Solène Baptiste

Boris

Ivan

Lorenzo

Shuo-Wen Carlos

Keywords: blue green red PSW blue 70 16, 514 1 Herschel/ green 100 16, 642 6, 7 Herschel/ red

Comprendre l'évolution des galaxies avec le temps cosmique est l'un des enjeux clés de l'astrophysique. Plusieurs questions se posent lorsque nous observons les galaxies distantes dans l'univers lointain : les galaxies à décalage vers le rouge élevé sont-elles plus riches en gaz ou leur efficacité de formation d'étoiles est-elle plus importante ? Les galaxies à flambée d'étoiles à décalage vers le rouge élevé sont-elles les analogues des LIRG et ULIRG locales, c'est-à-dire des galaxies en interaction ? Les galaxies lointaines massives, compactes, à forte formation d'étoiles, sont-elles les ancêtres des galaxies elliptiques ? Quelle est la fraction de la formation des étoiles qui est masquée par la poussière à z > 2 (c.-a-d. au-delà du midi cosmique de la formation stellaire) ? Quelle est la fraction de galaxies trop obscurcies pour être détectées par les relevés existants dans les domaines optiques et proche infrarouge ? La présence d'un noyau actif affecte-t-elle les propriétés physiques d'une galaxie ?

Le plus grand sondage cosmologique à 1.1mm réalisé avec l'interféromètre ALMA sur lequel j'ai travaillé lors de ma thèse de doctorat offre une occasion unique d'aborder ces questions. Cette observation a été réalisée dans une région du ciel, le champ GOODS-Sud, qui bénéficie des observations les plus profondes du télescope spatial Hubble, des observatoires infrarouges Spitzer et Herschel, ainsi que des données de l'observatoire X Chandra et l'interféromètre radio VLA. Ces observations à 1.1mm avec ALMA complètent donc ce panorama multi-longueurs d'onde, et font de cette région du ciel un laboratoire de premier plan pour l'étude de l'évolution des galaxies.

L'observation avec ALMA nous permet d'observer cette région du ciel sans être affecté par la limite de confusion qui affectait les observations du satellite Herschel, et de chercher des galaxies plus éloignées. Pour la première fois, nous pouvons étudier la formation d'étoiles obscurcie par la poussière à z > 2 sur une surface assez grande pour réduire les différents biais d'observation.

Une grande partie de cette thèse a été consacrée à l'exploitation scientifique de cette image cosmologique à 1.1 mm. Pour ce faire, nous avons analysé les données interférométriques, caractérisé précisément le sondage, défini des seuils de détectabilité et des indicateurs permettant de quantifier la crédibilité des détections, et effectué des simulations. Nous avons ensuite extrait et identifié les galaxies présentes sur l'image. Cette analyse montre que les relevés ALMA peuvent révéler de nouvelles galaxies qui ne sont pas détectées par les relevés les plus profonds effectués avec le télescope spatial Hubble. Ces galaxies "sombres" comptent parmi les galaxies les plus massives et les plus distantes de cette région du ciel. La découverte de ces nouvelles galaxies sombres, qui représentent de l'ordre de 10 à 20% des détections ALMA, suggère que le nombre de galaxies massives formant des étoiles dans l'univers lointain pourrait être beaucoup plus important que prévu. Ces travaux ont également permis de déterminer les propriétés des galaxies détectées par ALMA, à travers la modélisation de leurs distributions d'énergie spectrale : le taux de formation d'étoiles, les masses de gaz et de poussières, la température des poussières, le temps nécessaire à une galaxie pour consommer son gaz, la relation entre la luminosité infrarouge et la luminosité radio, l'excès de la composante infrarouge dans le spectre d'une galaxie. L'analyse de ces résultats suggère que les galaxies massives à fort décalage vers le rouge épuisent leur gaz par la formation d'étoiles.

De plus, la caractérisation précise de ce grand relevé ALMA a permis d'estimer le nombre de galaxies dans le ciel par unité de surface et de densité de flux. Cette étude montre également que les galaxies détectées avec ALMA hébergent une fraction beaucoup plus élevée de noyaux actifs que les galaxies massives équivalentes à des décalages vers le rouge similaires. Cependant, l'origine de cette propriété reste à déterminer. Il n'est notamment pas possible de dire à ce stade s'il existe une relation de causalité ou si la formation d'étoiles poussiéreuse et l'activité des noyaux actifs sont toutes deux activées par la même cause, par exemple une fusion galactique.

Enfin, nous avons mesuré la taille de ces galaxies détectées par ALMA à 1.1 mm, en utilisant plusieurs méthodes. Bien qu'elles aient des dimensions dans le proche infrarouge comparables à celles de la majorité des galaxies ayant les mêmes masses et les mêmes décalages vers le rouge, leur zone d'émission de poussière, c'est-à-dire la région trac ¸ant la partie obscure de la formation des étoiles, est relativement compacte et a une taille comparable aux galaxies passives à z ∼ 2. De plus, un nombre significatif de ces galaxies ont une faible fraction de gaz, tout en maintenant un taux élevé de formation d'étoiles. Cela signifie que si elles continuent à former des étoiles à ce rythme sans réapprovisionnement en gaz, elles épuiseront leurs réservoirs de gaz sur des échelles de temps cosmiques relativement courtes (∼ 100 Myr). Tous ces différents indicateurs conduisent à penser que ces galaxies sont les ancêtres idéales des galaxies passives à z ∼ 2.

INTRODUCTION

Global context 1.An expanding universe

The Great Debate It will soon be a century ago, on April 26, 1920, that what every astronomer knows as the Great Debate took place at the Smithsonian Museum of Natural History. At the beginning of the last century, a particularly hot subject agitated the world of astronomy: what was the real nature of nebulae. The term nebulae referred to any diffuse object of the sky. Many of these diffuse objects were known since antiquity, but it was the astronomer Charles Messier who, at the end of the 18th century, attempted to make an exhaustive list of them by drawing up a catalog of 110 objects. This great debate saw two astronomers confront each other: Harlow Shapley and Heber Curtis. While the latter thought that nebulae were extragalactic objects, that is, distant objects located beyond our galaxy, Shapley argued in favor of the Milky Way being the entire Universe, and put forward arguments suggesting that these nebulae were close objects located within our galaxy 1 .

No definite conclusion emerged from this great debate at the time, but it had the merit of focusing attention on this crucial issue, and inspiring generations of astronomers. These astronomers, a few years later, will accredit Curtis' thesis thanks to the observation of a category of standard candles, the Cepheids 2 . The characterization of the relationship between the period and luminosity (thus making Cepheids excellent tools for distance measurements) made by Henrietta Swan Leavitt in 1908 (Leavitt and[START_REF] Leavitt | Periods of 25 Variable Stars in the Small Magellanic Cloud[END_REF], and then by Ejnar Hertzsprung [START_REF] Hertzsprung | Über die räumliche Verteilung der Veränderlichen vom δ Cephei-Typus[END_REF], [START_REF] Shapley | On the Nature and Cause of Cepheid Variation[END_REF], and [START_REF] Hubble | Cepheids in Spiral Nebulae[END_REF], demonstrated that the distance to the Cepheids inside the Andromeda nebula was incompatible with the dimensions of our Milky Way.

This opening of the boundaries of the Universe, from our galaxy to a Universe with billions of galaxies moving relative to each other, is undoubtedly one of the greatest paradigm shifts that the Universe has ever known, similar to the passage from a geocentric world in which we occupy the predominant place, to a heliocentric world in which the sun has the place of choice. The subtlety of a Universe that is not centered on us is that it most likely does not have a center, or centers 2 Chapter 1. Introduction everywhere, as Blaise Pascal famously summarizes it: the universe "is a sphere whose center is everywhere, the circumference is nowhere" 3 (Les Pensées (1670), II, 72 by Blaise Pascal).

The first pieces of evidence

In 1913, with the Brashear spectrograph on the 24-inch refractor telescope at the Lowell Observatory in Flagstaff, Arizona [START_REF] Thompson | Vesto Slipher and the First Galaxy Redshifts[END_REF], Vesto Slipher brought the first observational evidence of a universe whose limit exceeds that of our Milky Way, and also that the Universe seemed to be expanding. After measuring the radial velocity of Andromeda's (M31) cloud cover in 1913 [START_REF] Slipher | The radial velocity of the Andromeda Nebula[END_REF], Vesto Slipher expanded his sample to 15 nebulae in 1915 [START_REF] Slipher | Spectrographic Observations of Nebulae[END_REF], and then to 25 two years later [START_REF] Slipher | Nebulae[END_REF]. Of these 25 clouds, 21 have positive radial velocities -that is, they move away from us. If the velocity distributions of the nebulae were randomly distributed, if they were equally likely to move away from or towards the Earth, the probability of finding such an imbalance in the results is less than 1 in 2000 4 . The average velocity of the 21 nebulae moving away from us 5 is 640 km.s -1 , which is much faster than the speed of the stars inside the Milky Way.

The confirmation

Georges Lemaître, priest and professor of physics at the Catholic University of Louvain understood the importance of these measurements, using Vesto Slipher's observations. In 1927, he wrote a paper "A homogeneous Universe of constant mass and increasing radius accounting for the radial velocity of extragalactic nebulae" [START_REF] Lemaître | Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques[END_REF] in which he explains: "Using 42 nebulae from the Hubble and Strömberg lists [lists that used Vesto Slipher's radial velocity measurements, Stromberg 1925, N.D.A.], and taking into account the proper speed of the sun [...], we find an average distance of 0.95 million parsecs and a radial velocity of 600Km./sec, or 625Km./sec at 10 6 parsecs. We will therefore adopt": R /R = v/rc (1.1) Lemaitre, therefore, states a law of proportionality between the speed of galaxies and their distance from the observer, and proposes a constant value of the proportionality. This is what every astronomy student knows as Hubble's Law. However, this predates the publication of Edwin Hubble's famous paper by two years. Unfortunately, as it is written in French in Les Annales de la Société Scientifique de Bruxelles, which did not have an international reputation, this paper did not have the impact it should have had. It was translated in 1931 Lemaître (1931a), but Eq. 1.1 (Eq. 24 in Lemaitre's original paper) does not appear in the translation. Many theories have circulated about this mysterious disappearance (e.g., van den Bergh, 2011) but the mystery seems to have been solved by the discovery of an original letter addressed to the publisher [START_REF] Livio | Lost in translation: Mystery of the missing text solved[END_REF] in which Georges Lemaitre explains his choice not to reproduce his equation: "I did not find advisable to reprint the provisional discussion of radial velocities which is clearly of no actual interest". Lemaitre's paper, unlike Hubble's, does not simply give a relationship between the speed of distance of galaxies and their distance, he explains this phenomenon by the expansion of the Universe (Lemaître, 1931a) and evokes the beginning of the universe [START_REF] Lemaître | The Beginning of the World from the Point of View of Quantum Theory[END_REF] 3. The origin of this quotation is regularly debated. This sentence exists in a similar form in the pen Nicholas of Cusa or Giordano Bruno.

4. Pr{X≥21}= 1 -21 k=0 C k 25 p k ×0.5 (25-k) = 0.0005 with C k 25 the coefficient of the pair. 5. The four nebulae with negative radial velocities (M31, M32, M33, and M8) are nebulae of the local group [START_REF] Baade | The Globular Cluster NGC 2419[END_REF]. They are linked together by the force of gravity that dominates in relation to the expansion of the Universe.

1.1. Global context 3 by its theory of the primitive atom, the real anchor of the big bang. This law is now known as the "Hubble-Lemaître law". This decision was taken after a recommendation dated August 30, 2018, during the 30th meeting of the International Astronomical Union 6 , which was then decided on October 29, 2018. It can be expressed as explained in the following.

As shown in Fig. 1.1 of Hubble's original article [START_REF] Hubble | A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae[END_REF] 7 , if v r is the recession rate of distant nebulae and d their distance from us, there is a linear relationship between v r and d: However, this Hubble-Lemaître law cannot be applied to all distances. If z << 1:

v r = H o × d (1.2)
z v r c (1.3) v r cz H 0 × d. (1.4)
For galaxies with high redshifts (z > 1), this law is no longer valid, and the distance of the galaxies follows the equations of general relativity.

The Relativist Revolution

The real revolutions concerning our vision of the Universe took place in 1905 [START_REF] Einstein | Zur Elektrodynamik bewegter Körper[END_REF] and 1915 [START_REF] Einstein | Die Feldgleichungen der Gravitation[END_REF], with the publication of Albert Einstein's two famous papers presenting the theories of special and general relativity, respectively. These theories lay the foundations 6. https://www.iau.org/static/archives/announcements/pdf/ann18029e.pdf 7. We would like to point out that in this article, Edwin Hubble uses the determination of galaxy velocities performed by V. Slipher without ever mentioning it.

Chapter 1. Introduction of modern astrophysics. General relativity is based on the cosmological principle, discussed below.

Cosmological principle

There are two parts to the cosmological principle:

-Generalized Copernican principle (we do not occupy a particular place in space) -Isotropy and homogeneity (the general appearance of the Universe does not depend on the position of the observer)

Several pieces of observational proof statistically validate this cosmological principle. One of the most convincing proofs is the prediction in 1948 of the Cosmic Microwave Background (CMB) 8 by Ralph Alpher and Robert Herman (Alpher and Herman, 1948a,b) then its discovery 9 sixteen years later, in 1964 by A. [START_REF] Penzias | A Measurement of Excess Antenna Temperature at 4080 Mc/s[END_REF] with the 20-foot horn-reflector antenna [START_REF] Crawford | A Horn-Reflector Antenna for Space Communication[END_REF] at the Crawford Hill Laboratory, Holmdel, New Jersey. The discovery of the CMB not only supports the hypothesis of an expanding universe, and by extension the Big-Bang hypothesis, but also, through the observation of near-perfect isotropy, measured with great precision by Cosmic Background Explorer (COBE), the Wilkinson Microwave Anisotropy Probe (WMAP), and the Planck satellite. Another observation confirms the hypothesis of an isotropic and homogeneous universe -the distribution of radio sources.

The number density and brightness of distant radio galaxies show that the Universe is globally isotropic 10 .

The vision of space and time is also transformed by linking these two entities into a single equation describing the structure of the space around us. The notion of distances is transformed, and paradoxes can appear. For example, the angular size of an object may, after a certain distance, increase (see Fig. 1.2). In addition, in this paradigm, by the distortion of space-time, the light from a distant galaxy could be bend around a massive object and magnify it, allowing us to see it as if it were under a lens.

Problematic

An essential question at the forefront of astronomy is to understand how galaxies assemble their baryonic mass into stars and supermassive black holes (SMBHs), and how this assembly depends on internal factors (e.g., gravitational instabilities, feedback from a supernova or AGNs) and external (dark matter halo, mergers) factors. Deep field surveys like GOODS have gathered exceptional multiwavelength data from X-ray through to radio wavelengths to allow astronomers to attack these questions in many ways. They provide thousands of galaxies with spectroscopic and photometric redshifts back to z = 8 and beyond, stellar population properties and masses, galaxy structure from HST, star formation rates (SFRs) from UV and FIR data, and pinpoint AGN accretion in different modes (i.e., radiative, obscured and unobscured) over a wide dynamic range of luminosity and Eddington ratio. A broad picture has emerged portraying the rise and fall of cosmic star formation and SMBH growth, and the organization of star formation into an evolving SFR-M * "main sequence" for the majority of galaxies (e.g., Schreiber et al., 2015, and references therein).

Several questions then arise: Are high redshift galaxies rich in gas, or is star formation efficiency more important at high redshift? Are starburst galaxies at high redshift analogues of LIRG or ULIRG galaxies, i.e., mainly interacting galaxies? Are massive, compact, highly star-forming galaxies the progenitors of elliptical galaxies at z = 2? What is the rate of galaxy formation at z > 2 (i.e., beyond the cosmic noon of star formation)? Which part of the formation of high redshift galaxies is too obscured to have been detected by the surveys that have been carried out so far? Does the presence of an AGN modify the physical properties of a galaxy?

To answer these questions, a large, contiguous region was observed with ALMA during the autumn of 2016 in one of the most observed region in the sky, the deep part of the GOODS-South field. This region benefits from some of the deepest observations of the Hubble Space Telescope and the Spitzer and Herschel infrared observation satellites, as well as X-ray data from the Chandra Telescope and the Very Large Array (VLA) radio interferometer. The observations at 1.1mm from ALMA, therefore, complete this multiwavelength panorama and make this region of the sky a leading laboratory for the study and evolution of galaxies. The observation with ALMA will allow us to observe this region of the sky without being affected by the confusion limit of Herschel, and to search for deeper regions of the sky. For the first time, with ALMA, we can observe the sky over a large enough surface to reduce cosmic variance and observe galaxy star formation at z > 2.

During the three years of this PhD., I have had the great opportunity to play a central role in the processing and data analysis of this largest ever ALMA survey. An overview of the history of the formation and evolution of massive, dusty, high redshift galaxies is beginning to emerge of the fog little by little thanks to these observations. It is this vision that I will explain in this thesis manuscript.

Chapter 1. Introduction

In the introduction, we will see that galaxies, whose extragalactic nature we have known for less than a century, can, thanks to the formalism of general relativity and to multiwavelength observations, tell us a part of the history of the Universe. We will also take the time to explain the origin of these questions and place this work in a more general context to identify and characterize precisely the issues we are trying to answer.

In the second chapter, we will present the framework of these observations, the GOODS-South field and the specificity of millimeter observations with a large interferometer. In the next chapter, we will explain how we constructed scientifically exploitable images from ALMA data, and how we were able to acquire a sufficiently precise knowledge of these images to detect galaxies and extract fluxes from them.

We will then explain, in the following chapter, that this flux-limited sample has allowed us, after many simulations and after the correction of several biases, to carry out counts, i.e., to know the number of sources per unit area at different fluxes that are present in our visible and accessible Universe.

We will then see that the search for these sources could be completed, using previous optical observations using HST data, and near-infrared using both the IRAC filters of the Spitzer space telescope and the Magellan telescope, in order to have the most unbiased galaxy sample possible. We present a method, which can be used for other blind surveys, to detect galaxies above the threshold imposed by a purity criterion.

In the following chapter, we will show that this blind survey has allowed us to detect galaxies that had previously been missed by HST observations. These galaxies, optically dark, represent about 20% of our blind detections. These galaxies are interesting because they are particularly dusty, massive, and distant. Taking these galaxies into account could change our vision of star formation in massive high redshift galaxies and change our understanding of the star formation density in the first billions of years after the Big Bang. We will also see that these optically dark galaxies could turn out to be excellent tracers of overdensities at high redshift.

The galaxies detected in this work will be analyzed using a multiwavelength approach. We will see that these massive and compact galaxies, with high star formation rates and gas deficiencies, are the ideal progenitors of compact elliptical galaxies at z > 2. This population of progenitors of distant elliptical galaxies is still poorly constrained, and escapes most of the current observations made with the Hubble Space Telescope.

On the origin of elliptical galaxies 1.3.1 Galaxy classification

Before the Hubble tuning fork

Historically, the first work on the classification of galaxies according to their morphologies was done by Max Wolf in 1908[START_REF] Wolf | Die Klassifizierung der kleinen Nebelflecken[END_REF]. This classification was only made possible by advances in astrophotography techniques that have been developed a few years earlier. Indeed, to the naked eye, it is impossible to identify the smallest detail of a galaxy. Less than 50 years after the first astrophotography (daguerreotype of the Moon taken on March 23, 1840, by John William Draper from the roof of New York University), Isaac Roberts made for the first time, in 1887, using a 20 inch aperture reflecting telescope, a photograph 11 with high enough quality to be able to distinguish the spiral arms of the nearest spiral galaxy to ours, the Andromeda galaxy. This work was published 6 years later in A Selection of Photographs of Stars, Star-clusters and Nebulae [START_REF] Roberts | A Selection of Photographs of Stars, Star-Clusters and Nebulae, together with Information concerning the Instruments and the Methods employed in the pursuit of Celestial Photography[END_REF]. [START_REF] Wolf | Die Klassifizierung der kleinen Nebelflecken[END_REF] was the first study to differentiate, in a linear sequence, galaxies that do not have structures (type d to k), spirals (types r to w).

The Hubble tuning fork

In Extragalactic nebulae, based on 400 extragalactic nebulae for which Holetschek determined the magnitudes [START_REF] Hubble | Extragalactic nebulae[END_REF], Edwin Hubble proposes a classification of galaxies according to their morphology in a diagram that is now known as the Hubble tuning fork, or the Hubble sequence.

"The classification of these nebulae is based on structure, the individual members of a class differing only in apparent size and luminosity" [START_REF] Hubble | Extragalactic nebulae[END_REF]. FIGURE 1.3: Classification of galaxies made by Edwin Hubble commonly known as the Hubble tuning fork. From: [START_REF] Hubble | Realm of the Nebulae[END_REF].

This classification was illustrated 10 years later with the famous Hubble tuning fork diagram (see Fig. 1.3) in The Realm of the nebulae [START_REF] Hubble | Realm of the Nebulae[END_REF]. This diagram is divided into two parts: elliptical and spiral galaxies. On the left side of Fig. 1.3, we can see the elliptical galaxies without defined structures. Within these elliptical galaxies, stars are dominated by random motions. These elliptical galaxies are classified from E0 to E7. The number characterizes the degree of ellipticity of the galaxy, where the higher this number is, the more elliptical the galaxy is, and the smaller this number is, the more spherical the galaxy is. The ellipticity of a galaxy can be defined by:

e = 1 - a b (1.5)
where a and b are the length of the galaxy's major and minor axis respectively.

The number next to the E corresponds to the number of the decimal of Eq. 1.5. The EO galaxies Chapter 1. Introduction will therefore be spherical, while the E7 labeled galaxies will be very elongated. No galaxy with an ellipticity greater than 0.7 has been found by Edwin Hubble. "The structural transition is so smooth and continuous that the selection of division points for further classification is rather arbitrary." [START_REF] Hubble | Extragalactic nebulae[END_REF] On the right side of the Hubble tuning fork are the spiral galaxies. Spiral galaxies are themselves subdivided into two parts, "normal" spiral galaxies (from Sa to Sc) and barred spiral galaxies (from SBa to SBc). The lowercase letters correspond to the compactness of the galaxies. The most compact spiral galaxies are designated with the letter a while the more aerial, larger galaxies inherit the letter c.

The "node" of this tuning fork is composed of a rather particular family of nebulae, the lenticular galaxies (S0). These galaxies make the connection between elliptical and spiral galaxies.

In addition to elliptical and spiral nebulae, Hubble introduces the notion of irregular galaxies.

There are two types of irregular galaxies (Irr I and Irr II). The purpose of this classification was to be complete, so that each galaxy could fall into a category. Although the Hubble tuning fork classification is still used today, many attempts at improvement or substitution have been proposed (e.g., [START_REF] De Vaucouleurs | Classification and Morphology of External Galaxies[END_REF][START_REF] Sandage | The Hubble Atlas of Galaxies[END_REF][START_REF] Sandage | Classification and Stellar Content of Galaxies Obtained from Direct Photography[END_REF][START_REF] Sandage | A Revised Shapley-Ames Catalog of Bright Galaxies[END_REF].

Although the division between elliptical and spiral galaxies is still in effect today, the interpretation of the tuning fork has evolved. Hubble thought that galaxies evolved from left to right in his diagram. He thought that young galaxies were elliptical (early-type galaxies) and gradually evolve towards more complexity by forming spiral arms (late-type galaxies). These temporal terms between the "early", "middle" and "late" were central to Edwin Hubble's vision of the evolution of nebulae. Subsequent observations, notably [START_REF] Toomre | Galactic Bridges and Tails[END_REF] and the future of infrared astronomy, seem to contradict this initial interpretation. Spiral galaxies seem to be young, intermediate-mass galaxies, rich in gas and forming stars. Elliptical galaxies seem more compact, more massive and almost without gas. One of the possible origins of elliptical galaxies could be the merging of two spiral galaxies. This merging could be followed by an intense episode of star formation (a starburst) and then a transformation of their morphology. The morphology of a galaxy could, therefore, be an indicator of the environment of a galaxy. The more galaxies evolving in a dense environment, the more likely it is that galaxies will merge and that a galaxy will become elliptical. This also explains why elliptical galaxies are more often in dense environments.

This transformation in the morphology of a galaxy, as well as the timescale and mechanisms causing the transformation of a spiral to an elliptical galaxy, are still poorly known phenomena, and observations of a large region of the sky with ALMA could give crucial information to understand the death of a galaxy, and understand how a galaxy forming stars in a secular way stops (or at least significantly reduces) its star formation rate (SFR).

The quest for progenitors of elliptical galaxies at high redshift

The primary progenitors of passive compact galaxies at z ∼ 2 are largely unknown (e.g., Williams et al., 2014;[START_REF] Straatman | The Sizes of Massive Quiescent and Star-forming Galaxies at z ∼ 4 with ZFOURGE and CANDELS[END_REF][START_REF] Wang | A dominant population of optically invisible massive galaxies in the early Universe[END_REF]. Current observations are ineffective in finding this galaxy population, which is paradoxically very massive. As the most massive galaxies are also the dustiest (see Chapter 7), UV observations are not efficient to detect them (see Sect. 1.4). Only (sub)millimeter observations have the capacity to constrain this galaxy population.

The mechanisms causing the drop in star formation in galaxies are largely unknown. This is one of the main questions in the study of galaxy evolution: why and how do galaxies stop forming stars?

The study of distant and massive galaxies is crucial to understand our models of galaxy formation and evolution, as they are the ideal candidate progenitors of compact quiescent galaxies at z∼2 (Barro et al. 2013;Williams et al. 2014;van der Wel et al. 2014;Kocevski et al. 2017, see also Elbaz et al. 2018). Massive star-forming galaxies at z > 2 are rare; to be able to detect them, it is essential to cover the largest possible area of the sky. It is for this region that it was decided to carry out the largest survey with ALMA to discover very massive galaxies forming large quantities of stars. These galaxies cannot continue to form stars for long periods. If this was the case, they would become much more massive than the most massive galaxies we have observed at z = 1, or in the local universe.

Unlike many studies that have been carried out with ALMA in recent years, the galaxies we will study in this thesis have not been selected as compact galaxies in the H-band. They are fluxselected at 1.1mm. Due to the low dispersion of the main sequence (MS; e.g., Noeske et al., 2007;[START_REF] Elbaz | The reversal of the star formation-density relation in the distant universe[END_REF][START_REF] Daddi | Multiwavelength Study of Massive Galaxies at z˜2. I. Star Formation and Galaxy Growth[END_REF][START_REF] Pannella | Star Formation and Dust Obscuration at z ∼ 2: Galaxies at the Dawn of Downsizing[END_REF]Schreiber et al., 2015), this selection is equivalent to a mass selection. We will see how these galaxies detected by ALMA, not selected for their compact size in H-band, can give us indications on the end-of-life scenarios of a galaxy at z > 2. Before getting to the heart of the matter, we will introduce, in the next paragraph, the notion of bimodality of galaxies, to reveal the life and death scenarios of galaxies.

The galaxy bimodality

In the same way that it is possible to differentiate galaxies through their morphology (which can be seen as a proxy for the angular momentum of the galaxy), it is also possible to differentiate galaxies according to their stellar populations. Massive stars, with a short lifetime (< 100 Myr) and are therefore tracers of star formation, will typically have a blue color, while low mass, long lifetime stars (> 10 Gyr) will have a red color. This color distinction therefore makes it possible to differentiate star-forming galaxies from galaxies that are no longer forming stars (passive galaxies) 12 .

When galaxies are placed on a color-magnitude diagram (or a color-stellar mass diagram), we note that they can be separated into two distinct populations, a blue cloud and a red sequence (e.g., [START_REF] Visvanathan | The color -absolute magnitude relation for E and S0 galaxies. I. Calibration and tests for universality using Virgo and eight other nearby clusters[END_REF][START_REF] Visvanathan | Colour-absolute magnitude relation for spiral galaxies[END_REF][START_REF] Strateva | Color Separation of Galaxy Types in the Sloan Digital Sky Survey Imaging Data[END_REF][START_REF] Baldry | Quantifying the Bimodal Color-Magnitude Distribution of Galaxies[END_REF][START_REF] Dekel | Galaxy bimodality due to cold flows and shock heating[END_REF][START_REF] Schawinski | The green valley is a red herring: Galaxy Zoo reveals two evolutionary pathways towards quenching of star formation in early-and late-type galaxies[END_REF]. This transition between the two galaxy populations is visible in Fig. 1.4. The vast majority of star-forming spiral galaxies are located in the blue cloud, while passive elliptical galaxies are located on the red sequence. This boundary is not always strict, recent studies have shown that elliptical galaxies can be on the blue side (e.g., [START_REF] Yi | Galaxy Evolution Explorer Ultraviolet Color-Magnitude Relations and Evidence of Recent Star Formation in Early-Type Galaxies[END_REF][START_REF] Kannappan | E/S0 Galaxies on the Blue Color-Stellar Mass Sequence at z = 0: Fading Mergers or Future Spirals[END_REF][START_REF] Schawinski | Galaxy Zoo: a sample of blue early-type galaxies at low redshift*[END_REF] or spiral galaxies on the red side [START_REF] Van Den Bergh | A new classification system for galaxies[END_REF][START_REF] Masters | Galaxy Zoo: passive red spirals[END_REF]. The low presence of gas is also not a sufficient criterion for the high reduction of star formation in elliptical galaxies (e.g., [START_REF] Gobat | The unexpectedly large dust and gas content of quiescent galaxies at z > 1.4[END_REF]. These observations are not anecdotal; this shows that there are mechanisms that Late-type galaxies FIGURE 1.4: u-r color-mass diagram corrected for reddening using the Sloan Digital Sky Survey (SDSS; [START_REF] York | The Sloan Digital Sky Survey: Technical Summary[END_REF][START_REF] Abazajian | The Seventh Data Release of the Sloan Digital Sky Survey[END_REF], the Galaxy Evolution Explorer (GALEX; [START_REF] Martin | The Galaxy Evolution Explorer: A Space Ultraviolet Survey Mission[END_REF]) and the Galaxy Zoo project [START_REF] Lintott | Galaxy Zoo: morphologies derived from visual inspection of galaxies from the Sloan Digital Sky Survey[END_REF][START_REF] Lintott | Galaxy Zoo 1: data release of morphological classifications for nearly 900 000 galaxies[END_REF]. The two peaks of the galaxy distribution according to their colors and masses are visible on the top left panel. The division is made into Early-type galaxies (top right panel) and Late-type galaxies (bottom right panel). The scatter of the dispersion in Early-type galaxies is smaller than that of Late-type galaxies. This is why these two populations are called the red sequence and blue cloud respectively. Green lines show the green valley. Figure from [START_REF] Schawinski | The green valley is a red herring: Galaxy Zoo reveals two evolutionary pathways towards quenching of star formation in early-and late-type galaxies[END_REF].

stop star formation that are not necessarily induced by (or dependent on) the morphological transformation of galaxies or the complete absence of cold gas.

To differentiate star-forming galaxies from passive galaxies in this thesis we will use a separation based on two colors, to break the age-dust degeneracy (e.g., [START_REF] Wuyts | What Do We Learn from IRAC Observations of Galaxies at 2 < z < 3.5?[END_REF]Williams et al., 2009;[START_REF] Whitaker | The NEWFIRM Medium-band Survey: Photometric Catalogs, Redshifts, and the Bimodal Color Distribution of Galaxies out to z ˜3[END_REF]. We will use the rest-frame color criterion given by Williams et al. (2009) applied at all redshifts and stellar masses, as suggested by Schreiber et al. (2015):

U -V < 1.3 V -J >
1.6 U -V < 0.88 × (V -J) + 0.49 (1.6) The characteristic stellar mass that separates these two populations of galaxies M * 3× 10 10 M [START_REF] Dekel | Galaxy bimodality due to cold flows and shock heating[END_REF]. We will see in the rest of this thesis that this critical stellar mass also defines the lower mass limit of our detections and makes the galaxies studied in this thesis a unique laboratory to understand the transition mechanisms between active and passive 1.3. On the origin of elliptical galaxies 11

U-V V-J -1 0 1 2 0 1 2 0<z<1 -1 0 1 2 1<z<2 -1 0 1 2 2<z<3 -1 0 1 2 3<z<4 -1 0 1 2 4<z<5 FIGURE 1
.5: Rest-frame U -V vs. V -J with the boundaries presented in Eq.1.6 for five redshift bins performed with ZFOURGE (Straatman et al., 2016) data. Star-forming galaxies are represented in blue while quiescent galaxies are represented in red.

galaxies. This sample will investigate the physical origin of the critical mass where the separation between passive and active galaxies occurs.

This bimodality can be expressed in different ways. We have seen the division in color and magnitude (or stellar mass, e.g., [START_REF] Baldry | Quantifying the Bimodal Color-Magnitude Distribution of Galaxies[END_REF][START_REF] Hogg | The Dependence on Environment of the Color-Magnitude Relation of Galaxies[END_REF][START_REF] Blanton | Relationship between Environment and the Broadband Optical Properties of Galaxies in the Sloan Digital Sky Survey[END_REF], but it can also be expressed in other ways, for example by looking at color in relation to the environment (e.g, [START_REF] Balogh | The Bimodal Galaxy Color Distribution: Dependence on Luminosity and Environment[END_REF][START_REF] Kauffmann | The environmental dependence of the relations between stellar mass, structure, star formation and nuclear activity in galaxies[END_REF][START_REF] Blanton | The Scale Dependence of Relative Galaxy Bias: Encouragement for the "Halo Model" Description[END_REF], star formation rate in relation to the age of the stellar population (e.g., [START_REF] Kauffmann | The dependence of star formation history and internal structure on stellar mass for 10 5 low-redshift galaxies[END_REF][START_REF] Madgwick | Galaxy spectral parametrization in the 2dF Galaxy Redshift Survey as a diagnostic of star formation history[END_REF], the gas to-stellar mass ratio (e.g., [START_REF] Kannappan | Linking Gas Fractions to Bimodalities in Galaxy Properties[END_REF], the bulge-to disc ratio (e.g., [START_REF] Blanton | Relationship between Environment and the Broadband Optical Properties of Galaxies in the Sloan Digital Sky Survey[END_REF], the luminosity/mass functions (e.g., [START_REF] Baldry | Quantifying the Bimodal Color-Magnitude Distribution of Galaxies[END_REF][START_REF] Bell | The Optical and Near-Infrared Properties of Galaxies. I. Luminosity and Stellar Mass Functions[END_REF], the excess of X-ray flux (e.g., [START_REF] Mathews | Hot Gas in and around Elliptical Galaxies[END_REF][START_REF] Osmond | The GEMS project: X-ray analysis and statistical properties of the group sample[END_REF], and the size as a function of stellar mass (e.g., van der Wel et al., 2014, see [START_REF] Dekel | Galaxy bimodality due to cold flows and shock heating[END_REF][START_REF] Cattaneo | Modelling the galaxy bimodality: shutdown above a critical halo mass[END_REF] for a review).

Passive galaxies constitute only a minority of the number of galaxies (∼ 30% at z = 0), but are dominant in mass, with stellar masses contributing ∼70% to the total mass of the galaxies (e.g., [START_REF] Hogg | The K correction[END_REF][START_REF] Bell | The Optical and Near-Infrared Properties of Galaxies. I. Luminosity and Stellar Mass Functions[END_REF][START_REF] Baldry | Quantifying the Bimodal Color-Magnitude Distribution of Galaxies[END_REF]. These passive galaxies have been detected at all redshifts up to z ∼4 (e.g., [START_REF] Glazebrook | A high abundance of massive galaxies 3-6 billion years after the Big Bang[END_REF][START_REF] Straatman | A Substantial Population of Massive Quiescent Galaxies at z ˜4 from ZFOURGE[END_REF][START_REF] Spitler | Exploring the z = 3-4 Massive Galaxy Population with ZFOURGE: The Prevalence of Dusty and Quiescent Galaxies[END_REF][START_REF] Glazebrook | A massive, quiescent galaxy at a redshift of 3.717[END_REF][START_REF] Schreiber | Near infrared spectroscopy and star-formation histories of 3 ≤ z ≤ 4 quiescent galaxies[END_REF] which means that star formation may be faster and more efficient than most models predict.

This bimodality of galaxies raises several questions. One of them is the origin of such high masses in passive galaxies. There is a mass transition between active and passive galaxies (e.g., [START_REF] Dekel | The dissipative merger progenitors of elliptical galaxies[END_REF][START_REF] Faber | Galaxy Luminosity Functions to z ˜1 from DEEP2 and COMBO-17: Implications for Red Galaxy Formation[END_REF]. One of the explanations given for this is a slow evolution of the mass of passive galaxies through a series of gas-poor, or "dry" mergers [START_REF] Faber | Galaxy Luminosity Functions to z ˜1 from DEEP2 and COMBO-17: Implications for Red Galaxy Formation[END_REF].

Another origin that will be discussed in this manuscript is the rapid mass growth of massive galaxies at high redshift.

One of the questions underlying galaxy bimodality is also to know which scenarios trigger star formation in galaxies, and why at some point this star formation stops. In particular, we are interested in whether this cessation of star formation is due to internal mechanisms (supernova, AGN) or if the environment plays an important role (e.g., [START_REF] Dressler | Galaxy morphology in rich clusters: implications for the formation and evolution of galaxies[END_REF][START_REF] Kauffmann | The environmental dependence of the relations between stellar mass, structure, star formation and nuclear activity in galaxies[END_REF][START_REF] Balogh | The Bimodal Galaxy Color Distribution: Dependence on Luminosity and Environment[END_REF][START_REF] Hogg | Cosmic Homogeneity Demonstrated with Luminous Red Galaxies[END_REF]. It is important to tracing back the star-formation in the galaxy to understand this bimodality.

Star formation in galaxies

Star forming galaxies follow a tight correlation (scatter of σ = 0.2-0.3 dex, [START_REF] Speagle | A Highly Consistent Framework for the Evolution of the Star-Forming "Main Sequence" from z ˜0-6[END_REF], Whitaker et al. 2015) between their star formation rate and stellar mass. This so-called 'Main Sequence' (Noeske et al. (2007)) represents ∼70% of the total galaxy population. This main sequence, which extends over at least 4 orders of magnitudes in mass [START_REF] Santini | Star formation and mass assembly in high redshift galaxies[END_REF] was first characterized for local galaxies (z ≈ 0; [START_REF] Brinchmann | The physical properties of star-forming galaxies in the low-redshift Universe[END_REF][START_REF] Salim | UV Star Formation Rates in the Local Universe[END_REF]) then extended to more distant galaxies (z ≈ 1; Noeske et al. (2007); [START_REF] Elbaz | The reversal of the star formation-density relation in the distant universe[END_REF], z =2 [START_REF] Pannella | Star Formation and Dust Obscuration at z ∼ 2: Galaxies at the Dawn of Downsizing[END_REF]Rodighiero et al., 2011;[START_REF] Whitaker | A Large Population of Massive Compact Post-starburst Galaxies at z > 1: Implications for the Size Evolution and Quenching Mechanism of Quiescent Galaxies[END_REF], z = 3 [START_REF] Magdis | On the stellar masses of IRAC detected Lyman Break Galaxies at z ˜3[END_REF][START_REF] Kurczynski | Evolution of Intrinsic Scatter in the SFR-Stellar Mass Correlation at 0[END_REF], z = 4 (Schreiber et al., 2015;[START_REF] Pannella | GOODS-Herschel: Star Formation, Dust Attenuation, and the FIR-radio Correlation on the Main Sequence of Star-forming Galaxies up to z ∼4[END_REF]Tomczak et al., 2016), z = 5 [START_REF] Tasca | The evolving star formation rate: M * relation and sSFR since z ∼ 5 from the VUDS spectroscopic survey[END_REF], and z = 6 [START_REF] Salmon | The Relation between Star Formation Rate and Stellar Mass for Galaxies at 3.5 < z <= 6.5 in CANDELS[END_REF].

This relationship evolves with redshift (see Fig. 1.6). While a galaxy with a stellar mass of 10 11 M located on the main sequence forms on average ∼ 25 M per year at a redshift ∼ 0.5, a galaxy of the same mass will produce on average 10 times more stars at z = 3. However, the scatter in the MS remains constant over both cosmic time and the stellar mass of the galaxies (Tomczak et al., 2016). This suggests that the main mode of growth in a galaxy is secular. On the other hand, the mechanism of slow and secular formation of galaxies involves a gas refill process. Indeed, if a galaxy only has its own gas reserves (M gas,mol /M * ∼1 for a galaxy of ∼ 10 11 M at z ∼2; [START_REF] Tacconi | PHIBSS: Unified Scaling Relations of Gas Depletion Time and Molecular Gas Fractions[END_REF], this galaxy would exhaust these reserves in only ∼ 650 million years. If we observe this galaxy, and all those in this configuration, it would mean that we live in a privileged time, which would tend to violate the generalized Copernican principle. About 90% of star formation occurs on the main sequence in the universe, essentially in disk-like galaxies (e.g., [START_REF] Wuyts | Galaxy Structure and Mode of Star Formation in the SFR-Mass Plane from z ˜2.5 to z ˜0.1[END_REF][START_REF] Combes | The Evolution of Gas Content and Star Formation from z=3 to z=0[END_REF], with only about 10% in starburst galaxies.

In the rest of this thesis, we will use the equation parameterized by Schreiber et al. (2015) to calculate the star formation rate of a galaxy on the main sequence:

log 10 (SF R ms ) = m -m 0 + a 0 r -a 1 [max(0, m -m 1 -a 2 r)]
2 (1.7) where m 0 = 0.5 ± 0.07, a 0 = 1.5 ± 0.15, a 1 = 0.3 ± 0.08, m 1 = 0.36 ± 0.3 and a 2 = 2.5 ± 0.6 the SF Rms is given in units of M yr -1 (see Fig. 1.6).

Recently, several studies have suggested that this relationship does not follow a power-law but seems to flatten for the most massive galaxies (e.g., [START_REF] Whitaker | Galaxy Structure as a Driver of the Star Formation Sequence Slope and Scatter[END_REF]Schreiber et al., 2015;[START_REF] Lee | A Turnover in the Galaxy Main Sequence of Star Formation at M * ∼ 10 10 M for Redshifts z > 1.3[END_REF]Tomczak et al., 2016;[START_REF] Popesso | The main sequence of star-forming galaxies -I. The local relation and its bending[END_REF] 13 . This flattening could bring into question the fast transition between the star-forming galaxies and the quenched galaxy population, as strongly suggested by the apparent dichotomy with few galaxies between these two populations (in the green valley).

The star formation main sequence seems to be the consequence of a proportionality between star formation density (Σ SF R ) and gas density (Σ gas ). The beginnings of this proportionality were set out in van den [START_REF] Van Den Bergh | The Luminosity Function of Population I[END_REF], before [START_REF] Schmidt | The Rate of Star Formation[END_REF] made it explicit: 1.8) 13. However, we note that some studies (e.g., [START_REF] Speagle | A Highly Consistent Framework for the Evolution of the Star-Forming "Main Sequence" from z ˜0-6[END_REF][START_REF] Rodighiero | A multiwavelength consensus on the main sequence of star-forming galaxies at z ∼ 2[END_REF] do not find this flattening FIGURE 1.6: Evolution of the average SFR of star-forming galaxies as a function of stellar mass and redshift. The filled colored circles are the result of stacking stacking analysis, while the gray curves show the best-fit relation for the main sequence. Figure from Schreiber et al. (2015).

Σ SF R ∝ (Σ gas ) n (
This relationship was later refined through measurements of H α , H I and CO in a sample of normal spiral galaxies combined with starburst galaxies: [START_REF] Kennicutt | The Global Schmidt Law in Star-forming Galaxies[END_REF]:

Σ SF R = (2.5 ± 0.7) × 10 -4 Σ gas 1M pc -2 1.4±0. [START_REF] Schreiber | Jekyll & Hyde: quiescence and extreme obscuration in a pair of massive galaxies 1.5 Gyr after the Big Bang[END_REF] M yr-1kpc-2 (1.9) where the gas refers to the the sum of both the atomic and molecular gas content.

This law which is now known as Schmidt-Kennicutt law (SK;[START_REF] Schmidt | The Rate of Star Formation[END_REF][START_REF] Kennicutt | The rate of star formation in normal disk galaxies[END_REF][START_REF] Kennicutt | The Global Schmidt Law in Star-forming Galaxies[END_REF], and tells us than the star formation is proportional to the density of the gas content (see Fig.1.7). This law also tells us that the denser a region of a galaxy is in gas, the more intense the star formation is 14 . The SK law is not linear (see Fig. 1.7); it can be divided into three distinct regimes:

-Σ gas < 9 M pc -2 : The efficiency of gas in producing stars drops drastically (e.g., [START_REF] Kennicutt | The star formation law in galactic disks[END_REF][START_REF] Martin | Star Formation Thresholds in Galactic Disks[END_REF][START_REF] Schaye | Star Formation Thresholds and Galaxy Edges: Why and Where[END_REF][START_REF] Bigiel | The Star Formation Law in Nearby Galaxies on Sub-Kpc Scales[END_REF]. There is a threshold below which Schmidt-Kennicutt law no longer works. -15 < Σ gas < 200 M pc -2 . Normal regime of SK law -Σ gas > 200 M pc -2 : molecular surface density is higher. Σ SF R is more important than for SK law. This regime corresponds to starburst galaxies and could reflect real changes in the ISM of these galaxies. [START_REF] Bigiel | The Star Formation Law in Nearby Galaxies on Sub-Kpc Scales[END_REF] showing the evolution of the SFR density as a function of the total gas surface density. In addition, the three distinctly different regimes (indicated by the vertical lines) of the star-formation law are also shown. Figure from [START_REF] Bigiel | The Star Formation Law in Nearby Galaxies on Sub-Kpc Scales[END_REF].

Starburst galaxies

In contrast to quenched galaxies, there is a galaxy population with much higher star formation rates than normal, for a galaxy of given stellar mass and redshift (see Fig. 1.7). Although there are several definitions for starburst galaxies, based on the SFR or the birth-rate parameter (b = SFR(t now )/ SFR(t) , [START_REF] Kennicutt | The rate of star formation in normal disk galaxies[END_REF][START_REF] Heckman | On the Nature and Implications of Starburstdriven Galactic Superwinds[END_REF], the definition we have adopted in this thesis is to consider that a galaxy is starburst if the SFR is 4 or higher than the main sequence (e.g., Rodighiero et al., 2011). This definition is not completely satisfactory. In the two-star-formation-mode (2SFM) formalism introduced by Sargent et al. (2012), see Fig. 1.8, star-forming galaxies can be separated, depending on their distance from the main sequence (RSB = sSFR/ sSFR M S , where sSFR = SFR/M * is the specific star formation rate, i.e., the SFR per unit stellar mass), into two galaxy populations that can be modelled by a double Gaussian. This would mean that there are a number of starburst galaxies belonging to the starburst Gaussian distribution but having an RSB close to 1. This population of starburst galaxies on the main sequence has been studied by (Elbaz et al., 2018), who show that gas depletion time (t dep ,= M gas /SFR, i.e. the characteristic time a galaxy needs to empty its gas reserves by assuming a constant SFR and no replenishment of gas) is a key parameter for distinguishing these galaxies. We will see that we have also identified this type of galaxy population in this study.

Starburst galaxies represent only 2% of the stellar mass but 10% of the SFRD at z = 2 and M * > 10 10 M . Rodighiero et al. (2011) showed that starburst galaxies were not just an extension of MS galaxies, but that there was a dichotomy between these two populations of galaxies.

1.3. On the origin of elliptical galaxies The spectra of the MS and SB galaxies also differ (e.g., [START_REF] Kinney | Template Ultraviolet to Near-Infrared Spectra of Star-forming Galaxies and Their Application to K-Corrections[END_REF][START_REF] Lanc ¸on | Near-IR spectral evolution of dusty starburst galaxies[END_REF]. The distribution of stars is not identical between these two galaxy populations -we can see an increase in the IR8 ratio (L IR /L 8 ), corresponding to the total infrared brightness over the brightness at 8µm (Elbaz et al., 2011), in the starburst galaxies. In other words, it is the relationship between dust emission and PAH emission (see Sect. 1.4). PAHs are more easily destroyed than dust in photo-dissociation regions near stars. A PAH deficit means that starburst galaxies are more compact and could result from the merging of galaxies that is known to make galaxies more compact in the near universe. The dust temperature also follows two distinct trends for MS and SB galaxies (e.g., Schreiber et al., 2018c;[START_REF] Donevski | Towards a census of high-redshift dusty galaxies with Herschel. A selection of "500 µm-risers[END_REF][START_REF] Jin | Discovery of four cold dusty galaxies at z=3.62-5.85[END_REF], with higher dust temperatures in starburst galaxies.

Several questions arise from these observation. Do all galaxies experience a starburst phase in their existence? Is it a unique phenomenon in the history of the galaxy, or on the contrary, is it repeated periodically? What are the causes of these star formation outbreaks?

Many studies have attempted to link the post-starburst phase of galaxies with quenching (e.g., [START_REF] Whitaker | A Large Population of Massive Compact Post-starburst Galaxies at z > 1: Implications for the Size Evolution and Quenching Mechanism of Quiescent Galaxies[END_REF][START_REF] Yesuf | From Starburst to Quiescence: Testing Active Galactic Nucleus feedback in Rapidly Quenching Post-starburst Galaxies[END_REF][START_REF] Maltby | The structure of post-starburst galaxies at 0.5 < z < 2: evidence for two distinct quenching routes at different epochs[END_REF]. There are similarities and continuities between the growth of the bulge due to a starburst phase and the quenching of galaxies [START_REF] Tran | Field E+A Galaxies at Intermediate Redshifts (0.3 < z < 1)[END_REF], which leads to a change in morphology between disk-dominated and elliptical. This morphological change can be characterized by a change in the Sérsic index (Sérsic, 1963, see Fig. 1.9), which is equal to 1 for disk galaxies, and at least 4 for elliptical galaxies. Galaxies in the starburst phase often have a Sérsic index between these values (e.g., [START_REF] Goto | 266 E+A galaxies selected from the Sloan Digital Sky Survey Data Release 2: the origin of E+A galaxies[END_REF][START_REF] Mendel | Towards a physical picture of star formation quenching: the photometric properties of recently quenched galaxies in the Sloan Digital Sky Survey[END_REF]. [START_REF] Marrone | Galaxy growth in a massive halo in the first billion years of cosmic history[END_REF]. n = 0.5 corresponds to a Gaussian profile while n=1 and n = 4 correspond to exponential and de Vancouleurs profiles respectively. The surface brightness and the radius are given in arbitrary units.

In this thesis we will attempt to uncover which mechanisms may be at the origin of the increase in the surface brightness at the center of a galaxy, and we will study the hypothesis of a violent episode of compact star formation in the center of the galaxy, as the origin of the increase in the Sérsic index [START_REF] Toft | Submillimeter Galaxies as Progenitors of Compact Quiescent Galaxies[END_REF].

In addition, we will also focus on galaxy sizes as an indicator of quenching (van der Wel et al., 2014). Indeed, as we will show in Chapter 8, finding massive, star-forming galaxies with very compact star formation sizes may be a sign that they will soon become quenched. On average, the size of early-type galaxies evolves rapidly (e.g., [START_REF] Toft | Hubble Space Telescope and Spitzer Imaging of Red and Blue Galaxies at z ˜2.5: A Correlation between Size and Star Formation Activity from Compact Quiescent Galaxies to Extended Star-forming Galaxies[END_REF][START_REF] Van Dokkum | Confirmation of the Remarkable Compactness of Massive Quiescent Galaxies at z ˜2.3: Early-Type Galaxies Did not Form in a Simple Monolithic Collapse[END_REF][START_REF] Newman | Can Minor Merging Account for the Size Growth of Quiescent Galaxies? New Results from the CANDELS Survey[END_REF][START_REF] Cassata | Constraining the Assembly of Normal and Compact Passively Evolving Galaxies from Redshift z = 3 to the Present with CANDELS[END_REF][START_REF] Morishita | The Evolution of Galaxy Size and Morphology at z ˜0.5-3.0 in the GOODS-N Region with Hubble Space Telescope/WFC3 Data[END_REF]van der Wel et al., 2014). We will also discuss the different mechanisms that can drive the evolution of a galaxy, such as the negative feedback of an AGN, ram pressure, morphological quenching, and major mergers.

The hidden star-formation at high redshift

Over the last 8 billion years, the cosmic star formation density has decreased by a factor ∼ 10 (e.g., Madau and Dickinson, 2014). One of the major enigmas in astrophysics is to understand why the Universe reaches a peak around z = 2 and why it is now so ineffective at generating stars.

The study of cosmic star formation is crucial to validate cosmological models. To be able to estimate the star formation rate density (SFRD), it is necessary to observe a large enough field of view, deep enough and with multiwavelength coverage to be able to derive both redshifts and star formation rates. Among the first estimates of the SFRD, we can cite the work of [START_REF] Lilly | The Canada-France Redshift Survey: The Luminosity Density and Star Formation History of the Universe to Z approximately 1[END_REF] who used the 4-m Canada-France-Hawaii Telescope, the Canada-France Redshift Survey 1.4. The hidden star-formation at high redshift (CFRS), and [START_REF] Madau | High-redshift galaxies in the Hubble Deep Field: colour selection and star formation history to z˜4[END_REF] who use the Hubble Ultra Deep Field. These two studies, which were carried out almost simultaneously, used galaxy UV emission to derive the star formation rate. Although the work of [START_REF] Lilly | The Canada-France Redshift Survey: The Luminosity Density and Star Formation History of the Universe to Z approximately 1[END_REF] focused mainly on galaxies with redshifts less than 1; one of the most striking results of this survey was to show that the star formation rate has declined drastically from z = 1 until now (see Fig. 1.10). FIGURE 1.10: Cosmic star formation history of the Universe from UV observation in the Hubble Deep Field. The filled dots come from [START_REF] Lilly | The Canada-France Redshift Survey: The Luminosity Density and Star Formation History of the Universe to Z approximately 1[END_REF] while the diagonal crosses come from Steidel et al. (1996), and the squares from [START_REF] Madau | High-redshift galaxies in the Hubble Deep Field: colour selection and star formation history to z˜4[END_REF]. Figure from [START_REF] Madau | High-redshift galaxies in the Hubble Deep Field: colour selection and star formation history to z˜4[END_REF].

Since then, several other surveys have explored the sky in order to build the star formation history (SFH) and trace the stellar mass build-up in galaxies to higher redshift (e.g., [START_REF] Steidel | Lyman Break Galaxies at Redshift z ˜3: Survey Description and Full Data Set[END_REF][START_REF] Giavalisco | The Great Observatories Origins Deep Survey: Initial Results from Optical and Near-Infrared Imaging[END_REF][START_REF] Bouwens | A Census of Star-forming Galaxies in the Z ˜9-10 Universe based on HST+Spitzer Observations over 19 Clash Clusters: Three Candidate Z ˜9-10 Galaxies and Improved Constraints on the Star Formation Rate Density at Z ˜9.2[END_REF]. However, the evolution of star formation rate density is only currently constrained by infrared observations from the local Universe until the cosmic peak around z∼2 (see Fig.1.11). Due to the lack of infrared surveys able to detect normal star-forming galaxies at z > 2, the actual contribution of dust-obscured galaxies to the cosmic star formation history at these redshifts remains largely unknown, especially at high masses where galaxies are known to be metal (e.g., [START_REF] Garnett | The Luminosity-Metallicity Relation, Effective Yields, and Metal Loss in Spiral and Irregular Galaxies[END_REF][START_REF] Tremonti | The Origin of the Mass-Metallicity Relation: Insights from 53,000 Star-forming Galaxies in the Sloan Digital Sky Survey[END_REF][START_REF] Gallazzi | The ages and metallicities of galaxies in the local universe[END_REF][START_REF] Mannucci | A fundamental relation between mass, star formation rate and metallicity in local and high-redshift galaxies[END_REF][START_REF] Yates | The relation between metallicity, stellar mass and star formation in galaxies: an analysis of observational and model data[END_REF][START_REF] Foster | Galaxy And Mass Assembly (GAMA): the mass-metallicity relationship[END_REF][START_REF] Kirby | The Universal Stellar Mass-Stellar Metallicity Relation for Dwarf Galaxies[END_REF][START_REF] Dayal | The physics of the fundamental metallicity relation[END_REF] and dust-rich (e.g., [START_REF] Heckman | The Ultraviolet Spectroscopic Properties of Local Starbursts: Implications at High Redshift[END_REF][START_REF] Boissier | The radial extinction profiles of late-type galaxies[END_REF][START_REF] Reddy | Dust Obscuration and Metallicity at High Redshift: New Inferences from UV, Hα, and 8 µm Observations of z 2 Star-forming Galaxies[END_REF]. Evidence already exists that the Lyman break galaxy (LBG) technique is missing a dominant population of massive dusty galaxies above a stellar mass of typically 5 × 10 10 M , because of their faintness and the redness of the UV slope (e.g., [START_REF] Van Dokkum | The Space Density and Colors of Massive Galaxies at 2 < z < 3: The Predominance of Distant Red Galaxies[END_REF][START_REF] Bian | The LBT Boötes Field Survey. I. The Rest-frame Ultraviolet and Nearinfrared Luminosity Functions and Clustering of Bright Lyman Break Galaxies at Z ˜3[END_REF]Wang et al., 2016). The star-formation rates (SFRs) of these high redshift galaxies are mostly estimated from UV measurements emitted by short-lived massive stars (e.g., [START_REF] Kennicutt | Star Formation in the Milky Way and Nearby Galaxies[END_REF]. This UV emission is strongly affected by the presence of dust in the interstellar medium (ISM). In order to correctly estimate the SFR, a dust correction needs to be applied using an extinction law (e.g., [START_REF] Meurer | Dust Absorption and the Ultraviolet Luminosity Density at z ˜3 as Calibrated by Local Starburst Galaxies[END_REF]Calzetti et al., 2000;[START_REF] Reddy | A multi-wavelength census of star formation at redshifts z equals 2[END_REF],a β slope (see Chapter 8, and the UV luminosity. This approach has proved effective for distant galaxies (e.g., [START_REF] Oesch | First Frontier Field Constraints on the Cosmic Star Formation Rate Density at z ∼ 10 -The Impact of Lensing Shear on Completeness of High-redshift Galaxy Samples[END_REF][START_REF] Bouwens | UV Luminosity Functions at Redshifts z ∼ 4 to z ∼ 10: 10,000 Galaxies from HST Legacy Fields[END_REF][START_REF] Mcleod | New redshift z ∼ 9 galaxies in the Hubble Frontier Fields: implications for early evolution of the UV luminosity density[END_REF] but suffers from caveats due to the large number of parameters that are poorly constrained (e.g., [START_REF] Cowie | New Insight on Galaxy Formation and Evolution From Keck Spectroscopy of the Hawaii Deep Fields[END_REF][START_REF] Pannella | Star Formation and Dust Obscuration at z ∼ 2: Galaxies at the Dawn of Downsizing[END_REF]. In particular, the extinction law could be different in the distant Universe, especially for galaxies with high star-formation rates (e.g., Rodighiero et al., 2011). For this reason, constraining galaxy infrared re-emission is essential to obtain a robust star formation tracer. FIGURE 1.11: Left panel: Evolution of the star formation rate density in UV (uncorrected for dust attenuation) and in IR. Left panel: combination of the UV and IR to derive the SFRD. The solid curve is the best-fit. Figures from (Madau and Dickinson, 2014). This is really one of the main goals of the survey in this study. Several scenarios can be imagined when we look back at the cosmic history of galaxy formation. Some authors suggest the possibility of a relatively constant star formation density when the Universe was young [START_REF] Rowan-Robinson | Extreme submillimetre starburst galaxies[END_REF], then a decline of star formation after the cosmic noon. Others on the contrary lean towards the hypothesis of a progressive increase in star formation density to the cosmic noon and then a progressive decline beyond. To be able to settle this debate and constrain the cosmic history of galaxy formation, one of the only ways is to carry out a broad survey exploring the infrared emission of galaxies. Until the advent of ALMA, infrared observations suffered from poor resolution or were much less efficient than optical observations, which generally meant that only galaxies biased towards the extremes could be analyzed. Thanks to this new domain of sensitivity, ALMA is able to unveil less extreme objects, bridging the gap between massive starbursts and more 'normal' galaxies. However, many previous ALMA studies have been based on biased samples, with prior selection (pointing) or a posteriori selection (e.g., based on HST detections) of galaxies, or in a relatively limited region of the sky. In this study, we present an unbiased view of a large (69 arcmin 2 ) region of the sky, without prior or a posteriori selection based on already known galaxies, in order to improve our understanding of dust-obscured star formation, and to investigate the main properties of these objects. We take advantage of one of the most potentially transformational outputs of ALMA -its ability to reveal a new class of galaxies through serendipitous detections. This is one of the main reasons for performing blind extragalactic surveys.

Dust only represents about 1% of the mass of the interstellar medium (for local galaxies, [START_REF] Draine | Interstellar Dust Grains[END_REF]), yet it considerably modifies the emission of a galaxy. Fig. 1.12 shows the part of the galaxy spectrum affected by dust absorption. The term dust incorporates several categories of chemical element, with a typical grain size of less than micron 15 .

In general, we can distinguish large grains (BG for Big Grains), very small grains (VSG for Very Small Grains) and aromatic molecules (PAH for Polycyclic Aromatic Hydrocarbon). This grain size issue is essential, because absorption is highest for wavelengths at the order of magnitude 15. the size distribution of dust grains can be represented by the following formula: dn = a -3.5 da, where dn is the number of grains with a radius between a and a + da [START_REF] Mathis | The size distribution of interstellar grains[END_REF].

of the size of the dust grains. For this reason, dust obscuration primarily affects UV and visible light. FIGURE 1.12: Spectral energy distribution of one galaxy selected from the galaxies detected in GOODS-ALMA. The difference between the solid and dotted curves (grey area) represents the part of the stellar emission that is absorbed by the dust. We have assumed an exponentially declining star formation history and a dust attenuation law as described by Calzetti et al. (2000).

In order to reach galaxies at high redshift, and to constrain the emission of dust from a galaxy, it is necessary to observe it in (sub)millimeter wavelengths. The rest-frame peak of a galaxy spectral energy distribution (SED) can vary between 72 and 125 µm for a dust temperature between 30 and 50 K (e.g., [START_REF] Casey | Dusty star-forming galaxies at high redshift[END_REF], corresponding to an observed peak between 288 and 500 µm at redshift 3. To constrain the shape of the SED, at least one measurement has to be made beyond this peak. This is why (sub)millimeter observations are necessary to constrain the IR luminosity of a galaxy. Thanks to the strong negative K-correction at submillimeter wavelengths (see Sect. 1.4.1), infrared emission does not suffer from distance attenuation, making submillimeter observations insensitive to redshift across a wide redshift range 2 < z < 10 (Blain et al., 2002). The Herschel Space Observatory [START_REF] Pilbratt | Herschel Space Observatory. An ESA facility for far-infrared and submillimetre astronomy[END_REF] was limited by a poor angular resolution (36" at 500µ). To overcome the difficulty caused by this angular resolution, it is necessary to deblend the sources based on deep observations made at shorter wavelengths. This has been done for the SPIRE filter Griffin et al. (2010) of Herschel (e.g., [START_REF] Roseboom | The Herschel Multi-tiered Extragalactic Survey: SPIRE-mm photometric redshifts[END_REF][START_REF] Merlin | T-PHOT: A new code for PSF-matched, prior-based, multiwavelength extragalactic deconfusion photometry[END_REF][START_REF] Wright | Galaxy And Mass Assembly: accurate panchromatic photometry from optical priors using LAMBDAR[END_REF][START_REF] Pearson | Main sequence of star forming galaxies beyond the Herschel confusion limit[END_REF][START_REF] Wang | A dominant population of optically invisible massive galaxies in the early Universe[END_REF] as well as for PACS (Poglitsch et al., 2010). Unfortunately, these techniques may, in some cases, prove to be imprecise for galaxies with low fluxes.

Other techniques such as stacking allow us to recover information on these weak sources [START_REF] Pannella | GOODS-Herschel: Star Formation, Dust Attenuation, and the FIR-radio Correlation on the Main Sequence of Star-forming Galaxies up to z ∼4[END_REF]; Schreiber et al. (2015); [START_REF] Álvarez-Márquez | Dust properties of Lyman-break galaxies at z ˜3[END_REF]. This technique is very efficient but only allows us to measure the statistical properties (average or median) of the galaxies studied. Any particularly interesting properties of an individual faint galaxy are therefore lost in the galaxy stack.

With ALMA, it is now possible to overcome the confusion limit and to detect galaxies with continuum emission below 1 mJy and a resolution lower than 1 arcsec, which enables more secure counterpart association. Some recent studies have measured (sub-)millimeter fluxes down to 0.2 mJy (e.g., Hatsukade et al., 2013;Carniani et al., 2015;Fujimoto et al., 2016;Aravena et al., 2016;[START_REF] Muñoz Arancibia | The ALMA Frontier Fields Survey. IV. Lensing-corrected 1.1 mm number counts in Abell 2744[END_REF].

K-correction

Following [START_REF] Kinney | Template Ultraviolet to Near-Infrared Spectra of Star-forming Galaxies and Their Application to K-Corrections[END_REF], the word k-correction comes from the expression K-term introduced in [START_REF] Wirtz | Über die Bewegungen der Nebelflecke[END_REF]. The letter K comes from the German word for constant: "konstante". Hubble (1936a) popularized the use of the letter K to introduce the notion of magnitude correction due to redshift. The K-correction is the correction that must be applied to a distant object to adjust its absolute magnitude from observed-frame to rest-frame. In other words, it is the ratio between the rest-frame luminosity of a galaxy and its observed-frame luminosity:

K(ν, z) = L ν(1+z) L ν (1.10)
What makes (sub)millimeter observations powerful is that in this wavelength domain, the kcorrection becomes particularly strong and negative. By convention, and in relation to the relative magnitudes that decrease when the observed flux increases, K-correction is designated negative when the density flux increases with increasing redshift, and is positive when the density flux decreases with increasing redshift. At these wavelengths, the emission of dust is described by a Rayleigh-Jeans spectrum with the following shape: 1.11) with β ∼ [1. (e.g., Chapman et al., 2005;Gordon et al., 2010;[START_REF] Greve | Submillimeter Observations of Millimeter Bright Galaxies Discovered by the South Pole Telescope[END_REF]Magnelli et al., 2012;[START_REF] Boselli | Far-infrared colours of nearby late-type galaxies in the Herschel Reference Survey[END_REF][START_REF] Bianchi | Vindicating single-T modified blackbody fits to Herschel SEDs[END_REF][START_REF] Rémy-Ruyer | Revealing the cold dust in lowmetallicity environments. I. Photometry analysis of the Dwarf Galaxy Survey with Herschel[END_REF]. This dust emissivity index may vary depending on the metallicity of the galaxy, the size distribution of dust grains and the location in the galaxy. For a "classic" galaxy, the Rayleigh-Jeans tail dominates at restframe wavelengths between 200µm and 1mm (see Sect. 1.5 for more details).

S ν ∝ ν 2+β (
The evolution of the flux density for a galaxy is given according to the following equation:

S ν = L ν 4πD 2 L (1.12)
where D L is the luminosity distance. This formula shows that the luminosity of a galaxy is uniformly diluted in a sphere with a radius D L . In Fig. 1.13, we show the luminosity distance as a function of redshift. We compare this luminosity distance with the function f(z) = A×(1+z) α with α = 1.5, 2 and 3. We can see that the luminosity distance evolves as (1+z) 2.5 for 0.25 < z < 1.25, (1+z) 2 for 1.25 < z < 2.25, and (1+z) 1.5 for 2.25 < z < 7.

By combining Eq. 1.11 and Eq. 1.12, we find that S ν (z) ∝ ν 2+β /4πD 2 L ∝ ν 2+β /(1+z) 2α ∝ ν 2+β rest (1+z) 2+β /(1+z) 2α ∝ (1+z) 2+β-2α . To have a flux density that does not change, 2+β -2α must be equal to 0. This is the case when 1.25 < z < 2.25 assuming β = 1.5. For higher redshifts, this factor becomes negative and the observed flux increases with redshift. This correction is highly dependent on the value of β, which in turn depends on the galaxy.

In this sense, submillimeter observations are unique in making dusty star-forming galaxies accessible from the peak of the star formation rate density (z ∼ 2, Madau and Dickinson 2014) up to z ∼ 5 [START_REF] Blain | Submillimetre Cosmology[END_REF]. In Fig. 1.14, we show the evolution of the flux density as a function of the redshift for one of our detecetd galaxies, which we will present in detail in this study (AGS1), through different filters from the mid infrared (24µm) to the radio (5cm). We can clearly see the drop in the mid-IR and radio flux density as a function of the redshift, while the 1.5. Probing galaxy properties using a multiwavelength approach 21 1 2 3 4 5 6 7

Redshift 10 1 10 2

Distance [Gpc]

∝(1+z) 1.5 ∝(1+z) 2 ∝(1+z) 2.5 Luminosity distance millimeter flux remains roughly constant, and has a tendency to increase slightly for redshifts higher than z = 2 (see Fig. 1.14 and 1.15).

Probing galaxy properties using a multiwavelength approach

In the late 1990s a population of galaxies was discovered at submillimeter wavelengths using the Submillimeter Common-User Bolometer Array (SCUBA; Holland et al. 1999) on the James Clerk Maxwell Telescope (see e.g., Smail et al. 1997;Hughes et al. 1998;Barger et al. 1998;Blain et al. 2002). These "submillimeter galaxies" or SMGs, are highly obscured by dust, typically located around z ∼2-2.5 (e.g., Chapman et al., 2003;Wardlow et al., 2011;Yun et al., 2012), massive (M > 7 × 10 10 M ; e.g., Chapman et al., 2005;Hainline et al., 2011;Simpson et al., 2014), gas-rich (f gas > 50%; e.g., Daddi et al., 2010), and have high star formation rates (SFR) -often greater than 100 M year -1 (e.g., Magnelli et al., 2012;Swinbank et al., 2014). This makes them significant contributors to cosmic star formation (e.g., Casey et al., 2013), often driven by mergers (e.g., Tacconi et al., 2008;Narayanan et al., 2010) and often hosting an active galactic nucleus (AGN; e.g., Alexander et al. 2008;Pope et al. 2008;Wang et al. 2013). With ALMA, we can now bridge the gap between massive starbursts and more normal galaxies: SMGs no longer stand apart from the general galaxy population .

Thanks to the survey presented in this thesis, and after the identification of galaxy counterparts, we will use a multiwavelength approach to better understand the evolution of distant galaxies. We will estimate key properties of galaxies to probe the evolution of the gas fraction, star formation rate, and depletion time of galaxies detected by ALMA.

Multiwavelength emission of a galaxy

Each element of a galaxy emits at a specific wavelength. A multiwavelength approach is, therefore, necessary to have a full overview of the galaxy, understand the different emission mechanisms, and derive its redshift. In this section, we will explain the different processes contributing to the emission of a galaxy for each wavelength domain, and present the techniques used to derive galaxy parameters. We will then discuss the techniques used to fit the SEDs.

Radio emission

In the absence of AGN, radio emission has two primary origins: synchrotron radiation from relativistic electrons and free-free emission from HII regions (e.g., [START_REF] Condon | Radio emission from normal galaxies[END_REF].

Synchrotron emission

Synchrotron radiation (magneto-bremsstrahlung) arises mainly from the end of life of massive stars. Stars with a mass higher than 8M [START_REF] Condon | Radio emission from normal galaxies[END_REF], but less than 40 or 50M [START_REF] Gilmore | The short spectacular life of a superstar[END_REF], will rapidly collapse and explode, resulting in Type II or Type Ib supernova. In the remains of the supernova (supernova remnant; SNR) the two fundamental ingredients of the synchrotron emission process coexist -high-energy electrons and a magnetic field (e.g., [START_REF] Urošević | On the radio spectra of supernova remnants[END_REF]. Relativistic electrons rotating around the magnetic field FIGURE 1.15: Infrared luminosity limit in the GOODS-ALMA field, from the infrared at 24µm to millimeter wavelengths at 1mm. Detection limits (given in parentheses for each filter) correspond to the detecion limit in the GOODS-South field (Elbaz et al., 2011;Schreiber et al., 2015). lines will generate synchrotron radiation. Synchrotron emission, which is non-thermal emission, is generated when the acceleration of the electron is in a plane perpendicular to its velocity. The emission is directed in the direction of velocity vectors. The acceleration of elections is generally due to multiple interactions of an electron on either side of the supernova shock wave [START_REF] Niklas | A radio continuum survey of Shapley-Ames galaxies at λ 2.8cm. II. Separation of thermal and non-thermal radio emission[END_REF].

I ν ∝ ν -α0 1 + (ν/ν b ) ∆α (1.13)
free-free emission "Free-free" emission (Thermal bremsstrahlung) is produced directly in HII regions, i.e. clouds of ionized hydrogen. The intensity of the free-free emission is proportional to the production rate of Lyman continuum photons. Free-free emission is produced when an electron scatters off another charged particle, such as a proton in a HII star-forming region. It is called free-free because the electron is free both before and after the interaction. HII regions are the regions around stellar formation sites, where atomic hydrogen has been ionized. It is the massive and young stars (typically OB stars) that ionize this interstellar environment. As these stars have a short life expectancy, HII and free-free emission regions trace the recent stellar formation. For the majority of galaxies, synchrotron emission is dominant at rest-frame frequencies below 30GHz, while the dust is dominant at frequencies higher than 200 GHz. Between these two frequencies, the free-free emission is greater than the other two other components (see Fig. 1.17).

It is massive stars (M ≥ 10 8 M ) that contribute to the heating of dust in the interstellar medium (and are therefore responsible for the infrared part of a galaxy's spectrum), and that also produce radio emission in HII regions (thermal free-free emission) and from supernova explosions (synchrotron emission). There is therefore a correlation between the radio and infrared emission of a galaxy.

Infrared emission

In the infrared, we can differentiate between 3 main domains: the near infrared (0.8µm -5µm), the mid infrared (5µm -25µm) and the far infrared (25µm -500µm).

Near-infrared emission is dominated by stars on the stellar main sequence, which are old, relatively small and cold (3000 -8000 K, see Fig. 1.18). These low mass stars (≤1M ) are the most numerous stars in a galaxy, and dominate the total mass of the galaxy 16 Near-infrared emission therefore makes it possible to trace the stellar mass of a galaxy directly. However, these not very massive stars are not the only contributors to the near IR emission -the presence of an active FIGURE 1.17: Observed radio-far infrared spectrum of M82. The measurements (black dots) were made by [START_REF] Klein | Radio continuum observations of M82[END_REF] and [START_REF] Carlstrom | H II regions in M82 -High-resolution millimeter continuum observations[END_REF]. The synchrotron emission (dot-dashed line), the free-free emission (dashed line), the dust component (dotted line) and the sum of the SED (solid line) are shown as a function of the frequency. For M82, the synchrotron emission is dominant for frequencies below 30GHz, while the dust is dominant for frequencies higher than 200 GHz. Between these two frequencies, the free-free emission is higher than the two other components. galactic nucleus may also contribute 17 . For this reason, the presence of an AGN can artificially overestimate the stellar mass derived for a galaxy. Indeed, as we will see in Chapter 8, it is not always straightforward to (i) know if the galaxy is hosting an AGN; (ii) subtract the AGN's contribution to the spectrum of the galaxy, and this subtraction is a source of great uncertainty. We will also see that, in the same way, AGN can introduce biases on the measurement of galaxy mass, and the measurement of infrared luminosity and therefore star formation rate in the far-infrared part of the galaxy SED.

PAHs and small dust grains dominate the mid-IR emission. The polycyclic aromatic hydrocarbons (PAHs) have their emission bands around 10µm. The brightest bands are located at ∼ 3.3, 6.2, 7.7, 8.6, 11.3 and 12.7 µm and are associated with the vibration, elongation and bending modes of the C-H and C-C bonds (e.g., [START_REF] Leger | Identification of the "unidentified" IR emission features of interstellar dust ?[END_REF][START_REF] Allamandola | Polycyclic aromatic hydrocarbons and the unidentified infrared emission bands: auto exhaust along the milky way[END_REF][START_REF] Li | The Carriers of the Interstellar Unidentified Infrared Emission Features: Aromatic or Aliphatic?[END_REF][START_REF] Galliano | Variations of the Mid-IR Aromatic Features inside and among Galaxies[END_REF]. For wavelengths greater than 10 µm, mid-infrared emission is associated with small grains. PAHs and small dust particles are not in thermal equilibrium (and cannot be modeled by a modified blackbody law (e.g., Boselli et al., 2011); this is why they have strong emission bands (see Fig. 1.16).

At greater than ∼50 µm, large grains are responsible for the majority of a galaxy's emission. In the far-infrared, the SED can be approximated by a simple modified black body. If we consider a single blackbody temperature for grains of dust, the SED can be modeled by the following formula Blain et al. (2002):

L ν = Ω ν B ν (T d ) (1.14)
10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9

[Angstrom] According to Wien's Law, the peak emission wavelength of a body depends on its temperature. The warmer the body is, the more it will emit at higher frequencies, and the colder it is, the lower wavelength its peak emission will be. That is why "cold" stars with temperatures ∼ 3000-5000 K emit in the near-infrared, and why we use millimeter wavelengths to study 20 -50K dust emission.

where Ω is the solid emission angle, ν the emissivity coefficient and B ν (T d ) is the Planck function which has the following form:

B ν (T d ) = 2h c 2 ν 3 exp( hν k B T d ) -1 [ergs -1 Hz -1 m -2 sr -1 ]. (1.15)
We can also rewrite this equation according to the wavelength 18 λ, and we will preferably use this notation in the rest of this thesis: .16) The emissivity coefficient can be approximated by:

B ν (T d ) = 2hc λ 3 1 exp( hc λk B T d ) -1 . ( 1
ν ∼ κ ν M dust [m 2 kg -1 ] (1.17)
where κ ν is the dust mass absorption coefficient at a given frequency. By injecting this term into Eq. (1.14), we obtain the following formula: [START_REF] Straatman | A substantial population of massive quiescent galaxies at z ~ 4 from ZFOURGE[END_REF] with:

M dust = L ν 4πκ ν B ν (T d ) (1.
L ν = S ν 4πD 2 L (1 + z) . (1.19)
Here, S ν is the observed flux density and D L is the luminosity distance.

18. We express Bν according to λ. However, we must be careful with the unit with which the emissivity of the black body is expressed because Bν (T )dνν, = B λ (T )dλ, and hence Bν (T ) = B λ (T ) λ 2 c .

By combining Eq. 1.18 and Eq. 1.19, we obtain:

M dust = S ν D 2 L (1 + z)κ ν B ν (T d ) (1.20)
where κ ν is defined as follows: .21) as the absorption coefficient of the dust mass at the given rest frame wavelength, with β = 1. 5 Gordon et al. (2010).

κ ν = κ 0 ν ν 0 β . ( 1
To be consistent with the model of Draine and Li (2007) (DL07) we adopt a value of κ 250 ,= 5.1 cm 2 g -1 obtained by [START_REF] Li | Infrared Emission from Interstellar Dust. II. The Diffuse Interstellar Medium[END_REF]. We calculate the uncertainties on M dust in the same way as DL07, using a Monte-Carlo simulation. Using Eq. 1.18:

L ν = 4πM dust κ ν B ν (T d ) = M dust 8πhκ 0 ν β 0 c 2 ν 3+β exp( hν k B T d ) -1 (1.22)
so that:

L ν ∝ ν 3+β exp( hν k B T d ) -1 (1.23)
which is the simplified form of the modified black body.

Wien's law gives us the dust temperature from the fit of the modified black body:

T = h × c 4.9651k B × λ pic = 2.898 10 -3 λ pic (1.24)
where h is the Planck constant, k B is the Boltzmann constant and c is the speed of light.

Optical and UV

UV emission is associated with the emission of young and massive stars. Young stars radiate predominantly in the ultraviolet and optical domains, and the youngest and most massive of them (OB type stars) will contribute primarily to far-ultraviolet emission. This is why UV brightness is a good indicator of massive star formation (e.g., [START_REF] Kennicutt | The rate of star formation in normal disk galaxies[END_REF][START_REF] Meurer | Starbursts and Star Clusters in the Ultraviolet[END_REF]. However, these young and massive stars are also mainly located in regions that are rich in gas and dust. They are therefore significantly affected by dust obscuration (e.g., [START_REF] Buat | The observation of the nearby universe in UV and in FIR: an evidence for a moderate extinction in present day star forming galaxies[END_REF][START_REF] Kong | Star formation history and dust content of galaxies drawn from ultraviolet surveys[END_REF][START_REF] Cortese | Ultraviolet dust attenuation in star-forming galaxies -II. Calibrating the A(UV) versus L T IR /L U V relation[END_REF]. We also see many emission lines produced in HII regions at UV wavelengths.

X-ray emission

The X-ray emission of a galaxy has several origins. It can come from diffuse hot gas, point source objects such as X-ray binaries or neutron stars, supernova, or the AGN accretion disk of galaxies, which is heated by viscous friction at temperatures ∼10 5 K. The X-ray emission can be divided into soft X-rays (0.1-2keV) and hard X-rays (2-100 keV).

SED fitting

There are several types of models and techniques to fit the spectral energy distribution of a galaxy, whether it is with radiative transfer models (e.g., [START_REF] Siebenmorgen | Dust in starburst nuclei and ULIRGs. SED models for observers[END_REF], empirical templates (e.g., [START_REF] Chary | Interpreting the Cosmic Infrared Background: Constraints on the Evolution of the Dust-enshrouded Star Formation Rate[END_REF][START_REF] Dale | The Infrared Spectral Energy Distribution of Normal Star-forming Galaxies[END_REF][START_REF] Dale | The Infrared Spectral Energy Distribution of Normal Starforming Galaxies: Calibration at Far-Infrared and Submillimeter Wavelengths[END_REF]Draine and Li, 2007;[START_REF] Draine | Andromeda's Dust[END_REF][START_REF] Rieke | Determining Star Formation Rates for Infrared Galaxies[END_REF], or energy balance techniques (e.g., da [START_REF] Da Cunha | A simple model to interpret the ultraviolet, optical and infrared emission from galaxies[END_REF]Nonino et al., 2009;[START_REF] Burgarella | Star formation and dust attenuation properties in galaxies from a statistical ultraviolet-to-far-infrared analysis[END_REF], for example.

In this thesis, we chose to model the spectral energy distributions mainly using CIGALE 19 [START_REF] Noll | Analysis of galaxy spectral energy distributions from far-UV to far-IR with CIGALE: studying a SINGS test sample[END_REF]Nonino et al., 2009;[START_REF] Burgarella | Star formation and dust attenuation properties in galaxies from a statistical ultraviolet-to-far-infrared analysis[END_REF]. When IR information is not available to fit a SED with CIGALE, we will match to the millimeter flux with the dust spectral energy distribution library 20 presented in Schreiber et al. (2018a). The calculation of the star formation rate is done by adding SFR U V (uncorrected for dust attenuation) to the SFR IR , with the method described in Chapter 8. We will also see that SFR total ∼ SFR IR in this chapter, but to be more accurate in our derivation of SFRs, we also include the contribution from SFR U V .

Throughout this thesis, we adopt a spatially flat ΛCDM cosmological model with H 0 = 70 kms -1 Mpc -1 , Ω m = 0.7 and Ω Λ = 0.3. We assume a Salpeter (Salpeter, 1955) Initial Mass Function (IMF). We use the conversion factor of M (Salpeter 1955 IMF) = 1.7 × M (Chabrier 2003 IMF). All magnitudes are quoted in the AB system (Oke and Gunn, 1983).

CHAPTER 2

SUMMARY OF THE WORK DONE IN THIS THESIS

During the three years of my Ph.D., I had the opportunity to work on several different projects.

In particular, I was in charge of the scientific exploitation of the largest deep survey on the sky with ALMA. I will explain these projects in detail in this manuscript. I have had the chance to work on all of the stages of conducting a research project, both upstream and downstream, by writing telescope proposals (for ALMA and VLA), by going directly to observe (VLT), by reducing and analyzing data (CASA, Gildas), by publishing and presenting my research at international conferences and being active in the international community preparing for future projects (TolTEC/LMT). I have also had the opportunity to collaborate, throughout my Ph.D., within major international collaborations (VANDELS, CANDELS and LMT) and have visited regularly colleagues in different institutes in order to exchange and compare viewpoints, and to work on joint projects.

Characterization of the survey and creation of a catalog

The precise characterization of an ALMA survey in the GOODS-South field, the identification of the galaxies present in this survey, the definition of detectability thresholds and indicators that can define the reliability of these detections. The objective was to find the best compromise between the number of sources detected, i.e., to have the most complete sample possible and to have as high reliability as possible, i.e., to ensure that detections are not due to noise. We chose to produce a blind catalog, without using other wavelengths for the selection process, which allowed us to detect sources without optical counterparts. By choosing to create a blind catalog, we allowed a small proportion of spurious sources to be included in our catalog. We quantified this proportion and found criteria for segregation between spurious and "real" sources.

I also created noise maps, using a sigma clipping technique, for our images at different resolutions. We compared several softwares both for source detection (Blobcat, AEGEAN, PyBDSM, Sextractor) and flux extraction (CASA, Blobcat, Galfit). An important part of my work has been to accurately measure the emitted fluxes of these galaxies, and through simulations to determine precisely which fraction of the galaxies could be detected in our maps.

I compared the number of detections, flux, etc., between clean and dirty images and chose to work with the dirty images in order to have better control of our data. To measure the fluxes correctly, we needed to know if the sources were resolved or point-like. This is an important point to be able to quantify the reliability of flux measurements. To measure the size of our detections, we combined several techniques. We stacked all of our detections together and compared them to the PSF size. We also used flux extraction tools to compare the residuals between a point source model (PSF) or a Gaussian or Sérsic profile. We used CASA and Gildas to perform the size analyses in the UV-plane.

30

Chapter 2. Summary of the work done in this thesis I also note an astrometry difference between ALMA and HST images. One systematic offset had already been found. After subtracting this offset, we unveil the presence of a non-negligible local offset, with a structured pattern, resulting from the way the HST maps were built. The precise knowledge of the astronomy of the GOODS-South field has enabled us to confirm in a robust way, the optical counterparts of our ALMA detections.

Number Counts

I computed the completeness of our observations using Monte Carlo simulations performed on a tapered image. I injected artificial sources in each slice to quantify the differences between the fluxes and sizes of the sources injected into the image and the fluxes and sizes measured. I also quantify and model the relation between the number of sources injected and the number of sources found, as a function of the flux and size. This knowledge of the completeness allows us to estimate, from the number of sources detected, and after correcting several observational biases which we will describe in detail in Chapter 5, the theoretical number of sources present, per unit area and per bin of flux, in the GOODS-South field. This work also led to the compilation of data from literature and the creation of a parametrization of the submillimeter number counts. This compilation and the computed fit has since been reused in scientific publications.

Using IRAC priors to probe fainter millimeter galaxies I took advantage of three other wavelengths in addition to our ALMA data (HST/WFC3 H-band, Spitzer/IRAC channel 1 and an ultradeep K s -band image) to lower the detection threshold from 4.8 to 3.5 σ, and thus increase our number of detections. In order to validate the robustness of these prior-based detections, we used statistical tests such as the Kolmogorov-Smirnov test.

The creation of an additional supplementary catalog, based on priors, has two advantages. The first is to increase the number of sources detected with ALMA and therefore have a more robust statistics on our derived properties. The second advantage is to be able to make a comparative study of the galaxies detected at higher flux, without priors and those detected with priors. This study revealed that detection with priors allows us to detect larger, less massive sources that span over a wider redshift range than the galaxies of the main catalog.

HST-dark galaxies

During the creation of our catalogs, blind and with priors, we detected several sources without optical counterparts. The advantage of a blind survey is that they can reveal the presence of sources missed by the HST, that we believe may represent the missing candidates responsible for the formation of massive elliptical galaxies. As these sources are rare, they highlight the importance of a survey over a larger area than other studies, as we have done here, despite the ALMA limited field of view.

I used several spectral energy distribution (SED) fitting tools, such as Le PHARE and EAZY, to estimate the stellar masses and redshifts of our sample. I investigated whether the flux of HSTgalaxies arose from neighboring galaxies by using SED models to also measure the redshifts and stellar masses of nearby galaxies, and estimated the dust temperature that nearby galaxies would need to have if they were responsible for generating the ALMA flux.

We found that all of the sources without an optical counterpart had an infrared counterpart, visible in deep Spitzer/IRAC images. I quantified the probability that these are chance alignments as a function of distance to the infrared counterpart, and we calculate for each HST-dark galaxy a percentage of random false associations through Monte Carlo simulations.

Properties of detected sources

I fit the multiwavelength SED with CIGALE to derive several properties of these galaxies. I also used the IDL routine DecompIR to split the IR-SED into AGN and host-galaxy components. These fits allowed us to calculate the dust masses of the galaxies. Based on these dust masses and an assessment of the metallicity of the galaxies, we were able to derive the gas mass. I compared the amount of gas found by this technique with other methods used in the literature. I also calculated the dust temperature using a modified blackbody model and compared the dust temperature of the ALMA detected galaxies to all of the galaxies lying in the GOODS-ALMA field. We aimed to confirm that the detection of ALMA sources was not biased due to a lower dust temperature therefore making it easier to detect these galaxies.

I was able, from the IR and UV luminosities, to determine the star formation rate of the galaxies detected with ALMA, and estimate the proportion of galaxies on the main sequence compared with the starburst galaxies.

I compared the size of galaxies calculated in the H-band, which are on the relation of uvj active galaxies (at the same mass and redshift), with the millimeter sizes, which are particularly compact. I also note that a significant part of our galaxy sample has abnormally low gas fractions while having a star formation rate higher than the main sequence.. The underlying question in the study is to understand whether these distant, dusty, massive, high star-forming galaxies can be the progenitors of passive galaxies that are known to be compact at z = 2. Thanks to radio observations of the GOODS-South field, we also studied the evolution of the ratio between infrared and radio luminosity as a function of redshift.

I also calculated the star formation efficiency of galaxies as a function of IR brightness density, confirmed that there is a strong relationship between these two quantities and parameterized it.

The more concentrated a galaxy's brightness surface is, the greater its star formation efficiency.

Contribution as a co-author

I was pleased to be able to collaborate with other researchers during my Ph.D., and to be involved in several papers as a co-author. The list of papers for which I contributed can be found in Chapter 11.

In particular, I contributed to D. Elbaz's paper on starbursts in and out of the star-formation main sequence. For this paper, I fit IR SEDs and AGN SEDs to derive the star formation rate, as well as the contribution to IR luminosity due to an AGN, for a sample of 7 galaxies.

I also participated in the VANDELS collaboration, in particular by observing high redshift galaxies within the Chandra Deep Field South and UKIDSS Ultra Deep Survey survey field, using the multi-object spectrograph VIMOS on the VLT. I am a co-author of two papers, by R. McLure and L. Pentericci respectively, presenting this project and the first results.

I am a co-author of a paper by W. Rujopakarn, who observed at high resolution (200-parsec resolution) with ALMA to reveal the morphology of the dust distribution in galaxies. I contributed to this paper by correcting the astrometry between ALMA and HST observations. I am also co-author of a paper by T. Wang on the proportion of optically-dark galaxies among massive galaxies in the early Universe. My primary contribution to this paper was to perform a compared analysis of the fluxes ratio between IRAC and ALMA for the optically dark galaxies detected in the GOODS-ALMA survey and the H-dropout sample from T. Wang.

I also reduced data from the combination of the NOEMA interferometer and the 30m IRAM antenna, to be able to measure the CO transition for a highly lensed galaxy. This study will be presented in Rujopakarn et al., in prep. In addition, I collaborated in the study of an optically dark galaxy, detected in GOODS-ALMA. This galaxy has the intriguing behavior of being located in the center of an overdensity of several galaxies at z ∼ 3.5 and being the most massive galaxy at z/,> 3 without an AGN in this part of the sky. This work will be presented in detail in Zhou et al. in prep. And finally, I provided a literature compilation of number counts for G. Popping and discussed with him about the redshift distribution. These results will be presented in Popping et al. in prep.

Observations and proposals

I observed during seven nights at the VLT on the wide field imager and multi-object spectrograph VIMOS for the VANDELS survey. VANDELS is an ESO spectroscopic survey targeting galaxies at z > 2.5 within the Chandra Deep Field South (CDFS) and UKIDSS Ultra Deep Survey (UDS) survey fields. The goal of this survey is to constrain the metallicity, dust content and star-formation rates of more than two thousand 2.5 < z < 5.5 galaxies with a high signal-to-noise ratio (minimum of 20 hours per source to a maximum of 80 hours per source). I had an active role in these observations, identifying the guide stars and adjusting the instrumental offset to be applied to the telescope to center the guide stars. I regularly measured the diffraction spot caused by these guide stars to control the quality of the observations and change the observed field when necessary.

During this Ph.D., I apply for several observation with ALMA and VLA as principal investigator.

The complete list of proposals (accepted and pending) is given in Chapter 12. The ALMA data of one of this proposal have just been delivered.

Teaching and outreach

I have devoted a significant part of my Ph.D. to science outreach and teaching activities. At university, during these last three years, I was a teaching assistant in Physics (mechanics, fluid mechanics, electrostatics, acoustics, imaging), and informatics. In addition to astronomy outreach and teaching activities that I regularly carry out in different associations, I have participated in several occasional events such as science cafés, debates in museums, observation evenings, thesis presentation contest or radio broadcast 1 .

I have also written outreach scientific articles for CEA's communication, through a "Highlight" 2 on the HST-dark galaxies detected by ALMA, an article for the Fundamental Research Division 3 , as well as an article in the monthly journal of CEA "Défis du CEA".

CHAPTER 3

GOODS-ALMA

In this chapter, we will discuss the deep fields in astronomy, explain why the GOODS-South field was chosen and observed by ALMA, and then detail the exceptional multiwavelength coverage of this part of the sky. We then explain in detail how ALMA images and noise maps were created and give the characteristics of these images.

Historical context

The history of deep contiguous fields in astronomy is closely linked to Robert Williams' pioneering choices. Director of the Space Telescope Science Institute (StSci), he decided, against the opinion of many of his collaborators, to dedicate a large part of his Director's Discretionary time to pointing the Hubble Space Telescope towards nothing. He chose a region of the sky (∼ 4 square arcminutes, RA = 12h 36m 49s, Dec. = +62 • 12 58 ;J2000), close to the seven brightest stars of the Big Dipper constellation, in which there were a low density of nearby bright stars, and which has a low Galactic extinction. This observation, which lasted 10 consecutive days (about 150 orbits) from December 18 to 30, 1995, of the region now known as the Hubble Deep Field [START_REF] Williams | The Hubble Deep Field: Observations, Data Reduction, and Galaxy Photometry[END_REF] revealed thousands of galaxies (e.g., [START_REF] Abraham | Galaxy morphology to I=25 mag in the Hubble Deep Field[END_REF][START_REF] Van Den Bergh | A Morphological Catalog of Galaxies in the Hubble deep Field[END_REF]. "The image provides both a new source of inspiration for those interested in the wonders of the universe, and the latest and greatest source of data in a long line of surveys that push the limits of technology to attempt to see what galaxies like our own looked like in their early stages of evolution" [START_REF] Ferguson | The Hubble Deep Field[END_REF]. This image, which has become one of the most famous in astronomy, has made it possible, by extrapolation, to have a first idea of the number of galaxies in our universe and trace back the cosmic history of star formation (see Sect. 1.4). This region was subsequently observed at many different wavelengths by several telescopes as we will detail in Sect. 3.3.

To test the isotropy and homogeneity of the Universe, another region of the sky was observed in 1998 October, this time in the southern hemisphere, the Hubble Deep Field-South (HDF-S; RA = 22h 32m 56.22s and declination of -60 • 33' 02.69"), in a program similar to the northern Hubble Deep Field [START_REF] Williams | The Hubble Deep Field South: Formulation of the Observing Campaign[END_REF][START_REF] Ferguson | The Hubble Deep Fields[END_REF]. One of the many results of this comparative analysis was to show that these two fields are qualitatively similar [START_REF] Casertano | WFPC2 Observations of the Hubble Deep Field South[END_REF].

The GOODS fields (GOODS-North and GOODS-South) are successors and extensions of the Hubble Deep Field (HDF). The launch of the Spitzer space telescope in 2003 allowed us to observe much larger fields. While the GOODS-North field is a direct extension of the HDF, the GOODS-South field was chosen to be part of the Chandra Deep Field South (CDF-S). This field was observed by the Chandra X-ray observatory [START_REF] Weisskopf | Advanced X-Ray Astrophysics Facility (AXAF)[END_REF], centered at RA 3h 32m 28.0s DEC -27 • 48 30 (J2000.0) [START_REF] Giacconi | The Chandra Deep Field South[END_REF][START_REF] Giacconi | First Results from the X-Ray and Optical Survey of the Chandra Deep Field South[END_REF][START_REF] Giacconi | Chandra Deep Field South: The 1 Ms Catalog[END_REF] and was chosen for its low 36 Chapter 3. GOODS-ALMA Galactic extinction, containing no stars brighter than m v ∼ 14 and being well located, such that this field is accessible to observations with 8 m class telescopes such as the VLT and Gemini (Giacconi et al., 2002). Because Milky Way gas did not make ideal observations in HDF-S for both VLT and X-observations with Chandra, another field was chosen, the GOODS-South field. The GOODS-South field is therefore centered on the Chandra Deep Field South.

This corresponds to the period of the Great Observatories four telescopes that were launched between 1990 and 2003 to observe the sky at four different wavelengths (see Fig. 3.1). The Hubble Space Telescope (HST) observes at optical, near ultraviolet and (since 1997 with the installation of the new WFC3 camera), in near infrared. The Compton Gamma Ray Observatory (CGRO) captured gamma-ray (and later, hard x-ray) emission. We can observe the infrared with the Spitzer Space Telescope (SST), and X-ray emission with the Chandra X-ray Observatory (CXO).

The GOODS-South field is also part of a larger program, The Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS, Koekemoer et al. (2011); Grogin et al. (2011)). This program was presented at an August 2013 press conference1 as "the largest project in the history of Hubble". The CANDELS program, which includes five deep fields (GOODS-South, GOODS-North, COSMOS, EGS and UDS), will be briefly presented in the next section.

CANDELS

This large survey, 902-orbit Multi-Cycle Treasury (MCT) was designed, among other things, to probe the evolution of galaxies and black holes at z ∼ 1.5-8, to have several observations of galaxies in the reionization era ("cosmic dawn"), study the growth and morphological transformation of galaxies, measure supernova rate evolution and test Type Ia supernovae to determine if they can be used as standard candles for cosmological use, to investigate the role and transformation induced by active galactic nucleus (AGN) activity and understand how star formation proceeds and how galaxies quench at z > 2 (Grogin et al., 2011). The focus of the observation of the five CANDELS fields was to use the brand new HST/WFC3 camera that was installed on Hubble in May 2009. This new camera, which allows us to reach extremely distant objects, is associated with HST/ACS in order to benefit from multi-wavelength coverage from optical to near infrared, covering a surface of about 800 arcmin 2 (Guo et al., 2013). The five CANDELS fields that are located in both the southern and northern celestial hemisphere include:

- To summarize, the CANDELS survey can be divided in two parts, ordered by depth in H-band: deep regions (CANDELS/Deep; 5σ point-source limit H = 27.7 mag) within a part of the GOODS-North and GOODS-South (∼ 125 arcmin 2 ), and wider regions (CANDELS/Wide; 5σ point-source limit H > 27 mag) within the other part of the GOODS fields, COSMOS, UDS and EGS (∼ 675 arcmin 2 ). The details are a little more complex, with some of these fields themselves being split into wide and deep regions.

In total, more than 250 000 galaxies (Grogin et al., 2011) were detected in the CANDELS program. In the following, we will focus in detail on one of these five fields, the GOODS-South field, that was chosen to be observed by ALMA. We will first describe the multi-wavelength coverage, the characteristics of this field and then finish by presenting the GOODS-ALMA survey, its purpose and how the ALMA observations were made.

Multi-wavelength coverage

The area covered by the GOODS-ALMA survey is ideally located, in that it profits from ancillary data from some of the deepest sky surveys at infrared (IR), optical and X-ray wavelengths including the Spitzer Extended Deep Survey (Ashby et al., 2013), the GOODS-Herschel Survey (Elbaz et al., 2011), the Chandra Deep Field-South (Luo et al., 2017) and ultra-deep radio imaging with the VLA (Rujopakarn et al., 2016). In addition, the region covered by ALMA in this survey corresponds to the region with the deepest HST-WFC3 coverage, and has also been chosen for a guaranteed time observation (GTO) program with the James Webb Space Telescope (JWST).

In this section, we describe all of the data that were used in the analysis of the ALMA data.

Optical/near-infrared imaging

We have supporting data from CANDELS; Grogin et al. 2011) with images obtained with the Wide Field Camera 3/infrared channel (WFC3/IR) and UVIS channel, along with the Advanced Camera for Surveys (ACS; Koekemoer et al. 2011. The area covered by this survey lies in the deep region of the CANDELS program (central one-third of the field). The 5-σ detection depth for a point-source reaches a magnitude of 28.16 for the H 160 filter (measured within a fixed aperture of 0.17 ; Guo et al. 2013). The CANDELS/Deep program also provides images in 7 other bands: the Y 125 , J 125 , B 435 , V 606 , i 775 , i 814 and z 850 filters, reaching 5-σ detection depths of 28.45, 28.35, 28.95, 29.35, 28.55, 28.84, and 28.77 mag respectively.

The Guo et al. (2013) catalog also includes galaxy magnitudes from the VLT, taken in the U -band with VIMOS (Nonino et al., 2009), and in the K s -band with ISAAC (Retzlaff et al., 2010) and HAWK-I (Fontana et al., 2014).

In addition, we use data coming from the FourStar Galaxy Evolution Survey (ZFOURGE, PI: I. Labbé) on the 6.5 m Magellan Baade Telescope. The FourStar instrument (Persson et al., 2013) observed the CDFS (encompassing the GOODS-South Field) through 5 near-IR medium-bandwidth filters (J 1 , J 2 , J 3 , H s , H l ) as well as broad-band K s . By combination of the FourStar observations in the K s -band and previous deep and ultra-deep surveys in the K-band, VLT/ISAAC/K (v2.0) from GOODS (Retzlaff et al., 2010), VLT/HAWK-I/K from HUGS (Fontana et al., 2014), CFHST/WIRCAM/K from TENIS (Hsieh et al., 2012) and Magellan/PANIC/K in HUDF (PI: I. Labbé), a super-deep detection image has been produced. The ZFOURGE catalog reaches a completeness greater than 80% to K s < 25.3 -25.9 (Straatman et al., 2016).

We use the stellar masses and redshifts from the ZFOURGE catalog, except when spectroscopic redshifts are available. Stellar masses have been derived from Bruzual and Charlot (2003) models (Straatman et al., 2016) assuming exponentially declining star formation histories and a dust attenuation law as described by Calzetti et al. (2000).

Mid/far-infrared imaging

Data in the mid and far-IR are provided by the Infrared Array Camera (IRAC; Fazio et al. 2004) at 3.6, 4.5, 5.8, and 8 Labbé et al., 2015).

The flux extraction and deblending in 24 µm imaging have been provided by Magnelli et al. (2009) to reach a depth of S 24 ∼30 µJy. Herschel images come from a 206.3 h GOODS-South observational program (Elbaz et al., 2011) and combined by Magnelli et al. (2013) with the PACS Evolutionary Probe (PEP) observations (Lutz et al., 2011). Because the SPIRE confusion limit is very high, we use the catalog of T. Wang et al. (in prep), which is built with a state-of-the art de-blending method using optimal prior sources positions from 24 µm and Herschel PACS detections.

Complementary ALMA data

As the GOODS-South Field encompasses the Hubble Ultra Deep Field (HUDF), we take advantage of deep 1.3-mm ALMA data of the HUDF. The ALMA image of the full HUDF reaches a σ 1.3mm = 35 µJy (Dunlop et al., 2017), over an area of 4.5 arcmin 2 that was observed using a 45-pointing mosaic at a tapered resolution of 0.7 . These observations were taken in two separate periods from July to September 2014. In this region, 16 galaxies were detected by Dunlop et al. (2017), 3 of them with a high SNR (SNR > 14), the other 13 with lower SNRs (3.51 < SNR < 6.63).

Chapter 3. GOODS-ALMA

We also take advantage of the recent ALMA twenty-six arcmin 2 survey of GOODS-S at onemillimeter (ASAGAO). This survey reaches a depth of 61 µJy beam -1 in a tapered map with a beam of 0 51 × 0 45.The observations were made during the month of September 2016 (Project code: 2015.1.00098.S, PI: K. Kohno) at 1.2mm. This survey is composed of 9 sub-surveys, each one was covered by 90-pointing mosaic in a C40-6 array configuration. In total, 45 sources were detected in this survey (combined with the HUDF-ALMA survey described above) with an SNR > 4.5.

Radio imaging

We also use radio imaging at 5 cm from the Karl G. Jansky Very Large Array (VLA). These data were observed during 2014 March -2015 September for a total of 177 hours in the A, B, and C configurations (PI: W. Rujopakarn). The images have a 0 31 × 0 61 synthesized beam and an rms noise at the pointing centre of 0.32 µJy.beam -1 (Rujopakarn et al., 2016). Here, 179 galaxies were detected with a significance greater than 3 σ over an area of 61 arcmin 2 around the HUDF field, with a rms sensitivity better than 1 µJy.beam -1 . However, this radio survey does not cover the entire ALMA area presented in this paper. We also use an other radio imaging at 10cm, also from the Karl G. Jansky Very Large Array (VLA; PI: W. Rujopakarn, private communication). This radio image, centered on the Hubble Ultra Deep Field (HUDF) encompasses the entire GOODS-ALMA field and was observed for a total of 177 hours (configurations A, B, & C) to reach a depth of σ rms = 0.32 µJy/beam with a resolution of ∼ 0.3".

X-ray

The Chandra Deep Field-South (CDF-S) was observed for 7 Msec between 2014 June and 2016 March. These observations cover a total area of 484.2 arcmin 2 , offset by just 32 from the centre of our survey, in three X-ray bands: 0.5-7.0 keV, 0.5-2.0 keV, and 2-7 keV (Luo et al., 2017). The average flux limits over the central region are 1.9 × 10 -17 , 6.4 × 10 -18 , and 2.7 × 10 -17 erg cm -2 s -1 respectively. This survey enhances the previous X-ray catalogs in this field, the 4 Msec Chandra exposure (Xue et al., 2011) and the 3 Msec XMM-Newton exposure (Ranalli et al., 2013). We will use this X-ray catalog to identify candidate X-ray active galactic nuclei (AGN) among our ALMA detections.

Spectroscopic-survey

In addition, the GOODS-South field, or in some cases its deepest region, the HUDF, has been the target of several spectroscopic observations (e.g., Le [START_REF] Le Fèvre | The VIMOS VLT Deep Survey. Public release of 1599 redshifts to I AB ≤24 across the Chandra Deep Field South[END_REF][START_REF] Szokoly | The Chandra Deep Field-South: Optical Spectroscopy[END_REF][START_REF] Mignoli | The K20 survey. VII. The spectroscopic catalogue: Spectral properties and evolution of the galaxy population[END_REF][START_REF] Ravikumar | New spectroscopic redshifts from the CDFS and a test of the cosmological relevance of the GOODS-South field[END_REF]Cimatti et al., 2008;Vanzella et al., 2008;[START_REF] Popesso | The great observatories origins deep survey. VLT/VIMOS spectroscopy in the GOODS-south field[END_REF]Wuyts et al., 2009;[START_REF] Balestra | The Great Observatories Origins Deep Survey[END_REF][START_REF] Silverman | The Extended Chandra Deep Field-South Survey: Optical Spectroscopy of Faint X-ray Sources with the VLT and Keck[END_REF]Le Fèvre et al., 2013;[START_REF] Morris | A WFC3 Grism Emission Line Redshift Catalog in the GOODS-South Field[END_REF][START_REF] Kriek | The MOSFIRE Deep Evolution Field (MOSDEF) Survey: Rest-frame Optical Spectroscopy for ˜1500 H-selected Galaxies at 1.37 < z &lt[END_REF]Momcheva et al., 2016;[START_REF] Mclure | The VANDELS ESO public spectroscopic survey[END_REF][START_REF] Urrutia | The MUSE-Wide Survey: survey description and first data release[END_REF]. In total, there are more than 20,000 galaxies for which spectroscopic redshifts have been determined in the GOODS-South field, including about 7750 in the GOODS-ALMA field.

Completeness

The mass completeness of the GOODS-South field with Herschel was studied by Schreiber et al. (2015). The results obtained in this study are reported in the Table 3.1. Completeness was obtained by generating a mock population with a given stellar mass, associating a brightness function with these galaxies and adding a Gaussian error. These results are on average 0.3 dex lower than the results of [START_REF] Pannella | GOODS-Herschel: Star Formation, Dust Attenuation, and the FIR-radio Correlation on the Main Sequence of Star-forming Galaxies up to z ∼4[END_REF], who estimated the completeness using a stellar population model from [START_REF] Rodighiero | The first Herschel view of the mass-SFR link in high-z galaxies[END_REF].

Over the range of redshifts and stellar masses of our ALMA detections, the CANDELS catalog is 90% complete. We give the number of galaxies in some of the main catalogs in To accommodate such a large number of pointings within the ALMA Cycle 3 observing mode restrictions, we divided this mosaic into six parallel, slightly overlapping, sub-mosaics of 141 pointing each. To get a homogeneous pattern over the 846 pointings, we computed the offsets between the sub-mosaics so that they connect with each other without breaking the hexagonal pattern of the ALMA mosaics.

Survey presentation

Each sub-mosaic (or slice) has a length of 6.8 arcmin, a width of 1.5 arcmin and an inclination (PA) of 70 deg (see Fig. 4.3). This required three execution blocks (EBs), yielding a total onsource integration time of ∼ 60 seconds per pointing (Table 3 .6). We determined that the highest frequencies of the band 6 is the optimal setup for a continuum survey and we thus set the ALMA correlator to Time Division Multiplexing (TDM) mode and optimised the setup for continuum detection at 264.9 GHz (λ = 1.13 mm) using four 1875 MHz-wide spectral windows centered at Chapter 3. GOODS-ALMA 255.9 GHz, 257.9 GHz, 271.9 GHz and 273.9 GHz, covering a total bandwidth of 7.5 GHz (see Fig. 3.8). The bandwidth of the four spectral windows at 255.9 GHz, 257.9 GHz, 271.9 GHz and 273.9 GHz are represented with blue line within the sideband in yellow. The atmospheric transmission curve is also display in gray. The TDM mode has 128 channels per spectral window, providing us with ∼37 km/s velocity channels. We illustrate, in Fig. 3.9 a source in the continuum image (bottom left image) as well as in a random channel (top left image). The spectrum of this detection is given on the central panel while an illustration of the stacking process, to produce the image in the continuum, is presented in Fig. 3.9, right panel. We also used these channels to investigate whether we could detect an emission line. This search did not reveal the presence of an emission line among our detections.

Observations were taken between the 1 st of August and the 2 nd of September 2016, using ∼40 antennae (see Table 3.6) in configuration C40-5 with a maximum baseline of ∼ 1500 m. J0334-4008 and J0348-2749 (VLBA calibrator and hence has a highly precise position) were systematically used as flux and phase calibrators, respectively. In 14 EBs, J0522-3627 was used as 3.5. Mosaic 47 bandpass calibrator, while in the remaining 4 EBs J0238+1636 was used. Observations were taken under nominal weather conditions with a typical precipitable water vapour of ∼ 1 mm.

Data reduction

All EBs were calibrated with CASA (McMullin et al., 2007) using the scripts provided by the ALMA project. Calibrated visibilities were systematically inspected and few additional flaggings were added to the original calibration scripts. Flux calibrations were validated by verifying the accuracy of our phase and bandpass calibrator flux density estimations.

Finally, to reduce computational time for the forthcoming continuum imaging, we time-and frequency-averaged our calibrated EBs over 120 seconds and 8 channels, respectively. Imaging was done in CASA using the multi-frequency synthesis algorithm implemented within the task CLEAN. Sub-mosaics were produced separately and combined subsequently using a weighted mean based on their noise maps. As each sub-mosaic was observed at different epochs and under different weather conditions, they exhibit different synthesized beams and sensitivities (Table 3.6). Sub-mosaics were produced and primary beam corrected separately, to finally be combined using a weighted mean based on their noise maps.

To obtain a relatively homogeneous and circular synthesized beam across our final mosaic, we applied different u, v tapers to each sub-mosaic. The best balance between spatial resolution and sensitivity was found with a homogeneous and circular synthesized beam of 0 29 Full Width Half Maximum (FWHM; hereafter 0 29-mosaic; Table 3 .6). This resolution corresponds to the highest resolution for which a circular beam can be synthesized for the full mosaic.

We also applied this tapering method to create a second mosaic with an homogeneous and circular synthesized beam of 0 60 FWHM (hereafter 0 60-mosaic; Table 3.6), i.e., optimised for the detection of extended sources. Mosaics with even coarser spatial resolution could not be created because of drastic sensitivity and synthesized beam shape degradations.

Due to the good coverage in the uv-plane (see Fig. 3.6) and because the sources present in our image do not cover a large dynamic range in flux densities (see Sect. 4.3), the lobes of our dirty beams do not carry significant amounts of flux (see Fig. 4.8). To prevent any bias generated by the CLEAN process, we decided to work with the dirty map. We have cleaned all maps imaged at the original beam size to test the possible gain that would result from the cleaning process. The noise in these clean maps is not significantly better (< 1%), suggesting that indeed it is not necessary to clean these maps. In Fig. 3.10, we show the clean (left panel) as well as the dirty beam (right panel).

Mosaic

The GOODS-ALMA field was observed by ALMA over a continuous area of ∼ 70 arcmin 2 via a mosaic of 846 pointings (see Fig. 3.13). The antenna half power beam width (HPBW) is: The projection of these beams according to each of the dimensions is also represented. Because the clean and the dirty beam are very similar and in order to prevent any bias generated by the CLEAN process, we decided to work with the dirty map.

θ P B = A × λ D (3.1) X [p x ]
with λ the observed wavelength and D the diameter of a single antenna. This field of view is therefore independent of the interferometer configuration. The factor A depends on the morphology of the observation instrument. A = 1.22 for a single dish and less than 1.22 for an interferometer. In our configuration, with a wavelength of 1.13 mm and an antenna diameter of 12 m, the HPBW is ∼ 23.3". The [START_REF] Ekers | Short Spacing Synthesis from a Primary Beam Scanned Interferometer[END_REF] theorem tell us that an interferometer does not just measure the angular scale

θ = λ/b (3.2)
with b the length of a baseline (distance between 2 antennas); but the interferometer can also measures all the angular scales

λ/(b + D) < θ < λ/(b -D) (3.3)
3.6. Noise map with D the diameter of an antenna. A few years later, [START_REF] Cornwell | Radio-interferometric imaging of very large objects[END_REF] understands that the Ekers theorem allows an interferometer to perform wide-field imaging [START_REF] Pety | Revisiting the theory of interferometric wide-field synthesis[END_REF] There is a decrease in sensitivity when you move away from the centre of the pointing (see Fig. 3.11). A primary beam correction was applied after the mosaic was created to compensate for this decrease in sensitivity and make the sensitivity uniform over the entire surface. The sensitivity of a mosaic also depends on the position and spacing of the different pointings. There are different patterns to form a mosaic. The most commonly used are the organization of pointings in rectangular grid or hexagonal grid (see Fig. 3.12). FIGURE 3.12: Example of different patterns to create a mosaic. Left panel: rectangular grid. The separation between the center of two pointings is λ/2D to meet the Nyquist sampling criteria. Right panel: Hexagonal grid. In this configuration the distance between 2 pointings is λ/( √ 3D). This last configuration requires more pointings to cover the same area as a rectangular grid but ensures a sensitivity close to the uniform universe.

For rectangular paving, the distance between the center of two pointings is λ/2D to meet the sampling criterion of [START_REF] Nyquist | Certain Topics in Telegraph Transmission Theory[END_REF]. For hexagonal paving, the distance between the center and two pointings is λ/( √ 3D). The pointings are therefore closer to each other, so more pointings are needed to cover the same area as for a rectangular grid. A hexagonal grid ensures a sensitivity close to the uniform with a minimum number of pointings (ALMA Partnership et al., 2016).

According to [START_REF] Cornwell | Radio-interferometric imaging of very large objects[END_REF], it is theoretically the optimal sampling of a field.

ALMA imposes a limitation on the number of pointings per observation block. The total number of pointings must be less than or equal to 150. 846 pointing is required to fully map the deepest part of the CANDELS program in GOODS-South, so this region has been divided into 6 slices containing 141 pointings (see Fig. 3.13).

The next generation of telescopes and (sub)millimeter survey will make it possible to get rid of these combinations of pointings by allowing continuous observations to be made directly by the On-The-Fly observing mode.

Noise map

Building of the noise map

We build the RMS-map of the ALMA survey by a k-σ clipping method. This method can be applied when the pixel distribution is Gaussian (or almost Gaussian), centered on zeros and when the sources are relatively punctual. It is also a very effective method to remove all outliers from an image such as cosmic rays [START_REF] Akhlaghi | Noise-based Detection and Segmentation of Nebulous Objects[END_REF]. This method is iterative, for each pixel of our image, we calculate the standard division (σ) and median (m) of all pixels contained in a square centered on the central pixel. The size of the region to be taken into account was determined by performing a series of tests. We calculated the median of the standard deviations as a function of the size of the region considered (see Fig. 3.14 and Table 3.4). We wanted to find the smallest region to best respect local variations in image sensitivity and be as accurate as possible, large enough that this region would not be affected by sources that might be present. In the end a size of 100 × 100 pixels was chosen from the map tapered at 0.60" (the pixel size is 0.1").

The pixels, inside this box, with values greater than 3 times the standard deviation (σ) from the median value were masked. This procedure was repeated 3 times unless the exit criteria is reached before then. One of the classic criteria used is to set a threshold beyond which the iterative process stops. We did not use this exit criterion but another one: if the standard deviation in step n+1 is greater than or equal to the standard deviation in step n+1, the process stops.

In steps of 4 pixels on the image map, the standard deviation was computed in a square of 100 × 100 pixels around the central pixel. The pixels, inside this box, with values greater than 3 times the standard deviation (σ) from the median value were masked. This procedure was repeated 3 times. Finally, we assign the value of the standard deviation of the non-masked pixels to the central pixel. The step of 4 pixels corresponds to a sub-sampling of the beam so, the noise should not vary significantly on this scale. The median value of the standard deviation is 0.176 mJy.beam -1 . In comparison, the Gaussian fit of the unclipped map gives a standard deviation of 0.182 mJy.beam -1 . We adopt a general value of rms sensitivity σ = 0.18 mJy.beam -1 . The average values for the 0 29-mosaic and the untapered mosaic are given in Table 3.6.

Sampling Theorem

To ensure that the information contained in the uv plane is not lost when the image is created, the pixel size has been carefully chosen. The pixel size must satisfy the Nyquist criteria [START_REF] Nyquist | Certain Topics in Telegraph Transmission Theory[END_REF] demonstrated a few years later by Shannon [START_REF] Shannon | Communication in the Presence of Noise[END_REF] With the exception of slice B, which has a higher average noise than the others (224 µJy), the average noise of the other slices is between 164 and 186 µJy (see Table3.6. The edge of the noise map does not benefit from the overlapping of several pointings and has a higher noise level than the rest of the map. In the analysis of the image tapered at 0.6", areas located on the edge and having a noise greater than 0.3 mJy.beam -1 will not be taken into account.

The pixel size in the image plane must therefore be at most half of the synthesized beam size and satisfy the following equation:

∆l < 1 2u max ∆m < 1 2v max (3.4)
In practice, to ease deconvolution the image must be created with a sampling greater than the Nyquist's criteria. [START_REF] Felli | Book-Review -Very Long Baseline Interferometry -Techniques and Applications[END_REF] for example, recommend choosing a pixel size so that there is 3 to 5 pixels across the FWHM. The pixel size chosen was therefore 0 1 for the 0 60 mosaic and 0 05 for the 0 29 mosaic and 0 05 for the untapered image.

Tapering

We have produced maps with different levels of tapering, in other words, apodize the (u,v) sampling by a Gaussian:

W (u, v) = exp - u 2 + v 2 t 2 (3.5)
with t the tapering parameter.

The use of tapering will considerably increase the detectability of an extended source. On the other hand, the spatial resolution is also degraded.

The tapering in our survey will allow both: (i) to reduce the number of independent beams; (ii) to prevent the resolution of extended sources.

The reduction in the number of beams induced by a purely statistical effect reduces the number of spurious detections. This is what we illustrated in the Table 3.5. If we set our detection threshold at 4σ, we expect 39 false detections in the image tapered at 0.60" while we can have 170 in the map at 0.60". However, by tapering our map, we also degrade the sensitivity of our detections: 4 σ corresponds on average to 0.47mJy in the map at 0.29", while it corresponds to 0.73mJy in the map at 0.60". We will discuss in detail, in the Sect. 4.3 the delicate balance to be found between reducing the number of spurious sources and the desire to have as complete a catalog as possible.

The tapering also allows to reveal extended sources that would have been missing in the map at 0.29". In Fig. 3.17, we show the example of two sources, the top line shows AGS18. This is the most extended source of our main catalog (see Sect. 4.3), it is neither detected in the untapered image nor in the mosaic at 0.29". On the other hand, the AGS3 source, which is a compact source, is detected at all resolutions. The size of this source in the image will be very similar to the size of the beam. From the mosaic and noise map, described in the previous chapter, we will present in this chapter the way we have proceeded to detect sources. We wanted to create a blind catalog, i.e., without being biased by information from other wavelengths in order to be able to include sources that would have been missed during previous surveys, for example with the HST.

In this Chapter, we will explain how we determined the threshold of detectability that allowed us to obtain the best compromise between the number of detections and the lowest possible number of spurious sources. We will then present the methods used to calculate the flux of galaxies. Finally, from the counterparts to which we have associated these sources, we will investigate some properties of our galaxies such as redshift and mass distributions. We will see that some of these galaxies do not have optical counterparts and devote Chapter 7 to these HST-dark galaxies.

Source Detection

The search for faint sources in high-resolution images with moderate source densities faces a major limitation. At the native resolution (0 .25 × 0 .23), the untapered ALMA mosaic encompasses almost four million independent beams, where the beam area is

A beam = π × FWHM 2 /(4ln(2)) 1 .
It results that a search for sources above a detection threshold of 4-σ would include as many as 130 spurious sources assuming a Gaussian statistics. Identifying the real sources from such catalog is not possible knowing that the total number of sources is ∼200. In order to increase the detection quality to a level that ensures a purity greater than 80% -in other words, the excess of sources in the original mosaic needs to be five times greater than the number of detections in the mosaic multiplied by (-1) -we have decided to use a tapered image and adapt the detection threshold accordingly.

By reducing the weight of the signal originating from the most peripheral ALMA antennae, the tapering reduces the angular resolution hence the number of independent beams. The lower 58 Chapter 4. Creation of the ALMA source catalog angular resolution presents the advantage of optimizing the sensitivity to point sources -we recall that 0 .24 corresponds to a proper size of only 2 kpc at z ∼1-3 -and therefore will result in an enhancement of the signal-to-noise ratio for the sources larger than the resolution.

We chose to taper the image with a homogeneous and circular synthesized beam of 0 .60 FWHM -corresponding to a proper size of 5 kpc at z ∼1-3 -having tested various kernels and finding that this beam was optimized for our mosaic, avoiding both a beam degradation and a too heavy loss of sensitivity. This tapering reduces by nearly an order of magnitude the number of spurious sources expected at a 4-σ level down to about 19 out of 600 000 independent beams. However, we will check in a second step whether we may have missed in the process some compact sources by also analyzing the 0 .29 tapered map.

We also excluded the edges of the mosaic, where the standard deviation is larger than 0.30 mJy.beam -1 in the 0 .60-mosaic. The effective area was thus reduced by 4.9% as compared to the full mosaic (69.46 arcmin 2 out of 72.83 arcmin 2 ).

To identify the galaxies present on the image, we used BLOBCAT (Hales et al., 2012). BLOBCAT is a source extraction software using a "flood fill" algorithm to detect and catalog blobs (see Hales et al. 2012). A blob is defined by two criteria:

-at least one pixel has to be above a threshold (σ p ) -all the adjacent surrounding pixels must be above a floodclip threshold (σ f ) where σ p and σ f are defined in number of σ, the local RMS of the mosaic.

A first guess to determine the detection threshold σ p is provided by the examination of the pixel distribution of the signal to noise map (S/N-map). The S/N-map has been created by dividing the 0 .60 tapered map by the noise map. Fig. 4.1 shows that the S/N-map follows an almost perfect Gaussian below S/N = 4.2. Above this threshold, a significant difference can be observed that is characteristic of the excess of positive signal expected in the presence of real sources in the image. However, this histogram alone cannot be used to estimate a number of sources because the pixels inside one beam are not independent of one another. Hence although the non-Gaussian behavior appears around S/N = 4.2 we performed simulations to determine the optimal values of σ p and σ f .

Threshold determination

We first conducted positive and negative -on the continuum map multiplied by (-1) -detection analysis for a range of σ p and σ f values ranging from σ p = 4 to 6 and σ f = 2.5 to 4 with intervals of 0.05 and imposing each time σ p ≥ σ f . The difference between positive and negative detections for each pair of (σ p , σ f ) values provides the expected number of real sources.

We then searched for the pair of threshold parameters offering the best compromise between (i) providing the maximum number of detections, and (ii) minimizing the number of spurious sources. The later purity criterion, p c , is defined as:

p c = N p -N n N p (4.1)
where N p and N n are the numbers of positive and negative detections respectively. To ensure a purity of 80% as discussed above, we enforced p c ≥ 0.8. This led to σ p = 4.8 σ when fixing the value of σ f = 2.7 σ (see Fig. 4.2-left). Below σ p = 4.8 σ, the purity criterion rapidly drops below 80% whereas above this value it only mildly rises. Fixing σ p = 4.8 σ, the purity remains roughly constant at ∼80±5% when varying σ f . We did see an increase in the difference between the number of positive and negative detections with increasing σ f . However, the size of the sources above σ f = 2.7 σ drops below the 0 .60 FWHM and tends to become pixel-like, hence non physical. This is because an increase of σ f results in a reduction of the number of pixels above the floodclip threshold (σ f ) that will be associated with a given source. This parameter can be seen as a percolation criterion that sets the size of the sources in a number of pixels.

Reversely reducing σ f below 2.7 σ results in adding more noise than signal and a reduction in the number of detections. We therefore decided to set σ f to 2.7 σ.

While we did not wish to impose a criterion on the existence of optical counterparts to define our ALMA catalog, we found that high values of σ f not only generate the problem discussed above, but also generate a rapid drop of the fraction of ALMA detections with an HST counterpart in the Guo et al. (2013) catalog, p HST = N HST /N p . N HST is the number of ALMA sources with an HST counterpart within 0 .60 (corresponding to the size of the beam). The fraction falls rapidly from around ∼80% to ∼60%, which we interpreted as being due to a rise of the proportion of spurious sources, since the faintest optical sources, for example, detected by HST-WFC3, are not necessarily associated with the faintest ALMA sources due to the negative K-correction at 1.1mm. This rapid drop can be seen in the dashed green and dotted pink lines of Fig. This confirms that the sources that are added to our catalog with a floodclip threshold greater than 2.7 σ are most probably spurious. Similarly, we can see in Fig. 4.2-left that increasing the number of ALMA detections to fainter flux densities by reducing σ p below 4.8 σ leads to a rapid drop of the fraction of ALMA detections with an HST counterpart. Again there is no wellestablished physical reason to expect the number of ALMA detections with an optical counterpart to decrease with decreasing S/N ratio in the ALMA catalog.

As a result, we decided to set σ p = 4.8 σ and σ f = 2.7 σ to produce our catalog of ALMA detections. We note that we only discussed the existence of HST counterparts as a complementary test on the definition of the detection thresholds but our approach is not set to limit in any way our ALMA detections to galaxies with HST counterparts.

Indeed, evidence for the existence of ALMA detections with no HST-WFC3 counterparts already exist in the literature. Wang et al. (2016) identified H-dropouts galaxies, that is galaxies detected above the H-band with Spitzer-IRAC at 4.5 µm but undetected in the H-band and in the optical.

The median flux density of these galaxies is F 870µm 1.6 mJy (Wang et al., in prep.). By scaling this median value to our wavelength of 1.1 mm (the details of this computation are given in Sect. 5.7), we obtain a flux density of 0.9 mJy, close to the typical flux of our detections (median flux ∼1 mJy, see Table 4.2).

Creation of the catalog

Using the optimal parameters of σ p = 4.8 σ and σ f = 2.7 σ described in Sect. 4.1 & 4.2, we obtained a total of 20 detections down to a flux density limit of S 1.1mm ≈ 880 µJy that constitute our main catalog. These detections are listed in Fig. 4.3, sorted by decreasing S/N. The comparison of negative and positive detections suggests the presence of 4±2 (assuming a Poissonian uncertainty on the difference between the number of positive and negative detections) spurious sources in this sample.

In the following, we assume that the galaxies detected in the 0 .60-mosaic are point-like. This hypothesis will later be discussed and justified in Sect. 4.6.1. In order to check the robustness of our flux density measurements, we compared different flux extraction methods and softwares: PyBDSM (Mohan and Rafferty, 2015); Galfit (Peng et al., 2010); Blobcat (Hales et al., 2012). The peak flux value determined by Blobcat refers to the peak of the surface brightness corrected for peak bias (see Hales et al. 2012). The different results were consistent, with a median ratio of F Blobcat peak /F PyBDSM peak = 1.04±0.20 and F Blobcat peak /F Galfit P SF = 0.93±0.20. The fluxes measured using psf-fitting (Galfit) and peak flux measurement (Blobcat) for each galaxy are listed in Table 4.2. We also ran CASA fitsky and a simple aperture photometry corrected for the ALMA PSF and also found consistent results. The psf-fitting with Galfit was performed inside a box of 5×5 centered on the source.

The main characteristics of these detections (redshift, flux, S/N, stellar mass, counterpart) are given in Table 4.2. We used redshifts and stellar masses from the ZFOURGE catalog (see Sect. 3.3).

We compared the presence of galaxies between the 0 .60-mosaic and the 0 .29-mosaic. Of the 20 detections found in the 0 .60 map, 14 of them are also detected in the 0 .29 map. The presence of a detection in both maps reinforces the plausibility of a detection. However, a detection in only one of these two maps may be a consequence of the intrinsic source size. An extended source is more likely to be detected with a larger beam, whereas a more compact source is more likely to be missed in the maps with larger tapered sizes and reduced point source sensitivity.

A first method to identify potential false detections was to compare our results with a deeper survey overlapping with our area of the sky. We compared the positions of our catalog sources with the positions of sources found by Dunlop et al. (2017) in the HUDF. This 1.3-mm image is deeper than our survey and reaches a σ 35 µJy (corresponding to σ = 52 µJy at 1.1mm) but overlaps with only ∼6.5% of our survey area. The final sample of Dunlop et al. (2017) was compiled by selecting sources with S 1.3 > 120 µJy to avoid including spurious sources due to the large number of beams in the mosaics and due to their choice of including only ALMA detections with optical counterparts seen with HST.

With our flux density limit of S 1.1mm ≈ 880 µJy any non-spurious detection should be associated with a source seen at 1.3mm in the HUDF, the impact of the wavelength difference being much smaller than this ratio. We detected three galaxies in the HUDF, that were also detected by Dunlop et al. (2017), UDF1, UDF2 and UDF3, all of which have S 1.3mm > 0.8 mJy. The other galaxies detected by Dunlop et al. (2017) have a flux density at 1.3 mm lower than 320 µJy, which makes them undetectable with our sensitivity.

We note however that we did not impose as a strict criterion the existence of an optical counterpart to our detections, whereas Dunlop et al. (2017) did. Hence if we had detected a source with no optical counterpart within the HUDF, this source may not be included in the Dunlop et al. (2017) catalog. However, as we will see, the projected density of such sources is small and none of our candidate optically dark sources fall within the limited area of the HUDF. We also note that the presence of an HST-WFC3 source within a radius of 0 .6 does not necessarily imply that is the correct counterpart. As we will discuss in detail in Sect. 4.6, due to the depth of the HST-WFC3 observations and the large number of galaxies listed in the CANDELS catalog, a match between the HST and ALMA positions may be possible by chance alignment alone (see Sect. 4.6). TABLE 4.1: Details of the positional differences between ALMA and HST-WFC3 for our catalog of galaxies identified in the 1.1mm-continuum map. Columns: (1) Source ID; (2),(3) IDs of the HST-WFC3 (from the CANDELS catalog) and ZFOURGE counterparts of these detections (the cross correlations between ALMA and HST-WFC3 and between ALMA and ZFOURGE are discussed in Sect. 4.6). b indicates HST-WFC3 galaxies located in a radius of 0 .

6 around the ALMA detection, although strong evidence presented in Sect. 7.3 suggests they are not the optical counterparts of our detections; (4), ( 5) RA and Dec of the sources in the ALMA image (J2000); ( 6), (7) Positions of HST-WFC3 H-band counterparts when applicable from Guo et al. (2013), ( 8), [START_REF] Williams | The progenitors of the compact early-type galaxies at high redshift[END_REF] Distances between the ALMA and HST source positions before (∆HST 1 ) and after (∆HST 2 ) applying the offset correction derived from the comparison with Pan-STARRS and GAIA; [START_REF] Huang | Four IRAC sources with an extremely red H -[3.6] color: passive or dusty galaxies at z > 4.5?[END_REF], [START_REF] Wang | Infrared color selection of massive galaxies at z > 3[END_REF] Offset to be applied to the HST source positions, which includes both the global systematic offset and the local offset; [START_REF] Swinbank | An ALMA survey of sub-millimetre galaxies in the Extended Chandra Deep Field South: the far-infrared properties of SMGs[END_REF] Distance from the closest IRAC galaxy. 1

For AGS15 we used the distance given in the ZFOURGE catalog (see Sect. 7.3).

4.4. Supplementary catalog 63

Supplementary catalog

After the completion of the main catalog, three sources that did not satisfy the criteria of the main catalog presented strong evidence of being robust detections. We therefore enlarged our catalog, in order to incorporate these sources into a supplementary catalog.These three sources are each detected using a combination of σ p and σ f giving a purity factor greater than 80%, whilst also ensuring the existence of an HST counterpart.

The galaxy AGS21 has a S/N = 5.83 in the 0 .29 tapered map, but is not detected in the 0 .60 tapered map. The non-detection of this source is most likely caused by its size. Due to its dilution in the 0 .60-mosaic, a very compact galaxy detected at 5 σ in the 0 .29-mosaic map could be below the detection limit in the 0 .60-mosaic. The ratio of the mean RMS of the two tapered maps is 1.56, meaning that for a point source of certain flux, a 5.83 σ measurement in the 0 .29-mosaic becomes 3.74 σ in the 0 .60-map.

The galaxy AGS22 has been detected with an S/N = 4.9 in the 0 .60 tapered map (σ p = 4.9 and σ f = 3.1). With σ p and σ f values more stringent than the thresholds chosen for the main catalog, it may seem paradoxical that this source does not appear in the main catalog. With a floodclip criterion of 2.7 σ, this source would have an S/N just below 4.8, excluding it from the main catalog. This source is associated with a faint galaxy that has been detected by HST-WFC3 (ID CAN DELS = 28952) at 1.6 µm (6.6 σ) at a position close to the ALMA detection (0 .28).

Significant flux has also been measured at 1.25 µm (3.6 σ) for this galaxy. In all of the other filters, the flux measurement is not significant (< 3 σ). Due to this lack of information, it has not been possible to compute its redshift. AGS22 is not detected in the 0 .29-mosaic map with p c > 0.8. The optical counterpart of this source has a low H-band magnitude (26.8±0.2 AB), which corresponds to a range for which the Guo et al. (2013) catalog is no longer complete. This is the only galaxy (except the three galaxies most likely to be spurious: AGS14, AGS16 and AGS19) that has not been detected by IRAC (which could possibly be explained by a low stellar mass). The probability of the ALMA detection being spurious, within the association radius 0 .6 of a H-band source of this magnitude or brighter, is 5.5%. For these reasons, we did not consider it as spurious.

The galaxy AGS23 was detected in the 0 .60 map just below our threshold at 4.8 σ, with a combination σ p = 4.6 and σ f = 2.9 giving a purity criterion greater than 0.9. This detection is associated with an HST-WFC3 counterpart. It is for these two reasons that we include this galaxy in the supplementary catalog. The photometric redshift (z = 2.36) and stellar mass (10 11.26 M ) both reinforce the plausibility of this detection.

(2) Survey of GOODS-S at One-millimeter (ASAGAO). We also note the pointed observations of AGS1 presented in Barro et al. (2017), and those of AGS13 by Talia et al. (2018). For the two sources marked by a †, the hypothesis a of a point-like source is no longer valid. We therefore apply correction factors of 2.3 and 1.7 to the peak flux values of AGS17 and AGS18 respectively, to take into account the extended flux emission of these sources.

(3) (4) (5) (6) (7) (8) (9)
4.5. Astrometric correction 65

Astrometric correction

The comparison of our ALMA detections with HST (Sect. 4.3) in the previous section was carried out after correcting for an astrometric offset, which we outline here. In order to perform the most rigorous counterpart identification and take advantage of the accuracy of ALMA, we carefully investigated the astrometry of our images. Before correction, the galaxy positions viewed by HST were systematically offset from the ALMA positions. This offset has already been identified in previous studies (e.g., Maiolino et al., 2015;Rujopakarn et al., 2016;Dunlop et al., 2017).

In order to quantify this effect, we compared the HST source positions with detections from the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS). This survey has the double advantage to cover a large portion of the sky, notably the GOODS-South field, and to observe the sky at a wavelength similar to HST-WFC3. We used the Pan-STARRS DR1 catalog provided by Flewelling et al. (2016) and also included the corresponding regions issued from the GAIA DR1 (Gaia Collaboration et al., 2016). Cross-matching was done within a radius of 0 .5. In order to minimize the number of false identifications, we subtracted the median offset between the two catalogs from the Guo et al. (2013) catalog positions, after the first round of matching. We iterated this process three times. In this way, 629 pairs were found over the GOODS-South field.

To correct for the median offset between the HST and ALMA images, the HST image coordinates needed to be corrected by -96±113 mas in right ascension, α, and 261±125 mas in declination, δ, where the uncertainties correspond to the standard deviation of the 629 offset measurements.

This offset is consistent with that found by Rujopakarn et al. (2016) of ∆α = -80±110 mas and ∆δ = 260±130 mas. The latter offsets were calculated by comparing the HST source positions with 2MASS and VLA positions. In all cases, it is the HST image that presents an offset, whereas ALMA, Pan-STARRS, GAIA, 2MASS and VLA are all in agreement. We therefore deduced that it is the astrometric solution used to build the HST mosaic that introduced this offset. We will discuss this offset in more detail Sect. 6.3. These local offsets are larger in the periphery of GOODS-South than in the center, and close to zero in the HUDF field. The local offsets can be considered as a distortion effect. The offsets listed in Table 4.1 include both effects, the global and local offsets. The separation between HST and ALMA detections before and after offset correction, and the individual offsets applied for each of the galaxies are indicated in Table 4.1 and can be visualized in Fig. 4.4. We applied the same offset corrections to the galaxies listed in the ZFOURGE catalog.

This accurate subtraction of the global systematic offset, as well as the local offset, does not however guarantee a perfect overlap between ALMA and HST emission. The location of the dust emission may not align perfectly with the starlight from a galaxy, due to the difference in ALMA and HST resolutions, as well as the physical offsets between dust and stellar emission that may exist. In Fig. 4.5, we show the ALMA contours (4 to 10 σ) overlaid on the F160W HST-WFC3 images after astrometric correction. In some cases (AGS1, AGS3, AGS6, AGS13, AGS21 for example), the position of the dust radiation matches that of the stellar emission; in other cases, (AGS4, AGS17 for example), a displacement appears between both two wavelengths. Finally, in some cases (AGS11, AGS14, AGS16, and AGS19) there are no optical counterparts. We will discuss the possible explanations for this in Sect. 7.3.

Identification of counterparts

We searched for optical counterparts in the CANDELS/GOODS-South catalog, within a radius of 0 .6 from the millimeter position after applying the astrometric corrections to the source positions described in Sect. 4.5. The radius of the cross-matching has been chosen to correspond to the synthesized beam (0 .60) of the tapered ALMA map used for galaxy detection. Following Condon (1997); [START_REF] Condon | The NRAO VLA Sky Survey[END_REF], the maximal positional accuracy of the detection in the 1.1mm map is given by θ beam /(2×S/N). In the 0 .60-mosaic, the positional accuracy therefore ranges between 26.5 mas and 62.5 mas for our range of S/N (4.8-11.3), corresponding to physical sizes between 200 and 480 pc at z = 3.

Despite the high angular resolution of ALMA, the chance of an ALMA-HST coincidence is not negligible, because of the large projected source density of the CANDELS/GOODS-South catalog. Fig. the distance to its closest HST neighbor using the source positions listed in Guo et al. (2013).

We repeated this procedure 100 000 times inside and outside the HUDF. The probability for a position randomly selected in the GOODS-South field to fall within 0.6 arcsec of an HST source is 9.2% outside the HUDF, and 15.8% inside the HUDF. We repeated this exercise to test the presence of an IRAC counterpart with the Ashby et al. (2015) catalog (green histogram).

The probability to randomly fall on an IRAC source is only 2.1%. With the detection threshold determined in Sect. 4.1, 80% of the millimeter galaxies detected have an HST-WFC3 counterpart, and four galaxies remain without an optical counterpart. We cross-matched our detections with the ZFOURGE catalog.

Fig. 4.7 shows 3 .5 × 3 .5 postage stamps of the ALMA-detected galaxies, overlaid with the positions of galaxies from the CANDELS/GOODS-South catalog (magenta double crosses), ZFOURGE catalog (white circles) or both catalogs (sources with an angular separation lower than 0 .4, blue circles). These are all shown after astrometric correction. Based on the ZFOURGE catalog, we found optical counterparts for one galaxy that did not have an HST counterpart: AGS11, a photometric redshift has been computed in the ZFOURGE catalog for this galaxy. The redshifts of AGS4 and AGS17 as given in the CANDELS catalog are unexpectedly low (z = 0.24 and z = 0.03, respectively), but the redshifts for these galaxies given in the ZFOURGE catalog (z = 3.76 and z = 1.85, respectively) are more compatible with the expected redshifts for galaxies detected with ALMA. These galaxies, missed by the HST or incorrectly listed as local galaxies are particularly interesting galaxies (see Sect. 7.3). AGS6 is not listed in the ZFOURGE catalog, most likely because it is close (< 0 .7) to another bright galaxy (ID CAN DELS = 15768). These galaxies are blended in the ZFOURGE ground-based K s -band images. AGS6 has previously been In some cases (AGS1, AGS3, AGS6, AGS13, AGS21 for example), the position of the dust radiation matches that of the stellar emission; in other cases, (AGS4, AGS17 for example), a displacement appears between both two wavelengths. Finally, in some cases (AGS11, AGS14, AGS16, and AGS19) there are no optical counterparts. We will discuss the possible explanations for this in Sect. 7. HST (blue, orange) or IRAC (green) neighbor as a function of distance. We computed this probability by Monte Carlo simulation using the distribution of galaxies listed in the CANDELS/GOODS-South catalog. Due to the presence of the HUDF within the GOODS-South field, we cannot consider that the density of HST galaxies is uniform, and we consider these two fields separately (blue inside and orange outside the HUDF). detected at 1.3 mm in the HUDF, so we adopt the redshift and stellar mass found by Dunlop et al. (2017). The consensus CANDELS zphot from Santini et al. (2015) is z = 3.06 (95% confidence: 2.92 < z < 3.40), consistent with the value in Dunlop et al. (2017).

Galaxy sizes

Correctly estimating the size of a source is an essential ingredient for measuring its flux. As a first step, it is imperative to know if the detections are resolved or unresolved. In this section, we discuss our considerations regarding the sizes of our galaxies. The low number of galaxies with measured ALMA sizes in the literature makes it difficult to constrain the size distribution of dust emission in galaxies. Recent studies (e.g., Barro et al., 2016;Rujopakarn et al., 2016;Elbaz et al., 2018;Ikarashi et al., 2017;Fujimoto et al., 2017) with sufficient resolution to measure ALMA sizes of galaxies suggest that dust emission takes place within compact regions of the galaxy. Two of our galaxies (AGS1 and AGS3) have been observed in individual pointings (ALMA Cycle 1; P.I. R.Leiton, presented in Elbaz et al. 2018) at 870 µm with a long integration time (40-50 min on source). These deeper observations give more information on the nature of the galaxies, in particular on their morphology. Due to their high S/N (∼100) the sizes of the dust emission could be measured accurately: R 1/2maj = 120±4 and 139±6 mas for AGS1 and AGS3 respectively, revealing extremely compact star-forming regions corresponding to circularized effective radii of ∼1 kpc at redshift z ∼2. The Sérsic indices are 1.27±0.22 and 1.15±0.22 for AGS1 and AGS3 respectively: the dusty star-forming regions therefore seem to be disk-like. Based on their sizes, their stellar masses (> 10 11 M ), their SFRs (> 10 3 M yr -1 ) and their redshifts (z ∼2), these very compact galaxies are ideal candidate progenitors of compact quiescent galaxies at Size measurements of galaxies at (sub)millimeter wavelengths have previously been made as part of several different studies. Ikarashi et al. (2015) measured sizes for 13 AzTEC-selected SMGs. The Gaussian FWHM range between 0 .10 and 0 .38 with a median of 0 .20 +0 . 03 -0 . 05 at 1.1 mm. Simpson et al. (2015a) derived a median intrinsic angular size of FWHM = 0 .30±0 .04 for their 23 detections with a S/N > 10 in the Ultra Deep Survey (UDS) for a resolution of 0 .3 at 870 µm. Tadaki et al. (2017) found a median FWHM of 0 .11±0.02 for 12 sources in a 0 .2resolution survey at 870 µm. Barro et al. (2016) use a high spatial resolution (FWHM ∼0 .14) to measure a median Gaussian FWHM of 0 .12 at 870 µm, with an average Sérsic index of 1.28. For Hodge et al. (2016), the median major axis size of the Gaussian fit is FWHM = 0 .42±0 .04 with a median axis ratio b/a = 0.53±0.03 for 16 luminous ALESS SMGs, using high-resolution (∼0 .16) data at 870 µm. Rujopakarn et al. (2016) found a median circular FWHM at 1.3 mm of 0 .46 from the ALMA image of the HUDF (Dunlop et al., 2017). González-López et al. (2017) studied 12 galaxies at S/N ≥ 5, using 3 different beam sizes (0 .63 × 0 .49), (1 .52 × 0 .85) and (1 .22 × 1 .08). They found effective radii spanning < 0 .05 to 0 .37±0 .21 in the ALMA Frontier Fields survey at 1.1mm. Ikarashi et al. (2017) obtained ALMA millimeter-sizes of 0 .08 -0 .68 (FWHM) for 69 ALMA-identified AzTEC SMGs with an S/N greater than 10. These galaxies have a median size of 0 .31. These studies are all broadly in agreement, revealing compact galaxy sizes in the sub(millimeter) regime of typically 0 .3±0 .1. Size measurements require a high S/N detection to ensure a reliable result. The S/N range of our detections is 4.8-11.3. Following Martí-Vidal et al. (2012), the reliable size measurement limit for an interferometer is:

θ min = β λ c 2 S/N 2 1/4 × θ beam 0.88 θ beam √ S/N (4.2)
where λ c is the value of the log-likelihood, corresponding to the cutoff of a Gaussian distribution to have a false detection and β is a coefficient related to the intensity profile of the source model and the density of the visibilities in Fourier space. This coefficient usually takes values in the range 0.5-1. We assumed λ c = 3.84 corresponding to a 2 σ cut-off, and β = 0.75. For θ beam = 0 .60 and a range of S/N between 4.8 and 11.3, the minimum detectable size (FWHM) therefore varies between 0 .16 and 0 .24. Using the 0 .60-mosaic map, the sizes of a large number of detections found in previous studies could therefore not be reliably measured.

To quantitatively test if the millimeter galaxies are resolved in our survey we performed several tests. The first test was to stack the 23 ALMA-detections and compare the obtained flux profile with the profile of the PSF. However, in the mosaic map, each slice has its own PSF. We therefore also needed to stack the PSFs at these 23 positions in order to obtain a global PSF for comparison. Fig. 4.8 shows the different PSFs used in this survey in the 0 .60-mosaic. The FWHM of each PSF is identical, the differences are only in the wings. The stack of the 23 PSFs for the 23 detections and the result of the source stacking in the 0 .60-mosaic is shown in Fig. 4.9. The flux of each detection is normalized so that all sources have the same weight, and the stacking is not skewed by the brightest sources.

Size stacking to measure the structural parameters of galaxies is at present a relatively unexplored area. This measurement could suffer from several sources of bias. The uncertainties on the individual ALMA peak positions could increase the measured size in the stacked image, for example. On the other hand, due to the different inclination of each galaxy, the stacked galaxy could appear more compact than the individual galaxies (e.g., Hao et al., 2006;Padilla and Strauss, 2008;Li et al., 2016). Alternatively, some studies (e.g., van Dokkum et al., 2010) indicate that size stacking gives reasonably accurate mean galaxy radii. In our case, the result of the size stacking is consistent with unresolved sources or marginally resolved at this resolution which corresponds to a physical diameter of 4.6 kpc at z = 3. We compared the PSF flux extraction method with Gaussian and Sérsic shapes. As our sources are not detected with a particularly high S/N, and in order to limit the number of degrees of freedom, the Sérsic index was frozen to n = 1 (exponential disk profile, in good agreement with Hodge et al. 2016 andElbaz et al. 2018 for example), assuming that the dust emission is disklike. Fig. 4.10 shows the residuals for the three different extraction profiles. The residuals are very similar between the point source, Gaussian and Sérsic profiles, suggesting that the approximation that the sources are not resolved is appropriate, and does not result in significant flux loss. We also note that, for several galaxies, due to large size uncertainties, the Gaussian and Sérsic fits give worse residuals than the PSF fit (AGS4 for example).

For the third test, we took advantage of the different tapered maps. We compared the peak flux for each detection between the 0 .60-mosaic map and the 0 .29-mosaic map. The median ratio is S 0 . 29 peak /S 0 . 60 peak = 0.87±0.16. This small decrease, of only 10% in the peak flux density between the two tapered maps suggests that the flux of the galaxies is only slightly more resolved in the 0 .29-mosaic map.

In order to test the impact of our hypothesis that the sources can be considered as point-like in the mosaic tapered at 0 .60, we fit their light profiles with a circular Gaussian in the uv-plane using uvmodelfit in CASA (we also tested the use of an asymmetric Gaussian but the results remained similar although with a lower precision due to the larger number of free parameters in the fit). The sizes that we obtained confirmed our hypothesis that our galaxies are particularly compact since 85% of the sources (17 out of 20 robust detections) exhibit a FWHM smaller than (Dunlop et al., 2017), the black dash-dotted line shows the ASPECS sample (Aravena et al., 2016), the red dotted line shows the ALMA Frontier Fields Survey (González-López et al., 2017) and the yellow dotted line shows the ASAGAO survey (Ueda et al., 2018). Short coloured lines at the top of the figure indicate the median redshifts for these four studies. 0 .25 (in other words the half-light radius is twice smaller than this value). The median size of our sample of 20 galaxies is 0 .18 (see the distribution of sizes in Fig. 4.11). This analysis shows that two sources are outliers with sizes of 0 .41±0 .03 and 0 .50±0 .08, for AGS17 and AGS18 respectively. For these two sources, the assumption of point-like sources is not valid and leads to an underestimate of the actual flux densities by a factor of 2.3 and 1.7 respectively. This correction has been applied to the list of peak flux densities provided in Table 4.2. Having performed these tests, we concluded that for all of the detections, except AGS17 and AGS18, the approximation that these sources appear point-like in the 0 .60-mosaic map is justified. For the two remaining sources, we applied a correction given above. Our photometry was therefore performed under this assumption.

Mass and redshift

We now study the physical properties of the ALMA detected sources, taking advantage of the wealth of ancillary data available for the GOODS-South field.

Redshift distribution

Among the 17 ALMA-detected sources for which redshifts have been computed, six have a spectroscopic redshift (AGS1, AGS2, AGS3, AGS9, AGS12, AGS13 and AGS18) determined by Kurk et al. (2013), and recently confirmed by Barro et al. (2017), Momcheva et al. (2016), Vanzella et al. (2008), Mobasher (private communication), Inami et al. (2017), Kriek et al. (2008) and Dunlop et al. 2017 -from a private communication of Brammer -respectively. The redshift distribution of these 17 ALMA sources is presented in Fig. 4.12, compared to the distributions of four other deep ALMA blind surveys (Dunlop et al., 2017;Aravena et al., 2016;González-López et al., 2017;Ueda et al., 2018). Of the 17 sources, 15 are in the redshift range z = 1.9 -3.8. Only two galaxies (AGS4 and AGS11) have a redshift greater than 4 (z phot = 4.32 and 4.82 respectively). We discuss these galaxies further in Sect. 7.3. The mean redshift of the sample is z = 3.03±0.17, where the error is computed by bootstrapping. This mean redshift is significantly higher than those found by Dunlop et al. (2017), Aravena et al. (2016), González-López et al. (2017) and Ueda et al. (2018) who find distributions peaking at 2.13, 1.67, 1.99 and 2.28 respectively. The median redshift of our sample is 2.92±0.20, which is a little higher than the value expected from the models of Béthermin et al. (2015), which predict a median redshift of 2.5 at 1.1 mm, considering our flux density limit of ∼874 µJy (4.8 σ). Our limiting sensitivity is shallower than that of previous blind surveys: 0.184 mJy here compared with 13 µJy in Aravena et al. (2016), 35 µJy in Dunlop et al. (2017), [START_REF] Wang | SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES): faint-end counts at 450 μm[END_REF][START_REF] Casey | Characterization of SCUBA-2 450 μm and 850 μm selected galaxies in the COSMOS field[END_REF][START_REF] Geach | The SCUBA-2 cosmology legacy survey: blank-field number counts of 450-μm-selected galaxies and their contribution to the cosmic infrared background[END_REF][START_REF] Geach | The SCUBA-2 cosmology legacy survey: 850 μm maps, catalogues and number counts[END_REF][START_REF] Béthermin | Submillimeter number counts at 250 μm, 350 μm and 500 μm in BLAST data[END_REF][START_REF] Smolčić | The VLA-COSMOS 3 GHz large project: continuum data and source catalog release[END_REF][START_REF] Sobral | Slicing COSMOS with SC4K: the evolution of typical Lyα emitters and the Lyα escape fraction from z ~ 2 to 6[END_REF][START_REF] Finkelstein | Effects of dust geometry in Lyα galaxies at z = 4.4[END_REF][START_REF] Steidel | Spectroscopic confirmation of a population of normal star-forming galaxies at redshifts z > 3[END_REF][START_REF] Bouwens | UV luminosity functions at redshifts z ~ 4 to z ~ 10: 10,000 galaxies from HST legacy fields[END_REF][START_REF] Brammer | A fast, public photometric redshift code[END_REF][START_REF] Kriek | An ultra-deep near-infrared spectrum of a compact quiescent galaxy at z = 2.2[END_REF][START_REF] Calzetti | The dust opacity of star-forming galaxies[END_REF][START_REF] Landy | Bias and variance of angular correlation functions[END_REF][START_REF] Limber | The analysis of counts of the extragalactic nebulae in terms of a fluctuating density field[END_REF][START_REF] Croom | Radio-quiet QSO environments -I. The correlation of QSOs and bJ < 23 galaxies[END_REF][START_REF] Peebles | Principles of Physical Cosmology[END_REF] µJy in González-López et al. ( 2017) and 89 µJy in Ueda et al. (2018). However our survey covers a larger region on the sky: 69 arcmin 2 here, compared to 1 arcmin 2 , 4.5 arcmin 2 , 13.8 arcmin 2 and 26 arcmin 2 for these four surveys respectively. The area covered by our survey is therefore a key parameter in the detection of high redshift galaxies due to a tight link between 1.1mm luminosity and stellar mass, as we will show in the next section. The combination of two effects: a shallower survey allowing us to detect only brighter SMGs, which are more biased toward higher redshifts (e.g., Pope et al., 2005), as well as a larger survey allowing us to reach more massive galaxies, enables us to open the parameter space at redshifts greater than 3, as shown in Fig. 4.12. This redshift space is partly or totally missed in smaller blind surveys. We show in Fig. 4.13 the size of the recent ALMA survey as a function of their depth. We represented the surveys of Aravena et al. (2016);González-López et al. (2017); Dunlop et al. (2017); Hatsukade et al. (2018), as well as this work, color-coded as a function of the median redshift.

We can see in this figure a clear trend between the depth of the survey and the median redshift. The more the survey will be shallow, the higher the average redshift will be. This trend is parameterized in Béthermin et al. (2015). According to this study, a 1.1 mm survey with a flux density cut of 1 mJy would have a median redshift z = 2.5 while a survey with a flux density cut of 0.3 mJy would have a median redshift z = 2.

Another factor that greatly influences the average redshift of a survey is the observed wavelength. For example, Béthermin et al. (2015); [START_REF] Casey | The Brightest Galaxies in the Dark Ages: Galaxies' Dust Continuum Emission during the Reionization Era[END_REF]; [START_REF] Magnelli | The IRAM/GISMO 2 mm Survey in the COSMOS Field[END_REF] have shown that the longer the observed wavelength, the higher the average redshift would be. For example, a survey at 2 mm is efficient to isolate the dusty star-forming galaxies with the highest redshift by excluding the majority of lower redshift galaxies due to the negative K-correction [START_REF] Casey | Taking Census of Massive, Star-Forming Galaxies formed <1 Gyr After the Big Bang[END_REF]. In the survey conducted by [START_REF] Magnelli | The IRAM/GISMO 2 mm Survey in the COSMOS Field[END_REF] with Goddard IRAM Superconducting Millimeter Observer (GISMO) at the IRAM 30m-telescope [START_REF] Staguhn | The GISMO Two-millimeter Deep Field in GOODS-N[END_REF] in the COSMOS field, all the detection but one lie above z ∼ 3. Finally, we can also note that lensed fields have on average higher z than non-lensed fields (e.g., [START_REF] Hezaveh | Effects of Strong Gravitational Lensing on Millimeterwave Galaxy Number Counts[END_REF]. We emphasize that the two HST-dark galaxies (see Chapter 7.3) for which the mass and redshift could be determined (AGS4 and AGS11) are the two most distant galaxies in our sample, with redshifts greater than 4.

Stellar Masses

Over half (10/17 of galaxies for which a stellar mass has been determined) of our galaxies have a stellar mass greater than 10 11 M (median mass of M = 1.1 × 10 11 M ). The population of massive and compact star-forming galaxies at z ∼ 2 has been documented at length (e.g., Daddi et al., 2005;van Dokkum et al., 2015), but their high redshift progenitors are to-date poorly detected in the UV. Our massive galaxies at redshifts greater than 3 might therefore give us an insight into these progenitors. Fig. 4.14 shows the stellar mass as a function of redshift for all of the UVJ active galaxies, listed in the ZFOURGE catalog, in our ALMA survey field of view. Star forming galaxies (SFGs) have been selected by a UVJ colour-colour criterion as given by Williams et al. (2009) and applied at all redshifts and stellar masses as suggested by Schreiber et al. (2015):

SF G =      U -V < 1.3, or V -J > 1.6, or U -V < 0.88 × (V -J) + 0.49 (4.3)
We will call them "UVJ active" and the complementary population of passive galaxies "UVJ passive". All galaxies not fulfilling these colour criteria (Eq. 4.3) are considered as quiescent galaxies and are excluded from our comparison sample (9.3% of the original sample). The ALMA detected galaxies in our survey are massive compared to typical SFGs detected in deep 4.14: Stellar mass versus redshift for the galaxies detected in our ALMA GOODS-South blind survey (red points). For comparison, the distribution of all of the galaxies, listed in the ZFOURGE catalog, in the same field of view is given in blue. Only UVJ active galaxies are shown. The two HST-dark galaxies for which we have estimated a photometric redshift (AGS4 and AGS11) are represented by open circles. The redshift of AGS11 is however uncertain. The green dashed line shows the position that would be occupied by a typical star-forming galaxylying on the median of the SFR-M star-formation main sequence (MS) -that would produce a 1.1mm flux density equal to our average detection limit of 0.88 mJy (4.8-σ) using the Spectral Energy Distribution (SED) library of Schreiber et al. (2018a). The dotted line illustrates the position of galaxies 3 times above the MS using the appropriate SEDs from the same library. Galaxies hosting an AGN that are undetected or detected by ALMA are identified with black dotes and yellow stars respectively. Inside the black dashed rectangle, 50% of the galaxies detected by ALMA host an AGN, while only 14% of the UVJ active galaxies undetected by ALMA host an AGN. optical and near-IR surveys like CANDELS, in the same redshift range (2 < z < 4), as shown in Fig. 4.14.

The high proportion of massive galaxies among the ALMA detected sources suggests that stellar mass can be a strong driver for a source to be detected by ALMA at high redshift (Dunlop et al., 2017). The strong link between detection and stellar mass is related to the underlying relation between stellar mass and star formation rate of SFGs (e.g., Noeske et al., 2007;Elbaz et al., 2011). Almost one third (7/24) of the galaxies previously cataloged in the field of view of this study with M > 10 11 M and 2 < z < 3 are also detected with ALMA. The position of our galaxies along the main sequence of star formation (MS) will be studied Chapter 8. We observe a lack of detections at redshift z < 2, driven by both a strong positive K-correction favouring higher redshifts and a decrease in the star formation activity at low redshift. Indeed, the specific star formation rate (sSFR), defined as the ratio of galaxy SFR to stellar mass, drops quickly at lower redshifts (z < 2), whereas this rate increases continuously at greater redshifts (e.g., Schreiber et al., 2015). In addition, very massive galaxies (stellar mass greater than 10 11 M ) are relatively rare objects in the smaller co-moving volumes enclosed by our survey at lower redshift. To detect galaxies with these masses, a survey has to be sufficiently large. The covered area is therefore a critical parameter for blind surveys to find massive high redshift galaxies.

In order to estimate the selection bias relative to the position of our galaxies on the main sequence, we show in Fig. 4.14 the minimum stellar mass as a function of redshift that our survey can detect, for galaxies on the MS of star formation (green dashed line), and for those with a SFR three times above the MS (green dotted line). To determine this limit, we calculate the SFR of a given MS galaxy, based on the galaxy stellar mass and redshift as defined in Schreiber et al. (2015). From this SFR and stellar mass, the galaxy SED can also be calculated using the Schreiber et al. (2018a) library. We then integrate the flux of this SED around 1.1mm.

It can be seen that the stellar mass detection limit corresponding to MS galaxies lies at higher stellar mass than all of the galaxies detected by our ALMA survey (as well as all but one of the other star-forming galaxies present in the same region). This means that our survey is unable to detect star-forming galaxies below the main sequence. We can quantify the offset of a galaxy from the main sequence, the so-called "starburstiness" (Elbaz et al., 2011), by the ratio SFR/SFR M S , where SFR M S is the average SFR of "main sequence" galaxies computed from Schreiber et al. (2015). We also indicate our detection limit for galaxies with SFR/SFR M S = 3. In this case, 7 of the 17 galaxies shown lie above the limit. To have been detected, these galaxies must therefore have SFRs at least larger than the SFR M S , the other ten galaxies must have a SFR at least three times above the MS. This highlights that our survey is biased towards galaxies with high SFRs.

AGN

In this Section, we discuss the presence of AGN within the 20 most robust ALMA detections, i.e., rejecting the 3 spurious detections with no IRAC counterpart (AGS14, AGS16 and AGS19 marked with a star in Table 4.2) but including 3 of the supplementary sources (AGS21, AGS22 and AGS23). We find an X-ray counterpart for 65% of them (13/20) in the 7 Msec X-ray survey of GOODS-South with Chandra (Luo et al., 2017). Most of these galaxies were classified as AGN in the catalog of Luo et al. (2017) that identifies as AGN all galaxies with an intrinsic 0.5-7.0 keV luminosity higher than L X,int = 3 × 10 42 erg.s -1 , among other criteria. However, our ALMA galaxies being biased towards highly star-forming galaxies, we decided to increase the minimum X-ray luminosity to a three times stronger X-ray luminosity threshold to avoid any contamination by star-formation. We also consider as AGN the galaxies exhibiting a hard X-ray spectrum. Hence, we adopt here the following criteria to identify AGN: either (i) L X,int > 10 43 erg.s -1 (luminous X-ray sources) or (ii) Γ < 1.0 (hard X-ray sources). As the redshifts adopted by Luo et al. (2017) are not always the same as ours, when necessary we scaled the X-luminosities to our redshifts using Eq. 1 from Alexander et al. (2003), and assuming a photon index of Γ = 2. Using these conservative criteria, we find that 8 ALMA galaxies host an X-ray AGN (marked with a yellow star in Fig. 4.14). In order to compare the AGN fraction among ALMA detections with galaxies undetected by ALMA with similar masses and redshifts, we restrict our comparison to galaxies with M > 3 × 10 10 M and 1.8 < z < 4.5 (rectangle in black dotted lines in Fig. 4.14). In this area encompassing 16 ALMA detections, we find that 50% of the ALMA sources host an AGN (8/16) as compared to only 14% (23/160) of the star-forming galaxies undetected by ALMA located in this same area (selected using the UVJ criteria recalled in Eq. 4.3 in the ZFOURGE catalog). The presence of a large fraction of AGN among the galaxies detected by ALMA may reflect the fact that the ALMA sources are experiencing a starburst (well above the MS marked with a green dashed line in Fig. 4.14), possibly triggered by a merger that may dramatically reduce the angular momentum of the gas and drive it towards the centre of the galaxies (e.g., Rovilos et al., 2012;Gatti et al., 2015;Lamastra et al., 2013) or violent disk instabilities (Bournaud et al., 2012). In addition, the high AGN fraction may be driven by the link between the presence of an AGN and the compactness of their host galaxy. Elbaz et al. (2018), Chang et al. (2017) and Ueda et al. (2018) suggest that the proportion of galaxies hosting an AGN increases with IR luminosity surface density. As discussed in Sect. 5.5.5, the size, and therefore the compactness of a galaxy, increases the likelihood of an ALMA detection at our angular resolution. Alternatively ALMA might preferentially detect galaxies with a high gas, hence also dust, content, more prone to efficiently fuel the central black hole and trigger an AGN. This fraction of galaxies with a high X-ray luminosity (L X,int > 10 43 erg.s -1 ) seems to be significantly higher than that found in some other ALMA surveys, in particular in Dunlop et al. (2017) (2/16) or Ueda et al. (2018) (4/12).

Conclusion

The GOODS-ALMA survey covers an area of 69 arcmin 2 matching the deepest HST-WFC3 coverage of the GOODS-South field at 1.1 mm and at a native resolution of ∼0 .24. We used a 0 .60 tapered mosaic due to the large number of independent beams at the native resolution. A comparison of the HST source positions with existing catalogs such as Pan-STARRS allowed us to correct the HST astrometry of the GOODS-South field from both a global and local offset (equivalent to a distortion map, see also Dickinson et al. in prep.). We find a median offset between the HST and ALMA images of -94±42 mas in right ascension, α, and 262±50 mas in declination, δ. The main conclusions from our study are listed below.

-20 galaxies brighter than 0.7 mJy at 1.1mm. We detect in total 20 sources above a detection threshold that guarantees an 80% purity (less than 20% chance to be spurious). Among these 20 galaxies (with an SNR > 4.8), we expect 4±2 spurious galaxies from the analysis of the inverted map and we identify 3 probably spurious detections with no HST nor Spitzer-IRAC counterpart, consistent with the expected number of spurious galaxies. An additional three sources with HST counterparts are detected either at high significance in the higher resolution map, or with different detection-algorithm parameters ensuring a purity greater than 80%. Hence we identify in total 20 robust detections. -Pushing further in redshift the blind detection of massive galaxies with ALMA. The sources exhibit flux densities ranging from 0.6 to 2 mJy, have a median redshift (and rms) of z = 2.92±0.20 and stellar mass of M = (1.1±0.4) × 10 11 M . By comparison with deeper but smaller ALMA extragalactic surveys (Aravena et al. 2016;Dunlop et al. 2017;González-López et al. 2017;Ueda et al. (2018)), our redshift distribution is shifted to higher values even though our survey is shallower. This is due to the low surface density of massive, metal hence dust-rich, galaxies at high redshifts. The size of the ALMA survey is therefore a key parameter to detect high redshift galaxies. -Exceptionally high AGN fraction. We find a high proportion of AGNs in our ALMA 1.1mm sample with 40% (8 out of 20 robust detections) detected in the 7Msec Chandra Xray survey of GOODS-South in the 0.5-7.0 keV band with a X-luminosity greater than 10 43 erg.sec -1 . Limiting our analysis to the ALMA sources with a redshift and stellar mass determination, we find that 50% of the ALMA sources located in a well-defined stellar mass (M > 3 × 10 10 M ) -redshift (z∼1.8-4.5) range host an AGN as compared to 14% only for the galaxies located within the same zone but undetected by ALMA. This excess AGN contribution may be due to the fact that the ALMA galaxies are preferentially in a starburst mode due to our detection limit -hence possibly experiencing a merger -or/and that the high-resolution of ALMA favours unresolved, hence compact, sources knowing that the mechanism that leads to such compact star-formation may also trigger an AGN.

CHAPTER 5

NUMBER COUNTS

Motivation of the number counts

Number counts make it possible to model the flux distribution of sources in the sky. The great strength of this modelling approach is that it is done without any a priori knowledge, and therefore is not biased on the nature of the galaxies observed. It is, for example, not necessary to know the redshift or the mass of the galaxies. In addition to that, they set key constraints on galaxy evolution models using only one single filter or frequency band. However, detailed analysis of the observations and characterization and correction of observational biases must be carried out in order to obtain an accurate model of the evolution of galaxy density as a function of fluxes.

In this section, we will briefly present the reasons for conducting these number counts and explain the two types of number counts we have conducted. We will then explain the different biases to which we have been exposed and the tests and simulations we have performed to correct these biases. We will then compare the results we have obtained with those obtained in other surveys or models. Finally, we will use the parameterization of our number counts to estimate the contribution of the resolved sources detected in this survey to the Cosmic Infrared Background.

The observation in 1964 of the Cosmic Microwave Background (CMB) by [START_REF] Penzias | A Measurement of Excess Antenna Temperature at 4080 Mc/s[END_REF] opened a new era in the history of astronomy and the understanding of the evolution of the universe. Thirty years later, another discovery, less well known to the general public, also had a profound impact on our understanding of the evolution of galaxies: a significant part of the Extragalactic Background Light (EBL) is detected at infrared or millimetre wavelengths (see Fig. 5.1;[START_REF] Puget | Tentative detection of a cosmic far-infrared background with COBE[END_REF]Fixsen et al. 1998;Dole et al. 2006). We will discuss the contribution of the Cosmic Infrared Background (CIB) to the EBL in detail in Sect 5.10. The first survey carried out with single-dish telescopes at submillimeter wavelengths, which detected only galaxies with a flux greater than a few mJy (e.g., Barger et al., 1998;[START_REF] Eales | The Canada-UK Deep Submillimeter Survey: First Submillimeter Images, the Source Counts, and Resolution of the Background[END_REF][START_REF] Smail | The nature of faint submillimetreselected galaxies[END_REF], showed that only a small part of this Cosmic Infrared Background was resolved into galaxies. Herschel studies have now shown that the CIB can be resolved [START_REF] Lagache | Evidence for dust emission in the Warm Ionised Medium sing WHAM data[END_REF]Dole et al., 2006;[START_REF] Berta | Dissecting the cosmic infra-red background with Herschel/PEP[END_REF]. One of the key questions that motivates (sub)millimetre surveys and galaxy number counts is to know what proportion of the CIB is coming from dust re-processed stellar emission of high redshift galaxies.

The different forms of number counts

Cumulative number counts

The aim of cumulative number counts is to model the number of galaxies per unit area with a flux greater than S ν . The interpretation of the cumulative number counts is straightforward.

On the y-axis is the number of sources with a flux greater than a given flux per unit area. On the other hand, since these are cumulative number counts, the number of low-flux sources is dependent on the number of high-flux sources. The slightest error or uncertainty is propagated to all the number counts.

Differential number counts

The aim of differential number counts is to model the number of galaxies per unit area with a flux between S ν and S ν + dS ν . One of the advantages of using differential number counts compared to cumulative number counts is the absence of correlation of the counts between the different bins. However, the differential number counts are sensitive to the lower number of detections per flux density bin.

Number counts in a static Euclidean universe

If we lived in a static Euclidean universe, then the number counts would be a breeze to predict. Inside a sphere of radius R, the number of sources would not evolve in this sphere. The relationship between flux density and luminosity would simply be given by:

S ν = L ν 4πR 2 (5.1)
The number of sources can be expressed within a sphere of radius R by:

N = Ω 4π R 0 N 0 4πr 2 dr = Ω 3 N 0 R 3 (5.2)
with N 0 the number of sources per unit volume. The number of sources is therefore proportional to the cube of the radius of this sphere (N ∝ R 3 ). Moreover, Eq. 5.1 tells us that the flux of a source is inversely proportional to the radius of the sphere squared (S ν ∝ R -2 ). By combining these two proportionality relationships, we see that N ∝ S -3/2 ν for cumulative number counts.

N = Ω 3 N 0 L ν 4π 3/2 S -3/2 ν (5.3)
For differential counts, we find that N ∝ S

-5/2 ν . dN dS ν = Ω 2 N 0 L ν 4π 3/2 S -5/2 ν (5.4)
It is common to represent number counts normalized to the Euclidean trend, i.e., by multiplying them by flux to the power of 2.5 (units of mJy 1.5 deg -2 , see Fig. 5.2). However, in the rest of our study, we do not represent the counts in Euclidean-normalized units, in order to be consistent with the latest published studies.

Unfortunately (for the implicit interpretation of the number counts), we do not live in a Euclidean universe, so the flux of galaxies varies with redshift. We therefore have to consider the K-correction (see Sect. 1.4.1). Moreover, the spectrum of a galaxy evolves according to the redshift, meaning that a distant galaxy will not have, for example the same stellar population, nor the same size, nor the same dust temperature, and thus does not have the same SED as a nearby galaxy. It is also important to note that in a non-Euclidean universe, the radius of the sphere is no longer constant, and evolves with cosmic time. It is therefore no longer the radius that must be taken into account, but the luminosity distance. This luminosity distance varies as (1+z) α , with α evolving with the redshift (see Fig. 1.13).

In a non-Euclidean universe, the flux of a galaxy evolves as:

S ν (z) = L ν(1+z) (z) 4πD 2 l (5.5)

(Sub)millimeter surveys over contiguous areas of the sky

In this section we discuss the surveys performed with 850µm < λ < 3 mm. During the last decades, many (sub)millimetre surveys have been carried out by many instruments, for example, the Submillimetre Common-User Bolometer Array (SCUBA; Holland et al. 1999) on the James Clerk Maxwell Telescope, the Large APEX Bolometer Camera (LABOCA; [START_REF] Siringo | The Large APEX BOlometer CAmera LABOCA[END_REF] on the Atacama Pathfinder Experiment (APEX; [START_REF] Güsten | The Atacama Pathfinder EXperiment (APEX) -a new submillimeter facility for southern skies[END_REF]; the Max Planck Millimeter Bolometer Array (MAMBO; [START_REF] Kreysa | Bolometer array development at the Max-Planck-Institut fuer Radioastronomie[END_REF]) on 30 meter telecope at the Institut de Radio Astronomie Millimetrique (IRAM); the AzTEC camera [START_REF] Wilson | The AzTEC mm-wavelength camera[END_REF] and the the Atacama Submillimeter Telescope Experiment (ASTE; [START_REF] Ezawa | The Atacama Submillimeter Telescope Experiment (ASTE)[END_REF]) and Bolocam [START_REF] Glenn | Bolocam: a millimeter-wave bolometric camera[END_REF] on the Caltech Submillimeter Observatory (CSO), the Goddard IRAM Superconducting Millimeter Observer (GISMO) at the IRAM 30m-telescope [START_REF] Staguhn | The GISMO Two-millimeter Deep Field in GOODS-N[END_REF][START_REF] Magnelli | The IRAM/GISMO 2 mm Survey in the COSMOS Field[END_REF] as well as with interferometer such as ALMA.

In order to be able to constrain the number counts, surveys have been carried out at different depths (see Fig. 5.3). This allows both the faint and bright ends of the number counts to be constrained. The first surveys carried out by SCUBA at the end of the 1990s covered small areas.

The development of more efficient instruments, such as SCUBA-2, has made it possible to carry out surveys covering a larger area but the depth remains limited by the confusion noise (see Sect. 5.5.7). Recently, thanks to the advent of the Atacama Large Millimeter/submillimeter Array (ALMA) and its capabilities to perform both high-resolution and high-sensitivity observations, our view of galaxies detected in (sub)millimeter wavelenghts has become increasingly refined.

The high angular resolution compared to single-dish observations reduces drastically the uncertainties of source confusion and blending, and provides new opportunities for robust galaxy identification and flux measurement. The ALMA sensitivity permits the detection of sources down to 0.1 mJy (e.g., Carniani et al., 2015), the analysis of populations of dust-poor high-z galaxies (Fujimoto et al., 2016) or main sequence (MS; see Sect. 1.3.4) galaxies (e.g., Papovich et al., 2016;Dunlop et al., 2017;Schreiber et al., 2017), and also demonstrates that the extragalactic background light (EBL) can be resolved partially or totally by faint galaxies (S < 1 mJy; e.g., Hatsukade et al. 2013;Ono et al. 2014;Carniani et al. 2015;Fujimoto et al. 2016). Thanks to this new domain of sensitivity, ALMA is able to unveil less extreme objects, bridging the gap between massive starbursts and more normal galaxies: SMGs no longer stand apart from the general galaxy population (e.g. Dunlop et al., 2017;Elbaz et al., 2018).

Soon, large millimeter surveys are planned to cover unparalleled areas of the sky, whether in the short term with the TolTEC at the Large Millimeter Telescope (LMT; Bryan 2018), the SPT3G at the SPT, NIKA-2 camera [START_REF] Adam | The NIKA2 large-field-of-view millimetre continuum camera for the 30 m IRAM telescope[END_REF] at the IRAM 30m-telescope, the Chajnantor Sub/Millimeter Survey Telescope (CSST; Golwala 2018) or in the longer term with the Origins Space Telescope (OST; [START_REF] Battersby | The Origins Space Telescope[END_REF]). 0.5" 1" 10" 20" We have used the same set of simulations that we used for the completeness analysis.

10

ALMA SCUBA SCUBA-2 LABOCA MAMBO GISMO AzTEC NIKA2 ALMA SCUBA SCUBA-2 LABOCA MAMBO GISMO AzTEC NIKA2

Bias estimation

In this section, we will discuss the different biases that we have estimated and corrected in order, from our observations, to be able to trace back the number of galaxies present in the sky per unit of surface area.

Deboosting fluxes

In this section, we evaluate the effect of flux boosting. Galaxies detected with a relatively low S/N tend to be boosted by noise fluctuations (see Hogg and Turner 1998;Coppin et al. 2005;Scott et al. 2002). To estimate the effect of flux boosting, we used the same set of simulations that we used for completeness estimations (see Sect. 5.5.5).

The results of our simulations are shown in Fig. 5.4. The boosting effect is shown as the ratio between the input and output flux densities as a function of the measured S/N. For point sources, we observed the well-known flux boosting effect for the lowest S/Ns. This effect is not negligible for the faintest sources in our survey. At 4.8 σ, the flux boosting is ∼15%, and drops below 10% for an S/N greater than 5.2. We estimated the de-boosted flux by dividing the measured flux by the median value of the boosting effect as a function of S/N (red line in Fig. 5.4).

Purity

We parameterize the purity criterion (see Eq. 6.1 and Fig. The histogram showing the number of positive and negative sources (see Fig. 5.5) is not intuitive to read. At σ p = 4.8, we have 20 positive sources for 4 negative ones, which is a purity rate of 80%. That does not mean that it is strictly each one of the 20 sources that has an 80 percent chance of being false. With a detection threshold of 4.8σ, the S/N range of our detections is ∼4.8-11. Each source has a probability of being false equal to its purity estimated at the S/N of its detection.

Eddington Bias

As sources with lower luminosities are more numerous than sources with higher luminosities, assuming that the noise is Gaussian distributed gives rise to an overestimation of the number counts in the lowest flux bins. Sir Arthur Stanley Eddington, in 1913, proposed a formula to correct the statistical effects of magnitude distribution between the observed magnitude distribution and the "true" magnitude distribution (Eddington, 1913). After [START_REF] Dyson | A method for correcting series of parallax observations[END_REF] had studied in detail a particular form of Eddington bias in the distribution of stellar parallaxes, Sir Arthur Stanley Eddington proposed a literal form of this bias [START_REF] Eddington | The correction of statistics for accidental error[END_REF].

We also corrected for the effects of the Eddington bias (Eddington, 1913). We simulated a realistic number of sources (the slope of the number counts were computed using the coefficients given in Table 5.2) and added Gaussian noise to each simulated source. The correction factor for each flux bin was therefore the ratio between the flux distribution before and after adding the noise. The bias is that when Gaussian noise is added to the flux density F ν +δF ν , since the number of low flux density galaxies is much higher than the number of high flux sources, the number of sources artificially entering the counts because of the noise fluctuations at low flux density is higher than the number of galaxies artificially leaving the number counts at higher flux density. This creates a bias between the "real" source number per flux density interval and the observed number (see Fig. 5.6). In order to correct this effect, we simulated a realistic number of sources (the slope of the number counts is computed using the coefficients given in Table 5.2) and add Gaussian noise to each simulated source. The correction factor for each flux bin is therefore the ratio between the flux distribution before and after adding the noise.

Flux density [mJy]

dN/dS FIGURE 5.6: Distribution of the number of galaxies calculated according to the set of parameters given in Table 5.2 ; blue curve) as a function of flux density, and when a Gaussian noise is added (green distribution). The difference between the two curves represents the Eddington bias.

Effective Area

As the sensitivity of our 1.1mm ALMA map is not uniform, we defined an effective area where a source with a given flux can be detected with an S/N > 4.8 σ, as shown in Fig. 5.7. Our map is composed of six different slices -one of them, slice B, presents a noise 30% greater than the mean of the other five, whose noise levels are comparable. The total survey area is 69.46 arcmin 2 , with 90% of the survey area reaching a sensitivity of at least 1.06 mJy.beam -1 . We considered the relevant effective area for each flux density in order to compute the number counts. We considered the total effective area over all slices in the number counts computation. Total FIGURE 5.8: As the noise map is not uniform (see Table 3.6 and Fig. 3.16), we have split the effective area according to the slices (different dashed lines for each slices) in addition to the total area shown by the solid line. For each slice, excluding slice B, 50% of the effective area is reached between 0.7-0.9 mJy, or 1.1mJy for slice B. Normalized flux 0.0" 0.1" 0.2" 0.3" 0.4" 0.5" 0.6" 0.7" 0.8" FIGURE 5.9: Convolution of a source (Gaussian form) of different sizes with a Gaussian of 0.6" (representing the PSF). Half of the FWHM of this convolution is given by the dotted lines. The integrated flux is the same for all convolutions.

Completeness

For the same integrated flux, the more compact a source will be, the easier its detection will be (see Fig. 5.9). Basically, if we consider that the shape of the source is Gaussian and that the PSF is Gaussian too:

f (x) = 1 √ 2πσ f e -( x-µ f ) 2 2σ 2 f and g(x) = 1 √ 2πσ g e - (x-µg) 2 2σ 2 g (5.7)
The convolution of these two Gaussians will be given by 1 :

x 0 f (x -τ )g(τ )dτ = f ⊗ g (5.8) F -1 [F (f (x))F (g(x))] = f (x) ⊗ g(x)
(5.9)

F (f (x)) = 1 √ 2πσ f ∞ -∞ e -x 2 2σ 2 f e -2πik(x +µ f ) dx = e -2πikµ f √ 2πσ f ∞ -∞ e -x 2 2σ 2
f e -2πikx dx (5.10) We assessed the accuracy of our catalog by performing completeness tests. The completeness is the probability of a source to be detected in the map. We computed the completeness of our observations using Monte Carlo simulations performed on the 0 .60-mosaic map. We injected 50 artificial sources in each slice. Each source was convolved with the PSF and randomly injected on the dirty map tapered at 0 .60 (see Fig. 5.10. In total, for each simulation run, 300 sources with the same flux were injected into the total map (see Fig. 5.11). In view of the size of the map, the number of independent beams and the few number of sources detected in our survey, we can consider, to first order, that our dirty map can be used as a blank map containing only noise, and that the probability to inject a source exactly at the same place as a detected galaxy is negligible.

P f ⊗g (x) = F -1 [F (f (x))F (g(x))] = 1 2π σ 2 f + σ 2 g e -( x-( µ f +µg )) 2 2 ( σ 2 f +σ 2 g ) (5.11)
The probability that at least two point sources, randomly injected, are located closer than FWHM (p b ) is:

p b = 1 - k = n-1 k = 0 N b -k N b (5.12)
where N b is the number of beams in the full mosaic and n is the number of injected sources. For each one of the six slices of the survey, we have ∼100 000 independent beams at the resolution of 0 .60. The probability of having source blending for 50 simulated sources in one map is therefore ∼1%. We then counted the number of injected sources detected with σ p = 4.8 σ and σ f = 2.7 σ, corresponding to the thresholds of our main catalog. We injected 300 artificial sources of a given flux, and repeated this procedure 100 times for each flux density. Our simulations cover the range S ν = 0.5-2.4 mJy in steps of 0.1 mJy. Considering the resolution of the survey, it would be reasonable to expect that a non-negligible number of galaxies are not seen as point sources but extended sources (see Sect. 4.6.1). We simulated different sizes of galaxies with Gaussian FWHM between 0 .2 and 0 .9 in steps of 0 .1, as well as point-source galaxies, to better understand the importance of the galaxy size in the detectability process. We matched the recovered source with the input position within a radius of 0 .6. As a result of our simulations, we determined that at 1.2 mJy, our sample is 94±1% complete for point sources. This percentage drastically decreases for larger galaxy sizes. For the same flux density, the median detection rate drops to 61±3% for a galaxy with FWHM ∼0 .3, and to 9±1% for a FWHM ∼0 .6 galaxy. This means, that for a galaxy with an intrinsic flux density of 1.2 mJy, we are more than ten times more likely to detect a point source galaxy than a galaxy with FWHM ∼0 .6.

The size of the millimeter emission area plays an essential role in the flux measurement and completeness evaluation. In order to roughly estimate this effect, we assumed that ALMA sizes are 1.4 times smaller than the size measured in HST H-band (as derived by Fujimoto et al. 2017 using 1034 ALMA galaxies). We are aware that this size ratio is poorly constrained at the present time, but such relations have been observed in several studies (see Sect. 4.6.1). For example, of the 12 galaxies presented by Laporte et al. (2017), with fluxes measured using ALMA at 1.1mm (González-López et al., 2017), seven of them have a size measured by HST F140W/WFC3 similar to the size measured in the ALMA map. On the other hand, for the remaining five galaxies, their sizes are approximately two times more compact at millimeter wavelengths than at optical wavelengths. This illustrates the dispersion of this ratio.

Cosmic variance

When studying relatively small fields and wanting to extend this result to the whole sky, there is an observational uncertainty, based on the variation in density of large scale structures. Indeed, it is not always clear whether the part of the sky we are observing is representative of the whole sky, or whether we are looking at a region that is particularly rich or poor in galaxies. This variation, which depends on the size of the area studied, as well as the masses and redshifts of the observed galaxies, is called the cosmic variance. This cosmic variance is particularly important when the studied area is small, the galaxies are massive, and the redshifts high. Unfortunately, it is precisely these characteristics that define the field and the galaxies that we study in GOODS-ALMA. The relative cosmic variance can be defined by:

σ 2 v = N 2 -N 2 N 2 - 1 N (5.13)
where N 2 and N 2 are the mean and the variance of the probability to have N objects within a volume V. The last term in this equation corresponds to the Poissonian uncertainty.

Following [START_REF] Peebles | The large-scale structure of the universe[END_REF] and Moster et al. (2011):

σ 2 v = 1 V 2 V dV a dV b ξ(|r a -r b |) (5.14)
where ξ is the two-point correlation function of the sample .

The cosmic variance is therefore dependent on the galaxy population studied. For example, extremely red objects (EROs) at z ∼ 1.2 in the GOODS fields will have a relatively high cosmic variance (∼ 0.4-0.6), much higher than the LBG population at z ∼ 3, because the LBG population is much less clustered than the ERO population [START_REF] Somerville | The Redshift Distribution of Near-Infrared-Selected Galaxies in the Great Observatories Origins Deep Survey as a Test of Galaxy Formation Scenarios[END_REF].

Cosmic variance was not taken into account in the calculation of the errors. Above z = 1.8 and up to the redshift of the farthest galaxy in our catalog at z = 4.8, the strong negative Kcorrection at this wavelength ensures that the selection of galaxies is not redshift-biased. The cosmic variance, although significant for massive galaxies in a small solid angle, is counterbalanced by the negative K-correction, which makes the redshift interval of our sources (∆z = 3 in Eq. 12 in Moster et al. 2011) relatively large, spanning a comoving volume of 1400 Gpc 3 . Based on Moster et al. (2011), the cosmic variance for our sources is ∼15 %, which does not significantly affect the calculation of the errors on our number counts.

There are also other types of bias, such as cosmic bias (e.g., [START_REF] Szapudi | Cosmic statistics of statistics[END_REF], but this is negligible in our case in relation to cosmic variance [START_REF] Colombi | The cosmic distribution of clustering[END_REF], and is therefore not taken into account.

Confusion limit

This becomes the limiting factor when the observation is deep. As the number of low flux sources is greater than the number of bright sources, the deeper the observation is, the more the distance between two galaxies decreases. For SCUBA-2 for example, the confusion limit at 850 µm is approximately 1.7 mJy (4σ; Cowie et al. (2018). This limit corresponds to a SFR of ∼220

M yr -1 (Kroupa IMF). For ALMA, the beam size is considerably smaller than for single dishtelescopes. If we assume a Poissonian distribution of sources, the probability that two sources brighter than S lim are closer than the size of the beam is given by:

P (< θ min ) = 1 -e -πN θ 2 (5.15)
In practice, this probability is even lower, and current extraction techniques allow us to detect two sources that are separated by a distance up to 0.8θ [START_REF] Dole | Predictions for Cosmological Infrared Surveys from Space with the Multiband Imaging Photometer for SIRTF[END_REF].

N = - ln (1 -P (< θ min )) πθ 2 (5.16)
In the end with ALMA, in the case of this study, we are not limited by the confusion limit and the noise confusion is negligible and will not be taken into consideration.

Comparison with other surveys

We were able to extend the range of fluxes studied in the number counts by integrating previous (sub)millimetre number counts studies: Lindner et al. ( 2011 2017). We took advantage of our ALMA survey to open the parameter space in terms of surface-flux and to limit the cosmic variance due to the small size of previous ALMA surveys, which tends to strongly bias the number counts. In addition, the large size of our survey allows us to detect massive galaxies with high redshift that have been missed by smaller ALMA surveys.

There is a gap in the compilation of the (sub)millimetre number counts (see Fig. 5.13) at the level of our flux range, i.e. between 0.8 and 1.5mJy. Our study will therefore help to fill this gap.

In addition, there is a tension in the literature for fluxes > 1.5mJy. Some studies such as Geach et al. (2017) or Scott et al. (2012) that have been carried out on single dish telescopes show systematically higher counts than those carried out with ALMA for these flux ranges. There could be a blending phenomenon for galaxies with the highest fluxes when observing with a single dish telescope . These counts with ALMA (e.g., Karim et al., 2013;[START_REF] Simpson | The SCUBA-2 Cosmology Legacy Survey: ALMA Resolves the Bright-end of the Sub-millimeter Number Counts[END_REF] were done with a shorter wavelength (λ = 870 µm). The conversion factor between 870µm and 1.1mm described in detail Sect. 5.7 can suffer from great uncertainties. This ALMA survey is therefore ideal for fixing this tension.

At low flux, we can note that the deepest counts were carried out in small and lensed regions (e.g., Fujimoto et al., 2016). Here again, great uncertainties regarding number counts may appear in this for these regions of the sky. We will discuss in detail these sensitive surveys in the conclusion of this chapter.

Estimation of number counts

We use sources with an S/N greater than 4.8 from the main catalog to create cumulative and differential number counts. We need to take into account the contamination by spurious sources, completeness effects, and flux boosting in order to compute these number counts.

The contribution of a source with flux density S i ± dS i to the cumulative number counts is given by: dN (S i ) where p c (S i ) is the purity criterion as defined in Eq. 6.1 at the flux density S i , A ef f (S i ) and C(S i , R circ ALMA ) are the effective area and the completeness for the flux interval dS i , as shown in Fig. 5.12 and Fig. 5.7. The completeness is strongly correlated with the sizes of the galaxies. To estimate the completeness, galaxies that do not have measured sizes in the H-band (van der Wel et al., 2012) are considered as point sources otherwise we use R circ ALMA = R circ H /1.4 (see Sect. 5.5.5).

dS i = p c (S i ) A ef f (S i )C(S i , R circ ALMA ) × dN obs (S i ) dS i (5.17) 5.7. Estimation of number counts 97 S ν N(> S ν ) N cum S ν dN/dS ν N diff mJy deg -2 mJy mJy -1 deg -2 (1) (2) (3) (4) (5) (6
The cumulative number counts are given by the sum over all of the galaxies with a flux density higher than S:

N (> S) = Si>S p c (S i ) A ef f (S i )C(S i , R circ ALMA ) × dN obs (S i ) dS i × dS i (5.18)
Errors are computed by Monte-Carlo simulations, added in quadrature to the Poisson uncertainties. The derived number counts are provided in Tab. 5.1. AGS19 is located at a position where the noise is artificially low, and has therefore not been taken into account

In Fig. 5.13, we compare our results with previous studies (Lindner et al., 2011;Scott et al., 2012;Karim et al., 2013;Hatsukade et al., 2013;[START_REF] Simpson | The SCUBA-2 Cosmology Legacy Survey: ALMA Resolves the Bright-end of the Sub-millimeter Number Counts[END_REF]Oteo et al., 2016;Hatsukade et al., 2016;Aravena et al., 2016;Fujimoto et al., 2016;Umehata et al., 2017;Geach et al., 2017;Dunlop et al., 2017). To standardize these previous studies, the different flux densities are scaled to 1.1 mm using a Modified Black Body (MBB) model, assuming a dust emissivity index β = 1.5 (e.g., Gordon et al., 2010), a dust temperature T d = 35 K (eg. Chapman et al., 2005;Kovács et al., 2006;Coppin et al., 2008), and a redshift of z = 2.5 (e.g., Wardlow et al., 2011;Yun et al., 2012). These values have also been chosen to be consistent with Hatsukade et al. (2016). The different flux densities were therefore scaled to 1.1 mm using the relations S 1.1mm /S 1.2mm = 1.29, S 1.1mm /S 1.3mm = 1.48 and S 1.1mm /S 870µm = 0.56. It is a real challenge to standardize these previous studies because instruments, observational techniques or resolution often vary between studies. Some of these counts have been computed from individual pointings, by brightness selection, or by serendipitous detections. Observations with a single dish or a low resolution can also overestimate the number counts for the brightest fluxes, because of blending effects (see Ono et al. 2014). Another non-negligible source of error can come from an inhomogeneous distribution of bright galaxies. An underdensity by a factor of two of submillimeter galaxies with far infrared luminosities greater than 2 × 10 12 L in the extended Chandra deep field south (ECDFS) compared to other deep fields has been revealed by Weiß et al. (2009).

(1.3mm) Hatsukade+16 (1.1mm) Hatsukade+13 (1.3mm) Fujimoto+16 (1.2mm) Umehata+16 (1.1mm) Aravena+16 (1.2mm) Oteo+15 (1.2mm) Karim+13 (870 m) Simpson+15 (870 m) Scott+12 (1.1mm) Lindner+11 (1.2mm) Geach+17 (850 m) FIGURE 5
.13: 1.1-mm cumulative number counts derived using the corrections described in Sect. 5.7, for the sources detected at > 4.8 σ in the main catalog. AGS19 is located at a position where the noise is artificially low, and has therefore not been taken into account. Previous (sub)millimetre cumulative number counts are also shown (Lindner et al., 2011;Scott et al., 2012;Karim et al., 2013;Hatsukade et al., 2013;Ono et al., 2014;[START_REF] Simpson | The SCUBA-2 Cosmology Legacy Survey: ALMA Resolves the Bright-end of the Sub-millimeter Number Counts[END_REF]Oteo et al., 2016;Carniani et al., 2015;Hatsukade et al., 2016;Aravena et al., 2016;Fujimoto et al., 2016;Umehata et al., 2017;Geach et al., 2017;Dunlop et al., 2017). The different fluxes are scaled to 1.1 mm flux densities using S1.1mm/S1.2mm = 1.29, S1.1mm/S1.3mm = 1.48, S1.1mm/S870µm = 0.56. From the study of Umehata et al. (2017), we use only sources which do not have z = 3.09, (i.e. we are excluding the protocluster members). Results from single-dish surveys are shown with unfilled pentagon markers and are only indicative, they are not considered for model fitting. The grey curve shows the best-fit Schechter function (with 1-σ) uncertainties, and the red curve shows the best-fit DPL function (with 1-σ).

Despite those potential caveats, the results from our ALMA survey in the GOODS-South field are in good agreement with previous studies for flux densities below 1 mJy. For values above this flux density, two different trends coexist as illustrated in Fig. 5.13: our counts are similar to those found by Karim et al. (2013), but below the trend characterized by Scott et al. (2012). These two previous studies have been realized under different conditions. The effects of blending, induced by the low resolution of a single dish observation, as with Scott et al. (2012), tend to overestimate the number counts at the bright-end (Ono et al., 2014;Karim et al., 2013;Béthermin et al., 2017). We indicate these points on the Fig. 5.13 on an indicative basis only.

The differences in wavelength between the different surveys, even after applying the scaling corrections above, can also induce scatter in the results, especially for wavelengths far from 1.1mm.

(1.1mm) Fujimoto+16 (1.2mm) Umehata+16 (1.1mm) Ono+14 (1.2mm) Carniani+15 (1.1mm) Karim+13 (870 m) Scott+12 (1.1mm) Lindner+11 (1.2mm) Geach+17 (850 m) FIGURE 5
.14: 1.1-mm differential number counts derived using the corrections described in Sect. 5.7, for the sources detected at > 4.8 σ in the main catalog. AGS19 is located at a position where the noise is artificially low, and has therefore not been taken into account. Previous (sub)millimetre differential number counts are also shown (Lindner et al., 2011;Scott et al., 2012;Karim et al., 2013;Ono et al., 2014;Carniani et al., 2015;Hatsukade et al., 2016;Fujimoto et al., 2016;Umehata et al., 2017;Geach et al., 2017). The different fluxes are scaled to 1.1 mm flux densities using S1.1mm/S1.2mm = 1.29, S1.1mm/S1.3mm = 1.48, S1.1mm/S870µm = 0.56. From the study of Umehata et al. (2017), we use only sources which do not have z = 3.09, (i.e. we are excluding the protocluster members). Results from single-dish surveys are shown with unfilled pentagon markers and are only indicative, they are not considered for model fitting. The grey curve shows the best-fit Schechter function (with 1-σ) uncertainties, the blue curve shows the model of Béthermin et al. (2017).

Parametrizing number counts

The cumulative source counts from the 20 detections in this study and the results from other interferometric blank surveys are fitted with a Double Power Law (DPL) function (e.g., Scott et al., 2002) given by:

N (> S) = N 0 S 0 S S 0 α + S S 0 β -1 (5.19)
and a modified Schechter (Schechter, 1976) function (e.g., Knudsen et al., 2008):

N (> S) = N 0 S 0 S S 0 α exp - S S 0 d S S 0 (5.20)
where N 0 is the normalization, S 0 the characteristic flux density and α is the faint-end slope. β is the bright-end slope of the number of counts in Eq. 5. the Trust Region Reflective algorithm for these two fitted-functions. The best-fit parameters are given in Table 5.2.

Comparison with models

We compare our results with an empirical model that predicts the number counts at far-IR and millimeter wavelengths, developed by Béthermin et al. (2017). This simulation, called SIDES (Simulated Infrared Dusty Extragalactic Sky), updates the Béthermin et al. (2012) model. These predictions are based on the redshift evolution of the galaxy properties, using a two starformation mode galaxy evolution model (see also Sargent et al. 2012).

The Béthermin et al. (2017) prediction is in good agreement with the number counts derived in this study, for the two bins with the lowest flux densities (see Fig. 5.14). For the highestflux density bin, the model is slightly above the data (∼1σ above the best Schechter fit for flux densities greater than 1 mJy). However, both the Béthermin et al. (2017) model and our data points are below the single-dish measurements for flux densities greater than 1 mJy. This disagreement between interferometric and single-dish counts is expected, because the boosting of the flux densities of single-dish sources by their neighbor in the beam (Karim et al., 2013;Hodge et al., 2013;Scudder et al., 2016). Béthermin et al. (2017) derived numbers counts from a simulated single-dish map based on their model and found a nice agreement with single-dish data, while the intrinsic number counts in the simulation are much lower and compatible with our interferometric study.

Contribution to the cosmic infrared background

The contribution of our ALMA sources to the extragalactic background light (EBL) is derived by integrating the derived number counts down to a certain flux density limit. Using the 20 (>4.8 σ) sources detected, we computed the fraction of the 1.1 mm EBL resolved into discrete sources. The integrated flux density is given by:

I(S > S lim ) = inf S lim dN (S) dS SdS (5.21)
We used the set of parameters given in Table 5.2 on the differential number counts. We compared our results with observations from the far infrared absolute spectrophotometer (FIRAS) on the cosmic background explorer (COBE), knowing that uncertainties exist on the COBE measurements (e.g., Yamaguchi et al., 2016). We used the equation given in Fixsen et al. (1998) to compute the total energy of the EBL:

I ν = (1.3 ± 0.4) × 10 -5 ν ν 0 0.64±0.12
P ν (18.5 + 1.2K) (5.22) where ν 0 = 100 cm -1 , and P ν is the familiar Planck function with I ν in erg.s -1 cm -1 Hz -1 sr -1 .

From this equation, we find that at 1.1 mm, the energy of the EBL is 2.87 nW.m -2 sr -1 .

As surface brightness is expressed in units of nW m-2 sr-1, we use the following conversion:

1nW.m -2 sr -1 = 3000 mJy/sr.

(5.23)

From Eq. 5.21 we can estimate the integrated EBL. For our data, the lowest flux density bin for differential counts S lim is 0.7 mJy, and we extrapolate to lower flux densities. We have resolved only 13.7 +9.6 -5.3 % of the EBL into individual galaxies at 0.7 mJy. This result is in good agreement with studies such as Fujimoto et al. (2016). In order to have the majority of the EBL resolved (e.g., Hatsukade et al. 2013;Ono et al. 2014;Carniani et al. 2015;Fujimoto et al. 2016), we would need to detect galaxies down to 0.1 mJy (about 50 % of the EBL is expected to be resolved at this value).

The extrapolation following the model of the differential number counts (see the coefficients in the Table 5.2) of the integrated flux density below S lim suggests a flattening of the number counts. The population of galaxies that dominate this background is composed of the galaxies undetected in our survey, with a flux density below our detection limit.

Conclusion

The derived differential and cumulative number counts of our 20 primary detections have allowed us to partly alleviate the degeneracy observed above 1 mJy.beam -1 in previous (sub)millimetre studies. However, we can note that due to our low detection rate, our uncertainties on the number counts are relatively high.

This work allowed us to set the number counts to 1.1mm using our survey and the main surveys carried out in (sub)-millimetres. We have configured them with a Schechter function and a double power law. We can note the faint-end of the number counts was done through a cluster by taking advantage of a lensing. Fujimoto et al. (2016) with an ALMA survey at 1.2mm reached sources Down to ∼ 0.02 mJy. More recently, Muñoz Arancibia et al. ( 2018) has reached the same depths here too with lensed galaxies. There is a real doubt about the evolution of faint-end of the number counts compaction (i.e. one of the two models is not physical). Semi-analytical models such as Popping et al. in prep, coupling the UniverseMachine [START_REF] Behroozi | UniverseMachine: The Correlation between Galaxy Growth and Dark Matter Halo Assembly from z = 0 -10[END_REF] with empirical and theoretical relations on the dust emission are in good agreement with the trends found for galaxies with fluxes of > 0.1 mJy but present flattering for lower flux. This may mean that the faint-end of the number counts over small and lensed regions may not be extrapolated to all number counts.

Introduction

The formation and evolution of the most massive galaxies (M > 5×10 10 M ) at redshifts z > 2 is still largely debated. Their observed number density exceeds theoretical expectations assuming typical dark matter to stellar mass ratios (Steinhardt et al., 2016). The downsizing of galaxy formation challenges theoretical models which match either the low or high mass end but are unable to match both ends (e.g., Fontanot et al., 2009). The presence of a population of massive passive galaxies at z ∼2 with compact stellar surface densities challenges searches for their progenitors (?).

Since infrared (IR) wavelengths contribute to approximately half of the total Extragalactic Background Light (EBL; e.g., Dole et al. 2006), the study of dust-enshrouded star-formation in distant galaxies is an important tool to progress in our understanding of the evolution of massive galaxies. The first submillimeter extragalactic surveys (Smail et al., 1997;Barger et al., 1998;Hughes et al., 1998) performed with the Submillimetre Common-User Bolometer Array (SCUBA; Holland et al. 1999) on the James Clerk Maxwell Telescope (JCMT) have revealed a population of high redshift galaxies that are massive, highly obscured and have high star formation rates (SFRs). Recent observations using the Atacama Large Millimetre/submillimetre Array (ALMA), which provides a resolution more than an order of magnitude higher than SCUBA, has since refined our understanding of galaxy evolution by securing the identification of optical counterparts and allowing us to detect not only extreme galaxies (galaxies with particularly high star 104 Chapter 6. Using IRAC priors to probe fainter millimeter galaxies formation rates, e.g., starburst or lensed galaxies), but also "normal" galaxies that are secularly forming stars. This chapter extends our previous analysis (see Chapter 4) of a deep continuum 1.1mm survey with ALMA over an area of 69 2 . This survey is located in the Great Observatories Origins Deep Survey-South (GOODS-South) at a location covered with the deepest integrations in the H-band with the HST-WFC3 camera. Chapter 4, we limited our analysis to the blind detection of ALMA sources without considering prior information at other wavelengths. Due to the large number of independent beams in the high-resolution ALMA image, we were limited to the 4.8-σ detection limit. Here we extend the detection limit to 3.5-σ by cross-matching the ALMA detections with catalogs in the near and mid-infrared. The need for a good astrometric calibration led us to introduce an improved correction for the astrometry of the HST image of the GOODS-South field (hereafter GOODS-S).

Data

Additional data IRAC catalog

We use the Spitzer-Cosmic Assembly Near-Infrared Deep Extragalactic Survey (S-CANDELS; Ashby et al. 2015) catalog of galaxies detected at 3.6 and 4.5 µm with the Infrared Array Camera (IRAC; Fazio et al. 2004) aboard the Spitzer Space Telescope (Werner et al., 2004). The catalog (Ashby et al., 2015) -hereafter S-CANDELS catalog -that reaches a 5-σ depth of 26.5 mag (AB) includes 2627 galaxies in the GOODS-ALMA field, i.e. about 38 sources.arcmin -2 .

HST H-band catalog

The GOODS-ALMA area covers the deepest H-band part of the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS; Grogin et al. 2011) field (central one-third of the field). The point source catalog reaches a 5-σ depth of 28.16 mag (AB) in the H 160 filter (measured within a fixed aperture of 0.17 ; Guo et al. 2013). The surface density of galaxies detected at 1.6 µm with the Wide Field Camera 3 / infrared channel (WFC3/IR) within the GOODS-ALMA field is about 233 sources.arcmin -2 .

Near-infrared K s -band catalog

We use the 2.2 µm catalog described in Straatman et al. (2016) that uses an ultradeep image resulting from the combination of multiple observations in the K and K s bands from: (i) the very large telescope (VLT), which combines the images of GOODS-S done with the Infrared Spectrometer and array camera (ISAAC; Moorwood et al. (1999)) in the K s -band (Retzlaff et al., 2010) with the High Acuity Wide filed /K-band imager (Hawk-I; Kissler-Patig et al. 2008) image in the K-band (Fontana et al., 2014), (ii) the 6.5m Magellan Baade Telescope combining the K s -band image from the FourStar Galaxy Evolution Survey (ZFOURGE, PI: I. Labbé) using the FourStar near-infrared Camera (Persson et al., 2013) with the K-band image using the Persson's For each panel, the histogram of the offsets in RA and DEC is shown as well as a fit with a Gaussian function (orange curve). The position of the peak and the standard deviation of the Gaussian is indicated for each curve. The middle and the right panels show that there are no significant astrometric differences between ALMA and JVLA nor between JVLA and PS1, while The left panel shows the clear shift in both RA and DEC between the positions of 375 sources in common between the Pan-STARRS (PS) and HST images. We measure a systematic offset of ∆RA = -96 ± 83 mas and ∆Dec = 252 ± 107 mas. In addition, a local offset is presented in Fig. 6.2.

Auxillary Nasmyth infrared camera (PANIC; Martini et al. 2004) in the HUDF (PI: I. Labbé), (iii) the Canada-France-Hawaii Telescope (CFHT), with the K band image done with the wide-field infrared camera (WIRCam; Puget et al. (2004) as part of the Taiwan ECDFS near Infrared survey (TENIS; Hsieh et al. 2012).

The 5-σ point-source detection threshold in this ultradeep K s image reaches a magnitude between 26.2 and 26.5, which leads to an average galaxy surface density of about 168 sources.arcmin -2 .

Radio catalog

A radio image that encompasses the GOODS-ALMA field was observed with the Karl G. Jansky Very Large Array (VLA) at a frequency of 3 GHz (10 cm) and an angular resolution of ∼0 3 for a total of 177 hours (configurations A, B, & C; PI: W. Rujopakarn). Down to the average depth of the radio catalog within the GOODS-ALMA region of RMS = 2.1 µJy.beam -1 , the average surface density of radio sources is about 5 sources.arcmin -2 .

Astrometric correction of the HST image of GOODS-South

We describe Chapter 4 the presence of a systematic offset of ∆RA=-96±113 mas in right ascension, and ∆Dec=261±25 mas in declination between the ALMA and HST images. This offset, interpreted as a positional shift of the HST image with respect to all other reference frames, is in good agreement with the offset previously discussed in Dunlop et al. (2017) and Rujopakarn et al. (2016). For the GOODS-North field, the coordinates were shifted by approximately 0.3 arcsec, primarily in declination, compared to those of other astrometric reference datasets (Dunlop et al., 2017). However, this correction has not been made to the v2.0 release for GOODS-South, in part because no external astrometric reference data with both suitable absolute accuracy and faint source density (such as the SDSS) were available 1 . The offset used until now only corrects for the bulk global shift in astrometry but it does not account for the relative error in the astrometric calibration that was introduced in the building of the HST mosaic. In the following, we propose to determine this local correction that behaves like a distortion correction. This correction is important in the present study since we aim at using prior knowledge of existing sources from other wavelengths in order to push the ALMA detection limit to deeper levels.

0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.1 " 0.
We take advantage of the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) Data Release 2 (Flewelling et al., 2016). The offset between HST and Pan-STARRS images computed using an ensemble of 375 common detections (see Fig. 6.1 left panel) is comparable to the one presented chapter 4 : ∆RA = -96±83 mas and ∆Dec = 252±107 mas.

The comparison of the positions of 69 sources in common between our 3 GHz VLA catalog (5σ detections; Rujopakarn et al., in prep.) and Pan-STARRS within a radius of 0.6 shows that there is no offset between both images (Fig. 6.1 middle panel). To reduce the risk of misidentification, in all the astrometric analysis, we only retained galaxies that had been observed at least twice in the same filter during the Pan-STARRS survey. The average deviations are found to be ∆RA = 0 ± 98 mas and ∆Dec = 12 ± 160 mas.

Similarly, we find no offset between our ALMA sources (both the Main catalog presented chapter 4 and the supplementary catalog presented in the following) and their VLA counterparts for the 27 galaxies in common between both catalogs (Fig. 6.1, right panel). The average offset is ∆RA = 3 ± 113 mas and ∆Dec = 16 ± 93 mas well within the expected uncertainties for S/N ∼ 4 sources (Ivison et al., 2007;Hatsukade et al., 2018). Some of these sources come from the 6.4. ALMA Main and Supplementary catalogs 107 supplementary list discussed in the following of the paper, but since we applied this astrometric correction to the HST sources used as priors in the catalog production, we decided to present the astrometric correction upfront and to illustrate the positions of all our ALMA galaxies in this section.

The excellent agreement in the astrometry of VLA, ALMA, and Pan-STARRS implies that it is most likely the HST coordinate system that needs to be corrected.

After subtracting this systematic and global offset from the HST data, the residuals offsets present spatially coherent patterns (see Fig. 6.2). Each arrow represents the median offset between Pan-STARRS and HST positions, for a sliding median containing in average 30 points. This local offset varies with position in the GOODS-South field, and we refer to this as a distortion offset artificially introduced in the mosaicing of the HST data. The absolute value of the distortion offset is lower than the systematic offset, but it is not negligible, and can reach values higher than 0 15 at the edge of our GOODS-ALMA survey. A possible explanation for this local distortion may come from the process of making the HST maps themselves. Before the projection of the HST image onto the reference grid according to the World Coordinate System (WCS), a geometric distortion was applied using the WFC3 SMOV F606W data alone2 (Windhorst et al., 2011). This wavelength-independent geometric solution becomes greater for regions near the field edge (Windhorst et al., 2011), where the error on the correction itself also becomes very large. The combined effect of the global offset and distortion offset between the ALMA and HST positions is illustrated in Fig. 6.3 and listed in Table 6.1 both before and after applying the global offset of ∆RA = -96±83 mas and ∆Dec = 252±107 mas and the distortion offset. With the exception of two galaxies for which the offset between the ALMA detected position and that of HST is ∼0.4 (after correction of both the global offset and the distortion offsets, AGS27 and AGS35), all other galaxies have a difference in the two positions of < 0.27 . The average deviation after correction is -35 mas in RA and 47 mas in DEC for the sample of galaxies selected in this study.

(indicated by a magenta cross in Fig. 6.3). The updated RA and Dec positions derived for all galaxies in the Guo et al. (2013) catalog after the correction of both systematic and local offset are given at https://github.com/maximilienfranco/astrometry/.

ALMA Main and Supplementary catalogs 6.4.1 ALMA Main Catalog

The main ALMA catalog consists of 20 sources detected above 4.8 σ (see Chapter 4). This catalog was built without any prior assumption from a blind source extraction down to the 4.8 σ-limit using BLOBCAT (Hales et al., 2012).

The detection limit was set to S/N ≥ 4.8 due to the large number of independent beams that leads to spurious detections that become rapidly more numerous than the number of robust detections below this threshold despite the tapering at 0 60. Here the 4.8 σ-limit concerns the central pixel detection threshold (σ p = 4.8) and is associated with a constraint on the adjacent surrounding pixels that are included in the source if they pass a detection threshold of σ f = 2.7.

-0. This combination of parameters ensures an 80 % purity where the purity criterion p f defined as:

p f = N p -N n N p > 0.8 (6.1)
where N p and N n are the number of positive and negative detections. The negative detections refer to the detections in the inverse map (in other words detections in the continuum map multiplied by -1).

The initial catalog coming out of the blind source extraction contains 23 detections including 3 detections that we flagged as spurious Chapter 4 (marked with an asterisk in the Table 4.3).

Finding three spurious detections out of 23 detections matches the expected number of spurious sources obtained from the difference between positive and negative peaks above the 4.8 σ level of 4 with a Poissonian uncertainty of ±2. These three sources are the only ALMA detections in the list without any sign of an IRAC counterpart at λ = 3.6 or 4.5 µm (Spitzer/IRAC channels 1 and 2) despite the availability of ultra-deep IRAC data in this field (26.5 AB mag, Ashby et al. 2015). The possibility that these sources are most likely spurious was later on confirmed by 2018) -AGS21 and AGS23 -or lie outside of the SCUBA-2 field of view -AGS22. We note however, that AGS22 is both at the very limit of our detection threshold and that it is the only galaxy of our list that does not show any IRAC counterpart. In view of the very large number of expected spurious detections at the 3.5σ limit that we plan to reach in the present paper, we will adopt the strategy to limit ourselves to the most secure ALMA detections, which exhibit a clear IRAC counterpart.

As a result, we will limit the original main sample to 19 galaxies only, leaving aside AGS22 for consistency.

ALMA Supplementary Catalog

Using IRAC counterparts to identify robust ALMA sources down to 3.5-σ

In the present paper, we propose to use counterparts at other wavelengths to identify robust ALMA detections below the 4.8-σ limit of the Main Catalog described in Sect. 6.4.1. This approach is similar in the philosophy to a prior source extraction approach, except that we start from the ALMA blind source extraction at a lower threshold and then only keep sources with counterparts already identified in the near and mid infrared.

We start with the list of sources detected with the same algorithm than the Main Catalog but push it down to the σ p =3.5 limit. A total of 1077 sources are detected down to this threshold, most of which are spurious simply due to the large number of independent beams (more than one million in the 0"60 tapered map). Indeed the inverse map exhibits an equivalently large, even larger, number of detections of 1157. The number of detections at this level obviously depends on noise fluctuations but does not preclude the existence of real positive sources. Hence we cannot rely on Eq. 6.1 to calculate the probability that a source is real from a purely blind detection approach.

We observed Chapter 4 that all the ALMA robust detections of the Main Catalog present an IRAC counterpart, hence we start by imposing the requirement that all candidate detections exhibit an IRAC counterpart. We note that this criterion may lead us to reject real ALMA sources without any IRAC counterpart with the possible consequence to bias our sample towards the most massive galaxies, but this is for the sake of the robustness of the sources. ALMA sources without any IRAC counterpart may well exist (see e.g. Williams et al. 2019) and would be particularly interesting to analyse, but this is out of the scope of the present paper, since including sources without IRAC counterparts would imply including a significant number of hazardous sources in the sample.

In the process of cross-matching the ALMA and IRAC images, we identified several cases of IRAC sources that were present in the IRAC image but were not listed in the S-CANDELS catalog (see Sect. 6.2.1). These sources were systematically located close to one or several brighter IRAC sources. We therefore implemented a new source extraction for those sources taking care of modeling the neighboring sources to proceed to a clean de-blending of the IRAC sources. This allowed us to determine the S/N ratio of those sources and only keep real detections. In most cases, those sources exhibited a counterpart in either the H and K s band catalogs (described in Sect. 6.2.1,6.2.1). This led us to extend our counterpart search to the H and K s bands that we will use as priors to identify candidate IRAC sources that may have been missed in the original S-CANDELS catalog.

We choose the cross-matching radius between the positions of the ALMA detections and the IRAC, H and K band catalogs to be equal to the value of the largest FWHM. It is equal to 0 60, the FWHM of the tapered 1.1mm ALMA image, for the cross-match with the CANDELS H-band and ZFOURGE K-band catalogs, and it is equal to 1 95 for the cross-match with the IRAC channel 1 (3.6 µm) catalog (F W HM IRAC = 1.95" at 3.6 µm, F W HM IRAC = 2.05" at 4.5 µm). Before performing this cross-matching, we apply the astrometric correction to the CANDELS and ZFOURGE catalogs which use the HST reference frame, as described in Sect. 6.3.

A total of 204 sources detected with ALMA above 3.5σ at 1.1 mm have a counterpart in at least one of the three catalogs (see Fig. 6.4). In comparison, there are 182 detections above 3.5-σ that also fulfill these criteria in the inverse image. We recall that we used the H and K-band counterparts as priors to search for IRAC sources that may have been missed in the S-CANDELS catalog due to the presence of a bright neighbor.

We note that 84 % (16 out of 19 sources) of the ALMA sources in the Main Catalog described Chapter 4 have an IRAC counterpart closer than 0 3 (red dashed line in Fig. 6.5). Since our goal is not here to include all possible ALMA sources but to limit the Supplementary Catalog to the most robust candidates, we decided to impose a more stringent constraint on the association with IRAC counterparts by keeping as robust candidates those within a distance of 0 3. In total, 8 ALMA sources detected between 3.5σ and 4.8σ fulfill this criterion. This close association between ALMA and IRAC may be due in part to the fact that the FWHM of the IRAC images is limited by the pixel size rather than the diffraction limit, hence position accuracies may actually be better determined than the 1 95 FWHM of IRAC.

Looking at the remaining three sources in the Main Catalog, we noticed another interesting characteristics. They are all closer than 0 7 from their IRAC counterpart and nearly all exhibit a radio counterpart as well (2 out of 3). In fact, out of the 19 sources in the Main Catalog, 16 hence again 84 % exhibit a radio counterpart. We therefore chose to list in the Supplementary Catalog the sources that have both an IRAC and a radio counterpart closer than 0 7. This extra condition adds up an extra 6 ALMA sources detected between 3.5σ and 4.8σ.

In total, we end up with a list of 14 sources which fulfill the criteria of having an IRAC counterpart either (i) closer than 0 3 or (ii) closer than 0 7 but associated with a radio counterpart in the 3 GHz catalog.

It is possible that using these criteria does not allow us to detect all "real" ALMA detections with a S/N > 3.5 but these conservative criteria ensure a high purity rate. We performed Monte Carlo simulation to estimate the probability that an ALMA detection lies randomly close to a galaxy listed in the S-CANDELS catalog. We randomly define a position within GOODS-South and then measure the distance to its closest IRAC neighbour using the source positions listed in Ashby et al. (2015) for IRAC sources with S/N > 5. We repeat this procedure 100 000 times. The distance from the nearest IRAC galaxies, within a radius of 1.95" is given Table 6.1. In our supplementary catalog, for the farthest source of an IRAC source (0.64"), the percentage of a random IRAC association is 2.85 %. With the exception of one other source, the other detections have a probability of random IRAC association ≤ 1%.

We checked whether deeper surveys covering parts of the GOODS-S field could be used to validate or invalidate those ALMA Supplementary Catalog sources. The HUDF (Dunlop et al., 2017) and ASAGAO (Hatsukade et al., 2018) surveys reach a depth of RMS 35µJy at 1.3mm and RMS 6 µ Jy at 1.2 mm respectively. Using the same scaling factors as those presented Chapter 4, these depths convert to RMS 52 µJy and RMS 79 µJy respectively at the wavelength of 1.1mm of the present GOODS-ALMA survey. Only three ALMA 1.1mm sources from the Supplementary Catalog fall in the area covered by these deeper surveys and all of them were detected and listed in the associated catalogs (see Fig. 6.8). The sources AGS29 and AGS35 from our Supplementary Catalog were both detected within the ASAGAO survey and listed as the sources 18 and 26 respectively (Hatsukade et al., 2018). The source AGS38 falls within the HUDF survey and is listed as UDF16 (Dunlop et al., 2017). Hence our independent identification of sources down to the 3.5-σ level did not bring any spurious source without any counterpart in deeper ALMA surveys, instead all 3 sources in these deeper images are confirmed.

Supplementary catalog: optically dark galaxies

As discussed above, we searched for potential IRAC sources that were present in the IRAC images but missed in the S-CANDELS catalog because of the presence of a bright IRAC neighbor. Starting from the H and K-band images and catalogs, we identified two such sources, AGS24 and AGS25. Both are detected in the K-band, but neither of these two sources has been detected by the HST even in the 1.6 µm H-band (down to the 5σ limiting depth of H = 28 AB), hence they are HSTdark like 4 sources listed Chapter 4 and as also discussed in Wang et al. e.g., 2016;Elbaz et al. e.g., 2018;Schreiber et al. e.g., 2018c;Yamaguchi et al. e.g., 2019a.

The source AGS24 exhibits extended IRAC emission that is 0 36 away from the ALMA position. This is slightly larger than the 0 3 criterion but the source is also detected in the radio at 6 GHz (3.7σ) and 3 GHz (5.7σ). The S/N of this source is higher in the 0 29 mosaic than in the 0 60 tapered image, which suggests that it is particularly compact at 1.1 mm. This galaxy will be presented in detail in Zhou et al. (in prep), where a mass and photometric redshift are estimated to be z ∼ 3.5 and M = 1.82 +0. 27 -0.50 ×10 11 .

The source AGS25 is 0 1 away from its K-band counterpart in the ZFOURGE catalog (after applying the astrometric correction to the position of the ZFOURGE source), the source ID ZF OU RGE = 11353 with a magnitude K = 25.9 AB shown by a circle in Fig. 7.10. This source is not listed in the CANDELS catalog Guo et al. (2013), nor in the S-CANDELS catalog Ashby et al. (2015). It is marginally detected in radio at 5 and 10 cm with a S/N ratio close to 3. AGS25 is close (3 ) to a massive galaxy listed in CANDELS, ID CANDELS = 8067 with a stellar mass of M = 5.6×10 at a redshift of z spec = 1.038). ID CANDELS = 8067 is the bright neighbor that explains the absence of AGS25 in S-CANDELS. We subtracted it from the IRAC image by modeling a Sérsic profile with GALFIT Peng et al. (2010) and measured an IRAC flux density of 0.81±0.19 mJy (see Fig. 7.10). The IRAC source is 0 28 away from the ALMA position of AGS25.

Since the ALMA source is only 0 1 away from the ZFOURGE source ID ZF OU RGE = 11353, we use the stellar mass and redshift from the ZFOURGE catalog for this source. The characteristics of this galaxy make it particularly interesting, with z AGS25 = 4.66 +0.25 -0.26 and M ,AGS25 = 2.0×10 10 M . These properties are similar to those of the Main Catalog source AGS11, which is also an HSTdark galaxy, with z AGS11 = 4.83 +0.82 -0.76 and M ,AGS11 = 2.8×10 10 M .

We note that among the 4 HST-dark galaxies for which we were able to determine a stellar mass and redshift, there appear to be two distinct trends. Galaxies (AGS4 and AGS24) are among the most massive of all active uvj galaxies detected in the region covered by the ALMA survey. AGS4 has a stellar mass M = 2.81 +1.65 -1.03 ×10 11 M . In other words, it is the most massive galaxy at 4 < z < 5 in our catalogs. AGS24 has a stellar mass M = 1.82 +0. 27 -0.50 ×10 11 M . The other two HST-dark galaxies are of intermediate mass, but with a redshift higher than 4.5.

In total, we end up with a list of 16 sources in the Supplementary Catalog including the two HST-dark sources AGS24 and AGS25 which exhibit the strongest S/N ratio of the catalog. Their properties are listed in Table 6.1 and Table 6.2 .

Consistency test of the Supplementary Catalog: stellar mass distribution

If we compare the nature of the counterparts of ALMA detections above 3.5-σ in the image and the inverse image, we can see a difference that strengthens the solidity of the 16 sources of the Supplementary Catalog. There are 62 and 45 detections above 3.5-σ in the ALMA image that have a counterpart in the K-band in the ZFOURGE catalog in the image and inverse image 4), ( 5) Positions of HST-WFC3 H-band counterparts when applicable from Guo et al. ( 2013), ( 6), (7) Distances between the ALMA and HST source positions before (Dec∆HST 1 ) and after (∆HST 2 ) applying both the systematic and local offset correction presented in Sect. 6.3; ( 8), ( 9) Offset to be applied to the HST source positions, which includes both the global systematic offset and the local offset; [START_REF] Huang | Four IRAC sources with an extremely red H -[3.6] color: passive or dusty galaxies at z > 4.5?[END_REF] respectively. The stellar mass distributions of both samples are represented by dashed black and green lines for the image and inverse image respectively in Fig. 6.7. Both histograms show the same behavior at masses below 10 10 M but there are nearly no galaxies above this mass threshold in the inverse image while there is a second bump in the histogram of the sources in the real image. Massive galaxies being rarer than low mass ones, the probability to get an association with such galaxy is lower and the fact that there is a second bump at high masses in the real image suggests that these may be real. The Supplementary Catalog histogram shown in filled grey matches very nicely this second bump of massive galaxies. We recall that we did not impose any criterion of brightness or mass in the selection of the Supplementary Catalog but only distances to IRAC, K-band and radio sources. If we limit ourselves to the galaxies above a stellar mass of 10 10 M , we can see that the number of sources in the Supplementary Catalog is close to the difference between the image and inverse image.

In the sample of cross-matched galaxies from the positive image, 21/62 galaxies (∼ 34 %) have a stellar mass greater than 10×10 10 M , compared with only 2/45 galaxies (∼4 %) in the inverse image (see Fig. 6.7). A Kolmogorov-Smirnov (KS) test on these data gives a p-value of 3.9×10 -3 between these two samples, meaning that the likelihood that the two samples were drawn from the same distribution is extremely low. When we remove the sample of 16 galaxies listed in Table 6.1, the two samples become more similar. The p-value from a KS test then reaches 0.71. This means that once the galaxies in our study have been removed, the detections that remain have as high a probability of originating from the same parent sample as the inverse image detections, so that they are no longer statistically different from noise.

This suggests that not only the Supplementary Catalog is robust but also that there is little margin for an extra population of real sources that we would have missed. 2),( 3),( 4) IDs of the HST-WFC3 (from the CANDELS catalog), ZFOURGE and IRAC (SEDS catalog) counterparts of these detections; ( 5),( 6) Photometric redshifts from the CANDELS catalog (Guo et al., 2013), zCLS, and ZFOURGE catalog (Straatman et al., 2016), zZF (note that AGS24 has a photometric redshift of z 3.5 determined by Zhou et al. (in prep.,see Sect. 6.4.2) ; ( 7) Spectroscopic redshift when available (see Sect. 6.5.1), flagged with a "sp" exponent to avoid confusion; (8) S/N of the detections in the 0 60 mosaic. This S/N is given for the peak flux; ( 9) Flux and error on the flux as explained in Sect. 6.5.2;

(10) Stellar mass from the ZFOURGE catalog with the exception of AGS24, marked with a †, the determination of the stellar mass of this galaxy will be presented in Zhou et al. (in prep.) ; [START_REF] Wang | Infrared color selection of massive galaxies at z > 3[END_REF] 3GHz flux density from VLA (PI W.Rujopakarn.)

Catalog

The positions of the ALMA sources listed in the Main and Supplementary catalogs are shown in Fig. 6.8 where they can be compared to the locations of other ALMA surveys. The postage-stamp images of the sources are shown in Appendix 6.14.

Redshifts and stellar masses

Except for the two HST-dark galaxies, AGS24 and AGS25 (discussed in Sect. 6.4.2), all sources listed in the ALMA Supplementary Catalog have been attributed a photometric redshift by the CANDELS (Guo et al., 2013) and ZFOURGE (Straatman et al., 2016) teams. The two sources of photometric redshifts listed in the Col.( 5) and Col.( 6) of Table 6.2 are in excellent agreement (see Fig. 6.9-left). Excluding AGS35 (whose redshift given in the ZFOURGE catalog, z = 9.48 is much higher than that given by the CANDELS catalog, z = 2.99), the average of |z HST -z ZFOURGE | /(1 + (z HST +z ZFOURGE )/2) for the galaxies that have redshifts in both catalogs is 0.03.

A total of 38 % of the galaxies in the Supplementary Catalog (6/16) have been attributed a spectroscopic redshift:

-AGS26: z spec = 1.619 determined with VLT/FORS2 (Vanzella et al., 2008).

-AGS29: z spec = 1.117 from the VIMOS VLT Deep Survey (Le Fèvre et al., 2013).

-AGS30: z spec = 0.65 from the HST/ACS slitless grism spectroscopy of the PEARS program (Ferreras et al., 2009). In this paper, we will take, with the exception of AGS36 which has an inconsistent redshift (zAGS37,ZF OU RGE = 9.47 and for which we will take the data from the CANDELS catalog), the redshifts and stellar masses are given from the ZFOURGE catalog. Fèvre et al., 2013). -AGS37: z spec = 1.956 determined using the Spitzer Infrared Spectrograph (Wuyts et al., 2009;Fadda et al., 2010) and confirmed with the 3D-HST survey (Momcheva et al., 2016). -AGS38: z spec = 1.314 determined with VLT/FORS2 (Vanzella et al., 2008).

We note that two additional spectroscopic redshifts have been determined for galaxies in the Main Catalog since the publication of F18.

-AGS6, previously reported at z = 3.00, has been observed by the ALMA Spectroscopic Survey Large Program (ASPECS-LP; Decarli et al. 2019) in the Hubble Ultra-Deep Field, giving a z spec = 2.698 from the transition of CO(3-2) at 93.51 GHz. This spectroscopic redshift confirms the redshift also found by MUSE, at the same position (Boogaard et al., 2019). -AGS18, previously reported at z = 2.794, has also been observed in the ASPECS-LP survey, giving a z spec = 2.696 from the transition of CO(3-2) at 93.51 GHz. This spectroscopic redshift again confirms the one found by MUSE at the same position Boogaard et al. (2019). In the following, we will adopt for each source (i) the spectroscopic redshift when available, otherwise (ii) the photometric redshift from the ZFOURGE catalog (except for AGS35 for which we use the CANDELS redshift). These redshifts are given in Table 6.2.

We note that the redshift range of the Supplementary Catalog covers a wider dynamic range than the sources of the Main Catalog including two low redshift sources (z ∼ 0.6), with no equivalent in the Main Catalog. These two sources will be discussed in detail in a following Chapter.

The stellar masses of the Main and Supplementary catalogs have been chosen from the ZFOURGE catalog (except AGS35, for the reasons mentioned above). They were multiplied by a factor 1.7 to scale them from the Chabrier IMF to a Salpeter IMF. Both catalogs provide gobally consistent stellar masses with no systematic offset, the median of the ratio M ,CANDELS /M ,ZFOURGE = 1.06 (see Fig. 6.9-right).

Flux and size measurements

Flux densities of the Supplementary Catalog sources were measured by fitting the light profiles with a circular Gaussian in the uv-plane using uvmodelfit in CASA (McMullin et al., 2007). Due to the low S/N (3.5 < S/N < 4.8), we have opted for a circular Gaussian rather than an asymmetric Gaussian, in order to limit the number of free parameters. We use the formula given by Martí-Vidal et al. (2012) as in Chapter 4 to determine the minimum size that can be reliably measured in the uv-plane as a function of the S/N ratio of the source for an interferometer :

θ beam 0.88 θ beam √ S/N (6.2)
We use the S/N of the tapered map at 0 60 and θ beam = 0 60. Galaxies for which the circular Gaussian fit in the uv-plane give a size (FWHM) smaller than θ beam , the size limit given by Flux uvmodelfit / Flux peak FIGURE 6.10: Ratio between the flux extracted using uvmodelfit in CASA and the peak flux as a function of the size of the galaxy for the supplementary catalog. When the measured size is below the reliable size measurement limit (see Eq. 6.2), we consider the size given by Eq. 6.2 as an upper limit. The horizontal solid line indicates flux uvmodelfit = peak flux. The dotted lines show a 15 percent deviation from this equality. For galaxies larger than 0.25" (vertical dotted line), the approximation of a point source is no longer valid, and we assume the flux value derived from uvmodelfit for these galaxies.

Eq. 6.2, we set the size of the galaxy to θ beam and use the peak flux density measured on the direct image. This choice is expected to lead to slightly underestimated flux densities since it implies that sources are assumed to be point-like while the typical size measured for distant ALMA galaxies is on average close to 0 3 (Simpson et al. 2015a;Ikarashi et al. 2017;Elbaz et al. 2018). Assuming a point-like source for a real size extension of 0 3 FWHM would lead to an underestimation of the real flux density by a factor F real /F peak =1.2 (see Fig. 6.11) but in the absence of a robust size measurement, we decided to keep the peak flux values having in mind that they may be lower by about 20 %. Using the measurements coming out of uvmodelfit would lead to larger uncertainties for those sources with no reliable size measurement.

For galaxies whose sizes measured using uvmodelfit are larger than this limit (see Fig. 6.10), we keep the size given by uvmodelfit. For these galaxies, the peak flux approximation is no longer valid and we keep the integrated flux given by uvmodelfit. The flux density of each galaxy, as well as its uncertainty, are listed in Table 6.2. The sizes measured by uvmodelfit, the detection limit derived from the Eq. 6.2 and the size of the galaxies are given Table 6.3.

In order to check whether our flux density measurements were underestimated by a large factor, we computed the expected ALMA flux density that those sources would have if they had been located on the star-formation main sequence (MS; Noeske et al. 2007;Rodighiero et al. 2011;Elbaz et al. 2011). Since a large fraction of the ALMA sources are actually starbursting and above the MS, this assumption only provides a rough estimate of a lower-limit to the ALMA flux densities. We used the infrared spectral energy distributions (IR SED) from the library presented in Schreiber et al. (2018c), with the stellar masses and redshifts listed in Table 6.1 as input parameters. The measured, F ALM A , and predicted, F SED , flux densities exhibit a ratio F ALM A /F SED ranging from 0.73 to 5.2 with a median (average) of 2.4 (2.7) suggesting that about 50 % of the galaxies of the Supplementary Catalog fall within the factor 2 dispersion of the MS, the remaining half being in a starburst phase. None of the measured flux densities fall more than 25 % below the predicted MS ALMA flux density, which suggests that our flux density measurements are probably not largely underestimated.

Comparison of the properties of the ALMA galaxies from

the Main and Supplementary catalogs

Redshifts

The redshifts of the Supplementary Catalog covers a wider range (z= 0. 65 -5.36) than the sources of the Main Catalog (z= 1.95 -4.82). Galaxies with a redshift greater than z=4.5 represented 5 % of the Main Catalog (1/19), they make 19 % of the Supplementary Catalog (3/16, see Fig. 6.12). On the other extreme, none of the Main Catalog sources were detected below z=1.9 whereas 38 % (6/16) of the sources in the Supplementary Catalog are found in this lower redshift range. Despite these differences, the median redshifts of both catalogs are similar, z = 2.70 and 2.56 for the Main and Supplementary catalogs, showing that there is no systematic shift in redshift between both catalogs but a wider dynamic range for the Supplementary Catalog. This median redshift is also similar to Stach et al. (2019), who derive a median redshift of 2.61± 0.09. We found no correlation between redshift and flux density of the Supplementary Catalog sources.

Stellar Masses

All galaxies detected in GOODS-ALMA have a stellar mass greater than M = 2×10 10 M . The median stellar mass of galaxies from the Supplementary Catalog, M Supp = 6.6×10 10 M , is twice lower than that from galaxies in the Main Catalog, M Main = 1.1 ×10 11 M . Hence by pushing down the ALMA detection limit using IRAC priors, we have reached more normal galaxies, with less extreme stellar masses, and extended the redshift range of the ALMA sources.

We can now compare the galaxies detected by GOODS-ALMA, combining the Main and Supplementary catalogs, to their parent sample of distant star-forming galaxies taken from the ZFOURGE catalog after selecting only the UVJ active galaxies (Williams et al. 2009, using the same definition as in Chapter 4, see Fig. 6.12).

GOODS-ALMA detects nearly half (46%, 6/13) of the most massive star-forming galaxies with log 10 (M /M ) =11-12 in the range 2 < z < 2.5. Pushing further in redshift to 2.5 < z < 3, GOODS-ALMA also sees nearly half of the star-forming galaxies with log 10 (M /M ) =10. 7-11 (44%, 7/16). At even further redshifts of 3 < z < 4, GOODS-ALMA detects 38% (3/8) of the most massive galaxies (log 10 (M /M ) =11-12). .12: Stellar mass as a function of redshift for the galaxies detected in Chapter 4 (red points) and in this work (gray points). For comparison, the distribution of all of the galaxies, listed in the ZFOURGE catalog, in the same field of view is given in blue. Only UVJ active galaxies are shown. For each bins of redshift (z = 0.5) and stellar mass (log10(M ) = 0.5), with a yellow shade, the fraction of sources detected by ALMA compare to the uvj active galaxies in GOODS-ALMA. The optically dark galaxies for which redshifts and masses have been derived are represented by open circles. The upper panel shows the compared distribution of redshift between all the UVJ active galaxies in GOODS-ALMA and the ALMA-detected galaxies while the right panel shows the stellar mass distribution. The median of the redshift and of the stellar mass are shown in these two panels. The median redshift is 2.56 for the galaxies presented in this paper, compared to 2.70 in Chapter 4, while the median stellar mass is 6.7×10 10 M in this study, compared to 1.1×10 11 M in Chapter 4.

In total, GOODS-ALMA detects about 30 % (11/37) of the most massive star-forming galaxies with a redshift 2 < z < 4 (log 10 (M /M ) =11 -12).

Sizes

The sizes of the sources of the Main and Supplementary catalogs were derived by fitting a circular Gaussian in the uv-plane using uvmodelfit in CASA. We find that by pushing down the detection limit to 3.5-σ using IRAC priors, we have been able to identify galaxies with nearly twice larger ALMA sizes. The median ALMA 1.1mm FWHM of the galaxies in the Supplementary Catalog is indeed 0 32 as compared to 0 18 for the galaxies in the Main Catalog. When accounting for the redshift of the sources, we find that the physical circularized half-light radius of the new sources in the present Supplementary Catalog (R 1/2 = FWHM/2) is 1.3 kpc as compared to only 0.65 kpc for the Main Catalog. If we take into account the fact that the Supplementary sources exhibit twice lower stellar masses, this implies that pushing down the ALMA detection limit using priors, we were able to identify lower mass galaxies in which dust-enshrouded star-formation extends over twice larger sizes. 6.13: Cumulative fraction of sources with a FWHM below a given size for the main (red) and the supplementary catalog (gray). These sizes are computed by fitting the ALMA detections with a circular Gaussian in the uv-plane using uvmodelfit in CASA. The shaded areas correspond to the integration of the individual uncertainties of the sizes of each detection.

In Fig. 6.13, we show the cumulative fraction of sources with a major axis below a given size for the Main (red) and Supplementary (grey) catalogs. This figure clearly shows that the galaxies detected in the main catalog are generally more compact than the supplementary catalog: 80% of the galaxies in the Main Catalog have a FWHM below 0 24, whereas in the Supplementary Catalog, 80% the sources have a size above 0 27 arcsec. The size below which 80 % of the galaxies in the Supplementary Catalog are found is twice larger with a FWHM of 0 49. This shows that while the projected sizes of dust-enshrouded star-formation probed by ALMA are globally small for massive and distant galaxies, the new sources that we present here in the Supplementary Catalog do not extend the sample to much lower flux densities but to sources with a wider extension of the dust emission. This explains in part why these sources were not detected in the Main Catalog. Although their integrated flux densities may be equal (and sometimes higher) than sources in the Main Catalog, this flux is diluted into several beams and therefore drops below the detection limit for the central beam.

We recall that this increase in the ALMA sizes measured in the Supplementary Catalog remains such that globally the ALMA emission extends over much smaller sizes than their H-band sizes, confirming that the ALMA sources are particularly compact at 1.1 mm (e.g., Chen et al., 2015;[START_REF] Simpson | The SCUBA-2 Cosmology Legacy Survey: ALMA Resolves the Bright-end of the Sub-millimeter Number Counts[END_REF]Rujopakarn et al., 2016;Elbaz et al., 2018;Calistro Rivera et al., 2018, see also Franco et al., in prep). 6.7. Conclusion 123

How complete is the Main plus Supplementary catalog ?

The average noise in the GOODS-ALMA image is RMS=0.182 mJy, hence the 3.5-σ limit of the Supplementary Catalog converts into a detection limit of about 0.64 mJy. We note that since the RMS of the noise varies across the image, because it is subdivided in 6 slices taken at different epochs, sources may be detected below 0.64mJy (a source was detected at 0.55mJy).

The various studies that have carried out millimetric counts (e.g., Hatsukade et al., 2013;Oteo et al., 2016;Aravena et al., 2016;Umehata et al., 2017;Fujimoto et al., 2017;Dunlop et al., 2017;Franco et al., 2018;Hatsukade et al., 2018) allow us to estimate an expected galaxy surface density that varies between 2000 and 3500 galaxies.deg 2 above 0.65 mJy at 1.1 mm. Over the size of 69.5 arcmin 2 of the GOODS-ALMA survey, this amounts to an estimated number of sources ranging between 39 and 48. In comparison, we have now extended the number of detections in GOODS-ALMA to 35 galaxies. This number is not far from the expected one, especially when one accounts for cosmic variance, and suggests that the present sample may be more than 70 % complete above 0.65 mJy.

Conclusion

Using prior information at 3.6 and 4.5 µm from IRAC (combined with deep HST H-band and ground-based Ks-images), we were able to explore the presence of galaxies detected at 1.1mm with ALMA down to the 3.5-σ limit. This was done despite the extremely large number of independent beams in the ALMA image even after tapering from 0 29 to 0 6.

In order to avoid introducing spurious associations, we restricted the new sample to ALMA detections with either an IRAC counterpart closer than 0 3 or closer than 0 6 but with a radio counterpart as well. In two cases, we used the K-band image to deconvolve IRAC sources that were missed by previous studies because of their close proximity to bright IRAC neighbors. These two galaxies do not exhibit any counterpart in the HST images, hence they are HST-dark, but both present a radio counterpart. In total we find 16 galaxies in the Supplementary Catalog that bring the total sample of GOODS-ALMA 1.1mm sources to 35 galaxies. This number is between 70 and 90 % of the predicted number of galaxies expected to be detected at 1.1 mm above 0.65 mJy as derived from existing millimeter number counts. We now detect in GOODS-ALMA between a third and half of the most massive star-forming galaxies (log 10 (M /M ) = 11 -12) depending on the redshift range within 2 < z < 4.

The redshift range of the Supplementary Catalog covers a wider dynamic range (z = 0. 65 -5.36) than the sources of the Main Catalog (z = 1.95 -4.82), with no systematic shift in the median redshift of z 2.6. The typical physical size of the new sources in the present Supplementary Catalog (1.3 kpc) is twice larger than that of the Main Catalog sources (0.65 kpc). The lower surface brightness of these sources explains partly why they were not detected in the Main Catalog. Hence, pushing down the ALMA detection limit using IRAC priors allowed us to reach twice less massive galaxies (median stellar mass M = 6.6×10 10 M ) in which dust-enshrouded star-formation extends over twice larger sizes. However, this increase in the ALMA sizes is not large enough to question the fact that the ALMA emission globally extends over much smaller sizes than the H-band light, confirming that the ALMA sources are particularly compact at 1.1 mm.

Finally, we used a comparison of nearly 400 galaxies in common between HST and Pan-STARRS in the GOODS-ALMA field to show that the astrometry of the HST image does not only suffer from a global astrometric shift, as already discussed in previous papers, but also from local shifts that draw the equivalent of a distortion map that was artificially introduced in the process of building the mosaic of the GOODS-South HST image. We present a solution to correct for this distortion and use this correction in our identification of counterparts. We note that in some cases, the absence of this correction led previous studies to attribute the wrong counterpart to ALMA detections. This will be discussed in more detail in a paper in preparation.

Outline of the problem

The primary progenitors at z ∼ 2 of massive galaxies are largely unknown from the current state of our observations (e.g., Williams et al., 2014;[START_REF] Straatman | The Sizes of Massive Quiescent and Star-forming Galaxies at z ∼ 4 with ZFOURGE and CANDELS[END_REF][START_REF] Wang | A dominant population of optically invisible massive galaxies in the early Universe[END_REF].

Understanding this missing element is essential in order to constrain the star formation density beyond the peak of cosmic star formation (z ∼ 2; Madau and Dickinson 2014), to understand the massive end of the main sequence at high redshift, and more generally the evolution of massive galaxies at these high redshifts.

We will see in this chapter that the galaxies detected by ALMA in this survey, particularly the optically dark galaxies, are ideal candidates to be the progenitors of the massive, compact, passive galaxies at z ∼ 2. We will first present a brief history of previous discoveries of HST-dark galaxies, and then define this term more specifically. We will then present the 6 HST-dark galaxies that we find in the GOODS-ALMA field, which are missed by the HST but unveiled by ALMA. Then, we will discuss the hypothesis that these galaxies are tracers of overdensities, and the implications of HST-dark galaxies on the cosmic density of star-formation.

History

The history of optically dark galaxies is closely linked to the history of (sub)-millimetre surveys. This begins with Smail et al. (1997), one of the first submillimeter surveys "of the distant universe" of two lensing clusters (lensed galaxies at z = 0.37 and z = 0. 33) observed at two submillimeter wavelengths with SCUBA (450µm and 850µm; see Fig. 7.1).

Two years later, [START_REF] Smail | The discovery of ERO counterparts to faint submillimetre galaxies[END_REF] used ground-based near-IR (2µm) images of these two lensing clusters to find the counterparts to the luminous submillimeter galaxies they had previously 130 Chapter 7. HST-dark galaxies found. These near-IR observations did not show apparent optical counterparts corresponding to the SCUBA sources. Color constraints implied that these two galaxies with no optical counterparts had a redshift greater than 2, that therefore did not belong to the lensing clusters themselves.

However, the findings we present in this section are significantly different from these first cases of submillimeter galaxies with no optical counterparts. Indeed, it is rather different to discuss the absence of a counterpart of a (sub)millimeter source when the size of the (sub)millimeter beam is greater than 15", compared with 0.25", as with our survey. In the former case, the counterpart is not necessarily easy to identify, and it is often only possible to give the probability of association with a submillimeter source. The advent of interferometers allowing subarcsecond resolution has changed this picture. Since the commissioning of the Submillimeter Array (SMA, [START_REF] Ho | The Submillimeter Array[END_REF]) several high redshift galaxies without optical counterparts have been discovered. For example, [START_REF] Tamura | Submillimeter Array Identification of the Millimeter-selected Galaxy SSA22-AzTEC1: A Protoquasar in a Protocluster[END_REF] present the discovery of a galaxy undetected at wavelengths < 3 µm, which is located in a protocluster at z = 3.09 in SSA2 [START_REF] Steidel | A Large Structure of Galaxies at Redshift Z approximately 3 and Its Cosmological Implications[END_REF]. This observation is particularly interesting because, in our field, ALMA unveils several HST-dark galaxies which could be part of an overdensity. We will discuss the implications of these observations in Sect. 7.6.

The advent of ALMA marked the beginning of a new era. ALMA allows deep resolved surveys to be carried out (e.g., Walter et al., 2016;Dunlop et al., 2017;[START_REF] González-López | The ALMA Spectroscopic Survey in the HUDF: CO emission lines and 3 mm continuum sources[END_REF], reaching rms levels down to 30µJy.

Unfortunately, obtaining deep observations in small areas is not very efficient in finding opticallydark galaxies. These sources are, for those currently known, particularly massive and distant galaxies, hence rather rare, with surface densities that suffer from strong cosmic variance (Wang et al., 2016). The more massive a galaxy is, the more metal-rich (e.g. [START_REF] Garnett | The Luminosity-Metallicity Relation, Effective Yields, and Metal Loss in Spiral and Irregular Galaxies[END_REF][START_REF] Tremonti | The Origin of the Mass-Metallicity Relation: Insights from 53,000 Star-forming Galaxies in the Sloan Digital Sky Survey[END_REF][START_REF] Gallazzi | The ages and metallicities of galaxies in the local universe[END_REF][START_REF] Mannucci | A fundamental relation between mass, star formation rate and metallicity in local and high-redshift galaxies[END_REF][START_REF] Yates | The relation between metallicity, stellar mass and star formation in galaxies: an analysis of observational and model data[END_REF][START_REF] Foster | Galaxy And Mass Assembly (GAMA): the mass-metallicity relationship[END_REF][START_REF] Kirby | The Universal Stellar Mass-Stellar Metallicity Relation for Dwarf Galaxies[END_REF][START_REF] Dayal | The physics of the fundamental metallicity relation[END_REF] and dust-rich (e.g. [START_REF] Heckman | The Ultraviolet Spectroscopic Properties of Local Starbursts: Implications at High Redshift[END_REF][START_REF] Boissier | The radial extinction profiles of late-type galaxies[END_REF][START_REF] Reddy | Dust Obscuration and Metallicity at High Redshift: New Inferences from UV, Hα, and 8 µm Observations of z 2 Star-forming Galaxies[END_REF] it will be. The gravitational potential of the galaxy will prevent dust and metal from escaping from the galaxy [START_REF] Pannella | GOODS-Herschel: Star Formation, Dust Attenuation, and the FIR-radio Correlation on the Main Sequence of Star-forming Galaxies up to z ∼4[END_REF][START_REF] Barone | The SAMI Galaxy Survey: Gravitational Potential and Surface Density Drive Stellar Populations. I. Early-type Galaxies[END_REF] and prevents the metal-rich gas from being ejected from the galaxy, as it requires a higher escape velocity. There is a strong correlation between the stellar mass of a star-forming galaxy and its dust attenuation (e.g., [START_REF] Buat | GOODS-Herschel: dust attenuation properties of UV selected high redshift galaxies[END_REF][START_REF] Heinis | HerMES: dust attenuation and star formation activity in ultraviolet-selected samples from z∼ 4 to ∼ 1.5[END_REF][START_REF] Oteo | The ultraviolet to farinfrared spectral energy distribution of star-forming galaxies in the redshift desert[END_REF][START_REF] Pannella | GOODS-Herschel: Star Formation, Dust Attenuation, and the FIR-radio Correlation on the Main Sequence of Star-forming Galaxies up to z ∼4[END_REF]. The density of galaxies with stellar masses greater than 10 11 M at redshift greater 7.3. HST-dark galaxies in GOODS-ALMA 131 than 3.5 is lower than 0.1 arcmin -2 [START_REF] Davidzon | The COSMOS2015 galaxy stellar mass function . Thirteen billion years of stellar mass assembly in ten snapshots[END_REF]Williams et al., 2019). We would therefore expect no sources with these characteristics to reside in fields such as the HUDF. In addition, these massive and distant galaxies are mostly clustered [START_REF] Chiang | Galaxy Protoclusters as Drivers of Cosmic Star Formation History in the First 2 Gyr[END_REF], which increases the effects of cosmic variance and enhances the randomness of finding them in small areas.

To detect this type of sources, it is therefore essential to extend the search area by carrying out large surveys. This search can be performed by single-dish telescopes that have a large half power beam width (HPBW) antenna. For example, the JCMT and SCUBA-2 can cover large areas (e.g. Geach et al., 2017), but the angular resolution is low (θ ∼ 15" at 850 µm). Future large surveys are planned with the NIKA2 camera (θ ∼ 11" at 1.2 mm) on the 30m of IRAM (PIs: A.Beelen, G.Lagache & N.Ponthieu), for example, and with the TolTEC Camera (Bryan 2018, θ ∼ 5" at 1.1 mm) at the 50-meter Large Millimeter-wave Telescope (LMT, e.g., [START_REF] Pope | TolTEC/LMT Extragalactic Legacy Surveys: Completing our Census of Dust-Obscured Star Formation[END_REF].

Another solution is to multiply the pointings with an interferometer. The ALMA HPBW, with the configuration used in our analysis, is ∼ 23 .3. This requires a significant number of pointings to cover a large surface area (846 to cover a surface of 69arcmin 2 ). However, the advantage of the interferometer, despite the complexity of mapping large surfaces, is to benefit from an unprecedented angular resolution and thus to identify the counterparts of detected galaxies with high precision. Intermediate size surveys (ASAGAO, 26 arcmin 2 ), have subsequently allow the detection of some optically-dark galaxies Yamaguchi et al. (2019a), but larger surveys such as the one presented in this work are the ideal method to detect this type of object.

This notion of a HST-dark galaxy is obviously relative. In this work, we will use this term to refer to a galaxy that has not been detected in a catalog based on HST observations. This definition is somewhat problematic because it depends on the depth of HST observations. Indeed, if the HST detection limit of our survey had been shallower, we would have found many more HST-dark sources. In our survey, the detection at 5σ in H-band reaches a magnitude limit of 28.2 AB. The detection limit in H-band is also not uniform in the GOODS-ALMA field -for example, in HUDF9 [START_REF] Bouwens | Discovery of z ˜8 Galaxies in the Hubble Ultra Deep Field from Ultra-Deep WFC3/IR Observations[END_REF] the detection limit reaches 29.74 AB. Definitions can, therefore, disagree on this notion of HST-dark: those "absolute" definitions that are based only on the HST detection limit, and the more relative definitions based on a color difference, for example.

HST-dark galaxies in GOODS-ALMA

We have discovered a number of galaxies without H-band HST-WFC3 (1.6 µm) counterparts.

We discuss below the possibility that these detections are real HST-dark galaxies. Some ALMA detections that were previously attributed to an HST counterpart seem in fact to be either more distant galaxies, extremely close on the line of sight to another galaxy, hidden by a foreground galaxy, or too faint at optical rest-frame wavelengths to be detected by HST. It is already known that some of the most luminous millimeter or submillimeter galaxies can be completely missed at optical wavelengths (e.g., Huang et al., 2011;Caputi et al., 2012;Ono et al., 2014;Fujimoto et al., 2016;Wang et al., 2016;[START_REF] Schreiber | Near infrared spectroscopy and star-formation histories of 3 ≤ z ≤ 4 quiescent galaxies[END_REF][START_REF] Yamaguchi | ALMA twenty-six arcmin 2 survey of GOODS-S at onemillimeter (ASAGAO): Near-infrared-dark faint ALMA sources[END_REF]Williams et al., 2019), even in the deepest optical surveys, due to dust extinction.

Among the sources that do not have detections in the H-band of HST-WFC3, we distinguish between sources not detected by HST but detected by other instruments (we will discuss the particular importance of the IRAC filters), and sources undetected by HST as well as all of the other available instruments in the GOODS-South field (described in the Sect. 4.4). Of the 20 galaxies detected in our main catalog, seven (35%) do not present an obvious HST counterpart. This number is slightly higher than the expected number of spurious sources (4±2), predicted by the statistical analysis of our survey. To be more accurate, for three of these seven galaxies (AGS4, AGS15 and AGS17), an HST galaxy is in fact relatively close to the ALMA detection on the line of sight. However, strong evidence, presented below, suggest that these HST galaxies are not the counterparts of the ALMA detections, and without the resolution of ALMA we would falsely associate the counterparts. For the four other ALMA detections without HST-WFC3 counterparts within a radius of 0 .60, one of them (AGS11) has also been detected at other wavelengths.

In this section, we will discuss four particularly interesting cases of HST-dark galaxies (AGS4, AGS11, AGS15, and AGS17), and discuss our reasons for classifying the other three as spurious sources (see Fig. 7.2).

AGS4

AGS4 is a close neighbor of ID CAN DELS 8923. AGS4 is the fourth brightest detection in our survey, with a S/N greater than 9. The center of the ALMA detection is located at only 0 .38 from ID CAN DELS 8923, its closest neighboring galaxy. Before the astrometric correction (see Sect. 4.5), this distance was only 0 .21. This is, therefore, an example where the astrometric correction moves the ALMA galaxy away from the supposed counterpart. In Fig. 7.2, we can clearly see that the ALMA emission is offset from the observed H-band galaxy shown by the white arrow. This offset could be explained physically, for example, as a region extremely obscured by dust, within the same galaxy, greatly extinguishing the optical rest-frame emission, but still visible with ALMA. However, for AGS4, a series of clues suggest another explanation.

The first piece of evidence is the comparison between the IR SED at the position of the ALMA detection and the redshift of the optical galaxy. The redshift of the optical galaxy is z = 0.241, whereas the far IR SED peaks around 350 µm (see Fig. 7.5). If AGS4 was a dusty star-forming region in the outskirts of 8923, this infrared SED would suggest an abnormally cold dust temperature. It is, therefore, more probable that AGS4 is not part of ID CAN DELS 8923, and is a dusty distant galaxy. The fuzzy emission in the H-band HST image, exactly centered at the position of the ALMA detection (see Fig. 7.2) has not led to any detection in the CANDELS catalog. In the V -band HST images, only ID CAN DELS 8923 is present, seen to the South-East of the position of the ALMA detection (indicated by a white cross). No emission is visible at the exact position of the ALMA detection. In the z-band, a barely visible detection appears extremely close to the center of the image. The second clue is the detection of a galaxy with redshift z = 3.76 in the FourStar galaxy evolution survey, 0 .16 from the ALMA detection. This redshift is much more consistent with the peak of the IR SED. The ZFOURGE survey is efficient in detecting galaxies with redshifts between 1 and 4 by using a K s -band detection image (instead of H-band as used for the CANDELS survey), and also due to the high spectral resolution (λ/∆λ ≈ 10) of the medium-bandwidth filters which provide fine sampling of the Balmer/4000 Å spectral break at these redshifts (Tomczak et al., 2016). Furthermore, the stellar mass derived in the ZFOURGE catalog (10 10.50 M1 compared with 10 7.64 M in the CANDELS catalog) is more consistent with the expected mass of galaxies detected by ALMA. Indeed as shown in this paper, and as already shown by Dunlop et al. (2017), ALMA tends to reveal the most massive dusty galaxies.

The third piece of evidence is the presence, in the Spitzer-CANDELS catalog (Ashby et al., 2015), of a galaxy detected with the IRAC filers only 0 .1 from our ALMA detection. This IRAC galaxy has a magnitude of 22.51 at 3.6 µm, measured within an aperture of 2 .4 radius.

We also note that Rujopakarn et al. (2016) detect a radio galaxy at S/N ≈ 17 only 55 mas from the center of the ALMA detection shown in Fig. 7.2 (the positional accuracy of this VLA image is 40 mas). Additionally, AGS4 is detected in two of the three Chandra bands: 0.5-7.0 keV (full band; FB) and 0.5-2.0 keV (soft band; SB), but not at 2-7 keV (hard band; HB) from the 7 Ms Chandra observations of the GOODS-South field. The integrated X-ray flux is only 6.86 × 10 40 erg.s -1 , but this galaxy is classified as an AGN in the 7 Ms catalog.

The detection of a local galaxy at this position has been largely documented (e.g., Hsu et al., 2014;Skelton et al., 2014;Santini et al., 2015). In contrast, some studies present the galaxy located at this location as a distant galaxy. Cardamone et al. (2010) take advantage of the 18medium-band photometry from the Subaru telescope and the photometric redshift code EAzY (Brammer et al., 2008) to derive a redshift z = 3.60. Wuyts et al. (2008) find a redshift of z = 3.52 also using EAzY. We can also add a redshift determination by Rafferty et al. (2011) using the Zurich extragalactic Bayesian redshift analyzer (ZEBRA, Feldmann et al. 2006), at z = 2.92. These determinations of a high redshift by independent studies support the existence of a distant galaxy at this position.

Although close to one another, the two sources (ID CAN DELS 8923 and 8923b) were successfully de-blended using two light-profile models, determined by fitting the HST H-band image with Galfit. The two sources were then fit simultaneously using these two models on all of the available images, fixing the profiles to those observed in the H band. The SEDs of these two galaxies are shown in Fig. 7.3, in blue for the HST galaxy and in orange for the ALMA galaxy, together with the photometric redshift probability distribution for AGS4. The redshifts were estimated using EAZY. For the blue HST galaxy we found z = 0.09 +0.06 -0.07 , in good agreement with that found by Skelton et al. (2014). On the other hand, the redshift found for AGS4 is slightly higher than in ZFOURGE, with z AGS4 = 4.32 +0.25 -0.21 . However, we can also see a secondary peak in the redshift probability distribution, at the position of the ZFOURGE redshift. As the Balmer break is well established in the K-band, we consider that the redshift determination (z AGS4 = 4.32 +0.25 -0.21 ) is robust and we adopt this redshift for AGS4. The stellar mass of the ALMA galaxy was then computed with FAST (Kriek et al., 2009), and we found 10 11.45±0.2 M (probably slightly overestimated due to the presence of an AGN, suggested by a flux excess in the IRAC bands). The IR SED of this galaxy is shown in Fig. 7.5. For the first time, thanks to ALMA, we can argue that there exists, at this position, not one but two galaxies, close to each other on the line of sight.

AGS11

AGS11 is detected at 1.1 mm with a flux of 1.4 mJy (S/N∼8) without any counterpart in the deep HST image. However, the galaxy is also detected by IRAC, confirming the existence of a galaxy at this position (see Fig. 7.6). A galaxy was recently found, for the first time, in the ZFOURGE catalog at 0 .18 from the center of the ALMA position. This galaxy was not detected directly in the Magellan image but in a super-deep combined K s -band image at 4.5 σ. From this position, the flux in the IRAC-bands has been extracted with S/Ns of 26, 34, 8 and 8 at 3.6 µm, 4.5 µm, 5.8 µm and 8.0 µm respectively. This HST-dark galaxy falls in a projected overdensity on the sky, consisting of sources in the redshift range 3.42 ≤ z ≤ 3.56 and brighter than K s < 24.9 (Forrest et al., 2017). This density has been computed by Forrest et al. (2017) using the 7 th nearest-neighbor technique (Papovich et al., 2010). This overdensity, centered at RA = 53.08, DEC = -27.85, extends beyond approximately 1.8 Mpc.

1.8"

HST galaxy 9" The redshift derived in the ZFOURGE catalog is z = 4.82, making it the farthest galaxy detected in this blind survey. However, we remain cautious regarding this redshift, as this entry has been flagged in the ZFOURGE catalog (use = 0) due to the S/N of this galaxy (4.7) being below the limit defining galaxies with good photometry (S/N ≥ 5). This galaxy is the only galaxy in our catalog flagged in the ZFOURGE catalog. AGS11 has not been detected in the 7 Ms Chandra survey.

The stellar mass, derived in the ZFOURGE catalog, 3.55 × 10 10 M , is consistent with the masses of all of the other ALMA galaxies found in this survey. What is particularly interesting in the multiwavelength images of this galaxy is that AGS11 is detectable only by ALMA and in the IRAC-bands (in non-stacked images). Outside of these wavelengths, no emission is detectable.

AGS15

AGS15 is at a distance of 0 .59 from its possible HST counterpart (ID CAN DELS 3818) after astrometric correction, corresponding to a physical distance of 4.33 kpc. This is the largest HST-ALMA offset in our entire catalog. The IRAC position, in contrast, matches much more closely with the ALMA position, with an offset of only 0 .14. The stellar mass of the optical galaxy, given by the ZFOURGE catalog (7.24 × 10 9 M ) would have made AGS15 a galaxy lying far from the median stellar mass (1.1 × 10 11 M ) of our survey. The redshift of ID CAN DELS 3818 (z = 3.46) is nevertheless consistent with the other redshifts found in this study. Moreover, we will see later in this chapter that this redshift is particularly interesting. It could correspond to the redshift of other HST-dark galaxies and a redshift of an overdensity in GOODS-ALMA (we will discuss this in detail when we discuss AGS24).

AGS17

AGS17 is a close neighbor (0 .27) of ID CAN DELS 4414 (z = 1.85). AGS17 is one of the three galaxies detected by Hodge et al. (2013) at 870µm in the ALMA field of view (along with AGS8 and AGS15 previously discussed). The counterpart of AGS17 was attributed to ID CAN DELS 4414 by Wiklind et al. (2014) with an offset between the ALMA detection and the corresponding F160W object of 0 .32. Again, there are indications that the identification may be false: the peak of the IR SED is ∼400 µm (see Fig. 7.7), suggesting a more distant galaxy. To be detected with the flux densities reported in Table 4.2, a galaxy at z = 1.85 would have an extraordinarily high star formation rate (∼820±240 M yr -1 ), using the IR SEDs of Schreiber et al. (2018a). If truly associated with the CANDELS counterpart, this galaxy would be an extreme starburst with an SFR 59±17 times greater than the SFR M S . Galaxies with these properties cannot be ruled out, as galaxies with much higher star formation rates (and offsets from the main sequence) have already been observed (e.g., Pope et al., 2005;Fu et al., 2013). However, such objects are relatively rare. In addition, the stellar mass of ID CAN DELS 4414 (10 10 M ) is inconsistent with the trend of the other detections (more than one order of magnitude below the median stellar mass of our catalog).

Another galaxy (ID CAN DELS 4436) is relatively close (0 .57) to the ALMA detection. The position of the ALMA detection, which is between ID CAN DELS 4414 and ID CAN DELS 4436, could be the signature of a major merger occurring between these two galaxies. The emission observed by ALMA could result in this case from the heating of the dust caused by the interaction of these two galaxies, but the redshift determination of 0.92 +0.04 -0.18 by Le PHARE (Arnouts et al., 1999;Ilbert et al., 2006) dismisses this hypothesis.

After subtraction of the two galaxies close on the line of sight (ID CAN DELS 4414 and 4436) in the HAWK-I image, a diffuse source is revealed (half-light radius = 1 .55±0 .12, Sersic index = 1.0). Lower resolution ALMA observations would be needed in order to correctly measure the total submm flux of this extended source.

We also note the position of the IRAC source, which is located only 0 .06 from the ALMA detection.

AGS24

This galaxy will be presented in detail in Zhou et al., in prep. This galaxy is the only galaxy added to the supplementary catalog (see Chapter 6) that was not detected using prior information, but instead, by slightly lowering the threshold (S/N = 3.9) in the tapered map to 0 .60. The S/N of this source is higher in the 0 .29 mosaic which suggests that this source is particularly compact. This galaxy has been detected in the radio band at 6 GHz (3.7σ) and 3 GHz (5.7σ). In Fig. 7.8, we show the emission of this galaxy at different wavelengths, from the H band, at 1.6µm to the 10cm radio. While for all wavelengths below the IRAC filter, the galaxy is invisible, it appears, at the position of the ALMA detections, from the IRAC filters. It was possible, by the same method as that used to determine the AGS4 redshift, to determine the AGS24 redshift (z = 3.5, see Fig. 7.9). The fact that this galaxy is located at z 3.5 is particularly interesting, this galaxy could be at the center of an overdensity at z 3.5. We will discuss this hypothesis in detail in Sect. 7.5. (Elbaz et al., 2011). The SED of AGS17 (bottom), which has no known redshift, is simply presented with an interpolation between the observed flux densities to illustrate that it peaks around 400 µm. This peak is inconsistent with the redshifts of the two optical sources with IDCANDELS 4414 (z = 1.85) and 4436 (z = 0.92).

AGS25

This detection is not listed in the CANDELS catalog (Guo et al., 2013), nor the S-CANDELS catalog (Ashby et al., 2015), nor is it detected in X-ray (Luo et al., 2017). This galaxy is marginally detected in radio at 5 and 10 cm.

In Chapter 4 , we showed that the presence of ALMA detection alone was not sufficient to qualify a galaxy as HST-dark. The four HST-dark galaxies presented in Chapter 4 (AGS4, AGS11, AGS15, and AGS17) have at least one feature in common -the presence of an IRAC detection.

The presence of an IRAC detection was until now the element that validated the blind HST-dark detection. We do not exclude that there may be HST-dark galaxies detected by ALMA, and without IRAC counterparts, but these galaxies will have to be tested further before they can be considered as robust. The case of AGS25 is rather special. AGS25 is close (3") to one of the galaxies ID CANDELS = 8067, which is very (M * = 5.6×10 10 M ) for its redshift (z spec = 1.038). The IRAC emission of this galaxy is large and extends to the position of AGS25. It is therefore probable that the emission of AGS25 in IRAC filters is blended with the emission of ID CANDELS = 8067. We see in Fig. 7.12 that the IRAC contours around the galaxies extend to the side of the ALMA detection. We performed deblending (source subtraction) to see if we could detect emission in the IRAC filter at the position of the ALMA detection. We did this by modeling a Sérsic profile with GALFIT (Peng et al., 2010).

After subtraction of the Sérsic model (see Fig. 7.10), we found IRAC emission. Moreover at less than 0 .1 from the ALMA position (after astrometric correction, see Sect. 6.3), a galaxy is listed in the ZFOURGE catalog (ID ZF OU RGE = 11353, shown by a circle in Fig. 7.10),with a magnitude in K band = 25.9 AB. The subtraction with GALFIT suggests that the source is not present in Ashby et al. (2015) only because of blending In this study, we will use this mass and redshift, derived from the ZFOURGE catalog.

The characteristics of this galaxy make it particularly interesting, with z AGS25 = 4.66 +0.25 -0.26 and M * ,AGS25 = 2.0×10 10 M . These properties are similar to those of AGS11, z AGS11 = 4.83 +0.82 -0.76 , M * ,AGSC11 = 2.8×10 10 M .

Among the 6 HST-dark galaxies for which we were able to determine a mass and redshift, there appear to be two distinct trends. Galaxies AGS4 and AGS24 are among the most massive of all active uvj galaxies detected in the region covered by the ALMA survey. AGS4 has a mass M * = 2.81 +1. 65 -1.03 × 10 11 . In other words, it is the most massive galaxy at 4 < z < 5 in our catalogs. AGS24 has a stellar mass M * = 1.82 +0. 27 -0.50 × 10 11 . Two HST-dark galaxies are of intermediate mass, but with a redshift higher than 4.5 (see Fig. 6.12) and for the two remaining galaxies, neither the mass nor the redshift have been estimated for the moment. The HST-dark galaxies could therefore be very massive galaxies (M * >10 11 M ) at z > 3.5. These massive galaxies are almost non-existent at z > 4.5 (in the volume defined by GOODS-ALMA), so we find HST-dark galaxies at these redshift with smaller stellar masses.

Verification of dubious galaxies

For several sources, there was a relatively large offset between the position of the ALMA detection and the position of the HST counterpart (see Table 4.1 and Table 6.1). This is the case, for example for AGS20 (see Fig. 7.11; left panel) which displays an offset of ∼0.3" between optical and infrared detections. We can ask ourselves for this source if ALMA detects an obscured part of the galaxy, not visible in optics or if it is two separate galaxies. In the rest of this paragraph, we will call the part "ALMA" the one that is in the center of Fig. 7.11; left panel) and we will call the HST part, the part clearly visible in this image. We will try to determine the characteristics of these two emissions separately to determine if we can find the signature of a distant galaxy at the ALMA emission level, which would show that they are two different galaxies. If the determined redshifts are comparable, this study will not allow us to decide between the fusion of two galaxies, one highly dust-obscured or if the dusty star formation region of this galaxy is offset of the stellar light visible in H-band. As for AGS4, the two possible sources (optical and submillimeter) were then fit simultaneously using these two light-profile models (using GALFIT) on all of the available images, fixing the profile to that observed in the H-band (see Fig. 7.11; right panel). The blue curve represents the spectral energy distribution for the galaxy clearly visible in optics, while the orange curve represents the spectral energy distribution at the ALMA position and which becomes dominant from the K band. The characteristics of these two parts taken separately are given in Table 7.1.

The spectral energy distribution of the ALMA galaxy is very attenuated, while the other is virtually dust-free and has little star formation. The redshifts of the ALMA part and the optical part are coherent (see Table 7.1). The probability density of the redshift of the HST part gives a single peak and is well constrained to z = 2.47. For the ALMA part, the probability density allows a redshift to z=2.4 or z=2.8. This last value corresponds to the redshift determined in the ZFOURGE catalog. On the other hand, z=2.4 is better compatible with the redshift of the other galaxy, which is much better constrained. We will therefore tend to favour z=2.4. With the information we have, it is difficult to decide whether it is a galaxy merger or a dark part within the galaxy. The determination of the redshift around z = 2.5 would require a spectroscopic validation. In any case, we think we can eliminate the hypothesis of a distant galaxy masked by a bright HST galaxy, as it was the case for AGS4.

Spitzer/IRAC a loyal ally for HST-dark galaxies identification

Our four HST-dark galaxies (AGS4, AGS11, AGS15, and AGS17) have at least one feature in common, the presence of an IRAC detection and the fact that this IRAC detection is closer on the sky than the unrelated HST detection (see Table 4.1). The IRAC detections come from the Ashby et al. (2015) catalog, except for AGS15 where the position comes from the ZFOURGE catalog, using the Labbé et al. (2015) survey. The offset between the IRAC and HST sources might suggest that they are different sources. Fig. 7.12 shows the IRAC contours at 3.6 µm centered on the ALMA detection, superimposed over the HST H-band image. The presence of IRAC detections at these distances from the ALMA galaxies is a very strong driver for the identification of sources. The probability of random IRAC association is between one and two orders of magnitude less likely than random HST association for this range of distances, as shown in Fig. 4.6 and Table 7.2. The selection of ALMA candidates from galaxies detected in IRAC channels 1 and 2 but missed by HST-WFC3 at 1.6 µm has already been experimented successfully by T. Wang et al. (in prep.), and seems to be a good indicator to detect HST-dark ALMA galaxies.

As each of our HST-dark galaxies has different features, we will discuss each galaxy individually.

Of the total 23 detections in this survey, 7 do not show an HST H-band counterpart. This lack of counterpart could arise from an occultation of the optical counterpart by a foreground galaxy, faint emission at optical wavelengths, or a spurious ALMA detection.

For the four galaxies previously discussed (AGS4, AGS11, AGS15 and AGS17), we observe a signal with IRAC at 3.6 µm and 4.5 µm, despite the limiting sensitivity of IRAC (26 AB mag at 3 σ for both 3.6 and 4.5 µm; Ashby et al. 2015) being lower than HST-WFC3 (28.16 AB mag at 5 σ for F160W; Guo et al. 2013) in the respective images. Furthermore, two of the galaxies (AGS15 and AGS17) have already been detected at submillimetre wavelengths (870 µm) by Hodge et al. (2013).

The other three galaxies (AGS14, AGS16 and AGS19) are not detected at any other wavelength hence there is a high probability that they are spurious. This number is in good agreement with the expected number of spurious sources for our sample (4±2).

Fig. 4.4 gives us a glimpse into how sources can be falsely associated with an HST galaxy. When the offset correction is applied, the three galaxies shown with magenta lines move further away from the center position (∆δ = 0, ∆α = 0), rather than closer to it

The IRAC detections seem to be particularly useful to confirm the existence of a source. In the main catalog, except for the three galaxies that we consider as spurious, all others are also detected in the IRAC filters.

In conclusion, we have detected 20% HST-dark galaxies (4 out of 20 robust detections) with a counterpart confirmed at least by IRAC. This proportion may depend in a manner that we cannot address here on the depth of the optical and millimeter images. Knowing that these HST-dark galaxies are dust, hence metal, rich they are likely progenitors of the most massive galaxies seen at z = 0, hence potentially hosted by massive groups or clusters of galaxies. Two of these HST-dark galaxies have a tentative redshift of z = 4.82 and z = 3.76, we, therefore, expect these galaxies to be located at z > 3 [START_REF] Wang | A dominant population of optically invisible massive galaxies in the early Universe[END_REF]. These two galaxies are already massive (10 10.55 M and 10 10.50 M respectively), suggesting that this population of galaxies is particularly interesting for understanding massive galaxy formation during the first billion years after the Big Bang. Spectroscopy with the JWST NIRSpec instrument will permit very sensitive spectroscopic detection of Hα emission at z < 6.6, and hence an important new tool to measure redshifts of these HST-dark galaxies. GOODS-South will undoubtedly be a venue for extensive JWST spectroscopy, including Guaranteed Time Observations. Spectral scan observations with ALMA can also be a powerful tool to determine the distances, and hence physical properties, of this intriguing population of HST-dark galaxies.

The HST-dark galaxy as an overdensity tracer

The presence of several overdensities in the South GOODS field has been established for several years. For example, [START_REF] Salimbeni | A comprehensive study of large-scale structures in the GOODS-SOUTH field up to z ∼ 2.5[END_REF] describe the presence of several overdensities at z ∼ 0.7, at z ∼ 0.96, z ∼ 1.05, and at z ∼ 2.3. These different z peaks can be visualized in Fig. 7.13 (Zhou et al., in prep) which shows in grey, the redshift distribution of galaxies in the GOODS-ALMA field.

These overdensities underline high-density structures. The analysis of these large scale structures is essential to understand the evolution of galaxies. These structures can link the primordial fluctuations of the cosmic diffuse background with the current galaxies (e.g., [START_REF] White | The Impact of the CMB on Large-Scale Structure[END_REF][START_REF] Boughn | A correlation between the cosmic microwave background and large-scale structure in the Universe[END_REF][START_REF] Efstathiou | Large-angle correlations in the cosmic microwave background[END_REF], they can also probe the distribution of the dark matter halo around the galaxies (e.g., [START_REF] Springel | The Aquarius Project: the subhaloes of galactic haloes[END_REF][START_REF] Taylor | Dark Matter Halos from the Inside Out[END_REF][START_REF] Piras | The mass dependence of dark matter halo alignments with large-scale structure[END_REF] and can be used to study the environmental effects on galaxies (e.g., [START_REF] Treu | A Wide-Field Hubble Space Telescope Study of the Cluster Cl 0024+16 at z = 0.4. I. Morphological Distributions to 5 Mpc Radius[END_REF][START_REF] Mei | Evolution of the Color-Magnitude Relation in High-Redshift Clusters: Early-Type Galaxies in the Lynx Supercluster at z ˜1.26[END_REF][START_REF] Rettura | Compact Massive Early-type galaxies in the z = 1.2 cluster[END_REF]. [START_REF] Castellano | A Photometrically Detected Forming Cluster of Galaxies at Redshift 1.6 in the GOODS Field[END_REF], analyses an overdensity at z ∼ 1.6 while Forrest et al. (2017) focuses on an overdensity at z = 3.47. It is this last overdensity that will interest us here. Forrest et al. (2017) The overdensity described in Forrest et al. (2017), therefore, corresponds spatially to the region in which AGS24 was discovered but also corresponds with the redshift determined by SED fitting. In Fig. 7.14, we show the ratio between the density within 2 Mpc comoving distance (ρ) to the the average number density over this field with 3.42 ≤ z ≤ 3.57 within the GOODS-ALMA field as well as the position of AGS24 in red, and the positions of AGS11, AGS15 and AGS17 (Zhou et al., in prep).

In addition, from the redshift, it was possible to estimate a mass for AGS24 using FAST++ . The stellar mass determined in this way is M = 1.82 +0. 27 -0.50 × 10 11 M . This would make this galaxy the most massive galaxy of this overdensity with a mass of ∼ 10 times more massive than the second most massive galaxy with z ∼ 3 -4 within this region [START_REF] Ginolfi | Molecular gas on large circumgalactic scales at z = 3.47[END_REF]).

We will discuss in Sect. 7.6 the possible implications of these HST-dark galaxies in understanding the evolution of galaxies and their possible contribution to the cosmic density of star formation among the most massive galaxies at high redshift. The position of AGS24 at the center of this overdensity and especially its mass makes this galaxy a candidate of a future bright cluster galaxy (BCG) or central dominant (cD) galaxy (Zhou et al., in prep).

In addition, the other HST-dark galaxies, i.e., AGS11, AGS15, AGS17, seem to be positioned in the overdensity region (see Fig. 7.14). Although the AGS11 redshift that we have taken from the CANDELS catalog (z AGS11 = 4.82) is higher than the redshift of this overdensity, the SED of AGS11 could be fit with z ∼ = 3.5. In Fig. 7.15, which was taken from the ZFOURGE database (http://zfourge.tamu.edu/DR2017/CDFS/object_pages/7500/7589.html), we can see that the Balmer break could fall between the H-band and the K-band which could possibly lead to a redshift z ∼ 3.5. It is therefore not excluded that AGS11 may be part of this overdensity.

Finally, we calculated the probability that AGS11, AGS15, AGS17, and AGS24 would be located randomly so close to each other. To do this, we randomly injected 4 points into the area covered by the GOODS-ALMA survey and calculated the minimum area covered by a circle, including these four positions (see Fig. 7.16). We repeated this operation 10,000 times and compared the distribution of these surfaces to the area covered by the HST-dark sources AGS11, AGS15, AGS17, and AGS24. The surface area of the points thrown at random is higher than the surface area covered by the HST-dark galaxies in 99.6% of cases (see Fig. 7.16).

This means that despite the fact these sources have a low projected surface density, they seem to be clustered. A two-point correlation function will be presented in detail in Zhou et al., in prep to accurately estimate the clustering of massive galaxies at these redshifts.

Implications of HST-dark galaxies in cosmic density of star-formation

It is difficult with such fragmented information to constrain the physical properties of these optically dark galaxies or to determine their implication in the evolution of the galaxies. The redshift determination for the few galaxies for which a determination can be attempted is highly uncertain.

The precise quantification of this type of object, according to their mass and redshift interval is necessary to understand the involvement of HST-dark galaxies in the evolution of galaxies, to know if their density is compatible with massive, compact and passive galaxies at z ∼2.

We were recently able to serendipitously detect an HST-dark galaxy using data from only 8 ALMA pointings (Elbaz et al., 2018). This serendipitously-detected HST-dark galaxy suggests a blind detection rate of 1 galaxy per 8 pointings, similar to the 20% of HST-dark galaxies found among the galaxies detected by ALMA in this work. These optically dark galaxies are therefore probably not marginal among the most massive galaxies. However, it is necessary to have a larger statistics to be able to have robust estimations of the proportion of these galaxies among massive galaxies.

Recently, with some serendipitous detections found (2 + 3 less secure for Yamaguchi et al. 2019a) in the ASAGAO field, 1 for Williams et al. (2019) in the cosmos field, these two authors have tried to estimate the contribution of optically-dark sources to the cosmic star formation density (see Fig. 7.17). The underlying idea is to know if the density of star formation increases continuously from the observation of distant galaxies to the cosmic noon as for example in the models of Madau and Dickinson (2014) or if this density of stellar formation is relatively constant, before decreasing as in the models of [START_REF] Rowan-Robinson | The star formation rate density from z = 1 to 6[END_REF].

For our survey, an analysis of both the sources detected and by stacking sources too weak to have been individually detected to probe to fainter levels is underway to determine the cosmic SFRD of the GOODS-ALMA field.

Another method, not requiring broad survey analysis, was used by [START_REF] Wang | A dominant population of optically invisible massive galaxies in the early Universe[END_REF]. (black solid line and blue triangle). The contribution of the massive H-dropout (red dots), ALESS SMGSs (purple pentagons), H-dropout in semi-analytical models (orange squares) as well as the massive LBGs (M * > 10 10.3 M ; based on dust-corrected UV) are shown in this image. Right panel: Fraction of massive galaxies, in number, that are either detected as LBGs or H-dropouts for galaxies with 3.5 < z < 6.5. Figures from: [START_REF] Wang | A dominant population of optically invisible massive galaxies in the early Universe[END_REF] interesting targets across the GOODS-South, COSMOS and UDS fields. An observation of 1.8 min for each of these targets allowed the detection of 62% of this sample, i.e., 39 detected with a signal on noise S/N > 4 σ. The SED fitting allowed to derive a median redshift of 4 and an average stellar mass of M * ∼ 10 10.8 M confirming that these objects are for the most part very massive and distant. The analysis of the contribution of massive UV-bright galaxies and H-equivalent mass dropout showed that the latter contributed 10 times more to the cosmic star formation rate density for z > 3 (see Fig. 7.18; left panel). In addition, a numerical analysis showed that at high redshifts, the H-dropout population became dominant from a stellar mass of M * ∼10 10.25 M (see Fig. 7.18; right panel).

Conclusion

Although there may be pure ALMA detection (e.g., Williams et al., 2019), we validated in this study that Spiter/IRAC is an extremely powerful tool to confirm the existence of an ALMA source.

The complementarity of these two instruments can remove ambiguity about the identification of a counterpart, as has been the case for several HST-dark galaxies presented in this section. By using the color difference between H and IRAC bands, it is possible to find solid candidates for the counterparts of (sub)millimetric detections done with single dish telescopes. This counterpart association expertise will be particularly useful for surveys as for example with the Nika2 camera [START_REF] Adam | The NIKA2 large-field-of-view millimetre continuum camera for the 30 m IRAM telescope[END_REF] and especially for the NIKA2 Cosmological Legacy Survey (NIKA2 GT-LP-N2CLS, PI : G. Lagache, A. Beelen, N. Ponthieu). This identification will only be possible in regions of the sky for which there are deep IRAC data. CO CO CO CO CO CO CI( 609) CI( 371) CII( 158) OI( 145) NII( 122) OI( 63) NII( 205) FIGURE 7.19: Position of CO transitions and CI lines as a function of z and observed frequency for the 10 ALMA band, used here for the spectral z search for the HST-dark galaxies.

These HST-dark galaxies do not seem to be a marginal population of galaxies when considering massive, star-forming galaxies with high redshift. Their contribution to the SFRD even seems to be major for galaxies with a log 10 (M * /M ) > 10.5 at z > 3.5.

For the moment these galaxies are very strong candidates to be the progenitors of elliptical galaxies at z ∼ 2. We will discuss this possibility in Chapter 8.

To know precisely the redshift and the characteristics of these galaxies, we have written proposals with ALMA (accepted see appendix) and VLA (rejected). With ALMA we proposed to observe in band 4 to detect possible emission line of CO (CO , CO , CO or CO(4-3)), depending on the redshift of the considered source (see Fig. 7.19). To be able to determine the redshift of these sources in the most secure way possible, we will use the technique explained and used in [START_REF] Jin | Discovery of four cold dusty galaxies at z=3.62-5.85[END_REF] to confirm detection with a secondary emission line (H 2 0, CI, etc.). The data of part of the ν range ([136 -163 GHz]) has just been delivered. In this Chapter, we take advantage of the broad ALMA coverage as well as the large multiwavelength coverage in GOODS-South, to constrain the properties of galaxies detected by ALMA in GOODS-ALMA. We will explore the possibility that these galaxies detected by ALMA are the progenitors of passive elliptical galaxies at z ∼ 2.

To do this, we will first describe how we took advantage of our large multiwavelength coverage to fit both the spectral energy distributions (SEDs), and modified blackbody models (MBB) to the galaxies detected in GOODS-ALMA. We will explain how we derived the main physical parameters of the galaxies (M dust ,M gas , SFR, depletion time), before showing that the galaxies detected by ALMA are among the most massive galaxies in the GOODS-ALMA field. The majority of these galaxies are starbursts, or are located in the upper part of the Main Sequence. A significant part of the population, located around z = 2.5-3 has an abnormally low gas fraction. The size of these galaxies, although located on the trend of star-forming galaxies in H-band, have sizes measured with ALMA that are compatible with the sizes of passive galaxies (in H-band). These results suggest that we are observing progenitors of passive elliptical galaxies at z ∼ 2.

SED-fitting 8.1.1 Method

We fit the spectral energy distributions using two different methods, depending on whether or not the galaxy has an Herschel counterpart.

For galaxies that have a far-IR fluxes density measured by the Herschel space observatory, we employ the SED-fitting code CIGALE1 (Code Investigating Galaxies Emission: [START_REF] Noll | Analysis of galaxy spectral energy distributions from far-UV to far-IR with CIGALE: studying a SINGS test sample[END_REF]. We use the stellar population models of Bruzual and Charlot (2003) and the attenuation law of Calzetti et al. (2000). The IR SED fitting was performed using the dust infrared emission model given by Draine and Li (2007). The galaxy data are fit from the UV to millimeter observations. We independently fit the wavelengths from UV up to 16 µm, and 24 µm up to the millimeter wavelengths respectively (see Fig. 8.11). The radio portion has been added after the fitting process, using the FIR/radio correlation, with a constant ratio between FIR and radio luminosity of 2. 34 Yun et al. (2001). The parameters used in CIGALE were given by [START_REF] Ciesla | Identification of galaxies that experienced a recent major drop of star formation[END_REF] and are shown in Table 8.1.

In contrast, if the galaxy has no Herschel infrared counterpart, we fit the data with the dust spectral energy distribution library 2 presented in Schreiber et al. 2018a, and normalized to the ALMA flux density at 1.13 mm in the SED. We proceed iteratively. After fitting the galaxy with a MS SED, we compute the distance to the main sequence (R SB = SFR/SFR M S ) using the output IR luminosity (8-1000 µm) and the redshift. The R SB and the redshift of the galaxy can be used to calculate the dust temperature (T dust ) and the IR8 (L IR /L 8 ) from Eq. 18 and 19 of Schreiber et al. (2018c). IR8 can be used as an indication of the compactness of distant galaxies Elbaz et al. (2011). T dust and IR8 are therefore set to these newly calculated values in the SED-fitting process, and an updated SED is generated.

AGN subtraction

To fit an SED with an AGN component, we used the code decompIR by [START_REF] Mullaney | Defining the intrinsic AGN infrared spectral energy distribution and measuring its contribution to the infrared output of composite galaxies[END_REF]. This code proposes to fit an AGN according to the spectrum of a sample of host galaxies representative of galaxies with an AGN. The contribution of the AGN to the IR luminosity can lead to an overestimation of the dust infrared emission and therefore an overestimation of the SFR. The AGN SED, used in decompIR do not include the wavelength below 6µm.

To better characterize the contribution of AGNs to the total infrared luminosity of galaxies, we need to know their behavior at rest-frame wavelengths lower than 6µm, corresponding to the domain where the contribution of AGN is most important. Since this AGN model is only defined for wavelengths > 6 µm, we, therefore, used another AGN model for wavelengths shorter than 6µm.

We therefore use Decompir to extrapolate AGN emission to shorter wavelengths, using an AGN model from [START_REF] Kirkpatrick | The Role of Star Formation and an AGN in Dust Heating of z = 0[END_REF]. We combine the two models according to the recommendation of [START_REF] Mullaney | Defining the intrinsic AGN infrared spectral energy distribution and measuring its contribution to the infrared output of composite galaxies[END_REF]:

νF ν (5µm(AGN )) = νF ν (0.4µm(QSO)) (8.1)

Dust Temperature

For the sake of simplicity and comparison with previous studies, we measure the dust temperature by fitting an MBB model, following: where k B is Boltzmann's constant, h is the Planck constant, β is the dust emissivity spectral index, T dust is the dust temperature and L ν is the flux density. We have assumed a spectral index β = 1.5 (e.g., Kovács et al., 2006;Gordon et al., 2010). We fit the flux densities at λ rest ≥ 0.55λ peak using the MBB model as suggested by Hwang et al. (2010), and exclude the synchrotron contribution (λ obs < 5 mm). The criteria we have defined to select the points to be modelled with a MBB are as follows:

S ν ∝ ν 3+β exp( hν k B T d ) -1 (8.2)
-at least one data point between 0.55 × λ peak and λ peak .

-at least one data point beyond the submillimeter peak, with a wavelength lower than or equal to 1.1 mm. Galaxies selected in (sub)millimeter flux density are expected to be biased towards low dust temperatures (e.g. [START_REF] Magdis | On the stellar masses of IRAC detected Lyman Break Galaxies at z ˜3[END_REF][START_REF] Mcalpine | The nature of sub-millimeter and highly starforming galaxies in the EAGLE simulation[END_REF]. Indeed, for the same redshift and infrared brightness, the (sub)millimeter flux of a colder galaxy will be higher than that of a warmer galaxy. We investigated where the galaxies detected in the GOODS-ALMA survey are located in the IR Luminosity-Temperature plane (Fig. 8.2, left panel) and in the Redshift-Temperature plane (Fig. 8.2, right panel). For comparison, we also plot the temperature of all the galaxies located in GOODS-ALMA. We find that the galaxies detected by ALMA do not exhibit a systematic offset compared to those undetected by ALMA.

For an SMG, the dust temperature is correlated with the FIR luminosity (e.g. Wardlow et al., 2011). We have found a median dust temperature of 39.7 K for our sample. However, we see that setting the spectral index β = 1.5 has an influence on the temperature. We chose to fix it, in order to have fewer free parameters in our fit and to compare all galaxies consistently. If we had taken β = 2, the modified blackbody temperatures would have been slightly lower (1 -4 K lower). Note that we do not use this T d temperature to determine dust masses (see Sect. 8.2.1).

Derived parameters

Dust mass

Following Draine et al. (2007), we adopt the maximum starlight intensity relative to the local interstellar radiation field U max = 10 6 U , and the power-law index α = 2 in Eq. 8.3. The dust 8.2. Derived parameters 155 mass is implemented in the CIGALE code using the formula of Draine et al. (2007):

dM dust dU = (1 -γ)δ(U -U min ) + γM dust α -1 U 1-α min -U 1-α max U -α (8.3)
with U min ≤ U max , α = 1 and is the exponent of the power law describing the intensity distribution of the interstellar radiation field, and γ is the relative fraction of dust heated by each source. (Draine et al., 2007) showed that α = 2 and U max = 10 6 gave a good fit to a large sample of nearby galaxies from the Spitzer SINGS program.

Gas mass

One of the fundamental questions to understand these ALMA galaxies (which are SB or in the upper part of the MS, see Fig. 8.8) if they have an increased SFE (SFR/M gas ) compared with MS galaxies, or because they have larger gas reservoirs. For each galaxy, we calculated the gas mass M gas as well as the gas fraction f gas , defined by:

f gas = M gas M gas + M , (8.4)
To compute the gas mass, we assume a ratio between dust mass and gas mass depending only on metallicity. The ratio (δ GDR ) was directly derived by [START_REF] Leroy | The CO-to-H 2 Conversion Factor from Infrared Dust Emission across the Local Group[END_REF] in the local Universe, and can be applied to our sample, assuming that this relation is valid at all redshifts:

δ GDR = M gas M dust = (9.4 ± 1.1) -(0.85 ± 0.13)[12 + log(O/H)] (8.5)
where M gas = M (H 2 ) + M (H I ). At the redshifts of this study, the atomic hydrogen can be considered negligible compared to the molecular form (e.g. [START_REF] Leroy | The Star Formation Efficiency in Nearby Galaxies: Measuring Where Gas Forms Stars Effectively[END_REF][START_REF] Obreschkow | Compactness of cold gas in high-redshift galaxies[END_REF]Daddi et al., 2010).

We note that recent studies have found evidence for a steep increase in the gas to dust ratio of sub-solar metallicity galaxies at z∼2 compared with this local relation [START_REF] Coogan | Suppressed CO emission and high G/D ratios in z=2 galaxies with sub-solar gas-phase metallicity[END_REF]), but we do not expect this effect to be significant for our more massive, enriched galaxies. As we do not have direct metallicity measurements for our galaxies, we use the equation given by [START_REF] Genzel | The Metallicity Dependence of the CO -> H 2 Conversion Factor in z 1 Star-forming Galaxies[END_REF] to compute the metallicity:

12 + log(O/H) = -4.51 + 2.18log 10 (M /1.7) -0.0896 log 10 (M /1.7) 2 (8.6)
In this equation, we include a conversion factor (1/1.7) to transform the original formula from a Chabrier IMF to a Salpeter IMF. However, the metallicity can be underestimated for galaxies above the main sequence (e.g. [START_REF] Silverman | A Higher Efficiency of Converting Gas to Stars Pushes Galaxies at z ∼ 1.6 Well Above the Star-forming Main Sequence[END_REF], which could artificially increase the proportion of gas and conversely underestimate the gas depletion time (Elbaz et al., 2018). We compared our calculated metallicities to the metallicities obtained using the fundamental metallicity relation (FMR) of [START_REF] Mannucci | A fundamental relation between mass, star formation rate and metallicity in local and high-redshift galaxies[END_REF]:

with m = log 10 (M /1.7)-10, and s = log 10 (SFR/1.7). The median metallicity ratio between these two methods is 1.00 ± 0.01, where the uncertainty corresponds to the standard deviation. For our galaxy sample, both methods are therefore, in good agreement. The metallicities of these ALMA detected galaxies are however somewhat uncertain. The metallicity evolution is poorly constrained for galaxies at high redshift, as well as for starburst galaxies and galaxies with AGNs (e.g., [START_REF] Tan | A Deep Search for Molecular Gas in Two Massive Lyman Break Galaxies at z = 3 and 4: Vanishing CO-emission Due to Low Metallicity[END_REF][START_REF] Kewley | Theoretical Evolution of Optical Strong Lines across Cosmic Time[END_REF].

We also verified that the mass of gas derived by the method described above was in agreement with that derived using the method of [START_REF] Scoville | ISM Masses and the Star formation Law at Z = 1 to 6: ALMA Observations of Dust Continuum in 145 Galaxies in the COSMOS Survey Field[END_REF]. The [START_REF] Scoville | ISM Masses and the Star formation Law at Z = 1 to 6: ALMA Observations of Dust Continuum in 145 Galaxies in the COSMOS Survey Field[END_REF] method is based on the assumption that continuum measurements of the Rayleigh-Jeans tail can be used to estimate the mass of dust and therefore, the mass of gas. Since this method is based on the Rayleigh-Jeans tail, it can only be used at long wavelengths (λ > 250 µm). However, if the dust emission is optically thin, the Scoville et al. ( 2016) method may underestimate the gas mass [START_REF] Miettinen | An ALMA survey of submillimetre galaxies in the COSMOS field: Physical properties derived from energy balance spectral energy distribution modelling[END_REF]. At 1.13mm, the estimate of the gas mass can be written, according to equations Eq. 6 and Eq. 16 of [START_REF] Scoville | ISM Masses and the Star formation Law at Z = 1 to 6: ALMA Observations of Dust Continuum in 145 Galaxies in the COSMOS Survey Field[END_REF], as:

M mol = S ν × 5.12 × 10 10 × (1 + z) -4.8 × (d l ) 2 Γ 0 RJ Γ z RJ (8.8)
with S ν the flux at 1.13 mm in mJy and Γ z RJ is the correction for departure in the rest frame of the Planck function from Rayleigh-Jeans [START_REF] Scoville | ISM Masses and the Star formation Law at Z = 1 to 6: ALMA Observations of Dust Continuum in 145 Galaxies in the COSMOS Survey Field[END_REF]:

Γ RJ (T dust , ν obs , z) = hν obs × (1 + z)/(k b T dust ) e (hν obs ×(1+z)/k b T dust ) -1 (8.9)
where h is the Planck constant and k b is the Boltzmann constant.

Using a fixed dust temperature (25K), we find a difference between the calculated gas mass (M (gas, this work) ) and that derived following [START_REF] Scoville | ISM Masses and the Star formation Law at Z = 1 to 6: ALMA Observations of Dust Continuum in 145 Galaxies in the COSMOS Survey Field[END_REF]: M (gas, Scoville) /M (gas, this work) = 1.1 ± 0.5.

The gas mass is directly related to the depletion time by:

τ dep = M gas SF R (8.10)

SFR SFR IR

The infrared luminosity of each galaxy has been converted to SFR using the Kennicutt relation [START_REF] Kennicutt | The Global Schmidt Law in Star-forming Galaxies[END_REF] below:

SF R [M yr -1 ] = 1.72 × 10 -10 L IR (8.11) with L IR in L , and 8.12) where d l is the luminosity distance.

L IR [L ] = 4πd 2 l 1000µm 8µm F ν (λ) × c λ 2 dλ, (
In Fig. 8.3, we illustrate the distribution of SFRs as a function of redshift for the ALMA-detected galaxies. We also represent the theoretical detection limit of the galaxies present in the survey SFR [M yr -1 ] Detection limit 4.8σ Detection limit 3.5σ Main cat Supp. cat FIGURE 8.3: Star formation rate as a function of redshift, for galaxies from the main (red dots) and supplementary (gray dots) catalogs respectively. The SFR has been computed from the IR luminosity following Eq. 8.11. The detection limits at 4.8 σ(solid black line) and 3.5 σ(dashed black line) have also been computed from the IR library of Schreiber et al. (2018c), with a temperature evolving with redshift taking into account the average value of the rms at 0.182 mJy.

at the limit of 4.8σ (solid black line) used to create the main catalog, assuming a constant rms (rms = 0.182 mJy) over the whole map, as well as the 3.5σ (dashed black line) limit used to build the supplementary catalog. However, as the rms is not constant, and therefore may be lower at some points in the map, some galaxies (AGS21, for example) appear below this line.

We note that there is a galaxy (AGS37) that is clearly offset from the detection limit, with a SFR ∼ 10 M yr -1 . This galaxy is atypical, as it has the lowest redshift in our sample (z = 0.66, the same redshift as AGS30) and it also hosts a strong AGN with an X-ray luminosity = 1.39 10 43 erg.sec -1 . It is most likely because of this AGN emission that this galaxy was detected in our survey.

The SFR limit has been computed taking into account the main sequence SED from Schreiber et al. (2018a), with the temperature and the fraction of polycyclic aromatic hydrocarbon (PAH) emission evolving as a function of redshift. The IR luminosity was calculated by integrating the flux from the SED using Eq. 8.12, and was then converted into SFR using Eq. 8.11.

This IR luminosity limit allows us to detect galaxies down to an IR luminosity of 10 12 L at redshift z = 1.5, and down to 3×10 12 L at redshift z = 4. In other words, for an MS galaxy, this allows us to detect galaxies with a minimum stellar mass of 2.5 × 10 11 M , 1.8 × 10 11 M and 1.5 × 10 11 M for redshifts z = 2, z = 3 and z = 4 respectively, using Eq.9 of Schreiber et al. (2015).

Not surprisingly, the most IR luminous galaxies have been listed in the main catalog. However, we note the presence of a portion of galaxies from the supplementary catalog that are also among the most IR luminous galaxies. The size of the galaxies explains this behavior. The galaxies detected in the supplementary catalog generally have larger sizes than those in the main catalog (?). Even though the peak flux is fainter on average, the integrated flux can reach values close to those of the main catalog.

All galaxies except one can be classified as ultraluminous infrared galaxies (ULIRGs), with log 10 (L IR /L ) ≥ 11.9. Among these ULIRGs, one (AGS4) can be classified as a hyper-luminous infrared galaxy (HyLIRG). This galaxy has a high estimated redshift (z AGS = 4.32, but this estimation is highly uncertain because this source is optically dark (see F18). Its SFR is particularly high at SFR AGS = 2870 +146 -142 , and this galaxy is probably also a particularly massive galaxy (M * AGS4 ) ∼ 10 11.5 M , although there are also large uncertainties on its stellar mass). This galaxy is located above the main sequence, with an R SB of 2.77.

SFR U V

Massive galaxies are known to be heavily dust-obscured at z > 2 (e.g., Magnelli et al., 2009;[START_REF] Murphy | Calibrating Extinction-free Star Formation Rate Diagnostics with 33 GHz Free-free Emission in NGC 6946[END_REF]. While the SFR IR is derived from the dust emission, we also consider the unobscured contribution to the total SFR, observed through UV emission. For the most massive galaxies (M > 10 10.5 M ), the fraction of obscured to unobscured star formation (SFR IR /SFR IR+U V ) is greater than 90% [START_REF] Whitaker | The Constant Average Relationship between Dust-obscured Star Formation and Stellar Mass from z = 0 to z = 2.5[END_REF].

We derive L U V from the observed magnitude as follows:

L U V = 4πd 2 L ν 1600 10 -0.4(48.6+m) 1 + z (8.13)
where d L is the luminosity distance and m is the observed magnitude.

The SFR U V , uncorrected for dust attenuation, is in turn derived from the L U V , following [START_REF] Daddi | A New Photometric Technique for the Joint Selection of Star-forming and Passive Galaxies at 1.4 < ˜z < ˜2[END_REF]:

SF R U V = 2.17 × 10 -10 × L U V (8.14)
The total SFR (SFR tot = SFR U V + SFR IR ) is given in Table 8.2. The median contribution from SFR U V to SFR tot is only 1.3%.

AGN

Of the 1008 sources detected in Luo et al. (2017), 397 lie in the GOODS-ALMA field. We adopted a cross-matching radius of 0.6", after applying the offset correction (see Sect. 6.3). We found that 13/23 (6/20) of our main (supplementary) catalog galaxies had matches with the Luo et al.

(2017) catalog. However, the detection in X-ray is not definitive proof that a galaxy hosts an AGN. We corrected the Luo et al. ( 2017) catalog X-luminosity when redshift deviations were observed, using the following formula: .15) and assuming a fixed Γ = 2. In the following paragraphs, a galaxy will be considered as hosting an AGN if the galaxy has an X-Luminosity L X,int > 10 43 erg.s -1 (luminous X-ray sources). The SFRIR of these galaxies have been used. Galaxies with Herschel counterparts are color-coded as a function of the fgas. The other galaxies are represented by grey dots. We measured the distance to the MS using Eq. 9 from Schreiber et al. ( 2015) and its dispersion is 0.3 dex. We have rescaled all of the SFRs by multiplying by SFRMS(z)/SFRMS(z = 2.6), in order to maintain their relative positions with respect to the main sequence.

L X = 4πd 2 L (1 + z) Γ -2 f X . ( 8

IRX-β relation

The rest-frame UV slope, β, is defined following the equation (e.g [START_REF] Calzetti | Dust extinction of the stellar continua in starburst galaxies: The ultraviolet and optical extinction law[END_REF][START_REF] Meurer | Dust Absorption and the Ultraviolet Luminosity Density at z ˜3 as Calibrated by Local Starburst Galaxies[END_REF]:

F (λ) = λ β (8.16)
where F(λ) is in erg s -1 cm -2 Å-1 . We fit this power law relation between 1200 and 3000 Å. Of the 27 947 UVJ active galaxies (in the ZFOURGE catalog) encompassed by the GOODS-ALMA field, 520 have coverage in at least two photometric bands, as is needed to constrain β and a far IR counterpart. As the 2175 Å bump (existing both at low and high redshift, [START_REF] Conroy | Dust Attenuation in Disk-dominated Galaxies: Evidence for the 2175 Å Dust Feature[END_REF]; [START_REF] Buat | GOODS-Herschel: dust attenuation properties of UV selected high redshift galaxies[END_REF]) can bias the slope measurement in the case of sparse photometric sampling, we excluded the filter(s) that cover this wavelength [START_REF] Popping | Dissecting the IRX-β dust attenuation relation: exploring the physical origin of observed variations in galaxies[END_REF][START_REF] Tress | SHARDS: constraints on the dust attenuation law of star-forming galaxies at z ∼ 2[END_REF].

Using L U V and the UV slope, we can define the so-called 'infrared excess', defined as:

IRX = L IR L U V (8.17)
The IRX-β, calibrated on local galaxies, has been an important tool for estimating total SFRs when IR data are not available [START_REF] Overzier | Dust Attenuation in UV-selected Starbursts at High Redshift and Their Local Counterparts: Implications for the Cosmic Star Formation Rate Density[END_REF]. Indeed β is measured from UV filters, and can be used as a proxy to measure dust obscuration in galaxies (e.g., [START_REF] Adelberger | Multiwavelength Observations of Dusty Star Formation at Low and High Redshift[END_REF][START_REF] Daddi | Multiwavelength Study of Massive Galaxies at z˜2. I. Star Formation and Galaxy Growth[END_REF]. The dust attenuation (A UV ) is directly linked to IRX (e.g., [START_REF] Meurer | Dust Absorption and the Ultraviolet Luminosity Density at z ˜3 as Calibrated by Local Starburst Galaxies[END_REF]Calzetti et al., 2000;[START_REF] Buat | GOODS-Herschel: dust attenuation properties of UV selected high redshift galaxies[END_REF]. For [START_REF] Meurer | Dust Absorption and the Ultraviolet Luminosity Density at z ˜3 as Calibrated by Local Starburst Galaxies[END_REF], for example, the relation between IRX and the dust attenuation at 1600 Åis defined by: log 10 (IRX 1600 ) = log 10 (10 2015), ( 5) Gas mass derived from Eq. 8.5, (6) Gas fraction defined by fgas = Mgas/(Mgas + M ), (7) Dust temperature derived from a MBB model assuming β=1.5. † indicates galaxies without Herschel counterpart and whose LIR is determined only by the ALMA contribution. For these galaxies, we show the mass of gas as an indication but we do not use it in the rest of this paper.

This relationship, first defined at low redshift (e.g., [START_REF] Meurer | Dust Absorption and the Ultraviolet Luminosity Density at z ˜3 as Calibrated by Local Starburst Galaxies[END_REF]Calzetti et al., 2000) was refined using Galaxy Evolution Explorer (GALEX) data [START_REF] Overzier | Dust Attenuation in UV-selected Starbursts at High Redshift and Their Local Counterparts: Implications for the Cosmic Star Formation Rate Density[END_REF][START_REF] Takeuchi | Reexamination of the Infrared Excess-Ultraviolet Slope Relation of Local Galaxies[END_REF]. At high redshift, this relationship is still poorly constrained and the results are contradictory. While some studies show that galaxies at high redshift follow this local relationship (e.g. [START_REF] Fudamoto | The dust attenuation of star-forming galaxies at z ∼ 3 and beyond: New insights from ALMA observations[END_REF][START_REF] Bourne | Evolution of cosmic star formation in the SCUBA-2 Cosmology Legacy Survey[END_REF][START_REF] Mclure | The VANDELS ESO public spectroscopic survey[END_REF][START_REF] Koprowski | A direct calibration of thtae IRX-β relation in Lyman-break Galaxies at z = 3-5[END_REF], others claim that the results differ at high redshift. The most surprising aspect to note is that when results differ from the relationship, they can be located either under that relationship [START_REF] Capak | Galaxies at redshifts 5 to 6 with systematically low dust content and high [C II] emission[END_REF][START_REF] Álvarez-Márquez | Dust properties of Lyman-break galaxies at z ˜3[END_REF][START_REF] Pope | Early Science with the Large Millimeter Telescope: Detection of Dust Emission in Multiple Images of a Normal Galaxy at z>4 Lensed by a Frontier Fields Cluster[END_REF][START_REF] Bouwens | ALMA Spectroscopic Survey in the Hubble Ultra Deep Field: The Infrared Excess of UV-Selected z = 2-10 Galaxies as a Function of UV-Continuum Slope and Stellar Mass[END_REF][START_REF] Barisic | Dust Properties of C II Detected z ∼ 5.5 Galaxies: New HST/WFC3 Near-IR Observations[END_REF] or above this relationship (e.g. [START_REF] Oteo | Far-infrareddetected Lyman-break galaxies at z ˜3. Dust attenuation and dust correction factors at high redshift[END_REF].

We investigated how the galaxies detected by ALMA are positioned in the IRX-β plane. In The Galactic extinction correction for each filter [START_REF] Schlafly | Measuring Reddening with Sloan Digital Sky Survey Stellar Spectra and Recalibrating SFD[END_REF] wasn't taken into consideration in the fit process. This correction alters the final values of β by approximately 0.025 for the GOODS-South field [START_REF] Wang | Galaxy inclination and the IRX-beta relation: Effects on UV star-formation rate measurements at intermediate to high redshifts[END_REF], which is negligible compared to the median error on β.

For comparison with our sample, we have indicated the relationship derived by [START_REF] Meurer | Dust Absorption and the Ultraviolet Luminosity Density at z ˜3 as Calibrated by Local Starburst Galaxies[END_REF]:

IRX M eurer = 1.75 × (10 0.4 * (1.99 * (β+4.43)) -1) (8.19)
The factor 1.75 in Eq. 8.19 comes from the conversion between the FIR brightness used by [START_REF] Meurer | Dust Absorption and the Ultraviolet Luminosity Density at z ˜3 as Calibrated by Local Starburst Galaxies[END_REF] (40 to 120 µm) and IR luminosity (8 to 1000 µm) (Calzetti et al., 2000;[START_REF] Reddy | A multi-wavelength census of star formation at redshifts z equals 2[END_REF][START_REF] Bouwens | ALMA Spectroscopic Survey in the Hubble Ultra Deep Field: The Infrared Excess of UV-Selected z = 2-10 Galaxies as a Function of UV-Continuum Slope and Stellar Mass[END_REF].

We also give the relationship derived by (e.g. [START_REF] Prevot | The typical interstellar extinction in the Small Magellanic Cloud[END_REF][START_REF] Pettini | Infrared Observations of Nebular Emission Lines from Galaxies at Z ˜= 3[END_REF][START_REF] Smit | Inferred H#9082 Flux as a Star Formation Rate Indicator at z ˜4-5: Implications for Dust Properties, Burstiness, and the z = 4-8 Star Formation Rate Functions[END_REF][START_REF] Bouwens | ALMA Spectroscopic Survey in the Hubble Ultra Deep Field: The Infrared Excess of UV-Selected z = 2-10 Galaxies as a Function of UV-Continuum Slope and Stellar Mass[END_REF] for SMC-type dust correction:

IRX SM C = 10 0.4 * (1.1 * (β+2.23)) -1 (8.20)
Except for some rare outliers, we find that the galaxies detected by ALMA, whether in the blind catalog or the prior-based catalog, are consistent with the local relationship of [START_REF] Meurer | Dust Absorption and the Ultraviolet Luminosity Density at z ˜3 as Calibrated by Local Starburst Galaxies[END_REF]. Fig. 8.4 does not indicate a mass dependence for this relationship. On the other hand, some studies (e.g. [START_REF] Coppin | The SCUBA-2 Cosmology Legacy Survey: the submillimetre properties of Lyman-break galaxies at z = 3-5[END_REF][START_REF] Pannella | GOODS-Herschel: Star Formation, Dust Attenuation, and the FIR-radio Correlation on the Main Sequence of Star-forming Galaxies up to z ∼4[END_REF][START_REF] Fudamoto | The dust attenuation of star-forming galaxies at z ∼ 3 and beyond: New insights from ALMA observations[END_REF][START_REF] Álvarez-Márquez | Dust properties of Lyman-break galaxies at z ˜3[END_REF][START_REF] Mclure | The VANDELS ESO public spectroscopic survey[END_REF][START_REF] Koprowski | A direct calibration of thtae IRX-β relation in Lyman-break Galaxies at z = 3-5[END_REF] show a mass dependence of the IRX values for massive galaxies, where the dust attenuation is more significant for the most massive galaxies.

Infrared-radio correlation

The FIR/radio correlation (FRC; de Jong et al. e.g., 1984;Helou et al. e.g., 1985), first defined for local galaxies by the Infrared Astronomical Satellite (IRAS; [START_REF] Neugebauer | The Infrared Astronomical Satellite (IRAS) mission[END_REF], was later extended to intermediate redshifts (z∼0.1-1.5, (e.g. [START_REF] Yun | Radio Properties of Infrared-selected Galaxies in the IRAS 2 Jy Sample[END_REF][START_REF] Garrett | The FIR/Radio correlation of high redshift galaxies in the region of the HDF-N[END_REF][START_REF] Appleton | The Far-and Mid-Infrared/Radio Correlations in the Spitzer Extragalactic First Look Survey[END_REF][START_REF] Sargent | No Evolution in the IR-Radio Relation for IR-luminous Galaxies at z < 2 in the COSMOS Field[END_REF]) and then to even high redshift galaxies (e.g. Sargent et al., 2010a;[START_REF] Magnelli | The far-infrared/radio correlation and radio spectral index of galaxies in the SFR-M * plane up to z˜2[END_REF][START_REF] Delhaize | The VLA-COSMOS 3 GHz Large Project: The infrared-radio correlation of star-forming galaxies and AGN to z ∼ 6[END_REF]. One of the major outstanding questions is whether this relationship is evolving with redshift. Recent studies (e.g. Ivison et al., 2010;Sargent et al., 2010a;[START_REF] Magnelli | The far-infrared/radio correlation and radio spectral index of galaxies in the SFR-M * plane up to z˜2[END_REF][START_REF] Delhaize | The VLA-COSMOS 3 GHz Large Project: The infrared-radio correlation of star-forming galaxies and AGN to z ∼ 6[END_REF] support a dependence of this relationship on redshift. The capabilities of ALMA now allow for IR detections at high redshift, while having sufficient resolution to give increased confidence in optical counterparts. This infrared-radio correlation arises from the fact that massive stars (M ≥ 8 M ) contribute to the heating of dust in the interstellar medium (and are therefore responsible for the infrared part of the galaxy's spectrum), as well as producing radio emission in HII regions (thermal free-free emission), and from supernova explosions (synchrotron emission). Other phenomena could also come into play, such as the inverse Compton cooling (e.g. [START_REF] Condon | Radio emission from normal galaxies[END_REF][START_REF] Lacki | The Physics of the Far-infrared-Radio Correlation. I. Calorimetry, Conspiracy, and Implications[END_REF] (which depends on the ratio RSB = SFR/SFR M S or ionization parameter (e.g. [START_REF] Murphy | The Far-Infrared-Radio Correlation at High Redshifts: Physical Considerations and Prospects for the Square Kilometer Array[END_REF][START_REF] Schleicher | A new interpretation of the far-infrared -radio correlation and the expected breakdown at high redshift[END_REF]). This correlation is quantified by the parameter q F IR :

q F IR = log 10 L FIR [W] 3.75 × 10 12 -log 10 L 1.4GHz [W.Hz -1 ] (8.21)
where L FIR is the FIR luminosity integrated from rest-frame 42 to 122µm, and L 1.4GHz is the rest frame 1.4-GHz radio luminosity. The 1.4 GHz luminosities of our galaxies have been computed from 6 GHz radio observations (Rujopakarn et al. in prep.), following:

L 1.4GHz = 4πd 2 L (1 + z) 1-α S 3GHz × 1.4 3 -α (8.22)
where d L is the luminosity distance. We have assumed that the radio flux is k-corrected following S ν ∝ ν -α , with a synchrotron spectral index α = 0.8 [START_REF] Condon | Radio emission from normal galaxies[END_REF]; Ivison et al. (2010) between 1.4 and 3 GHz. According to Magnelli et al. (2012), the radio spectral index does not evolve significantly with redshift or distance from the MS. We therefore take a value of α = 0.8 for all of the galaxies in our sample.

The correlation between radio and FIR luminosity is tight (scatter of 0.26 dex, [START_REF] Yun | Radio Properties of Infrared-selected Galaxies in the IRAS 2 Jy Sample[END_REF] spanning over five orders of magnitude [START_REF] Price | New results on the radio-far-infrared relation for galaxies[END_REF]. This correlation can be used to segregate radio-loud AGNs from SFGs: the presence of an AGN may cause an excess of radio compared to IR luminosity. We compared our derived q F IR values with the relationship found by [START_REF] Magnelli | The far-infrared/radio correlation and radio spectral index of galaxies in the SFR-M * plane up to z˜2[END_REF], who studied the FRC across four extragalactic fields (GOODS-N, GOODS-S, ECDFS, and COSMOS). This study, shows an evolution of q F IR with redshift, with an increase in relative radio contribution as redshift increases:

q F IR = (2.35 ± 0.08) × (1 + z) α M (8.23)
with α M = -0.12 ± 0.04

On the other hand, this relationship does not evolve significantly with the offset from the main sequence [START_REF] Magnelli | The far-infrared/radio correlation and radio spectral index of galaxies in the SFR-M * plane up to z˜2[END_REF]. Due to the larger number of sources in common with our catalogs in the 3 GHz radio image than in the 6 GHz image (26 compared to 17), and because no source present at 6GHz is missing from the 3 GHz image, we have chosen the 3 GHz radio image to calculate our radio luminosities. The average ratio q F IR,3GHz /q F IR,6GHz for the 17 galaxies present in the two radio images is 1.02±0.06, where the uncertainty corresponds to the standard deviation.

In Fig. 8.5, we compare the q F IR of our galaxies with the relationship from [START_REF] Delhaize | The VLA-COSMOS 3 GHz Large Project: The infrared-radio correlation of star-forming galaxies and AGN to z ∼ 6[END_REF], as well as a local relationship [START_REF] Yun | Radio Properties of Infrared-selected Galaxies in the IRAS 2 Jy Sample[END_REF]). Among the 20 galaxies in the main catalog (F18), 15 are detected (S/N > 4.5) at 10 cm. Of the five that are not detected, three correspond to the galaxies that we have classified as spurious in F18 and that we have not analyzed in this thesis. More interestingly, the other two galaxies, not detected in radio and not classified as spurious, are HST-dark galaxies (AGS11 and AGS15), supporting the hypothesis that this population of galaxies is particularly distant. While the redshift of AGS11 has been estimated at z AGS11 = 4.8, making it the most distant galaxy of the blindly detected galaxies, the redshift of AGS15 could not be estimated. The strong negative K-correction applied to the Rayleigh-Jeans tail of the galaxy's SED keeps the observed millimeter flux constant over a wide range of redshifts (2 < z < 10; Blain et al. 2002). However, this correction applies less significantly to the radio continuum emission.

In the prior-based catalog, the proportion of galaxies detected by both ALMA and VLA is less significant, with only 11/17 (65%) having a detection with the VLA (SN > 3).

Overall, galaxies appear to follow the relationship defined by [START_REF] Magnelli | The far-infrared/radio correlation and radio spectral index of galaxies in the SFR-M * plane up to z˜2[END_REF]. Of the 24 galaxies for which we have both IR luminosity and robust VLA detections, only five galaxies are significantly offset from this relationship (q f ir > 2σ lower than the [START_REF] Magnelli | The far-infrared/radio correlation and radio spectral index of galaxies in the SFR-M * plane up to z˜2[END_REF] relation at a given redshift). Of these five galaxies, four have an X-ray detection > 10 43 erg.sec -1 and are classified as AGN in this study. A single galaxy, (AGS9) has a particularly low value of q F IR without an X-ray detection and is an excellent candidate to be a radio-loud AGN. Among the galaxies with a particularly low q F IR , we note that the largest difference with the relationship of [START_REF] Magnelli | The far-infrared/radio correlation and radio spectral index of galaxies in the SFR-M * plane up to z˜2[END_REF] is for the two galaxies in our sample that have a low redshift (z =0.66 and 1.10). These galaxies are very compact galaxies in the observed H-band (r e = 0.65 and 0.57 kpc respectively). They are the two galaxies that are below the size-mass relationship of the passive UVJ galaxies in Fig. 8.9, and have typical quasar characteristics.

On the other hand, and more interestingly, some galaxies lie above this trend. The majority of these outliers also host an AGN (AGS3, AGS4, AGS5, green stars in Fig. 8.5). These galaxies have particularly high star formation rates (SFR > 1000 M yr-1). We will discuss the relevance of classifying these galaxies as AGNs in this section.

8.3

The slow downfall of star-formation in z = 2-3 massive galaxies

Large fraction of our sample with low gas fractions

In this survey, we have detected particularly massive galaxies, the majority of which are beyond the cosmic noon at z ∼1-2. The study of the gas mass reservoirs is essential to understand how the galaxies will evolve with redshift and whether these galaxies could be the progenitors of passive galaxies at z ∼ 2. To obtain the most robust results possible, we have considered in the following section only galaxies with a Herschel counterpart. These are the galaxies marked by † in Table 8.2. In Fig. 8.6 (left panel), we compare the gas fraction of our galaxies as a function of their deviation from the MS, with the relationship presented in [START_REF] Tacconi | PHIBSS: Unified Scaling Relations of Gas Depletion Time and Molecular Gas Fractions[END_REF]: (8.24) In the same way, we compare the depletion time with the relationship presented in [START_REF] Tacconi | PHIBSS: Unified Scaling Relations of Gas Depletion Time and Molecular Gas Fractions[END_REF]: The dispersion is obtained by Monte-Carlo simulations. In order to compare the gas fractions of all of the galaxies in our sample, we have rescaled our gas fractions according to the median redshift and the stellar mass of our sample.

M gas /M * = 0.66 +0.22 -23 × R 0.53 SB .
τ dep = 322 +43 -38 × R -0.44 SB [M yr]. ( 8
We have rescaled this relationship to correspond to the median redshift (z med = 2.69) and the median stellar mass of our sample (M * ,med = 8.23 × 10 10 M ). To be able to directly compare the gas fraction of our galaxies to the relationship of [START_REF] Tacconi | PHIBSS: Unified Scaling Relations of Gas Depletion Time and Molecular Gas Fractions[END_REF], we have also scaled our gas fractions according to the median redshift and stellar mass of our sample. The gas fractions, before rescaling, are presented in Table 8.2.

The depletion times span a large range, between 20 and 600 Myr. The galaxies studied here show dependence between depletion time and distance to the main sequence, although very scattered.

About half of the GOODS-ALMA galaxies follow the f gas -R SB relation from (Tacconi et al. 2018, Eq. 20). However, we find a surprisingly large fraction (47%) of galaxies lying well below this relation, i.e., with excessively short depletion times. Interestingly, this fraction is not correlated with the starburstiness R SB , as defined by the distance to the MS. The galaxies with the shortest depletion times are also those with the lowest gas fraction. This is because despite exhibiting lower gas messes, these galaxies keep forming stars with a high SFR.

We note that all the ALMA galaxies experiencing a strong AGN episode with L X > 10 43 erg.sec -1 lie below the τ dep -R SB relation and f gas . This suggests that the low gas content and associated short depletion time of the galaxies may be due to the offset of the AGN feedback heating the surrounding extragalactic medium and preventing further the infall of gas. In other words, about half of the galaxies at these flux densities and redshift appear to suffer from starvation and constitute excellent candidate progenitors of z = 2 elliptical galaxies. To further investigate this possibility, we show in Sect.8.3.2 that the ALMA sizes, i.e., where the stars are formed, are consistent with the compact cores of z = 2 elliptical galaxies.

Although there is a trend between the R SB and the stellar mass of the galaxies, in that the less massive galaxies in our sample have a larger average R SB . We also investigate the evolution of depletion time as a function of the stellar mass. We found no correlation. This means that the star-formation efficiency (SFE = M gas /SFR = 1/τ dep ) does not change according to the mass of the galaxy. Galaxies transform their gas into stars at a rate independent of the stellar mass of the galaxy.

The gas fractions cover a significant range of values, between 0.2 and 0.9, with a median of 0.43 (mean = 0.48). We can see in Fig. 8.6 (left panel) that approximately half of the galaxies for which we have gas measurements are on the relationship of [START_REF] Tacconi | PHIBSS: Unified Scaling Relations of Gas Depletion Time and Molecular Gas Fractions[END_REF], taking into account the uncertainties on the gas measurement, and half of our sample are below. For galaxies below the relationship, we can see that this difference is even more pronounced when the galaxy is close to the main sequence.

These values are consistent with other studies, such as Wiklind et al. (2014). We do, however remark that for the two common galaxies between this work and Wiklind et al. (2014), there is a significant difference in the calculated gas fraction. These two common galaxies are outliers from the rest of the Wiklind et al. (2014) sample as they have gas fractions close to unity, and in fact, correspond to two HST-dark galaxies that were previously falsely attributed with optical counterparts. Interestingly, we see that a number of our galaxies are deficient in gas compared to the average population. We note that a significant number of these outliers are classified as AGN.

We note that a significant number of the outliers with low gas fraction are classified as AGN. We note that the presence of an AGN can influence the measurement of the stellar mass of the galaxy and artificially lower the calculated gas fraction of the galaxies. One of these galaxies has a low gas fraction (14%) and does not show any sign of an AGN. This galaxy is a particularly striking example of interacting galaxies, with strong tidal tails. This galaxy does not have a high star formation rate, it lies on the MS, but it does display a starburst-like behavior since it exhibits a short gas depletion time. This galaxy could, therefore, be a member of the population of galaxies described in Elbaz et al. (2018), a starburst galaxy hidden in the main sequence.

We find a negative correlation between the stellar mass and the gas fraction (see Fig. 8.7, right panel). The following equation characterizes this relationship:

f gas = (-0.55 ± 0.07) × log 10 (M * ) + 6.58 ± 0.78 (8.26)

A similar relationship has been found in other studies (e.g. [START_REF] Popping | An indirect measurement of gas evolution in galaxies at 0.5 < z < 2.0[END_REF][START_REF] Magdis | The Evolving Interstellar Medium of Star-forming Galaxies since z = 2 as Probed by Their Infrared Spectral Energy Distributions[END_REF][START_REF] Sargent | Regularity Underlying Complexity: A Redshift-independent Description of the Continuous Variation of Galaxy-scale Molecular Gas Properties in the Massstar Formation Rate Plane[END_REF][START_REF] Schinnerer | Gas Fraction and Depletion Time of Massive Star-forming Galaxies at z ˜3.2: No Change in Global Star Formation Process out to[END_REF]. Those galaxies hosting an AGN do not seem to occupy a particular position in Fig. 8.7. We also indicate in the left panel the distance to the main sequence as a function of the stellar mass. We can also see a clear negative correlation between the stellar mass and R SB . On the other hand, it is not possible to say whether selection effects are driving this trend. To be detected, a galaxy of low mass must have a larger R SB than a massive galaxy. On the other hand, we do not find massive galaxies (M * > 10 11 M with R SB > 6).

We also considered the evolution of depletion time as a function of the stellar mass. We found no correlation. This means that the star-formation efficiency (SFE = M gas /SFR = 1/τ dep ) does not change according to the mass of the galaxy. Galaxies transform their gas into stars at a rate independent of the stellar mass of the galaxy.

Galaxies with the lowest gas fractions and shortest depletion times also appear to be the most massive suggesting that are witnessing a slow downfall of the galaxies with the most massive galaxies dropping the first ones from forming stars to becoming elliptical galaxies, in a similar way to what had been shown ?.

Towards a reduction in the size of galaxies

Size

Several studies have reported the observation of massive star-forming galaxies, compact in the H-band (e.g., blue nuggets; Dekel and Burkert 2014). It has been proposed that these galaxies are the progenitors of massive, compact and passive galaxies at z = 2 (e.g., Barro et al., 2013;Williams et al., 2014;[START_REF] Toft | Submillimeter Galaxies as Progenitors of Compact Quiescent Galaxies[END_REF]van der Wel et al., 2014;Barro et al., 2016;Kocevski et al., 2017).

We have, thanks to the GOODS-ALMA survey, selected a sample of massive star-forming galaxies. These galaxies are among the most massive among the UVJ active galaxies (Williams et al. 2009, using the same definition as in F18) listed in the ZFOURGE catalog (see Fig. 12 in Franco et al., in prep). For example, with ALMA we have detected the most massive ZFOURGE galaxy in the redshift range 1 < z < 2, the most massive galaxy at 2 < z < 3, the second most massive galaxy at 3 < z < 4 and finally the most massive galaxy in the redshift range 4 < z < 5 (this galaxy is extremely faint in UV, so the determination of the mass may suffer from significant uncertainties). These galaxies cannot continue to form stars for long periods. If this were the case, they would become much more massive than the most massive galaxies we have observed at z = 1, or in the local universe.

These galaxies have not been selected as compact galaxies in the H-band. They are flux-selected. Due to the low dispersion of the main sequence, this selection is equivalent to a mass selection.

The compact H-band galaxies studied at z ∼ 2-3 have been proposed to be the progenitors of passive galaxies that are known to be compact at z ∼ 2.

We aim to study here whether galaxies that have not been selected to be compact in the H-band can also be the progenitors of compact galaxies at z = 2. To do this, we have compared the H-band sizes of the galaxies detected by ALMA with the H-band sizes of the galaxies present in Chapter 8. The slow downfall of star-formation in z = 2-3 massive galaxies

The majority of the galaxies studied in this thesis have a redshift between 2 and 4. We report in Fig. 8.9, left panel, H-band sizes of all galaxies with 2 < z < 4 located in the area defined by the GOODS-ALMA survey, as a function of stellar mass, in blue. We also show the H-band size of the ALMA-detected galaxies with black open markers. Galaxy sizes and Sérsic indices are obtained from van der Wel et al. ( 2014). These values have been computed by fitting a single-component Sérsic profile using GALFIT Peng et al. (2010), at both 1.4 and 1.6 µm. We focus here on the results at 1.6 µm. We also show the trends for the UVJ active and UVJ passive galaxies with blue and red lines respectively. These two relations were parametrized by van der Wel et al. ( 2014) following:

r eff = A (M * /5 × 10 10 )/1.7 α (8.27)
where R eff is the effective radius, in other words, the semi-major axis of the ellipse that contains half of the total flux of the best-fitting Sérsic model, in kpc. We use the following parameters: log 10 (A) = -0.06 ± 0.03, α = 0.79 0.07, and σlog 10 (R eff ) = 0.14 ± 0.03 for the early-type galaxies and log 10 (A) = 0.51 ± 0.01, α = 0.18 ± 0.02, and σlog 10 (R eff ) = 0.19 ± 0.01. for the late-type galaxies. We see that there is a significant difference in size between active and quiescent galaxies. The size of quiescent galaxies is on average larger than passive galaxies. Mosleh et al.

(2011) noted, for example, that the UV-bright galaxies with 10 10 < M < 10 11 and 0.5 < z < 3.5 are larger than quiescent galaxies in the same mass and redshift range by a factor 0.45 ± 0.09 dex.

For the vast majority of the ALMA detected galaxies (open black squares), the optical rest-frame sizes of these galaxies are comparable to the sizes of the H-band selected UVJ active galaxies (blue hexagons). We also over-plot, in Fig. 8.9, the compactness criterion given in Barro et al. (2013) and modified by Barro et al. (2016): 10.4 M kpc -1.5 (8.28)

M * r 1.5 e ≥ 10
Only three GOODS-ALMA galaxies are compact following the compactness criterion. These galaxies lie on the trend for quiescent galaxies. We note that those galaxies that do not follow the trend of star-forming galaxies systematically host an AGN. These galaxies, whose sizes are comparable with those of quenched galaxies, are galaxies that have already begun their quenching process. With the data available to us, it is not possible to distinguish between whether the compaction of the galaxy has triggered the AGN or, on the contrary, it is the presence of the AGN that has caused its compaction.

We also show the ALMA 1.1mm sizes in comparison to the H-band sizes in Fig. 8.9, right panel. The ALMA sizes for the main and supplementary catalogs are given in Franco et al., in prep. The size distribution differs slightly between the two samples. We showed in F18 that we were biased towards compact sources with our detection limit of 4.8σ. By lowering this detection threshold in the supplementary catalog, made possible as a result of basing our detections on priors, we are now detecting galaxies with larger sizes. For the 26 galaxies for which we have both HST H-band sizes and could measure the size with ALMA, we find that ALMA sizes are generally smaller, with a median FWHM HST /FWHM ALMA = 1.35. This ratio is in good agreement with that found by Fujimoto et al. (2017), who find a ratio of 1.4 between the H-band size and the size from ALMA at 870 µm, for a sample of 1034 ALMA sources. This value is also in good agreement with the studies of 2014). The density of the UVJ active galaxies (with 2 < z < 4) in the GOODS-ALMA field is represented by the blue hexagons.

The blue and red lines represent the trends of active and passive galaxies respectively, while the dashed lines give the scatter on these relations. The ALMA-detected galaxies are shown with black squares and the AGNs are marked with blue stars. Right panel: ALM A size-mass plane for the ALMA detected galaxies. For comparison, the trends for active and passive galaxies are also shown. We indicate the compactness criterion described in Eq. 8.28 to visualize which galaxies are compact in H-band.

of dust-obscured star formation, this result indicates compact dust-obscured star formation (at least more compact than optical emission) in the core of the galaxies studied here.

For these galaxies to be the progenitors of compact elliptical galaxies at z 2, they need to become more compact than their H-band size. The observed strong star formation activity concentrated in a small region of the galaxy can morphologically transform a galaxy into a more compact galaxy. Assuming that there is no addition of gas, the majority of these galaxies have gas reservoirs equal to or close to their stellar mass. If this gas is transformed into stars in the compact region of the emission detected by ALMA, these galaxies will become compact and gradually migrate into the location of the mass-size diagram reserved for passive galaxies.

In order for these galaxies to be the progenitors of compact elliptical galaxies at z = 2, they must also increase the surface brightness at their centers. Indeed, for the population of active UVJ galaxies contained in the region of our survey and measured in van der Wel et al. ( 2014), the average Sérsic index (<n active >) = 1.35. The average index for passive galaxies is (<n passive >) = 2.63, and can reach 4 [START_REF] Toft | Submillimeter Galaxies as Progenitors of Compact Quiescent Galaxies[END_REF]. For our galaxies we find <n AGS > = 1.08.

Our resolution and depth are not sufficient to derive a Sérsic index for the dust emission. However, we note that Hodge et al. (2016) and Elbaz et al. (2018) derived Sérsic indices from ALMA emission close to 1, implying that the dust emission is disk-like. This scenario of increasing the surface brightness in the centers of galaxies is compatible with strong star formation activity in the heart of the galaxy, as suggested by the small size of dust emission measured at 1.1mm.

Morphology

We here aim to look at the mechanisms that may have driven the gas in the center if the ALMA galaxies. This may be violent disc instabilities [START_REF] Dekel | Wet disc contraction to galactic blue nuggets and quenching to red nuggets[END_REF], or other dissipative processes, including mergers [START_REF] Wellons | The formation of massive, compact galaxies at z = 2 in the Illustris simulation[END_REF]. To investigate the role of mergers in the compaction process, we now investigate the morphology of the ALMA-detected galaxies.

Increasing numbers of observations have demonstrated that elliptical galaxies at z = 2 are particularly compact (e.g. [START_REF] Trujillo | The Size Evolution of Galaxies since z˜3: Combining SDSS, GEMS, and FIRES[END_REF][START_REF] Van Dokkum | Confirmation of the Remarkable Compactness of Massive Quiescent Galaxies at z ˜2.3: Early-Type Galaxies Did not Form in a Simple Monolithic Collapse[END_REF][START_REF] Conselice | The Evolution of Galaxy Structure Over Cosmic Time[END_REF]van der Wel et al., 2014). Major merger events can give rise to elliptical galaxies (e.g. [START_REF] Dekel | The dissipative merger progenitors of elliptical galaxies[END_REF][START_REF] Hopkins | A Unified, Merger-driven Model of the Origin of Starbursts, Quasars, the Cosmic X-Ray Background, Supermassive Black Holes, and Galaxy Spheroids[END_REF], but can also influence the compactness of the star-formation in galaxies (e.g. [START_REF] Wuyts | On Sizes, Kinematics, M/L Gradients, and Light Profiles of Massive Compact Galaxies at z ˜2[END_REF][START_REF] Ceverino | Early formation of massive, compact, spheroidal galaxies with classical profiles by violent disc instability or mergers[END_REF]. Due to their large stellar mass, which has generated and retained a large amount of metals, hence dust, against outflows (e.g. [START_REF] Dekel | The origin of dwarf galaxies, cold dark matter, and biased galaxy formation[END_REF][START_REF] Dekel | Feedback and the fundamental line of low-luminosity low-surfacebrightness/dwarf galaxies[END_REF][START_REF] Tremonti | The Origin of the Mass-Metallicity Relation: Insights from 53,000 Star-forming Galaxies in the Sloan Digital Sky Survey[END_REF], the galaxies detected in this study are extremely dust-obscured. In addition to this, their redshift makes them particularly faint in UV and optical filters. Some of them are Y -dropout (e.g., AGS5, AGS18), V -dropouts (e.g., AGS9, AGS10) or visible only in the K-band (AGS4, AGS11, etc.). The morphology of these galaxies is therefore difficult to obtain, and catalogs such as that of Huertas As a result, 61% (11/18) of our galaxies are classified as irregulars/mergers (two galaxies do not fit into any of the categories presented above). If we also take into account irregular disks, 78% (14/18) have an irregular morphology. Several galaxies show clear morphological characteristics of mergers, for example with large tidal tails. The galaxy AGS31 ,which exhibits large tidal tails, is an excellent illustration of this (see Fig. 6.14). For other galaxies, the interaction with another galaxy is more discrete or uncertain.

We compared these proportions against a control sample. We have for each one of the 18 galaxies for which we were able to determine a morphology from the Huertas-Company et al. (2015a) catalog, a galaxy closest to it in terms of redshift and stellar mass. This control sample exhibits significantly different morphological proportions. Only 6% (1/18) of these galaxies can be classified as irregulars/mergers, 22% (4/18) if we take into account irregular disks. The galaxy population detected by ALMA, therefore, tends to be on average biased towards irregular galaxies. By more precisely considering the morphological classification, we obtain in the sample galaxies detected by ALMA, on average f sph = 0.16, f disk = 0.50, f irr = 0.34 while for the control sample f sph = 0.40, f disk = 0.53, f irr = 0.07. While the disc fraction is relatively constant between these two samples, we are witnessing an inversion of the fraction between the irregulars and the spheroids.

We are therefore in the presence of a heterogeneous population of both secularly evolving disk and merger-type galaxies. This result is slightly higher with that found by models [START_REF] Hayward | What Does a Submillimeter Galaxy Selection Actually Select? The Dependence of Submillimeter Flux Density on Star Formation Rate and Dust Mass[END_REF][START_REF] Hayward | Submillimetre galaxies in a hierarchical universe: number counts, redshift distribution and implications for the IMF[END_REF], which predict that for a population of SMGs with S 1.1mm > 0.5 mJy, starforming galaxy-pairs account for ∼30-50 percent of the galaxies.

IR surface brightness as a prior for the remaining life-time of a galaxy

The role of compact star-formation in enhancing the efficiency of star-formation is illustrated in Fig. 8.10. Galaxies forming stars with the largest star-formation surface density, Σ SF R , experience the strongest star-formation episodes with the shortest depletion times.

The SFR surface density (Σ SF R ) can be defined as:

Σ SF R = SFR/(2πR 2 1.1mm ) (8.29)
where R 1.1mm the effective radius (see Sect. 8.3.2 for a description of the determination of the millimeter size).

We have found a strong negative correlation between Σ SF R and depletion time (see Fig. 8.10).

A similar trend was found in Elbaz et al. (2018). This correlation can be characterized by the following equation:

τ dep [M yr] = 1006 +584 -403 × Σ (-0.57±0.13) SF R . (8.30) 10 0 10 1 10 2 10 3 Σ SF R [M yr -1 kpc -2 ]

Conclusions

We have taken advantage of the excellent multiwavelength supporting data in the GOODS-South field and the largest contiguous ALMA survey to derive the physical properties of 33 ALMA fluxselected galaxies. This sample of galaxies comes both from purely blind detections (galaxies with a peak flux > 4.8 σ, see F18) and from an extension of this catalog that we have built down to the 3.5 σ limit using IRAC priors to probe fainter millimeter galaxies (see Chapter 6). These galaxies are massive (M ,med = 8.5 × 10 10 M ) and therefore rare, so in order to be able to detect and analyze them, a sufficiently large survey, such as GOODS-ALMA was needed. It is possible for the first time with this survey, covering ∼69 arcmin 2 . The analysis of the SEDs of these galaxies has made it possible to derive some of the physical properties of these galaxies. We are confronted with a heterogeneous population of galaxies. However, we highlight that about 50% of our galaxy sample exhibits a particularly small gas fraction. We remark that the most massive galaxies in our sample are also the galaxies with the lowest gas fractions. With their high star formation rates (the galaxies are mostly starbursts, or on the upper part of the main sequence) and without a gas refill mechanism, they will consume their gas reservoirs in a typical time of 100 Myr.

We also studied the sizes of these galaxies. The advantage of conducting a blind survey is that it does not impose a priori criteria for selecting the galaxies studied. The ALMA detected galaxies have observed H-band sizes comparable to the majority of galaxies with the same masses and redshifts, whereas their dust emission regions, i.e., the regions tracing the obscured part of the star formation, are relatively compact and have sizes comparable to passive galaxies at z ∼ 2.

We have investigated the link between depletion time and star formation surface density. We confirm the result showing a tight correlation between these two quantities. The denser the galaxy star-forming region is, the shorter the gas depletion time is. Mechanisms leading to a compaction of the obscured star-forming regions are to be confirmed, but a compact region massively forming stars at the center of a galaxy can lead to a rapid morphological transition from a spiral to a compact elliptical galaxy such as those observed at z ∼ 2, despite the fact that the ALMA selected galaxies are not yet compact in the H-band (they are not yet blue nuggets).

All of these different pieces of evidence indicate that our ALMA-detected galaxies are the ideal progenitors of passive galaxies at z ∼ 2 and a natural exhaustion of their gas reservoirs (slow downfall) is sufficient for this transition to happen quickly without needed to invoke a quenching mechanism. The large fraction of AGN among galaxies with the shortest depletion times and gas fractions suggest however that they may act by a starvation mechanism in preventing any further growth. 8.11: Optical to radio Spectral Energy Distributions created using the CIGALE code, for the main catalog galaxies. The UV and optical photometry is from the ZFOURGE catalog, the infrared measurements come from the Herschel catalog. The radio data at 5 cm is from Rujopakarn et al. (2016). The green (dark blue) lines fit the attenuated (unattenuated) stellar emission. The brown lines fit the dust emission and the purple fits the radio emission. The black is the sum of all emission components. The blue line shows the MBB fit. The lower panel shows the residuals between the observations and the model. CHAPTER 9 CONCLUSION My Ph.D. has focused on the study of galaxy infrared emission from the largest ALMA survey in the GOODS-South field. ALMA allows us to overcome the confusion limit that is present with the Herschel Space telescope, to reach greater redshifts while having an unprecedented resolution in this wavelength range. These observations are crucial to constrain the star formation history at high redshift, as they provide an unbiased view of star formation after the cosmic noon.

ALMA has been used mostly to observe previously known galaxies with individual pointings.

Here we perform a different mode of operation by observing an entire region of the sky, in order to have an unbiased view of this region and to shed new light on these galaxies and their properties. This is not the first blind survey carried out with ALMA, but it is currently the largest in thems of area.

One of the potentially transformational outputs of ALMA is its ability to reveal a new class of galaxies through serendipitous detections. This is also one of the main reasons for performing blind extragalactic surveys. Less efficient than pointed observations using pre-defined priors, blind surveys can provide a complete view on this new parameter space, specific to ALMA.

My thesis was divided into three main steps: the creation of a source catalog, the study of galaxy counts and the determination and analysis of galaxy properties.

Catalog creation

In the first part this manuscript we explained the motivations of submillimeter observations, the challenges and of the state of the art in the field, outlined the history of the deep fields in astronomy and in particular explained the genesis of the GOODS-South field, and why it was selected to be observed with the large interferometer ALMA. We also presented our survey design and the data reduction, as well as the combination of the six slices of our survey to create an homogeneous image. Although the native resolution of the survey was 0.2", we note that 0.2" was not the requested resolution. We decided to work almost exclusively in a map tapered at 0.6" to reduce the number of independent beams and thus reduce the number of purely statistical spurious detections, and also prevent the resolution of extended sources.

We analyzed the image to define detectability thresholds and indicators that could quantify the reliability of these detections. After comparing the performance of different source extraction tools, we created a catalog of 23 sources. We also attempted to estimate the size of the galaxies in order to verify whether or not they were resolved, and therefore whether the peak flux was a good estimator of the total flux or if, on the contrary, it was necessary to integrate this flux.

The average rms sensitivity of the 0 60-mosaic is σ 0.18 mJy.beam -1 (but varies within the six slices of the survey), and the 1.1mm flux densities of the galaxies range from 0.64 to 2 mJy. The 178 Chapter 9. Conclusion detection limit was set to S/N ≥ 4.8 due to the large number of independent beams that leads to spurious detections that become rapidly more numerous than the number of robust detections below this threshold, despite the tapering at 0 60. Despite this high detection threshold, we identified three sources that we considered to be spurious detections (indicated by an * in Table 4.2). Finding 3 spurious detections out of 23 detections matches the expected number of spurious sources obtained from the difference between positive and negative peaks above the 4.8 σ level (4±2). These three sources are the only ALMA detections we find without any sign of an IRAC counterpart at λ = 3.6 or 4.5 µm (Spitzer/IRAC channels 1 and 2), despite the ultra-deep IRAC data in this field (26.5 AB mag, Ashby et al. 2015).

The galaxies detected by ALMA are among the most massive galaxies present in the GOODS-ALMA field of view. All detected galaxies have a stellar mass M > 5 × 10 10 M . The median stellar mass of our catalog is M = (1.1±0.4) × 10 11 M .

We are pushing the blind detection of massive galaxies with ALMA further in redshift. The sources exhibit flux densities ranging from 0.6 to 2 mJy, and have a median redshift of z = 2.92±0.20. By comparison with deeper but smaller ALMA extragalactic surveys (Aravena et al. 2016;Dunlop et al. 2017;González-López et al. 2017;Ueda et al. 2018), our redshift distribution is shifted to higher values even though our survey is shallower. This is due to the low surface density of massive, metal-rich (and hence dust-rich) galaxies at high redshift. We show that the size of the ALMA survey is, therefore, a key parameter to detect high redshift galaxies.

Number counts

Due to the limited number of detections and uncertainties on the redshifts, it was not possible to derive luminosity functions. We have therefore carried out counts whose calculation depends only on the flux of galaxies (and detailed insight of the biases related to the image).

The derived differential and cumulative number counts of our 20 primary detections have allowed us to partly alleviate the degeneracy observed above 1 mJy.beam -1 in previous (sub)millimeter studies. However, we note that due to our low detection rate, our uncertainties on the number counts are relatively high.

This work allowed us to derive the number counts at 1.1 mm using our survey and the main surveys carried out at (sub)-millimeter wavelengths. We modelled them with both a Schechter function and a double power law. We note that the faint-end of the number counts was done using a cluster, taking advantage of lensing. Fujimoto et al. (2016) reached sources down to ∼ 0.02 mJy with an ALMA survey at 1.2mm. Semi-analytical models such as Popping et al. in prep., coupling the UniverseMachine Behroozi et al. (2019) with empirical and theoretical relations on the dust emission, are in good agreement with the trends found for galaxies with fluxes of > 0.1 mJy but present flattening for lower fluxes. This may mean that the faint-end of the number counts over small and lensed regions may not be extrapolated to all number counts.

The number counts show that ∼15% of the extragalactic background light at 1.1mm is resolved into discrete sources at 0.75 mJy. By extrapolation, ∼50% of the EBL is resolved at 0.1 mJy.

HST-dark galaxies

The recent discovery of a population of galaxies previously undetected by the Hubble Space Telescope (e.g., Wang et al., 2016;Elbaz et al., 2018;[START_REF] Schreiber | Near infrared spectroscopy and star-formation histories of 3 ≤ z ≤ 4 quiescent galaxies[END_REF]Franco et al., 2018;Yamaguchi et al., 2019a;Williams et al., 2019), has improved our understanding of the origin and formation of massive galaxies. These galaxies comprise 20% of the galaxies detected in GOODS-ALMA. Although these galaxies are undetected by the HST (at 5σ limiting depth H=28 AB at 1.6 µm), they are detectable through their thermal dust emission thanks to the depth and capabilities of ALMA. We were recently able to detect an HST-dark galaxy using data from only 8 ALMA pointings (Elbaz et al., 2018). This serendipitously-detected HST-dark galaxy suggests a blind detection rate of 1 galaxy per 8 pointings, similar to the 20% of HST-dark galaxies found among the galaxies detected by ALMA in Franco et al. (2018).

Among the 6 HST-dark galaxies for which we were able to determine masses and redshifts, there appear to be two distinct trends. Galaxies AGS4 and AGS24 are among the most massive of all active uvj galaxies detected in the region covered by the ALMA survey. AGS4 has a mass M * = 2.81 +1. 65 -1.03 ×10 11 . In other words, it is the most massive galaxy at 4 < z < 5 in our catalogs. AGS24 has a stellar mass M * = 1.82 +0.27 -0.50 ×10 11 . Two HST-dark galaxies are at intermediate mass, but with a redshift greater than 4.5 (see Fig. 6.12) and for the two remaining galaxies, neither the mass nor the redshift have been estimated for the moment.

We have only a relatively poor statistic on these HST-dark galaxies, but they appear to be clustered. Several of these galaxies (AGS11, AGS15, AGS17, and AGS24) may be at the same redshift, z,∼,3.5. The position of one of these galaxies, AGS24 at the center of the overdensity, as well as its mass, make this galaxy a candidate of a future bright cluster galaxy (BCG) or central dominant (cD) galaxy (Zhou et al., in prep). Several additional observations will be necessary to characterize this structure, and we successfully proposed for ALMA observation time (project ID: 2018.1.01079.S; PI: M. Franco). We have received the first results, and the analysis of these data will be done in the coming months.

These HST-dark galaxies do not appear to be a marginal population of galaxies when considering massive, star-forming galaxies at high redshift. A recent study that systematically analyzed HSTdark galaxies [START_REF] Wang | A dominant population of optically invisible massive galaxies in the early Universe[END_REF] shows that the contribution of HST-dark galaxies to the SFRD appears to be dominant for galaxies with log 10 (M * ) > 10.6 [START_REF] Wang | A dominant population of optically invisible massive galaxies in the early Universe[END_REF].

Using IRAC priors to probe fainter millimeter galaxies

We presented a new method for finding sources, involving lowering the detection limit. This method, based on previous detections in Spitzer/IRAC channel 1 (complemented by HST/WFC3 H-band data and an ultradeep K s -band image) made it possible to lower the search threshold from 4.8 to 3.5 σ. These detections were reinforced, a posteriori, by a statistical study of the distribution of all detections at 3.5σ in our image as well as a control sample. This method gives rise to the detection of 16 supplementary sources. The range of S/N for these sources is 3.6-4.6σ. We also note the presence of two low redshift sources at z < 1, which were not present in F18. The sources presented in this catalog are generally less compact than the sources presented in F18.

We have presented a detailed review of astrometry in the GOODS-South field. In addition to a systematic offset between HST and ALMA (∆α = -96±92 mas and ∆δ = 253±107 mas), we highlight the presence of a local offset, which can reach 0.15" at the edge of the GOODS-ALMA field.

Galaxy properties

Using multiwavelength coverage from the CANDELS program, we derived properties of galaxies detected with ALMA in the GOODS-ALMA field. We explored some of the main parameters driving the star-formation in these galaxies.

After verifying that the galaxies detected by ALMA were not biased towards galaxies with abnormally cold dust (which would have favored their detection), we took advantage of both the new Herschel deblended catalog to derived L IR as well as the L U V by modelling the SEDs of the galaxies. This allowed us to derive the star formation rates of the galaxies. We find that the majority of the galaxies detected have an infrared luminosity ≥ 10 12 L . The majority are starburst galaxies, with a star formation rate greater than 3 times that of the main sequence. The remaining galaxies populate the upper part of the main sequence.

We showed that we are confronted to a heterogeneous population of galaxies, with a significant part of this sample having an abnormally low gas fraction. We see a link between the fraction of gas and the stellar mass of the galaxies. The more massive a galaxy is, the smaller its gas fraction will be.

We have also studied the sizes of galaxies. Unlike other studies that selected the galaxies to be observed with ALMA to be particularly compact in H-band, and linked these galaxies (blue nuggets) to compact and passive galaxies, we have shown that the galaxies in our sample have standard H-band sizes (they follow the trend defined by van der Wel et al. 2014), while they are more compact in ALMA. The ALMA sizes are, for the most part, comparable with the sizes of passive galaxies with the same mass and redshift. Moreover, we have seen that the most massive galaxies in our sample are also the most compact. We confirmed that there is a link between the depletion time (τ dep = M gas /SFR) and the star formation rate (Σ SF R ). This demonstrates that the more compact the star-forming region is, the more efficient the galaxy will be in transforming its gas into stars and the shorter its lifetime (in the absence of replenishment) will be. Looking at the X-ray emission of the galaxies, we found that galaxies with strong X-emission (L X >10 43 erg.sec -1 ) i.e., which most probably host an AGN, are also the most compact galaxies, both in H and with ALMA, and also have the lowest τ dep . All of the conditions are met for these galaxies to be the progenitors of passive galaxies at z ∼ 2. At the same time, their masses are already comparable to the masses typical of passive galaxies. Their high star formation rates can not be sustained over a long period, or the galaxies would reach stellar masses that we have never observed for galaxies at z=3. Their concentrated star formation is also consistent with a morphological transformation of galaxies, with an increase in the Sérsic index due to increasing the surface brightness at their centers. The questions that now arise are which mechanisms concentrate the gas towards the centre of the galaxies and cause their death, to understand whether this can be explained by hydrodynamic instabilities, to explain more clearly the role of mergers and the environment in this compaction mechanism, to investigate the role of AGN at the end of a galaxy's life by better understanding positive and negative feedback from AGN, and their role in preventing the replenishment of galaxies, as well as studying other scenarios that make galaxies more compact.

CHAPTER 10

PERSPECTIVES

Contents

The work of this thesis opens many perspectives. In this thesis, we have presented the results of a survey carried out with ALMA with a native resolution of 0.24". This resolution was not the resolution originally requested (1"), which forced us to adapt our methodology by using techniques such as tapering. Tapering effectively enlarges the size of the beam, which allows us both to reduce the number of independent beams, thus reducing the number of purely statistical spurious detections, and also prevent the resolution of extended sources. Unfortunately, tapering also degrades the sensitivity of the observations.

In the last months of the thesis, the data from the same survey were delivered at the originally requested evolution. In this section, we will present the work we can carry out with this new map, how we can combine it with the high resolution image, and combine it with the different ALMA surveys done in the GOODS-South field. We will also see how we can use both of our resolutions to infer the properties of galaxies, and then present two projects. The first is to resolve the dust emission in a clumpy galaxy, and the second is to carry out a complete census in mass in the GOODS-ALMA field. Finally, we will briefly discuss the opportunities that will be offered in the coming years with the new generation of instruments (including the James Webb Space Telescope; JWST) and explain how our work can help prepare for these new fields of exploration.

Lower resolution image

We have recently received data from the same region of the sky as presented in this thesis, but at the originally requested, lower resolution (∼ 1.2"). In the rest of this chapter, we will call this image the "low-resolution" image, while the term "high-resolution image" refers to the image we analyzed in this Ph.D.

We have combined the high-resolution and low-resolution images to increase the sensitivity of the image. The theoretical rms of the combination of several images is obtained using the following formula:

σ 2 = 1 σ 2 -1/2 (10.1)
The low-resolution map has a beam varying from 1.2" to 1.5", depending on the slice. To take full advantage of the potential of these two maps, we have tapered them in order to have a circularized beam corresponding to the lowest resolution, i.e., 1.5". To analyze this data in the image plane as well as possible, we have cleaned the data using the task tclean of CASA, with natural weighting and a cell size of 0.2". We also produced a noise map using the same technique explained in Sect. 3.6 (sigma-clipping). The result of the combination the high and low resolution data is shown in Fig. 10.1. We can see that the difference between the distributions allows us to detect approximately three times more sources, and lowers the detection threshold before the number of negative sources rises drastically.

To get an initial idea of the number of detectable sources in this new image, we compared the detection numbers as a function of the threshold, in both the image and the inverse image (continuum map multiplied by -1). The purity index of 80% is reached at σ p = 4.4 with 57 positive detections against 11 negative ones. In Fig. 10.2, we show the histogram of the two distributions (positive and negative detections) that we put in perspective with the source distribution found in the low-resolution map (0.6").

In addition, high-and low-resolution maps can be used separately to probe the distribution of dust within the galaxy, and also to more easily constrain galaxy sizes.

The analysis of galaxies that have been missed in the high-resolution survey but detected in the low-resolution survey will also give us information both on the bias of our survey, and also on the evolution of the sizes of galaxies with redshift. It will give us information on the proportion of compact galaxies among massive galaxies and will give us a finer insight into the relationships between galaxy size, depletion time, the presence of an AGN and the gas fraction of galaxies. These maps, separated into both low and high resolution, will also allow in some cases to understand better the offset that can exist between the IR emission and the UV emission of galaxies.

Combined GOODS-South ALMA surveys

In addition, we have combined the different ALMA surveys that have been carried out in the GOODS-South field to create the deepest possible ALMA image of this region (see Fig. 10. 4 and Fig. 10.3). The image is comprised of 2494 pointings, combining the HUDF (Dunlop et al., 2017), ASAGAO (Hatsukade et al., 2018) and GOODS-ALMA (this work) surveys. This deep image can be used to further develop the analyses presented in this thesis, and in particular to calculate the star formation rate density based on the infrared emission of galaxies, and better constrain the evolution of the SFRD to redshifts greater than 3.

To conclude, the study of IR emission with ALMA of high redshift galaxies has motivated us to investigate two different directions using opposite methods. One is a systematic method to investigate all galaxies within 2 < z < 6 with a stellar mass above M * >5× 10 10 M . We want to avoid selection bias and have a complete picture of this category of galaxy. The second direction is to focus on a single galaxy located at z ∼ 2.8 that is partially extended and clumpy, so that the obscured star formation inside the clump of this high redshift galaxy can be analyzed in detail, and the dust distribution can be investigated. It is these two projects that we will present in this last part of this thesis.

Resolving the dust emission in a clumpy galaxy

During the exploration of the largest extragalactic blind survey with ALMA in the Great Observatories Origins Deep Survey-South (GOODS-South) field (2017.1.00755.S; PI: D. Elbaz); we detected and partially resolved the ALMA emission of one particularly extended and clumpy galaxy in the continuum at 1.13mm. We see that the clump emission is extended, as we have a significantly stronger detection when we integrate over the elongated clump region, compared when we consider the clumps as individual sources. The overarching question is now whether the clumps are physically associated, or if there is simply diffuse emission present between them.

If there is indeed a physical association between the IR clumps and the UV clumps, this would be the first detection of a galaxy where the majority of the dust-attenuated star formation (and therefore the total SFR) is coming from the clumps. This would mean that a significant part of the mass of galaxies could be generated in clumps, thus contributing to the growth of the galactic bulge without requiring major mergers.

Clumpy galaxies are prominent in the early Universe (z > 2; Förster [START_REF] Schreiber | SINFONI Integral Field Spectroscopy of z ˜2 UV-selected Galaxies: Rotation Curves and Dynamical Evolution[END_REF][START_REF] Elmegreen | Clumpy Galaxies in the Early Universe[END_REF]) and the clumpy structures are present for all galaxy types [START_REF] Elmegreen | Bulge and Clump Evolution in Hubble Ultra Deep Field Clump Clusters, Chains and Spiral Galaxies[END_REF]. One of the questions that arise is whether there is a spatial correlation between UV clumps and gas reservoirs. Although the definition of clumps is still uncertain, the typical stellar mass (M * ) of clumps is between 10 8 until 10 9 M (e.g., [START_REF] Elmegreen | Clumpy Galaxies in the Early Universe[END_REF]Guo et al., 2012, FIGURE 10.4: Primary beam coverage of the combined GOODS-ALMA, ASAGAO and HUDF-ALMA maps.

2015), and with typical sizes from few 100pc to 1kpc (e.g., [START_REF] Elmegreen | Clumpy Galaxies in the Early Universe[END_REF][START_REF] Livermore | Hubble Space Telescope Hα imaging of star-forming galaxies at z ∼ 1-1.5: evolution in the size and luminosity of giant H II regions[END_REF]. Clumps can represent between 20 and 50% of the total star formation rate (SFR) of the galaxy (e.g., Förster [START_REF] Schreiber | Constraints on the Assembly and Dynamics of Galaxies. II. Properties of Kiloparsec-scale Clumps in Rest-frame Optical Emission of z ˜2 Star-forming Galaxies[END_REF]. The study of clumps is essential to understand the evolution of galaxies, the bulge formation, star formation mechanisms, and the growth of the supermassive black hole. Until now, the vast majority of clump studies were carried out at UV wavelengths (e.g., Förster [START_REF] Schreiber | Constraints on the Assembly and Dynamics of Galaxies. II. Properties of Kiloparsec-scale Clumps in Rest-frame Optical Emission of z ˜2 Star-forming Galaxies[END_REF][START_REF] Guo | Multiwavelength View of Kiloparsec-scale Clumps in Star-forming Galaxies at z ˜2[END_REF]). ALMA's sensitivity and resolution now make it possible to explore sub-galactic scales in the (sub)millimeter wavelengths. This new space of observation parameters reveals contradictory results to previous studies. While [START_REF] Iono | Clumpy and Extended Starbursts in the Brightest Unlensed Submillimeter Galaxies[END_REF], [START_REF] Oteo | ALMACAL II: Extreme Star Formation Rate Densities in Dusty Starbursts Revealed by ALMA 20 mas Resolution Imaging[END_REF] or [START_REF] Hodge | ALMA Reveals Potential Evidence for Spiral Arms, Bars, and Rings in High-redshift Submillimeter Galaxies[END_REF] show evidence that a part of dust emission (∼2-20% of the total continuum emission in [START_REF] Hodge | ALMA Reveals Potential Evidence for Spiral Arms, Bars, and Rings in High-redshift Submillimeter Galaxies[END_REF]) comes from clump-like structures, others such as [START_REF] Gullberg | The Dust and [C II] Morphologies of Redshift ∼ 4.5 Sub-millimeter Galaxies at ∼ 200 pc Resolution: The Absence of Large Clumps in the Interstellar Medium at High-redshift[END_REF] or [START_REF] Rujopakarn | ALMA 200-parsec Resolution Imaging of Smooth Cold Dusty Disks in Typical z ∼ 3 Star-Forming Galaxies[END_REF] find a remarkably smooth distribution of cold dust emission within of a galaxy. Recently, [START_REF] Cibinel | ALMA constraints on star-forming gas in a prototypical z = 1.5 clumpy galaxy: the dearth of CO(5-4) emission from UV-bright clumps[END_REF] showed for a galaxy at z = 1.5 that the CO emission was undetectable down to the 3% level from the UV-bright clumps. We propose to use ALMA to probe the rest-frame emission at ∼240 µm of a particularly extended (diameter of 3" in H-band) and extremely clumpy galaxy. We want to use the accuracy of the ALMA observations to map the dust emission of this galaxy and quantify the infrared luminosity, the gas content (M gas ) and the star formation efficiency (SFE = SFR/M gas ) of the clumpy regions compared to the non-clumpy regions of the galaxy.

A galaxy at z=2.81 that may be forming the bulk of its stars in well-separated clumps

This galaxy is an ideal observational laboratory to study clumps. Indeed this galaxy is unusually large -its diameter, derived from a Hubble Space Telescope (HST)-WFC3 image at 1.6µm, was estimated to be ∼3", corresponding to a physical size of ∼25 kpc at z= 2.81. The clumps are distant from one another, which excludes any blending (see Fig. 10.6).

This galaxy has a redshift (z spec = 2.81) that is ideal to understand the crucial phase of the bulge formation. In addition, this galaxy presents no AGN contamination from the 7 Ms Source Catalogs (Chandra Deep Field-South Survey; Luo et al. 2017). This means that the star formation rate derived from infrared luminosity is most likely reliable.

This galaxy is located in the deepest part of the CANDELS field, and therefore benefits from excellent multiwavelength support. A first analysis shows that the 5 major clumps of this galaxy have different colors and therefore different dust obscurations. Indeed we can divide these clumps into two categories: the two southernmost clumps of the images are brighter in UV and redder than those present in the northern part. By studying this galaxy, and only one galaxy, we have the opportunity to analyze several types of clump. For 4 of these 5 clumps, redshifts and masses have been determined. Two of these redshifts have been confirmed by the instrument VIMOS as part of the VLT/VIMOS spectroscopy in the GOODS-South field [START_REF] Balestra | The Great Observatories Origins Deep Survey[END_REF], at z = 2.808 and z = 2.815 respectively. The photometric redshifts of the other two clumps are compatible with these measurements, at z = 2.94 and z = 2.93. Finally, neither the redshift nor the mass of the easternmost clump was determined. In addition, in the northern part, we also see two extra blobs, which are either a projection effect (redshifts have been measured at 0.041 and 0.036 respectively), or these redshifts are incorrect, and the two blobs are also part of the structure. Observation with ALMA will give us decisive information to distinguish between these two hypotheses.

The majority of galaxies studied with ALMA at high redshift to reveal clumps have been particularly massive galaxies (M * > 10 11 M ; e.g., [START_REF] Hodge | ALMA Reveals Potential Evidence for Spiral Arms, Bars, and Rings in High-redshift Submillimeter Galaxies[END_REF]) or lensed (e.g., the Cosmic Snake; [START_REF] Cava | Structural and dynamical modeling of WINGS clusters. I. The distribution of cluster galaxies of different morphological classes within regular and irregular clusters[END_REF]. The galaxy targeted here, with a smaller mass (M * = 3.6 × 10 10 M ; Chabrier 2003 IMF) will allow us to shed new light on less extreme galaxies.

In addition to a first estimation of the flux, thanks to SED fitting (uncertain due to uncertainties on the data near the peak of the SED at ∼ 300 µm (observed-frame); see right panel of Fig. 10.6),

we have also been able to estimate the integrated flux from a new mosaic of the GOODS-ALMA field, observed with a resolution of 1"2 imaging over 6.9' ×10' (2017.1.00755.S, PI: D. Elbaz).

0.5" [START_REF] Noll | Analysis of galaxy spectral energy distributions from far-UV to far-IR with CIGALE: studying a SINGS test sample[END_REF] and the photometry from the ZFOURGE catalog (Straatman et al., 2016).

Thanks to this object with ideal properties to study the clumps of galaxies, we plan to compare the number of UV clumps to the number of IR clumps. We would also like to derive the percentage of IR luminosity (and therefore the SFR) that comes from clumpy regions in comparison to the total infrared luminosity of the galaxy. We will also be able to determine the mass of dust and therefore the mass of gas. We will then calculate the proportion of gas inside these clumps and compare to simulations (see Fig. 10.7 and Fig. 10.8). FIGURE 10.7: From left to right: Mock observation of three different galaxies of different compactness seen at z=2.81 and with a 0.25" beam. The mock image represents the gas density of the galaxies, realized without any dust emission or absorption, and a face-on view of the galaxy. From left to right: Compact, less compact and intermediate compactness. The galaxies were simulated with the RAMSES hydrodynamical simulation code [START_REF] Teyssier | Cosmological hydrodynamics with adaptive mesh refinement. A new high resolution code called RAMSES[END_REF]. Each box is 20kpc wide. The black contours represent the clumps found by a clump finder algorithm.

We would also like to derive spatially resolved UV (β) from the HST images and compare the slope of β to the different IR emission regions. We plan to map the excess IR emission in the galaxy and compare it to existing studies (e.g., [START_REF] Gómez-Guijarro | Starburst to Quiescent from HST/ALMA: Stars and Dust Unveil Minor Mergers in Submillimeter Galaxies at z ∼ 4.5[END_REF] and models (e.g., [START_REF] Meurer | Dust Absorption and the Ultraviolet Luminosity Density at z ˜3 as Calibrated by Local Starburst Galaxies[END_REF]. We plan to quantify the star formation efficiency (SFE = SFR/M gas ) for each clump and compare it to other non-clumpy regions of the galaxy, and measure how the star formation rate within clumps deviates from the Schmidt-Kennicutt relation [START_REF] Zanella | An extremely young massive clump forming by gravitational collapse in a primordial galaxy[END_REF]. Simulations predict different signatures and clump shapes seen by ALMA, depending on the formation scenario of the galaxy. If the clumps are made of cold gas, a hierarchical formation of clumps will take place, i.e. the small clumps will gradually grow and form larger clumps in size (e.g., [START_REF] Bournaud | Rapid Formation of Exponential Disks and Bulges at High Redshift from the Dynamical Evolution of Clump-Cluster and Chain Galaxies[END_REF][START_REF] Inoue | Nonlinear violent disc instability with high Toomre's Q in high-redshift clumpy disc galaxies[END_REF]. On the other hand, if clumps are formed from hot gas, the opposite scenario is preferred -large structures will fragment and form small clumps. ALMA's resolution is sufficient to favor one hypothesis over another.

Complete census in mass

We propose to reach a complete census on the dusty star formation rate (SFR) of all galaxies within 2 < z < 6 with a stellar mass above M * > 5 × 10 10 M (red and green dots in Fig. 10.9) in the GOODS-ALMA field. This individual source follow-up will complement the existing ALMA detections that were obtained from the largest extragalactic blind survey covering the deepest part of the CANDELS field (HST-WFC3), in the Great Observatories Origins Deep Survey-South (GOODS-South) field over 6.9'×10' (GOODS-ALMA, 2015.1.00543.S, PI: D. Elbaz, Franco et al. 2018), as well as all existing pointings in the field available in the ALMA archives. All starforming galaxies in this mass and redshift range were predicted to exhibit flux densities above the 4-σ survey limit and yet only 13 % of them were detected. This survey is the largest ALMA survey and was obtained with two angular resolutions 0.2" (Cycle 3) and 1.2" (Cycle 5). The analysis of the high-angular resolution survey identified massive star-forming galaxies preferentially located in the redshift range z = 2 -4 with a few galaxies at z>4 (Franco et al., 2018). Among the population of galaxies with M * > 5×10 10 M -where the sensitivity limit of our survey allows us to detect typical SFR-M * main sequence galaxies at z = 2-4 -we found that only 13% of them were detected even after selecting only the star-forming ones from the UVJ color-color diagram to disentangle passive and star-forming galaxies. We found that nearly all of the detected galaxies experienced extremely compact star-formation. In order to determine whether this was a physical property systematically found in this mass and redshift range, or whether it was related to selection effects (despite tapering at 0.6 arcsec), we analyzed the lowresolution survey of the same area at 1.2". Thanks to the reduced number of independent beams, we were able to detect sources down to 1.7 times fainter flux limit, and surprisingly most of the newly detected ALMA sources fall below the mass limit of 5×10 10 M showing that the missing sources were not missed because they were extended. This suggests that compactness truly is a universal property of the massive star-forming galaxies at these redshifts and that the dispersion of SFR in this mass and epoch range is larger than expected by the extrapolation of the SFR-M* main sequence. In order to test this hypothesis with strong implications on our understanding of Dec (J2000) FIGURE 10.9: Left panel: Selection of the galaxies with M * > 5 × 10 10 M and 2 < z < 6. The black dots represent all of the galaxies in the GOODS-ALMA field. The green dots represent the selected galaxies in the mass and redshift range given above, while the red dots show the galaxies that have already been observed by ALMA (e.g., Aravena et al., 2016;Dunlop et al., 2017;Franco et al., 2018;Cowie et al., 2018;Hatsukade et al., 2018) and all the archive data.

Right panel: Spatial position of the GOODS-ALMA survey (solid black line) and of the galaxies, with the same color-coding than the left panel. The black solid line indicates the boundaries of the GOODS-ALMA survey.

the formation of massive ellipticals, we now need to reach a complete census on this parameter space area.

The majority of the galaxies detected in GOODS-ALMA are compact -∼85% have a size below 0.25", corresponding to a physical radius of 600 pc at z = 3 (Franco et al., 2018) suggesting these massive dusty star-forming galaxies could participate to the origin of the massive elliptical galaxies at z = 2, which are also known to be compact. The analysis of the sizes of the galaxies detected in GOODS-ALMA are in agreement with the results of other recent studies (e.g. [START_REF] Simpson | The SCUBA-2 Cosmology Legacy Survey: ALMA Resolves the Bright-end of the Sub-millimeter Number Counts[END_REF]Barro et al., 2016;Rujopakarn et al., 2016;Ikarashi et al., 2017;Fujimoto et al., 2017;Tadaki et al., 2017;Elbaz et al., 2018).

This complete census of star-formation in massive high-z galaxies will allow us to determine the rise of cosmic SFR density during the rise to cosmic noon (z∼2), quantify the relative amount of obscured star-formation above z>3 where it is mostly unknown in a complete way, reach a large enough statistical sample to disentangle rapid quenching from slow downfall of star-formation in massive galaxies. The systematic study of massive galaxies (M > 5 × 10 10 M ) during this period of rapid transition between star-forming and quenched galaxies [START_REF] Muzzin | The Evolution of the Stellar Mass Functions of Star-forming and Quiescent Galaxies to z = 4 from the COSMOS/UltraVISTA Survey[END_REF] is crucial to understanding the mechanism by which star formation ceases in these galaxies. We note that the need for such a wide area survey with ALMA is fundamental as demonstrated by the fact that the HUDF-ALMA survey (Dunlop et al., 2017) was highly inefficient in detecting distant galaxies most probably because the dusty distant galaxies need to be massive to be dusty, in order to maintain their metals from their deep potential well.

The fact that the majority of the missing galaxies with M * > 5 × 10 10 M remain undetected even at the 3σ level with the 1.2" resolution suggests that either these galaxies are not as dusty as expected, hence that only a small fraction of the massive galaxies have the expected dust mass, or that they are forming stars with a SFR much below the MS despite being UVJ active.

In both cases, this would change in a major way our understanding of star-formation in massive galaxies at z=2-4. This is the key epoch of the transition to cosmic noon from the higherredshift side, and of the formation of the massive ellipticals that end up being largely found compact at z∼2. Hence it is truly important to understand whether there is a variety of such galaxies or whether, as suggested by the SFR-M * sequence, there is a universal star-formation process in galaxies of a given mass and redshift range. It turns out that we found (papers in prep.) that the majority of the ALMA sources detected in this regime of mass and redshift were highly clustered, could this mean that the missing detections belong to galaxies less or more clustered. The most massive ALMA detection at z=3.5, AGS24, is an HST-dark source that we found to be located at the very center of an over-density of galaxies at z=3.5. This galaxy forms stars below the main sequence. The missing massive galaxies could also be those that experienced galaxy harassment, ram pressure stripping, and lost part of their gas reservoirs, in denser environments. They would then be useful tracers of high-density regions in the field. It may also be possible that at these masses and redshifts there is a high proportion of galaxies falling down from the MS, more than expected from the traditional 0.3 dex dispersion. This may be related to the building of what is often called the bending of the MS, in which galaxies at high masses exhibit lower SFR than the extrapolation of the MS slope. If we were able to show that there is a large dispersion of the SFR of galaxies in this mass and redshift range, much wider than expected by the MS, this would allow us to provide a statistical determination of the rapidity with which massive galaxies quench to become ellipticals. The timescale for this passage is fundamental to disentangle various models of massive galaxy formation such as compaction (e.g., [START_REF] Dekel | Wet disc contraction to galactic blue nuggets and quenching to red nuggets[END_REF][START_REF] Tacchella | Evidence for mature bulges and an inside-out quenching phase 3 billion years after the Big Bang[END_REF]Barro et al., 2017), major mergers versus minor mergers [START_REF] Gómez-Guijarro | Starburst to Quiescent from HST/ALMA: Stars and Dust Unveil Minor Mergers in Submillimeter Galaxies at z ∼ 4.5[END_REF], shock heating of the IGM [START_REF] Dekel | The dissipative merger progenitors of elliptical galaxies[END_REF] or simply consumption of the internal gas reservoirs (and preventing further infall by eg AGN activity, cf Peng et al. 2010;[START_REF] Maiolino | A supernova origin for dust in a high-redshift quasar[END_REF]) by quantifying the relative fraction of massive galaxies in the process of secular downfall of star-formation versus rapid quenching through the number density of galaxies in the SFR-M * plan. This will allow us in the process to determine in a complete manner the cosmic SFR density of M * > 5 × 10 10 M galaxies at z=2-4 including galaxies that were HST-dark, found by our two surveys and that could not be followed-up from prior selection techniques. Starting from a systematic blind survey is critical in this analysis.

Preparing the next generation of survey

Several large (sub)millimeter surveys are planned or are currently being observed. For example, the NIKA2 camera at the 30m IRAM telescope is observing the GOODS-South field (160 arcmin 2 ) and the COSMOS field (2000 arcmin 2 ) for 300h, at two different wavelengths (λ = 1mm and λ = 2mm). This is the "NIKA2 Cosmological Legacy Survey" (PIs: A.Beelen, G.Lagache & N.Ponthieu). Also, in the same way, the Large Millimeter Telescope (LMT), which is optimized for astronomical observations at millimeter wavelengths, has seen its diameter increase to 50m. This instrument is adapted, thanks to its observations mode, to carry out large surveys quickly. A Guaranteed Time Large Program was chosen to observe three of the CANDELS fields: UDS, COSMOS, and GOODS-South.

In the near future, the James Webb Space Telescope will be launched. The population of optically dark galaxies, missed by the HST, will be particularly interesting targets for the first JWST observations. Indeed, one of the objectives of the JWST is to reach more distant and fainter galaxies, including the epoch of reionization. The knowledge gained from the identification of galaxy counterparts and the identification of HST-dark sources in this study can be used to characterize the galaxies in the Extended Groth Strip (EGS), or those in the fields given above. EGS is at the heart of the Cosmic Evolution Early Release Science (CEERS) project, which is an Early Release Science (ERS) project of the James Webb Space Telescope (JWST). The JWST NIRCam 10.5. Preparing the next generation of survey 191 instrument will perform a mosaic of 10 pointings covering the majority (∼100 arcmin 2 ) of the EGS field. Over this region, we expect to find at least 10 HST-dark galaxies.

If other candidates of optically dark galaxies are discovered to be the central dominant galaxy in galaxy (proto-)clusters, this discovery may also change our understanding of these objects, especially in terms of the distribution of the mass within clusters, and the interactions between galaxies. One of the most uncertain and potentially transformational outputs of ALMA is its ability to reveal a new class of galaxies through serendipitous detections. This is also one of the main reasons for performing blind extragalactic surveys which can provide a complete view on this new parameter space, specific to ALMA. The present proposal targets a systematic identification of serendipitously found HST-dark galaxies in the GOODS-ALMA field to obtain or confirm spectroscopic redshifts from their CO lines. With their ultra-faint optical properties, this is the only way to determine whether there is really a 20% population of new, highly obscured galaxies in the distant Universe or whether these galaxies are actually nearby galaxies or regions of their neighbors but with abnormally low dust temperatures. With this proposal of 10h, we will (i) determine or confirm the redshifts of these sources, (ii) derive their molecular gas content, (iii) deduce their star formation efficiency. We will determine if these galaxies are observed during a starburst phase, determine whether they possess abnormally large molecular gas reservoirs and compare their CO conversion factor to that of.

No

Scientific justification

One of the most uncertain and potentially transformational outputs of ALMA is its ability to reveal a new class of galaxies through serendipitous detections. This is also one of the main reasons for performing blind extragalactic surveys. Blind surveys can provide a complete view on this new parameter space, specific to ALMA.

This proposal comes as a result of the observation by ALMA of the deepest part of the CANDELS field (HST -WFC3), in the Great Observatories Origins Deep Survey-South (GOODS-South) field, imaging over 6.9'×10' (2015.1.00543.S, PI: D. Elbaz). Thanks to the availability of very deep, panchromatic photometry at rest-frame UV, optical and NIR in this field, which also includes among the deepest available X-ray and radio maps, precise multi-wavelength analysis incorporating this crucial FIR data has been possible (Franco et al, 2018). This unbiased study, without prior selection, has allowed us to realize a flux limited census at 1.1 mm of all the galaxies present in the field.

A key outcome of this study was the uncovering of a population of candidates for high redshift (3 < z < 5) galaxies, too faint to be detected in the deepest HST -WFC3 images of the GOODS-South field, but detectable through their thermal dust emission thanks to the capabilities of ALMA. In total, 20% (4/20) of the sources detected in this survey are optically 'dark' galaxies, and strong evidence suggests that they are not spurious detections (Franco et al. 2018). This discovery, if confirmed, could significantly change our understanding of massive galaxy formation. The inferred redshifts of these galaxies place them at the "rising phase" of the cosmic star formation history, before the peak. This has important implications for understanding whether the apparently lower star formation rate densities at z >> 2, inferred mainly from UV rest-frame data, may be in part due to HST nondetection of a population of very dusty galaxies. This new population of galaxies, undetected by the HST but revealed by ALMA, has been reported in several recent papers (e.g. Wang et al. 2016, Fujimoto et al. 2016, Elbaz et al. 2018, Franco et al. 2018). These galaxies are ultra-faint at optical wavelengths, apparently very distant (z > 4 for the two galaxies for which photometric redshifts have been estimated) and highly obscured. New ALMA observations, and in particular spectral line observations, are therefore needed in order to further characterize and understand these galaxies. Currently, we have only continuum data at 265 GHz for these galaxies. ALMA is the only instrument able to reach the depths required to extract the spectra of these galaxies.

With these observations, we will (i) determine or confirm the redshifts of the HST -dark sources using a spectral scan for expected CO transitions, (ii) derive the galaxies' molecular gas contents, (iii) deduce their star formation efficiencies, SFE=SFR/Mgas. We will compare the molecular gas content derived from these proposed CO observations to the total gas mass derived from the galaxies' dust continuum, using our previous data. We can therefore investigate whether the HST -dark nature of these galaxies has an effect on other physical galaxy properties, such as the H 2 -to-CO conversion factor and gas-to-dust ratio, and explore what this tells us about the underlying nature of the galaxies.

This will allow us to reach the missing properties of galaxies undetected by the HST and to have a complete and precise view of all the galaxies, above the detection limit (0.8 mJy at 1.1 mm) in the GOODS-ALMA field.

These observations will allow us to answer the following questions:

• Are these HST -dark galaxies a distinct galaxy population, with characteristics (such as SFE, gas fraction...) distinguishable from those of the classical Star Forming Galaxy population?

• Could physical mechanisms other than dust obscuration be making these galaxies optically dark?

To answer these questions, we propose to study 6 galaxies unveiled by our ALMA continuum observations, which we briefly introduce the global properties of these galaxies in the following 1 section.

A hidden population of distant and massive galaxies

Although these 6 galaxies do not at first seem homogeneous, some common properties emerge from this sample of galaxies. Of these 6 galaxies, 5 were discovered during the ALMA-GOODS blind survey (4 are described in detail in Franco et al. 2018, the 5th in Franco et al. in preparation, andthe sixth (described in Elbaz et al. 2018) was present in the ALMA field of view as part of a follow-up of 8 z∼2 ULIRGs (PI R.Leiton, ALMA Cycle 1).

Secure identification : The presence of an ALMA detection alone does not make these galaxies HST-dark, it is the presence of a several pieces if concordant evidence that strongly indicate hat there is a galaxy at the position of the ALMA detection. Firstly, for all six galaxies, an IRAC detection is present within a radius of <0.2" from the ALMA position. The probability of having an ALMA detection at this distance from an IRAC source due to chance alone is <1%, giving a very strong argument to the credibility of these sources. In addition, for three of them (AGS4, AGS17 and AGS24), we detect a 1cm and 5cm flux at the position of the ALMA detection. As the radio part of the spectrum does not benefit from the strong negative K-correction, it is not unexpected that the radio fluxes are not present for the all of the most massive, distant galaxies. A population of apparently distant galaxies. For two of these HST-dark galaxies (GS8 and AGS4), which were located near the line of sight (0.3" and 0.4" respectively) of a galaxy detected in the optical, a redshift estimation has been determined . In Fig. 1, we clearly see that the ALMA emission is offset from the observed H-band galaxy, indicated by the white arrow. This offset could be explained physically, for example, as a region within the same galaxy extremely obscured by dust, greatly extinguishing the optical rest-frame emission revealed by ALMA. However, many things lead us to believe that they are two different galaxies, with the optical emission originating from the foreground and the infrared emission from the background. Without the high ALMA resolution of our survey, we would have falsely associated the two counterparts. In both cases, the peak of the far-IR emission obtained from the combination of Herschel and ALMA data was found between 350 and 400 µm, inconsistent with known SEDs for z = 1.616 (z = 0.3 respectively) galaxies. For GS8 and AGS4, the two sources (optical and submillimeter) were then fit simultaneously using these two light-profile models (using Galfit) on all of the available images, fixing the profile to that observed in the H band (see Fig. 2). In both cases, the redshifts found for the optical galaxies were coherent with previous values. As the Balmer break is well established in the K-band for the ALMA galaxy, we also consider the redshift determinations for the ALMA detections to be robust. We find the following redshifts: z GS8 = 3.24 ± 0.20 and z AGS4 = 4.32 +0.25 -0.21 . Additionally, for a third HST-dark galaxy, AGS11, despite the weak flux derived from several stacked images and the limited number of bands available, a redshift has been determined in the ZFOURGE catalogue (Straatman et al. 2016) at z = 4.82. This makes AGS11 the farthest galaxy detected in our blind survey (Franco et al. 2018). However, we remain cautious regarding this redshift. The top panels show the photometric redshift probability distributions for the two ALMA galaxies.

A population of apparently massive galaxies. The presence of an IRAC source for these galaxies not detected by the HST indicates a selection towards the most massive galaxies (Wang et al. 2015). ALMA also tends to preferentially detect the most massive galaxies (Franco et al. 2018). This is the third common property of these HST-dark galaxies: they are all very massive galaxies. The two galaxies presented in the previous section both have stellar masses greater than 10 11 M .

Description of observations

We propose to follow-up these six galaxies using band-4 spectral scan observations. As shown in Fig. 3, band-4 provides excellent line coverage from z=1 to z=5 (with a small gap between z=1.6 and z=2).

To estimate the necessary integration time, we base our calculations on the faintest of the six targeted galaxies (0.6 mJy at 1.1mm). Using a standard IR SED (Schreiber et al. 2018), we infer the total LIR from the ALMA 1.1mm flux, use the LIR -L CO relation (Daddi et al. 2015), and assume the typical SMG spectral line energy distributions from Bothwell et al. (2013) to infer the fluxes of the other CO lines. To optimize the overheads, we use the OT to select the smallest sensitivity for which the scan can be executed in a single SB in band 4. Using the position of the 1.1mm emission to extract the flux, reaching a S/N >5 for one line requires a 400 km.s -1 -averaged RMS of 0.20 mJy in band 4 for a time on source per pointing of less than 10 minutes for a total of 10.01h including calibration and overheads for the full proposal. The expected SNRs as a function of redshift are reported in Fig. 3. Recent claims have suggested that z∼4 galaxies become hard to detect in CO due to their reduced metal content (e.g. [START_REF] Tan | A Deep Search for Molecular Gas in Two Massive Lyman Break Galaxies at z = 3 and 4: Vanishing CO-emission Due to Low Metallicity[END_REF]. This is not an issue for our particular sample, because of the high attenuation which necessarily implies high metal abundances.

References:

Bothwell+13

Introduction

In the late 1990s a population of galaxies was discovered at submillimeter wavelengths using the Submillimeter Common-User Bolometer Array (SCUBA; Holland et al. 1999) on the James Clerk Maxwell Telescope (see e.g., Smail et al. 1997;Hughes et al. 1998;Barger et al. 1998;Blain et al. 2002). These "submillimeter galaxies" or SMGs are highly obscured by dust, typically located around z ∼ 2-2.5 (e.g., Chapman et al. 2003;Wardlow et al. 2011;Yun et al. 2012), massive (M > 7 × 10 10 M ; e.g., Chapman et al. 2005;Hainline et al. 2011;Simpson et al. 2014), gas-rich ( f gas > 50%; e.g., Daddi et al. 2010), with huge star formation rates (SFR) -often greater than 100 M yr -1 (e.g., Magnelli et al. 2012;Swinbank et al. 2014) -making them significant contributors to the cosmic star formation (e.g., Casey et al. 2013), often driven by mergers (e.g., Tacconi et al. 2008;Narayanan et al. 2010) and often host an active galactic nucleus (AGN; e.g., Alexander et al. 2008;Pope et al. 2008;Wang et al. 2013). These SMGs are plausible progenitors of present-day massive early-type galaxies (e.g., Cimatti et al. 2008;[START_REF] Michałowski | [END_REF].

Recently, thanks to the advent of the Atacama Large Millimeter/submillimeter Array (ALMA) and its capabilities to perform both high-resolution and high-sensitivity observations, our view of SMGs has become increasingly refined. The high angular resolution compared to single-dish observations reduces drastically the uncertainties of source confusion and blending, and affords new opportunities for robust galaxy identification and flux measurement. The ALMA sensitivity allows for the detection of sources down to 0.1 mJy (e.g., Carniani et al. 2015), the analysis of populations of dust-poor high-z galaxies (Fujimoto et al. 2016) or main sequence (MS; Noeske et al. 2007;Rodighiero et al. 2011;Elbaz et al. 2011) galaxies (e.g., Papovich et al. 2016;Dunlop et al. 2017;Schreiber et al. 2017), and also demonstrates that the extragalactic background light (EBL) can be resolved partially or totally by faint galaxies (S < 1 mJy; e.g., Hatsukade et al. 2013;Ono et al. 2014;Carniani et al. 2015;Fujimoto et al. 2016). Thanks to this new domain of sensitivity, ALMA is able to unveil less extreme objects, bridging the gap between massive starbursts and more normal galaxies: SMGs no longer stand apart from the general galaxy population.

However, many previous ALMA studies have been based on biased samples, with prior selection (pointing) or a posteriori selection (e.g., based on HST detections) of galaxies, or in a relatively limited region. In this study, we present an Article published by EDP Sciences A152, page 1 of 26 unbiased view of a large (69 arcmin 2 ) region of the sky, without prior or a posteriori selection based on already known galaxies, in order to improve our understanding of dust-obscured star formation and investigate the main properties of these objects.

We take advantage of one of the most uncertain and potentially transformational outputs of ALMA -its ability to reveal a new class of galaxies through serendipitous detections. This is one of the main reasons for performing blind extragalactic surveys.

Thanks to the availability of very deep, panchromatic photometry at rest-frame UV, optical and NIR in legacy fields such as great observatories origins deep survey-South (GOODS-South), which also includes among the deepest available X-ray and radio maps, precise multiwavelength analysis that include the crucial FIR region is now possible with ALMA. In particular, a population of high redshift (2 < z < 4) galaxies, too faint to be detected in the deepest HST-WFC3 images of the GOODS-South field has been revealed, thanks to the thermal dust emission seen by ALMA. Sources without an HST counterpart in the H-band, the reddest available (so-called HST-dark) have been previously found by color selection (e.g., Huang et al. 2011;Caputi et al. 2012Caputi et al. , 2015;;Wang et al. 2016), by serendipitous detection of line emitters (e.g., Ono et al. 2014) or in the continuum (e.g., Fujimoto et al. 2016). We will show that ∼20% of the sources detected in the survey described in this paper are HST-dark, and strong evidence suggests that they are not spurious detections.

The aim of the work presented in this paper is to exploit a 69 arcmin 2 ALMA image reaching a sensitivity of 0.18 mJy at a resolution of 0 60. We used the leverage of the excellent multiwavelength supporting data in the GOODS-South field: the cosmic assembly near-infrared deep extragalactic legacy survey (Koekemoer et al. 2011;Grogin et al. 2011), the Spitzer extended deep survey (Ashby et al. 2013), the GOODS-Herschel survey (Elbaz et al. 2011), the Chandra deep field-South (Luo et al. 2017) and ultra-deep radio imaging with the VLA (Rujopakarn et al. 2016), to construct a robust catalog and derive physical properties of ALMA-detected galaxies. The region covered by ALMA in this survey corresponds to the region with the deepest HST-WFC3 coverage, and has also been chosen for a guaranteed time observation (GTO) program with the James Webb Space Telescope (JWST).

This paper is organized as follows: in Sect. 2 we describe our ALMA survey, the data reduction, and the multiwavelength ancillary data which support our studies. In Sect. 3, we present the methodology and criteria used to detect sources, we also present the procedures used to compute the completeness and the fidelity of our flux measurements. In Sect. 4 we detail the different steps we conducted to construct a catalog of our detections. In Sect. 5 we estimate the differential and cumulative number counts from our detections. We compare these counts with other (sub)millimeter studies. In Sect. 6 we investigate some properties of our galaxies such as redshift and mass distributions. Other properties will be analyzed in Franco et al. (in prep.) and finally in Sect. 8, we summarize the main results of this study. Throughout this paper, we adopt a spatially flat ΛCDM cosmological model with H 0 = 70 kms -1 Mpc -1 , Ω m = 0.7 and Ω Λ = 0.3. We assume a Salpeter (Salpeter 1955) initial mass function (IMF). We used the conversion factor of M (Salpeter 1955, IMF) = 1.7 × M (Chabrier 2003, IMF). All magnitudes are quoted in the AB system (Oke & Gunn 1983).

ALMA GOODS-South survey data

Survey description

Our ALMA coverage extends over an effective area of 69 arcmin 2 within the GOODS-South field (Fig. 1), centered at α = 3 h 32 m 30.0 s , δ = -27 • 48 00 (J2000; 2015.1.00543.S; PI: D. Elbaz). To cover this ∼10 × 7 region (comoving scale of 15.1 Mpc × 10.5 Mpc at z = 2), we designed a 846-pointing mosaic, each pointing being separated by 0.8 times the antenna half power beam width (HPBW ∼ 23 3).

To accommodate such a large number of pointings within the ALMA Cycle 3 observing mode restrictions, we divided this mosaic into six parallel, slightly overlapping, submosaics of 141 pointing each. To get a homogeneous pattern over the 846 pointings, we computed the offsets between the submosaics so that they connected with each other without breaking the hexagonal pattern of the ALMA mosaics.

Each submosaic (or slice) had a length of 6.8 arcmin, a width of 1.5 arcmin and an inclination (PA) of 70 deg (see Fig. 1). This required three execution blocks (EBs), yielding a total on-source integration time of ∼60 s per pointing (Table 1). We determined that the highest frequencies of the band 6 were the optimal setup for a continuum survey and we thus set the ALMA correlator to Time Division Multiplexing (TDM) mode and optimized the setup for continuum detection at 264.9 GHz (λ = 1.13 mm) using four 1875 MHz-wide spectral windows centered at 255.9 GHz, 257.9 GHz, 271.9 GHz and 273.9 GHz, covering a total bandwidth of 7.5 GHz. The TDM mode has 128 channels per spectral window, providing us with ∼37 km s -1 velocity channels.

Observations were taken between the 1st of August and the 2nd of September 2016, using ∼40 antennae (see Table 1) in configuration C40-5 with a maximum baseline of ∼1500 m. J0334-4008 and J0348-2749 (VLBA calibrator and hence has a highly precise position) were systematically used as flux and phase calibrators, respectively. In 14 EBs, J0522-3627 was used as bandpass calibrator, while in the remaining 4 EBs J0238+1636 was used. Observations were taken under nominal weather conditions with a typical precipitable water vapor of ∼1 mm.

Data reduction

All EBs were calibrated with CASA (McMullin et al. 2007) using the scripts provided by the ALMA project. Calibrated visibilities were systematically inspected and few additional flaggings were added to the original calibration scripts. Flux calibrations were validated by verifying the accuracy of our phase and bandpass calibrator flux density estimations. Finally, to reduce computational time for the forthcoming continuum imaging, we time-and frequency-averaged our calibrated EBs over 120 s and 8 channels, respectively.

Imaging was done in CASA using the multifrequency synthesis algorithm implemented within the task CLEAN. Submosaics were produced separately and combined subsequently using a weighted mean based on their noise maps. As each submosaic was observed at different epochs and under different weather conditions, they exhibit different synthesized beams and sensitivities (Table 1). Submosaics were produced and primary beam corrected separately, to finally be combined using a weighted mean based on their noise maps. To obtain a relatively homogeneous and circular synthesized beam across our final mosaic, we applied different u, v tapers to each submosaic. The best balance between spatial resolution and sensitivity was found with a homogeneous and circular synthesized beam of 0 29 full A152, page 2 of 26 width half maximum (FWHM; hereafter 0 29-mosaic; Table 1). This resolution corresponds to the highest resolution for which a circular beam can be synthesized for the full mosaic. We also applied this tapering method to create a second mosaic with a homogeneous and circular synthesized beam of 0 60 FWHM (hereafter 0 60-mosaic; Table 1), in other words, optimized for the detection of extended sources. Mosaics with even coarser spatial resolution could not be created because of drastic sensitivity and synthesized beam shape degradations.

Due to the good coverage in the uv-plane (see Fig. 2) and the absence of very bright sources (the sources present in our image do not cover a large dynamic range in flux densities; see Sect. 4), we decided to work with the dirty map. This prevents introducing potential biases during the CLEAN process and we noticed that the noise in the clean map is not significantly different (<1%).

Building of the noise map

We built the rms-map of the ALMA survey by a k-σ clipping method. In steps of four pixels on the image map, the standard deviation was computed in a square of 100 × 100 pixels around the central pixel. The pixels, inside this box, with values greater than three times the standard deviation (σ) from the median value were masked. This procedure was repeated three times. Finally, we assigned the value of the standard deviation of the non-masked pixels to the central pixel. This box size corresponds to the smallest size for which the value of the median pixel of the rms map converges to the typical value of the noise in the ALMA map while taking into account the local variation of noise. The step of four pixels corresponds to a subsampling of the beam so, the noise should not vary significantly on this scale. The median value of the standard deviation is 0.176 mJy beam -1 . In comparison, the Gaussian fit of the unclipped map gave a standard deviation of 0.182 mJy beam -1 . We adopted a general value of rms sensitivity σ = 0.18 mJy beam -1 . The average values for the 0 29-mosaic and the untapered mosaic are given in Table 1.

Ancillary data

The area covered by this survey is ideally located, in that it profits from ancillary data from some of the deepest sky surveys at infrared (IR), optical and X-ray wavelengths. In this section, we describe all of the data that were used in the analysis of the ALMA detected sources in this paper.

Optical and near-infrared imaging

We have supporting data from the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS; Grogin et al. 2011) with images obtained with the wide field camera Notes. The slice ID, the date, the number of antennae, the time on target, the total time (time on target + calibration time), the resolution and the 1-σ noise of the slice are given. 3/Infrared Channel (WFC3/IR) and UVIS channel, along with the advanced camera for surveys (ACS; Koekemoer et al. 2011. The area covered by this survey lies in the deep region of the CANDELS program (central one-third of the field). The 5-σ detection depth for a point-source reaches a magnitude of 28.16 for the H 160 filter (measured within a fixed aperture of 0.17 Guo et al. 2013). The CANDELS/Deep program also provides images in seven other bands: the Y 125 , J 125 , B 435 , V 606 , i 775 , i 814 and z 850 filters, reaching 5-σ detection depths of 28.45, 28.35, 28.95, 29.35, 28.55, 28.84, and 28.77 mag respectively. The Guo et al. (2013) catalog also includes galaxy magnitudes from the VLT, taken in the U-band with VIMOS (Nonino et al. 2009), and in the K s -band with ISAAC (Retzlaff et al. 2010) and HAWK-I (Fontana et al. 2014).

In addition, we used data coming from the FourStar galaxy evolution survey (ZFOURGE, PI: I. Labbé) on the 6.5 m Magellan Baade telescope. The FourStar instrument (Persson et al. 2013) observed the CDFS (encompassing the GOODS-South field) through five near-IR medium-bandwidth filters (J 1 , J 2 , J 3 , H s , H l ) as well as broad-band K s . By combination of the FourStar observations in the K s -band and previous deep and ultra-deep surveys in the K-band, VLT/ISAAC/K (v2.0) from GOODS (Retzlaff et al. 2010), VLT/HAWK-I/K from HUGS (Fontana et al. 2014), CFHST/WIRCAM/K from TENIS (Hsieh et al. 2012) and Magellan/PANIC/K in HUDF (PI: I. Labbé), a super-deep detection image has been produced. The ZFOURGE catalog reaches a completeness greater than 80% to K s < 25.3-25.9 (Straatman et al. 2016).

We used the stellar masses and redshifts from the ZFOURGE catalog, except when spectroscopic redshifts were available. Stellar masses have been derived from Bruzual & Charlot (2003) models (Straatman et al. 2016) assuming exponentially declining star formation histories and a dust attenuation law as described by Calzetti et al. (2000).

Mid/far-infrared imaging

Data in the mid and far-IR are provided by the infrared array camera (IRAC; Fazio et al. 2004) at 3.6, 4.5, 5.8, and 8 µm, Spitzer multiband imaging photometer (MIPS; Rieke et al. 2004) at 24 µm, Herschel photodetector array camera and spectrometer (PACS; Poglitsch et al. 2010) at 70, 100 and 160 µm, and Herschel spectral and photometric imaging receiver (SPIRE; Griffin et al. 2010) at 250, 350, and 500 µm.

The IRAC observations in the GOODS-South field were taken in February 2004 and August 2004 by the GOODS Spitzer legacy project (PI: M. Dickinson). These data have been A152, page 4 of 26 supplemented by the Spitzer extended deep survey (SEDS; PI: G. Fazio) at 3.6 and 4.5 µm (Ashby et al. 2013) as well as the Spitzer-cosmic assembly near-infrared deep extragalactic survey (S-CANDELS; Ashby et al. 2015) and recently by the ultradeep IRAC imaging at 3.6 and 4.5 µm (Labbé et al. 2015).

The flux extraction and deblending in 24 µm imaging have been provided by Magnelli et al. (2009) to reach a depth of S 24 ∼ 30 µJy. Herschel images come from a 206.3 h GOODS-South observational program (Elbaz et al. 2011) and combined by Magnelli et al. (2013) with the PACS evolutionary probe (PEP) observations (Lutz et al. 2011). Because the SPIRE confusion limit is very high, we used the catalog of Wang et al. (in prep.), which is built with a state-of-the-art de-blending method using optimal prior sources positions from 24 µm and Herschel PACS detections.

Complementary ALMA data

As the GOODS-South field encompasses the Hubble Ultra Deep Field (HUDF), we took advantage of deep 1.3-mm ALMA data of the HUDF. The ALMA image of the full HUDF reaches a σ 1.3 mm = 35 µJy (Dunlop et al. 2017), over an area of 4.5 arcmin 2 that was observed using a 45-pointing mosaic at a tapered resolution of 0.7 . These observations were taken in two separate periods from July to September 2014. In this region, 16 galaxies were detected by Dunlop et al. (2017), three of them with a high S/N (S /N > 14), the other 13 with lower S/Ns (3.51 < S /N < 6.63).

Radio imaging

We also used radio imaging at 5 cm from the Karl G. Jansky Very Large Array (VLA). These data were observed during 2014 March-2015 September for a total of 177 h in the A, B, and C configurations (PI: W. Rujopakarn). The images have a 0 31 × 0 61 synthesized beam and an rms noise at the pointing center of 0.32 µJy beam -1 (Rujopakarn et al. 2016). Here, 179 galaxies were detected with a significance greater than 3σ over an area of 61 arcmin 2 around the HUDF field, with a rms sensitivity better than 1 µJy beam -1 . However, this radio survey does not cover the entire ALMA area presented in this paper.

X-ray

The Chandra deep field-South (CDF-S) was observed for 7 Msec between 2014 June and 2016 March. These observations cover a total area of 484.2 arcmin 2 , offset by just 32 from the center of our survey, in three X-ray bands: 0.5-7.0 keV, 0.5-2.0 keV, and 2-7 keV (Luo et al. 2017). The average flux limits over the central region are 1.9 × 10 -17 , 6.4 × 10 -18 , and 2.7 × 10 -17 erg cm -2 s -1 respectively. This survey enhances the previous X-ray catalogs in this field, the 4 Msec Chandra exposure (Xue et al. 2011) and the 3 Msec XMM-Newton exposure (Ranalli et al. 2013). We will use this X-ray catalog to identify candidate X-ray active galactic nuclei (AGN) among our ALMA detections.

Source detection

The search for faint sources in high-resolution images with moderate source densities faces a major limitation. At the native resolution (0 25 × 0 23), the untapered ALMA mosaic encompasses almost four million independent beams, where the beam area is A beam = π × FWHM 2 /(4ln( 2)). It results that a search for sources above a detection threshold of 4-σ would include as many as 130 spurious sources assuming a Gaussian statistics. Identifying the real sources from such catalog is not possible. In order to increase the detection quality to a level that ensures a purity greater than 80% -in other words, the excess of sources in the original mosaic needs to be five times greater than the number of detections in the mosaic multiplied by (-1) -we have decided to use a tapered image and adapt the detection threshold accordingly.

By reducing the weight of the signal originating from the most peripheral ALMA antennae, the tapering reduces the angular resolution hence the number of independent beams at the expense of collected light. The lower angular resolution presents the advantage of optimizing the sensitivity to point sources -we recall that 0 24 corresponds to a proper size of only 2 kpc at z ∼ 1-3 -and therefore will result in an enhancement of the signal-to-noise ratio (S/N) for the sources larger than the resolution.

We chose to taper the image with a homogeneous and circular synthesized beam of 0 60 FWHM -corresponding to a proper size of 5 kpc at z ∼ 1-3 -having tested various kernels and finding that this beam was optimized for our mosaic, avoiding both a beam degradation and a too heavy loss of sensitivity. This tapering reduces by nearly an order of magnitude the number of spurious sources expected at a 4-σ level down to about 19 out of 600 000 independent beams. However, we will check in a second step whether we may have missed in the process some compact sources by also analyzing the 0 29 tapered map.

We also excluded the edges of the mosaic, where the standard deviation is larger than 0.30 mJy beam -1 in the 0 60-mosaic. The effective area was thus reduced by 4.9% as compared to the full mosaic (69.46 arcmin 2 out of 72.83 arcmin 2 ).

To identify the galaxies present on the image, we used Blobcat (Hales et al. 2012). Blobcat is a source extraction software using a "flood fill" algorithm to detect and catalog blobs (see Hales et al. 2012). A blob is defined by two criteria:

at least one pixel has to be above a threshold (σ p ) all the adjacent surrounding pixels must be above a floodclip threshold (σ f ) where σ p and σ f are defined in number of σ, the local rms of the mosaic.

A first guess to determine the detection threshold σ p is provided by the examination of the pixel distribution of the S/N-map. The S/N-map has been created by dividing the 0 60 tapered map by the noise map. Figure 3 shows that the S/N-map follows an almost perfect Gaussian below S /N = 4.2. Above this threshold, a significant difference can be observed that is characteristic of the excess of positive signal expected in the presence of real sources in the image. However, this histogram alone cannot be used to estimate a number of sources because the pixels inside one beam are not independent of one another. Hence although the non-Gaussian behavior appears around S /N = 4.2 we performed simulations to determine the optimal values of σ p and σ f .

We first conducted positive and negative -on the continuum map multiplied by (-1) -detection analysis for a range of σ p and σ f values ranging from σ p = 4 to 6 and σ f = 2.5 to 4 with intervals of 0.05 and imposing each time σ p ≥ σ f . The difference between positive and negative detections for each pair of (σ p , σ f ) values provides the expected number of real sources.

We then searched for the pair of threshold parameters to find the best compromise between (i) providing the maximum number of detections, and (ii) minimizing the number of spurious sources. The later purity criterion, p c , is defined as:

p c = N p -N n N p (1)
where N p and N n are the numbers of positive and negative detections respectively. To ensure a purity of 80% as discussed above, we enforced p c ≥ 0.8. This led to σ p = 4.8σ when fixing the value of σ f = 2.7σ (see Fig. 4-left). Below σ p = 4.8σ, the purity criterion rapidly drops below 80% whereas above this value it only mildly rises. Fixing σ p = 4.8σ, the purity remains roughly constant at ∼80 ± 5% when varying σ f . We did see an increase in the difference between the number of positive and negative detections with increasing σ f . However, the size of the sources above σ f = 2.7σ drops below the 0 60 FWHM and tends to become pixel-like, hence non physical. This is because an increase of σ f results in a reduction of the number of pixels above the floodclip threshold (σ f ) that will be associated with a given source. This parameter can be seen as a percolation criterion that sets the size of the sources in a number of pixels. Reversely reducing σ f below 2.7σ results in adding more noise than signal and a reduction in the number of detections. We therefore decided to set σ f to 2.7σ. While we did not wish to impose a criterion on the existence of optical counterparts to define our ALMA catalog, we found that high values of σ f not only generate the problem discussed above, but also generate a rapid drop of the fraction of ALMA detections with an HST counterpart in the Guo et al. (2013) catalog, p HST = N HST /N p . N HST is the number of ALMA sources with an HST counterpart within 0 60 (corresponding to the size of the beam). The fraction falls rapidly from around ∼80% to ∼60%, which we interpreted as being due to a rise of the proportion of spurious sources, since the faintest optical sources, for example, detected by HST-WFC3, are not necessarily associated with the faintest ALMA sources due to the negative K-correction at 1.1 mm. This rapid drop can be seen in the dashed green and dotted pink lines of Fig. 4-right. This confirms that the sources that are added to our catalog with a floodclip threshold greater than 2.7σ are most probably spurious. Similarly, we can see in Fig. 4-left that increasing the number of ALMA detections to fainter flux densities by reducing σ p below 4.8σ leads to a rapid drop of the fraction of ALMA detections with an HST counterpart. Again there is no well-established physical reason to expect the number of ALMA detections with an optical counterpart to decrease with decreasing S/N ratio in the ALMA catalog.

As a result, we decided to set σ p = 4.8σ and σ f = 2.7σ to produce our catalog of ALMA detections. We note that we only discussed the existence of HST counterparts as a complementary test on the definition of the detection thresholds but our approach is not set to limit in any way our ALMA detections to galaxies with HST counterparts.

Indeed, evidence for the existence of ALMA detections with no HST-WFC3 counterparts already exist in the literature. Wang et al. (2016) identified H-dropouts galaxies, that is galaxies detected above the H-band with Spitzer-IRAC at 4.5 µm but undetected in the H-band and in the optical. The median flux density of these galaxies is F 870 µm 1.6 mJy (Wang et al., in prep.). By scaling this median value to our wavelength of 1.1 mm (the details of this computation are given in Sect. 5.4), we obtain a flux density of 0.9 mJy, close to the typical flux of our detections (median flux ∼1 mJy, see Table 3).

Catalog

Creation of the catalog

Using the optimal parameters of σ p = 4.8σ and σ f = 2.7σ described in Sect. 3, we obtained a total of 20 detections down to a flux density limit of S 1.1 mm ≈ 880 µJy that constitute our main catalog. These detections can be seen ranked by their S/N in Fig. 1. The comparison of negative and positive detections suggests the presence of 4 ± 2 (assuming a Poissonian uncertainty on the difference between the number of positive and negative detections) spurious sources in this sample.

In the following, we assume that the galaxies detected in the 0 60-mosaic are point-like. This hypothesis will later be discussed and justified in Sect. 4.5. In order to check the robustness of our flux density measurements, we compared different flux extraction methods and softwares: PyBDSM (Mohan & Rafferty 2015); Galfit (Peng et al. 2010); Blobcat (Hales et al. 2012). The peak flux value determined by Blobcat refers to the peak of the surface brightness corrected for peak bias (see Hales et al. 2012). The different results were consistent, with a median ratio of F Blobcat peak /F PyBDSM peak = 1.04 ± 0.20 and F Blobcat peak /F Galfit PSF = 0.93 ± 0.20. The fluxes measured using psf-fitting (Galfit) and peak flux measurement (Blobcat) for each galaxy are listed in Table 3. We also ran CASA fitsky and a simple aperture photometry corrected for the ALMA PSF and also found consistent results. The psf-fitting with Galfit was performed inside a box of 5 × 5 centered on the source.

The main characteristics of these detections (redshift, flux, S/N, stellar mass, counterpart) are given in Table 3. We used redshifts and stellar masses from the ZFOURGE catalog (see Sect. 2.4.1).

We compared the presence of galaxies between the 0 60mosaic and the 0 29-mosaic. Of the 20 detections found in the 0 60 map, 14 of them are also detected in the 0 29 map. The presence of a detection in both maps reinforces the plausibility of a detection. However, a detection in only one of these two maps may be a consequence of the intrinsic source size. An extended source is more likely to be detected with a larger beam, whereas A152, page 6 of 26 1), green dashed-line represents the percentage of positive detection with HST-WFC3 counterpart p HST and magenta dashed-line represents the percentage of positive detection with ZFOURGE counterpart p ZFOURGE . Gray dashed-lines show the thresholds σ p = 4.8σ and σ f = 2.7σ and the 80% purity limit. a more compact source is more likely to be missed in the maps with larger tapered sizes and reduced point source sensitivity.

A first method to identify potential false detections was to compare our results with a deeper survey overlapping with our area of the sky. We compared the positions of our catalog sources with the positions of sources found by Dunlop et al. (2017) in the HUDF. This 1.3-mm image is deeper than our survey and reaches a σ 35 µJy (corresponding to σ = 52 µJy at 1.1 mm) but overlaps with only ∼6.5% of our survey area. The final sample of Dunlop et al. (2017) was compiled by selecting sources with S 1.3 > 120 µJy to avoid including spurious sources due to the large number of beams in the mosaics and due to their choice of including only ALMA detections with optical counterparts seen with HST.

With our flux density limit of S 1.1 mm ≈ 880 µJy any nonspurious detection should be associated with a source seen at 1.3 mm in the HUDF 1.3 mm survey, the impact of the wavelength difference being much smaller than this ratio. We detected three galaxies that were also detected by Dunlop et al. (2017), UDF1, UDF2 and UDF3, all of which have S 1.3 mm > 0.8 mJy. The other galaxies detected by Dunlop et al. (2017) have a flux density at 1.3 mm lower than 320 µJy, which makes them undetectable with our sensitivity.

We note however that we did not impose as a strict criterion the existence of an optical counterpart to our detections, whereas Dunlop et al. (2017) did. Hence if we had detected a source with no optical counterpart within the HUDF, this source may not be included in the Dunlop et al. (2017) catalog. However, as we will see, the projected density of such sources is small and none of our candidate optically dark sources fall within the limited area of the HUDF. We also note that the presence of an HST-WFC3 source within a radius of 0 6 does not necessarily imply that is the correct counterpart. As we will discuss in detail in Sect. 4.4, due to the depth of the HST-WFC3 observations and the large number of galaxies listed in the CANDELS catalog, a match between the HST and ALMA positions may be possible by chance alignment alone (see Sect. 4.4).

Supplementary catalog

After the completion of the main catalog, three sources that did not satisfy the criteria of the main catalog presented strong evidence of being robust detections. We therefore enlarged our catalog, in order to incorporate these sources into a supplementary catalog.

These three sources are each detected using a combination of σ p and σ f giving a purity factor greater than 80%, whilst also ensuring the existence of an HST counterpart.

The galaxy AGS21 has an S /N = 5.83 in the 0 29 tapered map, but is not detected in the 0 60 tapered map. The nondetection of this source is most likely caused by its size. Due to its dilution in the 0 60-mosaic, a very compact galaxy detected at 5σ in the 0 29-mosaic map could be below the detection limit in the 0 60-mosaic. The ratio of the mean rms of the two tapered maps is 1.56, meaning that for a point source of certain flux, a 5.83σ measurement in the 0 29-mosaic becomes 3.74σ in the 0 60-map.

The galaxy AGS22 has been detected with an S /N = 4.9 in the 0 60 tapered map (σ p = 4.9 and σ f = 3.1). With σ p and σ f values more stringent than the thresholds chosen for the main catalog, it may seem paradoxical that this source does not appear in the main catalog. With a floodclip criterion of 2.7σ, this source would have an S/N just below 4.8, excluding it from the main catalog. This source is associated with a faint galaxy that has been detected by HST-WFC3 (ID CANDELS = 28 952) at 1.6 µm (6.6σ) at a position close to the ALMA detection (0 28). Significant flux has also been measured at 1.25 µm (3.6 σ) for this galaxy. In all of the other filters, the flux measurement is not significant (<3σ). Due to this lack of information, it has not been possible to compute its redshift. AGS22 is not detected in the 0 29-mosaic map with p c > 0.8. The optical counterpart of this source has a low H-band magnitude (26.8 ± 0.2 AB), which corresponds to a range for which the Guo et al. (2013) catalog is no longer complete. This is the only galaxy (except the three galaxies most likely to be spurious: AGS14, AGS16 and AGS19) that has not been detected by IRAC (which could possibly be explained by a low stellar mass). The probability of the ALMA detection being spurious, within the association radius 0 6 of a H-band source of this magnitude or brighter, is 5.5%. For these reasons, we did not consider it as spurious.

The galaxy AGS23 was detected in the 0 60 map just below our threshold at 4.8σ, with a combination σ p = 4.6 and σ f = 2.9 giving a purity criterion greater than 0.9. This detection is associated with an HST-WFC3 counterpart. It is A152, page 7 of 26 A&A 620, A152 (2018) Table 2. Details of the positional differences between ALMA and HST-WFC3 for our catalog of galaxies identified in the 1.1 mm-continuum map. 2),( 3) IDs of the HST-WFC3 (from the CANDELS catalog) and ZFOURGE counterparts of these detections (the cross correlations between ALMA and HST-WFC3 and between ALMA and ZFOURGE are discussed in Sect. 4.4). b indicates HST-WFC3 galaxies located in a radius of 0 6 around the ALMA detection, although strong evidence presented in Sect. 7 suggests they are not the optical counterparts of our detections; (4), ( 5) RA and Dec of the sources in the ALMA image (J2000); ( 6), ( 7) positions of HST-WFC3 H-band counterparts when applicable from Guo et al. (2013), ( 8), [START_REF] Williams | The progenitors of the compact early-type galaxies at high redshift[END_REF] distances between the ALMA and HST source positions before (∆ HST 1 ) and after (∆ HST 2 ) applying the offset correction derived from the comparison with Pan-STARRS and Gaia; [START_REF] Huang | Four IRAC sources with an extremely red H -[3.6] color: passive or dusty galaxies at z > 4.5?[END_REF], [START_REF] Wang | Infrared color selection of massive galaxies at z > 3[END_REF] offset to be applied to the HST source positions, which includes both the global systematic offset and the local offset; [START_REF] Swinbank | An ALMA survey of sub-millimetre galaxies in the Extended Chandra Deep Field South: the far-infrared properties of SMGs[END_REF] distance from the closest IRAC galaxy. (1) For AGS15 we used the distance given in the ZFOURGE catalog (see Sect. 7).

for these two reasons that we include this galaxy in the supplementary catalog. The photometric redshift (z = 2.36) and stellar mass (10 11.26 M ) both reinforce the plausibility of this detection.

Astrometric correction

The comparison of our ALMA detections with HST (Sect. 4.1) in the previous section was carried out after correcting for an astrometric offset, which we outline here. In order to perform the most rigorous counterpart identification and take advantage of the accuracy of ALMA, we carefully investigated the astrometry of our images. Before correction, the galaxy positions viewed by HST were systematically offset from the ALMA positions. This offset has already been identified in previous studies (e.g., Maiolino et al. 2015;Rujopakarn et al. 2016;Dunlop et al. 2017).

In order to quantify this effect, we compared the HST source positions with detections from the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS). This survey has the double advantage to cover a large portion of the sky, notably the GOODS-South field, and to observe the sky at a wavelength similar to HST-WFC3. We used the Pan-STARRS DR1 catalog provided by Flewelling et al. (2016) and also included the corresponding regions issued from the Gaia DR1 (Gaia Collaboration 2016).

Cross-matching was done within a radius of 0 5. In order to minimize the number of false identifications, we subtracted the median offset between the two catalogs from the Guo et al. (2013) catalog positions, after the first round of matching. We iterated this process three times. In this way, 629 pairs were found over the GOODS-South field.

To correct for the median offset between the HST and ALMA images, the HST image coordinates needed to be corrected by -96 ± 113 mas in right ascension, α, and 261 ± 125 mas in declination, δ, where the uncertainties correspond to the standard deviation of the 629 offset measurements. This offset is consistent with that found by Rujopakarn et al. (2016) of ∆α = -80 ± 110 mas and ∆δ = 260 ± 130 mas. The latter offsets were calculated by comparing the HST source positions with 2MASS and VLA positions. In all cases, it is the HST image that presents an offset, whereas ALMA, Pan-STARRS, Gaia, 2MASS and VLA are all in agreement. We therefore deduced that it is the astrometric solution used to build the HST mosaic that introduced this offset. As discussed in Dickinson et al. (in prep.), the process of building the HST mosaic also introduced less significant local offsets, that can be considered equivalent to a distortion of the HST image. These local offsets are larger in A152, page 8 of 26 8), ( 9) flags for detection by Blobcat in the 0 60-mosaic and 0 29-mosaic images, where at least one combination of σ p and σ f gives a purity factor (Eq. ( 1)) greater than 80%; [START_REF] Huang | Four IRAC sources with an extremely red H -[3.6] color: passive or dusty galaxies at z > 4.5?[END_REF] flux for detection greater than 3 σ by VLA (5 cm). Some of these sources are visible in the VLA image but not detected with a threshold >3σ. AGS8 and AGS16 are not in the field of the VLA survey; [START_REF] Wang | Infrared color selection of massive galaxies at z > 3[END_REF] absorption-corrected intrinsic 0.5-7.0 keV luminosities. The X-ray luminosities have been corrected to account for the redshift difference between the redshifts provided in the catalog of Luo et al. (2017) and those used in the present table, when necessary. For this correction we used Eq. ( 1) from Alexander et al. (2003), and assuming a photon index of Γ = 2; [START_REF] Swinbank | An ALMA survey of sub-millimetre galaxies in the Extended Chandra Deep Field South: the far-infrared properties of SMGs[END_REF] corresponding IDs for detections of the sources in previous (sub)millimeter ancillary data. UDF is for Hubble Ultra Deep Field survey (Dunlop et al. 2017) Survey of GOODS-S at One-millimeter (ASAGAO). We also note the pointed observations of AGS1 presented in Barro et al. (2017), and those of AGS13 by Talia et al. (2018). For the two sources marked by a †, the hypothesis a of a point-like source is no longer valid. We therefore apply correction factors of 2.3 and 1.7 to the peak flux values of AGS17 and AGS18 respectively, to take into account the extended flux emission of these sources.

the periphery of GOODS-South than in the center, and close to zero in the HUDF field. The local offsets can be considered as a distortion effect. The offsets listed in Table 2 include both effects, the global and local offsets. The separation between HST and ALMA detections before and after offset correction, and the individual offsets applied for each of the galaxies are indicated in Table 2 and can be visualized in Fig. 5. We applied the same offset corrections to the galaxies listed in the ZFOURGE catalog. This accurate subtraction of the global systematic offset, as well as the local offset, does not however guarantee a perfect overlap between ALMA and HST emission. The location of the dust emission may not align perfectly with the starlight from a galaxy, due to the difference in ALMA and HST resolutions, as well as the physical offsets between dust and stellar emission that may exist. In Fig. 6, we show the ALMA contours (4-10σ) overlaid on the F160W HST-WFC3 images after astrometric correction. In some cases (AGS1, AGS3, AGS6, AGS13, AGS21 for example), the position of the dust radiation matches that of the stellar emission; in other cases, (AGS4, AGS17 for example), a displacement appears between both two wavelengths. Finally, in some cases (AGS11, AGS14, AGS16, and AGS19) there are no optical counterparts. We will discuss the possible explanations for this in Sect. 7. Before correction After correction Fig. 5. Positional offset (RA HST -RA ALMA , Dec HST -Dec ALMA ) between HST and ALMA before (red crosses) and after (blue crosses) the correction of both a global systematic offset and a local offset. The black dashed circle corresponds to the cross-matching limit radius of 0 6. The gray dashed circles show a positional offset of 0 2 and 0 4 respectively. The magenta lines indicate the HST galaxies previously falsely associated with ALMA detections.

Identification of counterparts

We searched for optical counterparts in the CANDELS/GOODS-South catalog, within a radius of 0 6 from the millimeter position after applying the astrometric corrections to the source positions described in Sect. 4.3. The radius of the cross-matching has been chosen to correspond to the synthesized beam (0 60) of the tapered ALMA map used for galaxy detection. Following Condon (1997), the maximal positional accuracy of the detection in the 1.1 mm map is given by θ beam /(2 × S /N). In the 0 60-mosaic, the positional accuracy therefore ranges between 26.5 mas and 62.5 mas for our range of S/N (4.8-11.3), corresponding to physical sizes between 200 and 480 pc at z = 3.

Despite the high angular resolution of ALMA, the chance of an ALMA-HST coincidence is not negligible, because of the large projected source density of the CANDELS/GOODS-South catalog. Figure 7 shows a Monte Carlo simulation performed to estimate this probability. We separate here the deeper Hubble Ultra Deep Field (blue histogram) from the rest of the CANDELS-deep area (orange histogram). We randomly defined a position within GOODS-South and then measured the distance to its closest HST neighbor using the source positions listed in Guo et al. (2013). We repeated this procedure 100 000 times inside and outside the HUDF. The probability for a position randomly selected in the GOODS-South field to fall within 0.6 arcsec of an HST source is 9.2% outside the HUDF, and 15.8% inside the HUDF. We repeated this exercise to test the presence of an IRAC counterpart with the Ashby et al. (2015) catalog (green histogram). The probability to randomly fall on an IRAC source is only 2.1%.

With the detection threshold determined in Sect. 3, 80% of the millimeter galaxies detected have an HST-WFC3 counterpart, and four galaxies remain without an optical counter-part. We cross-matched our detections with the ZFOURGE catalog.

Figure 8 shows 3 5 × 3 5 postage stamps of the ALMAdetected galaxies, overlaid with the positions of galaxies from the CANDELS/GOODS-South catalog (magenta double crosses), ZFOURGE catalog (white circles) or both catalogs (sources with an angular separation lower than 0 4, blue circles). These are all shown after astrometric correction. Based on the ZFOURGE catalog, we found optical counterparts for one galaxy that did not have an HST counterpart: AGS11, a photometric redshift has been computed in the ZFOURGE catalog for this galaxy.

The redshifts of AGS4 and AGS17 as given in the CANDELS catalog are unexpectedly low (z = 0.24 and z = 0.03, respectively), but the redshifts for these galaxies given in the ZFOURGE catalog (z = 3.76 and z = 1.85, respectively) are more compatible with the expected redshifts for galaxies detected with ALMA. These galaxies, missed by the HST or incorrectly listed as local galaxies are particularly interesting galaxies (see Sect. 7). AGS6 is not listed in the ZFOURGE catalog, most likely because it is close (<0 7) to another bright galaxy (ID CANDELS = 15 768). These galaxies are blended in the ZFOURGE ground-based K s -band images. AGS6 has previously been detected at 1.3 mm in the HUDF, so we adopt the redshift and stellar mass found by Dunlop et al. (2017). The consensus CANDELS zphot from Santini et al. (2015) is z = 3.06 (95% confidence: 2.92 < z < 3.40), consistent with the value in Dunlop et al. (2017).

Galaxy sizes

Correctly estimating the size of a source is an essential ingredient for measuring its flux. As a first step, it is imperative to know if the detections are resolved or unresolved. In this section, we discuss our considerations regarding the sizes of our galaxies. The low number of galaxies with measured ALMA sizes in the literature makes it difficult to constrain the size distribution of dust emission in galaxies. Recent studies (e.g., Barro et al. 2016;Rujopakarn et al. 2016;Elbaz et al. 2018;Ikarashi et al. 2017;Fujimoto et al. 2017) with sufficient resolution to measure ALMA sizes of galaxies suggest that dust emission takes place within compact regions of the galaxy.

Two of our galaxies (AGS1 and AGS3) have been observed in individual pointings (ALMA Cycle 1; P.I. R. Leiton, presented in Elbaz et al. 2018) at 870 µm with a long integration time (40-50 min on source). These deeper observations give more information on the nature of the galaxies, in particular on their morphology. Due to their high S/N (∼100) the sizes of the dust emission could be measured accurately: R 1/2maj = 120 ± 4 and 139 ± 6 mas for AGS1 and AGS3 respectively, revealing extremely compact star-forming regions corresponding to circularized effective radii of ∼1 kpc at redshift z ∼ 2. The Sersic indices are 1.27 ± 0.22 and 1.15 ± 0.22 for AGS1 and AGS3 respectively: the dusty star-forming regions therefore seem to be disk-like. Based on their sizes, their stellar masses (>10 11 M ), their SFRs (>10 3 M yr -1 ) and their redshifts (z ∼ 2), these very compact galaxies are ideal candidate progenitors of compact quiescent galaxies at z ∼ 2 (Barro et al. 2013;Williams et al. 2014;van der Wel et al. 2014;Kocevski et al. 2017, see also Elbaz et al. 2018).

Size measurements of galaxies at (sub)millimeter wavelengths have previously been made as part of several different studies. Ikarashi et al. (2015) measured sizes for 13 AzTECselected SMGs. The Gaussian FWHM range between 0 10 and A152, page 10 of 26 In some cases (AGS1, AGS3, AGS6, AGS13, AGS21 for example), the position of the dust radiation matches that of the stellar emission; in other cases, (AGS4, AGS17 for example), a displacement appears between both two wavelengths. Finally, in some cases (AGS11, AGS14, AGS16, and AGS19) there are no optical counterparts. We will discuss the possible explanations for this in Sect. 7. Probability of a randomly selected position in the area defined by this survey to have at least one HST (blue, orange) or IRAC (green) neighbor as a function of distance. We computed this probability by Monte Carlo simulation using the distribution of galaxies listed in the CANDELS/GOODS-South catalog. Due to the presence of the HUDF within the GOODS-South field, we cannot consider that the density of HST galaxies is uniform, and we consider these two fields separately (blue inside and orange outside the HUDF).

(0 63 × 0 49), (1 52 × 0 85) and ( 122 × 1 08). They found effective radii spanning <0 05 to 0 37 ± 0 21 in the ALMA Frontier Fields survey at 1.1 mm. Ikarashi et al. (2017) obtained ALMA millimeter-sizes of 0 08-0 68 (FWHM) for 69 ALMAidentified AzTEC SMGs with an S/N greater than 10. These galaxies have a median size of 0 31. These studies are all broadly in agreement, revealing compact galaxy sizes in the sub(millimeter) regime of typically 0 3 ± 0 1.

Size measurements require a high S/N detection to ensure a reliable result. The S/N range of our detections is 4.8-11.3. Following Martí-Vidal et al. (2012), the reliable size measurement limit for an interferometer is:

θ min = β λ c 2 S /N 2 1/4 × θ beam 0.88 θ beam √ S /N (2)
where λ c is the value of the log-likelihood, corresponding to the cutoff of a Gaussian distribution to have a false detection and β is a coefficient related to the intensity profile of the source model and the density of the visibilities in Fourier space. This coefficient usually takes values in the range 0.5-1. We assumed λ c = 3.84 corresponding to a 2σ cut-off, and β = 0.75. For θ beam = 0 60 and a range of S/N between 4.8 and 11.3, the minimum detectable size (FWHM) therefore varies between 0 16 and 0 24. Using the 0 60-mosaic map, the sizes of a large number of detections found in previous studies could therefore not be reliably measured.

To quantitatively test if the millimeter galaxies are resolved in our survey we performed several tests. The first test was to stack the 23 ALMA-detections and compare the obtained flux profile with the profile of the PSF. However, in the mosaic map, each slice has its own PSF. We therefore also needed to stack the PSFs at these 23 positions in order to obtain a global PSF for comparison. Figure 9 shows the different PSFs used in this survey in the 0 60-mosaic. The FWHM of each PSF is identical, the differences are only in the wings. The stack of the 23 PSFs for the 23 detections and the result of the source stacking in the 0 60-mosaic is shown in Fig. 10. The flux of each detection is normalized so that all sources have the same weight, and the stacking is not skewed by the brightest sources.

Size stacking to measure the structural parameters of galaxies is at present a relatively unexplored area. This measurement could suffer from several sources of bias. The uncertainties on the individual ALMA peak positions could increase the measured size in the stacked image, for example. On the other hand, due to the different inclination of each galaxy, the stacked galaxy could appear more compact than the individual galaxies (e.g. Hao et al. 2006;Padilla & Strauss 2008;Li et al. 2016). Alternatively, some studies (e.g. van Dokkum et al. 2010) indicate that size stacking gives reasonably accurate mean galaxy radii. In our case, the result of the size stacking is consistent with unresolved sources or marginally resolved at this resolution which corresponds to a physical diameter of 4.6 kpc at z = 3.

The second test was to extract the flux for each galaxy using PSF-fitting. We used Galfit (Peng et al. 2010) on the 0 60mosaic. The residuals of this PSF-extraction are shown for the 6 brightest galaxies in Fig. 11. The residuals of 21/23 detections do not have a peak greater than 3σ in a radius of 1 around the source. Only sources AGS10 and AGS21 present a maximum in the residual map at ∼3.1σ.

We compared the PSF flux extraction method with Gaussian and Sersic shapes. As our sources are not detected with a particularly high S/N, and in order to limit the number of degrees of freedom, the Sersic index was frozen to n = 1 (exponential disk profile, in good agreement with Hodge et al. 2016 andElbaz et al. 2018 for example), assuming that the dust emission is disk-like. Figure 11 shows the residuals for the three different extraction profiles. The residuals are very similar between the point source, Gaussian and Sersic profiles, suggesting that the approximation that the sources are not resolved is appropriate, and does not result in significant flux loss. We also note that, for several galaxies, due to large size uncertainties, the Gaussian and Sersic fits give worse residuals than the PSF fit (AGS4 for example).

For the third test, we took advantage of the different tapered maps. We compared the peak flux for each detection between the 0 60-mosaic map and the 0 29-mosaic map. The median ratio is S 0 29 peak /S 0 60 peak = 0.87 ± 0.16. This small decrease, of only 10% in the peak flux density between the two tapered maps suggests that the flux of the galaxies is only slightly more resolved in the 0 29-mosaic map.

In order to test the impact of our hypothesis that the sources can be considered as point-like in the mosaic tapered at 0 60, we fit their light profiles with a circular Gaussian in the uv-plane using uvmodelfit in CASA (we also tested the use of an asymmetric Gaussian but the results remained similar although with a lower precision due to the larger number of free parameters in the fit). The sizes that we obtained confirmed our hypothesis that our galaxies are particularly compact since 85% of the sources (17 out of 20 robust detections) exhibit a FWHM smaller than 0 25 (in other words the half-light radius is twice smaller than this value). The median size of our sample of 20 galaxies is 0 18 (see the distribution of sizes in Fig. 12). This analysis shows that two sources are outliers with sizes of 0 41 ± 0 03 and 0 50 ± 0 08, for AGS17 and AGS18 respectively. For these two sources, the assumption of point-like sources is not valid and leads to an underestimate of the actual flux densities by a factor of 2.3 and 1.7 respectively. This correction has been applied to the list of peak flux densities provided in Table 3. Having performed these tests, we concluded that for all of the detections, except AGS17 and AGS18, the approximation that these sources appear point-like in the 0 60-mosaic map is justified. Forthetworemainingsources,weappliedacorrectiongivenabove. Our photometry was therefore performed under this assumption.

Number counts

Completeness

We assessed the accuracy of our catalog by performing completeness tests. The completeness is the probability for a source As each slice has a specific PSF, we stack the PSF corresponding to the position of each detection. The fluxes of each detection have been normalized, so that the brightest sources do not skew the results. Fluxes of the PSF and ALMA detections are normalized to 1. Flux profiles are taken across the East-west direction. The result is consistent with unresolved or marginally resolved sources at this resolution.

The insert in the top-right corner shows the same procedure for the 15 sources detected in the 0 29-mosaic (see Table 3).

to be detected in the map given factors such as the depth of the observations. We computed the completeness of our observations using Monte Carlo simulations performed on the 0 60mosaic map. We injected 50 artificial sources in each slice. Each source was convolved with the PSF and randomly injected on the dirty map tapered at 0 60. In total, for each simulation run, 300 sources with the same flux were injected into the total map. In view of the size of the map, the number of independent beams and the few number of sources detected in our survey, we can consider, to first order, that our dirty map can be used as a blank map containing only noise, and that the probability to inject a source exactly at the same place as a detected galaxy is negligible. The probability that at least two point sources, randomly injected, are located within the same beam (p b ) is:

p b = 1 - k=n-1 k=0 N b -k N b (3)
where N b is the number of beams and n is the number of injected sources. For each one of the six slices of the survey, we count ∼100 000 independent beams. The probability of having source blending for 50 simulated sources in one map is ∼1%.

We then counted the number of injected sources detected with σ p = 4.8σ and σ f = 2.7σ, corresponding to the thresholds of our main catalog. We injected 300 artificial sources of a given flux, and repeated this procedure 100 times for each flux density. Our simulations cover the range S ν = 0.5-2.4 mJy in steps of 0.1 mJy. Considering the resolution of the survey, it would be reasonable to expect that a non-negligible number of galaxies are not seen as point sources but extended sources (see Sect. 4.5). We simulated different sizes of galaxies with Gaussian FWHM between 0 2 and 0 9 in steps of 0 1, as well as point-source galaxies, to better understand the importance of the galaxy size in the detectability process. We matched the recovered source with the input position within a radius of 0 6.

Figure 13 shows the resulting completeness as a function of input flux, for different FWHM Gaussian sizes convolved by the PSF and injected into the map.

As a result of our simulations, we determined that at 1.2 mJy, our sample is 94 ± 1% complete for point sources. This percentage drastically decreases for larger galaxy sizes. For the same flux density, the median detection rate drops to 61 ± 3% for a galaxy with FWHM ∼ 0 3, and to 9 ± 1% for a FWHM ∼ 0 6 galaxy. This means, that for a galaxy with an intrinsic flux density of 1.2 mJy, we are more than ten times more likely to detect a point source galaxy than a galaxy with FWHM ∼ 0 6.

The size of the millimeter emission area plays an essential role in the flux measurement and completeness evaluation. We took the hypothesis that ALMA sizes are 1.4 times smaller than the size measured in HST H-band (as derived by Fujimoto et al. 2017 using 1034 ALMA galaxies). We are aware that this size ratio is poorly constrained at the present time, but such relations have been observed in several studies (see Sect. 4.5). For example, of the 12 galaxies presented by Laporte et al. (2017), with fluxes measured using ALMA at 1.1 mm (González-López et al. 2017), seven of them have a size measured by HST F140W/WFC3 similar to the size measured in the ALMA map. On the other hand, for the remaining five galaxies, their sizes are approximately two times more compact at millimeter wavelengths than at optical wavelengths. This illustrates the dispersion of this ratio.

Effective area

As the sensitivity of our 1.1 mm ALMA map is not uniform, we defined an effective area where a source with a given flux can be detected with an S /N > 4.8σ, as shown in Fig. 14. Our map is composed of six different slices -one of them, slice B, presents a noise 30% greater than the mean of the other five, whose noise levels are comparable. The total survey area is 69.46 arcmin 2 , with 90% of the survey area reaching a sensitivity of at least 1.06 mJy beam -1 . We considered the relevant effective area for each flux density in order to compute the number counts. We considered the total effective area over all slices in the number counts computation.

Flux boosting and Eddington bias

In this section, we evaluate the effect of flux boosting. Galaxies detected with a relatively low S/N tend to be boosted by noise fluctuations (see Hogg & Turner 1998;Coppin et al. 2005;Scott et al. 2002). To estimate the effect of flux boosting, we used the same set of simulations that we used for completeness estimations.

The results of our simulations are shown in Fig. 15. The boosting effect is shown as the ratio between the input and output flux densities as a function of the measured S/N. For point sources, we observed the well-known flux boosting effect for the lowest S/Ns. This effect is not negligible for the faintest sources in our survey. At 4.8σ, the flux boosting is ∼15%, and drops below 10% for an S/N greater than 5.2. We estimated the deboosted flux by dividing the measured flux by the median value of the boosting effect as a function of S/N (red line in Fig. 15).

We also corrected for the effects of the Eddington bias (Eddington 1913). As sources with lower luminosities are more numerous than bright sources, Gaussian distributed noise gives rise to an overestimation of the number counts in the lowest flux bins. We simulated a realistic number of sources (the slope of the number counts were computed using the coefficients given in Table 5) and added Gaussian noise to each simulated source. The correction factor for each flux bin was therefore the ratio between the flux distribution before and after adding the noise. The 1σ confidence intervals (dashed red lines) are overplotted. The solid black horizontal line corresponds to F out = F in (see text for details). We used the same set of simulations that we used for the completeness analysis.

Cumulative and differential number counts

We used sources with a S/N greater than 4.8 from the main catalog to create cumulative and differential number counts.

We needed to take into account the contamination by spurious sources, completeness effects, and flux boosting in order to compute these number counts.

The contribution of a source with flux density S i ± dS i to the cumulative number count is given by: dN(S i )

dS i = p c (S i ) A eff (S i )C(S i , R circ ALMA ) × dN obs (S i ) dS i (4)
where p c (S i ) is the purity criterion as defined in Eq. ( 1) at the flux density S i , A eff (S i ) and C(S i , R circ ALMA ) are the effective area and the completeness for the flux interval dS i , as shown in Figs. 13 and 14. The completeness is strongly correlated with the sizes of the galaxies. To estimate the completeness, galaxies that do not have measured sizes in the H-band (van der Wel et al. 2012) were considered as point sources, otherwise we used R circ ALMA = R circ H /1.4 (see Sect. 5.1). The cumulative number counts are given by the sum over all of the galaxies with a flux density higher than S :

N(>S ) = S i >S p c (S i ) A eff (S i )C(S i , R circ ALMA ) × dN obs (S i ) dS i × dS i (5)
Errors are computed by Monte-Carlo simulations, added in quadrature to the Poisson uncertainties. The derived number counts are provided in Table 4. AGS19 is located at a position where the noise is artificially low, and has therefore not been taken into account. In Fig. 16, we compare our results with previous studies (Lindner et al. 2011;Scott et al. 2012;Karim et al. 2013;Hatsukade et al. 2013Hatsukade et al. , 2016;;[START_REF] Simpson | The SCUBA-2 Cosmology Legacy Survey: ALMA Resolves the Bright-end of the Sub-millimeter Number Counts[END_REF]Oteo et al. 2016;Aravena et al. 2016;Fujimoto et al. 2016;Umehata et al. 2017;Geach et al. 2017;Dunlop et al. 2017). To standardize these previous studies, the different flux densities are scaled to 1.1 mm using a Modified Black Body (MBB) model, assuming a dust emissivity index β = 1.5 (e.g., Gordon et al. 2010) 1-mm cumulative (left panel) and differential (right panel) number counts derived using the corrections described in Sect. 5.4, for the sources detected at >4.8σ in the main catalog. AGS19 is located at a position where the noise is artificially low, and has therefore not been taken into account. Previous (sub)millimeter cumulative number counts are also shown (Lindner et al. 2011;Scott et al. 2012;Karim et al. 2013;Hatsukade et al. 2013Hatsukade et al. , 2016;;Ono et al. 2014;[START_REF] Simpson | The SCUBA-2 Cosmology Legacy Survey: ALMA Resolves the Bright-end of the Sub-millimeter Number Counts[END_REF]Oteo et al. 2016;Carniani et al. 2015;Aravena et al. 2016;Fujimoto et al. 2016;Umehata et al. 2017;Geach et al. 2017;Dunlop et al. 2017). The different fluxes are scaled to 1.1 mm flux densities using S Kovács et al. 2006;Coppin et al. 2008), and a redshift of z = 2.5 (e.g., Wardlow et al. 2011;Yun et al. 2012). These values have also been chosen to be consistent with Hatsukade et al. (2016). The different fluxes were therefore scaled to 1.1 mm using the relations S 1.1 mm /S 1.2 mm = 1.29, S 1.1 mm /S 1.3 mm = 1.48 and S 1.1 mm /S 870 µm = 0.56. It is a real challenge to standardize these previous studies because instruments, observational techniques or resolution often vary between studies. Some of these counts have been computed from individual pointings, by brightness selection, or by serendipitous detections. Observations with a single dish or a low resolution can also overestimate the number counts for the brightest galaxies, because of blending effects (see Ono et al. 2014). Another non-negligible source of error can come from an inhomogeneous distribution of bright galaxies. An underdensity by a factor of two of submillimeter galaxies with far infrared luminosities greater than 2 × 10 12 L in the extended Chandra deep field south (ECDFS) compared to other deep fields has been revealed by Weiß et al. (2009). Despite those potential caveats, the results from our ALMA survey in the GOODS-South field are in good agreement with previous studies for flux densities below 1 mJy. For values above this flux density, two different trends coexist as illustrated in Fig. 16: our counts are similar to those found by Karim et al. (2013), but below the trend characterized by Scott et al. (2012). These two previous studies have been realized under different conditions. The effects of blending, induced by the low resolution of a single dish observation, as with Scott et al. (2012), tend to overestimate the number counts at the bright-end (Ono et al. 2014;Karim et al. 2013;Béthermin et al. 2017). We indicate these points on the Fig. 16 on an indicative basis only.

The differences in wavelength between the different surveys, even after applying the scaling corrections above, can also induce scatter in the results, especially for wavelengths far from 1.1 mm. The cumulative source counts from the 20 detections in this study and the results from other multidish blank surveys are fitted with a Double Power Law (DPL) function (e.g., Scott et al. 2002) given by:

N(>S ) = N 0 S 0       S S 0 α + S S 0 β       -1 (6)
A152, page 16 of 26

Table 5. Best-fit parameters for the cumulative and differential number counts for a double power law function (Eq. ( 6)) and a Schechter function (Eq. ( 7)).

N (Schechter 1976) function (e.g., Knudsen et al. 2008):

N(>S ) = N 0 S 0 S S 0 α exp - S S 0 d S S 0 ( 7
)
where N 0 is the normalization, S 0 the characteristic flux density and α is the faint-end slope. β is the bright-end slope of the number of counts in Eq. ( 6). We used a least squares method with the trust region reflective algorithm for these two fitted-functions. The best-fit parameters are given in Table 5.

One of the advantages of using differential number counts compared to cumulative number counts is the absence of correlation of the counts between the different bins. However, the differential number counts are sensitive to the lower number of detections per flux density bin. Here we used ∆ log S ν = 0.2 dex flux density bins.

We compare our results with an empirical model that predicts the number counts at far-IR and millimeter wavelengths, developed by Béthermin et al. (2017). This simulation, called SIDES (Simulated Infrared Dusty Extragalactic Sky), updates the Béthermin et al. (2012) model. These predictions are based on the redshift evolution of the galaxy properties, using a two star-formation mode galaxy evolution model (see also Sargent et al. 2012).

The Béthermin et al. (2017) prediction is in good agreement with the number counts derived in this study, for the two bins with the lowest fluxes. For the highest-flux bin, the model is slightly above the data (∼1σ above the best Schechter fit for fluxes greater than 1 mJy). However, both the Béthermin et al. (2017) model and our data points are below the single-dish measurements for fluxes greater than 1 mJy. This disagreement between interferometric and single-dish counts is expected, because the boosting of the flux of single-dish sources by their neighbor in the beam (Karim et al. 2013;Hodge et al. 2013;Scudder et al. 2016). Béthermin et al. (2017) derived numbers counts from a simulated single-dish map based on their model and found a nice agreement with single-dish data, while the intrinsic number counts in the simulation are much lower and compatible with our interferometric study.

Cosmic variance was not taken into account in the calculation of the errors. Above z = 1.8 and up to the redshift of the farthest galaxy in our catalog at z = 4.8, the strong negative K-correction at this wavelength ensures that the selection of galaxies is not redshift-biased. The cosmic variance, although significant for massive galaxies in a small solid angle, is counterbalanced by the negative K-correction, which makes the redshift interval of our sources (∆z = 3 in Eq. ( 12) in Moster et al. 2011) relatively large, spanning a comoving vol-ume of 1400 Gpc 3 . Based on Moster et al. (2011), the cosmic variance for our sources is ∼15%, which does not significantly affect the calculation of the errors on our number counts.

Contribution to the cosmic infrared background

The extragalactic background light (EBL) is the integrated intensity of all of the light emitted throughout cosmic time. Radiation re-emitted by dust comprises a significant fraction of the EBL, because this re-emitted radiation, peaking around 100 µm, has an intensity comparable to optical background (Dole et al. 2006). The contribution of our ALMA sources to the EBL is derived by integrating the derived number counts down to a certain flux density limit. Using the 20 (>4.8σ) sources detected, we computed the fraction of the 1.1 mm EBL resolved into discrete sources. The integrated flux density is given by:

I(S > S lim ) = inf S lim dN(S ) dS S dS . (8)
We used the set of parameters given in Table 5 on the differential number counts. We compared our results with observations from the far infrared absolute spectrophotometer (FIRAS) on the cosmic background explorer (COBE), knowing that uncertainties exist on the COBE measurements (e.g., Yamaguchi et al. 2016). We used the equation given in Fixsen et al. (1998) to compute the total energy of the EBL:

I ν = (1.3 ± 0.4) × 10 -5 ν ν 0 0.64±0.12 P ν (18.5 + 1.2 K) (9)
where ν 0 = 100 cm -1 , and P ν is the familiar Planck function with I ν in erg s -1 cm -1 Hz -1 sr -1 . From this equation, we found that at 1.1 mm, the energy of the EBL is 2.87 nW m -2 sr -1 . From Eq. ( 8) we can estimate the integrated EBL light. Figure 17 shows this total integrated flux density. For our data, the lowest flux density bin for differential counts S lim is 0.8 mJy, and we extrapolate to lower flux densities. We have resolved only 13.5 +9.0 -8.6 % of the EBL into individual galaxies at 0.8 mJy. This result is in good agreement with studies such as Fujimoto et al. (2016). In order to have the majority of the EBL resolved (e.g., Hatsukade et al. 2013;Ono et al. 2014;Carniani et al. 2015;Fujimoto et al. 2016), we would need to detect galaxies down to 0.1 mJy (about 50 % of the EBL is resolved at this value).

The extrapolation of the integrated flux density below S lim suggests a flattening of the number counts. The population of galaxies that dominate this background is composed of the galaxies undetected in our survey, with a flux density below our detection limit.

Galaxy properties

We now study the physical properties of the ALMA detected sources, taking advantage of the wealth of ancillary data available for the GOODS-South field.

Redshift distribution

Among the 17 ALMA detected sources for which redshifts have been computed, six have a spectroscopic redshift (AGS1, AGS2, AGS3, AGS9, AGS12, AGS13 and AGS18) determined by Kurk et al. (2013), and recently confirmed by Barro et al. (2017), Momcheva et al. (2016), Vanzella et al. (2008), Mobasher (priv. comm.), Inami et al. (2017), Kriek et al. (2008) (2015) respectively. The blue line and shaded region show the results from this work and the associated uncertainty. The solid lines represent the model above the detection limits, and the dashed lines show the extrapolation below these limits. The gray shaded region shows the 1.1 mm cosmic infrared background measured by COBE (Fixsen et al. 1998).

and Dunlop et al. (2017) -from a private communication of Brammer -respectively. The redshift distribution of these 17 ALMA sources is presented in Fig. 18, compared to the distributions of four other deep ALMA blind surveys (Dunlop et al. 2017;Aravena et al. 2016;González-López et al. 2017;Ueda et al. 2018). Of the 17 sources, 15 are in the redshift range z = 1.9-3.8. Only two galaxies (AGS4 and AGS11) have a redshift greater than 4 (z phot = 4.32 and 4.82 respectively). We discuss these galaxies further in Sect. 7. The mean redshift of the sample is z = 3.03 ± 0.17, where the error is computed by bootstrapping. This mean redshift is significantly higher than those found by Dunlop et al. (2017), Aravena et al. (2016), González-López et al. (2017), and Ueda et al. (2018) who find distributions peaking at 2.13, 1.67, 1.99 and 2.28 respectively. The median redshift of our sample is 2.92 ± 0.20, which is a little higher than the value expected from the models of Béthermin et al. (2015), which predict a median redshift of 2.5 at 1.1 mm, considering our flux density limit of ∼874 µJy (4.8σ). Our limiting sensitivity is shallower than that of previous blind surveys: 0.184 mJy here compared with 13 µJy in Aravena et al. (2016), 35 µJy in Dunlop et al. (2017), [START_REF] Wang | SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES): faint-end counts at 450 μm[END_REF][START_REF] Casey | Characterization of SCUBA-2 450 μm and 850 μm selected galaxies in the COSMOS field[END_REF][START_REF] Geach | The SCUBA-2 cosmology legacy survey: blank-field number counts of 450-μm-selected galaxies and their contribution to the cosmic infrared background[END_REF][START_REF] Geach | The SCUBA-2 cosmology legacy survey: 850 μm maps, catalogues and number counts[END_REF][START_REF] Béthermin | Submillimeter number counts at 250 μm, 350 μm and 500 μm in BLAST data[END_REF][START_REF] Smolčić | The VLA-COSMOS 3 GHz large project: continuum data and source catalog release[END_REF][START_REF] Sobral | Slicing COSMOS with SC4K: the evolution of typical Lyα emitters and the Lyα escape fraction from z ~ 2 to 6[END_REF][START_REF] Finkelstein | Effects of dust geometry in Lyα galaxies at z = 4.4[END_REF][START_REF] Steidel | Spectroscopic confirmation of a population of normal star-forming galaxies at redshifts z > 3[END_REF][START_REF] Bouwens | UV luminosity functions at redshifts z ~ 4 to z ~ 10: 10,000 galaxies from HST legacy fields[END_REF][START_REF] Brammer | A fast, public photometric redshift code[END_REF][START_REF] Kriek | An ultra-deep near-infrared spectrum of a compact quiescent galaxy at z = 2.2[END_REF][START_REF] Calzetti | The dust opacity of star-forming galaxies[END_REF][START_REF] Landy | Bias and variance of angular correlation functions[END_REF][START_REF] Limber | The analysis of counts of the extragalactic nebulae in terms of a fluctuating density field[END_REF][START_REF] Croom | Radio-quiet QSO environments -I. The correlation of QSOs and bJ < 23 galaxies[END_REF][START_REF] Peebles | Principles of Physical Cosmology[END_REF] µJy in González-López et al. (2017) and 89 µJy in Ueda et al. (2018). However, our survey covers a larger region on the sky: 69 arcmin 2 here, compared to 1 arcmin 2 , 4.5 arcmin 2 , 13.8 arcmin 2 and 26 arcmin 2 for these four surveys respectively. The area covered by our survey is therefore a key parameter in the detection of high redshift galaxies due to a tight link between 1.1 mm luminosity and stellar mass as, we will show in the next section. The combination of two effects: a shallower survey allowing us to detect brighter SMGs, which are more biased toward higher redshifts (e.g., Pope et al. 2005), as well as a larger survey allowing us to reach more massive galaxies, enables us to open the parameter space at redshifts greater than 3, as shown in Fig. 18. This redshift space is partly or totally missed in smaller blind surveys.

We emphasize that the two HST-dark galaxies (see Sect. 7) for which the mass and redshift could be determined (AGS4 and AGS11) are the two most distant galaxies in our sample, with redshifts greater than 4. (Dunlop et al. 2017), the black dash-dotted line shows the ASPECS sample (Aravena et al. 2016), the red dotted line shows the ALMA Frontier Fields survey (González-López et al. 2017) and the yellow dotted line shows the ASAGAO survey (Ueda et al. 2018). Short colored lines at the top of the figure indicate the median redshifts for these four studies.

Stellar masses

Over half (10/17) of our galaxies have a stellar mass greater than 10 11 M (median mass of M = 1.1 × 10 11 M ). The population of massive and compact star-forming galaxies at z ∼ 2 has been documented at length (e.g., Daddi et al. 2005;van Dokkum et al. 2015), but their high redshift progenitors are to-date poorly detected in the UV. Our massive galaxies at redshifts greater than 3 might therefore give us an insight into these progenitors.

Figure 19 shows the stellar mass as a function of redshift for all of the UVJ active galaxies, listed in the ZFOURGE catalog, in our ALMA survey field of view. Star-forming galaxies (SFGs) have been selected by a UVJ color-color criterion as given by Williams et al. (2009) and applied at all redshifts and stellar masses as suggested by Schreiber et al. (2015):

SFG =          U -V < 1.3, or V -J > 1.6, or U -V < 0.88 × (V -J) + 0.49 . (10)
All galaxies not fulfilling these color criteria are considered as quiescent galaxies and are excluded from our comparison sample (9.3% of the original sample). The ALMA detected galaxies in our survey are massive compared to typical SFGs detected in deep optical and near-IR surveys like CANDELS, in the same redshift range (2 < z < 4), as shown in Fig. 19.

The high proportion of massive galaxies among the ALMA detected sources suggests that stellar mass can be a strong driver for a source to be detected by ALMA at high redshift (Dunlop et al. 2017). The strong link between detection and stellar mass is related to the underlying relation between stellar mass and star-formation rate of SFGs (e.g., Noeske et al. 2007;Elbaz et al. 2011). Almost one third (7/24) of the galaxies previously cataloged in the field of view of this study with M > 10 11 and 2 < z < 3 are also detected with ALMA. The position of our galaxies along the main sequence of 19. Stellar mass versus redshift for the galaxies detected in our ALMA GOODS-South blind survey (red points). For comparison, the distribution of all of the galaxies, listed in the ZFOURGE catalog, in the same field of view is given in blue. Only UVJ active galaxies are shown. The two HST-dark galaxies for which we have redshifts (AGS4 and AGS11) are represented by open circles. The redshift of AGS11 is however uncertain. The green dashed line shows the position that would be occupied by a typical star-forming galaxy -lying on the median of the SFR-M star-formation main sequence (MS) -that would produce a 1.1 mm flux density equal to our average detection limit of 0.88 mJy (4.8-σ) using the spectral energy distribution (SED) library of Schreiber et al. (2018). The dotted line illustrates the position of galaxies 3 times above the MS using the appropriate SEDs from the same library. Galaxies hosting an AGN that are undetected or detected by ALMA are identified with black dots and yellow stars respectively. Inside the black dashed rectangle, 50% of the galaxies detected by ALMA host an AGN, while only 14% of the UVJ active galaxies undetected by ALMA host an AGN.

star-formation will be studied in a following paper (Franco et al., in prep.).

We observe a lack of detections at redshift z < 2, driven by both a strong positive K-correction favoring higher redshifts and a decrease in the star formation activity at low redshift. Indeed, the specific star-formation rate (sSFR), defined as the ratio of galaxy SFR to stellar mass, drops quickly at lower redshifts (z < 2), whereas this rate increases continuously at greater redshifts (e.g., Schreiber et al. 2015). In addition, very massive galaxies (stellar mass greater than 10 11 M ) are relatively rare objects in the smaller co-moving volumes enclosed by our survey at lower redshift. To detect galaxies with these masses, a survey has to be sufficiently large. The covered area is therefore a critical parameter for blind surveys to find massive high redshift galaxies.

In order to estimate the selection bias relative to the position of our galaxies on the main sequence, we show in Fig. 19 the minimum stellar mass as a function of redshift that our survey can detect, for galaxies on the MS of star-formation (green dashed line), and for those with a SFR three times above the MS (green dotted line).

To determine this limit, we calculated the SFR of a given MS galaxy, based on the galaxy stellar mass and redshift as defined in Schreiber et al. (2015). From this SFR and stellar mass, the galaxy SED can also be calculated using the Schreiber et al. (2018) library. We then integrated the flux of this SED around 1.1 mm.

It can be seen that the stellar mass detection limit corresponding to MS galaxies lies at higher stellar mass than all of the galaxies detected by our ALMA survey (as well as all but one of the other star-forming galaxies present in the same region). This means that our survey is unable to detect star-forming galaxies below the main sequence. We can quantify the offset of a galaxy from the main sequence, the so-called "starburstiness" (Elbaz et al. 2011), by the ratio SFR/SFR MS , where SFR MS is the average SFR of "main sequence" galaxies computed from Schreiber et al. (2015). We also indicated our detection limit for galaxies with SFR/SFR MS = 3. In this case, 7/17 galaxies shown lie above the limit. To have been detected, these galaxies must therefore have SFRs at least larger than the SFR MS , the other ten galaxies must have a SFR at least three times above the MS. This highlights that our survey is biased toward galaxies with high SFRs.

AGN

In this Section, we discuss the presence of AGN within the 20 most robust ALMA detections, in other words, rejecting the three spurious detections with no IRAC counterpart (AGS14, AGS16 and AGS19 marked with a star in Table 3) but including three of the supplementary sources (AGS21, AGS22 and AGS23). We found an X-ray counterpart for 65% of them (13/20) in the 7 Msec X-ray survey of GOODS-South with Chandra (Luo et al. 2017). Most of these galaxies were classified as AGN in the catalog of Luo et al. (2017) that identifies as AGN all galaxies with an intrinsic 0.5-7.0 keV luminosity higher than L X,int = 3 × 10 42 erg s -1 , among other criteria.

A152, page 19 of 26 A&A 620, A152 (2018) Table 6. The probability of an HST or IRAC random association (RaA) between the ALMA detection and the closest HST and IRAC galaxies for the 4 HST-Dark galaxies discussed in Sect. 7

ID

AGS4 AGS11 AGS15 AGS17

HST RaA (%) 4.52 -9.14 2.12 IRAC RaA (%) 0.06 0.18 0.12 0.05 However, as our ALMA galaxies are biased toward highly starforming galaxies, we decided to increase the minimum X-ray luminosity to a three times stronger X-ray luminosity threshold to avoid any contamination by star-formation. We also considered as AGN the galaxies exhibiting a hard X-ray spectrum.

We therefore adopted here the following criteria to identify AGN: either (i) L X,int > 10 43 erg s -1 (luminous X-ray sources) or (ii) Γ < 1.0 (hard X-ray sources).

As the redshifts adopted by Luo et al. (2017) are not always the same as ours, when necessary we scaled the X-luminosities to our redshifts using Eq. ( 1) from Alexander et al. (2003), and assuming a photon index of Γ = 2.

Using these conservative criteria, we found that eight ALMA galaxies host an X-ray AGN (marked with a yellow star in Fig. 19). In order to compare the AGN fraction among ALMA detections with galaxies undetected by ALMA with similar masses and redshifts, we restricted our comparison to galaxies with M > 3 × 10 10 M and 1.8 < z < 4.5 (rectangle in black dotted lines in Fig. 19). In this area encompassing 16 ALMA detections, we found that 50% of the ALMA sources host an AGN (8/16) as compared to only 14% (23/160) of the star-forming galaxies undetected by ALMA located in this same area (selected using the UVJ criteria recalled in Eq. ( 10) in the ZFOURGE catalog).

The presence of a high percentage of AGN among the galaxies detected by ALMA may reflect the fact that the ALMA sources are experiencing a starburst (well above the MS marked with a green dashed line in Fig. 19), possibly triggered by a merger that may dramatically reduce the angular momentum of the gas and drive it towards the center of the galaxies (e.g., Rovilos et al. 2012;Gatti et al. 2015;Lamastra et al. 2013) or violent disk instabilities (Bournaud et al. 2012). In addition, the high AGN fraction may be driven by the link between the presence of an AGN and the compactness of their host galaxy. Elbaz et al. (2018), Chang et al. (2017), and Ueda et al. (2018) suggest that the proportion of galaxies hosting an AGN increases with IR luminosity surface density. As discussed in Sect. 5.1, the size, and therefore the compactness of a galaxy, increases the likelihood of an ALMA detection at our angular resolution. Alternatively, ALMA might preferentially detect galaxies with a high gas, hence also dust, content, more prone to efficiently fuel the central black hole and trigger an AGN.

This fraction of galaxies with a high X-ray luminosity (L X,int > 10 43 erg s -1 ) seems to be significantly higher than that found in some other ALMA surveys, in particular in Dunlop et al. (2017;2/16) or Ueda et al. (2018;4/12).

HST-dark galaxies

Some galaxies without H-band HST-WFC3 (1.6 µm) counterparts have been discovered. We discuss below the possibility that these detections may be real HST-dark galaxies. Some ALMA detections previously attributed to an HST counterpart seem in fact to be either more distant galaxies, extremely close on the line of sight to another galaxy, hidden by a foreground galaxy, or too faint at optical rest-frame wavelengths to be detected by HST.

It is already known that some of the most luminous millimeter or submillimeter galaxies can be completely missed at optical wavelengths (Wang et al. 2016), even in the deepest optical surveys, due to dust extinction. Some of these galaxies can also be undetected in the NIR (Wang et al. 2009).

Among the sources that do not have detections in the H-band of HST-WFC3, we distinguish the sources not detected by HST but detected by other instruments (we will discuss the importance of the IRAC filters), and sources undetected by HST and all of the other available instruments in the GOODS-South field (described in the Sect. 2.4).

Of the 20 galaxies detected in our main catalog, seven (35%) do not present an obvious HST counterpart. This number is slightly higher than the expected number of spurious sources (4 ± 2), predicted by the statistical analysis of our survey. To be more accurate, for three of these seven galaxies (AGS4, AGS15 and AGS17), an HST galaxy is in fact relatively close in the line of sight, but strong evidence, presented below, suggests that the HST galaxies are not the counterpart of the ALMA detections, and without the resolution of ALMA we would falsely associate the counterpart. For the four other ALMA detections without HST-WFC3 counterparts within a radius of 0 60, one of them (AGS11) has also been detected at other wavelengths. In this section, we will discuss four particularly interesting cases of HST-dark galaxies (AGS4, AGS11, AGS15 and AGS17), and discuss our reasons for classifying the other three as spurious sources.

Our four HST-dark galaxies (AGS4, AGS11, AGS15 and AGS17) have at least one feature in common, the presence of an IRAC detection and the fact that this IRAC detection is closer on the sky than the unrelated HST detection (see Table 6). The IRAC detections come from the Ashby et al. (2015) catalog, except for AGS15 where the position comes from the ZFOURGE catalog, using the Labbé et al. (2015) survey. The offset between the IRAC and HST sources might suggest that they are different sources. Figure 20 shows the IRAC contours at 3.6 µm centered on the ALMA detection, superimposed over the HST H-band image. The presence of IRAC detections at these distances from the ALMA galaxies is a very strong driver for the identification of sources. The probability of random IRAC association is between one and two orders of magnitude less likely than random HST association for this range of distances, as shown in Fig. 7 and Table 6. The selection of ALMA candidates from galaxies detected in IRAC channels 1 and 2 but missed by HST-WFC3 at 1.6 µm has already been experimented successfully by Wang et al. (in prep.), and seems to be a good indicator to detect HST-dark ALMA galaxies.

As each of our HST-dark galaxies have different features, we will discuss each galaxy individually.

AGS4

AGS4 is a close neighbor of ID CANDELS 8923. AGS4 is the fourth brightest detection in our survey with an S/N greater than 9. The center of the ALMA detection is located at only 0 38 from ID CANDELS 8923, its closest neighboring galaxy. Before astrometric correction, this distance was only 0 21. This is therefore an example where the astrometric correction moves the ALMA galaxy away from the supposed counterpart. In Fig. 21, we can clearly see that the ALMA emission is offset from the observed H-band galaxy shown by the white arrow in Fig. 21. This offset could be explained physically, for example, as a region extremely obscured by dust, within the same galaxy, greatly extinguishing the optical rest-frame emission that is revealed by ALMA. However, for AGS4, a series of clues suggest another explanation for this offset.

The first piece of evidence is the comparison between the IR SED at the position of the ALMA detection (the SEDs of all of the galaxies detected in this paper will be presented in a future publication, Franco et al., in prep.) and the redshift of the optical galaxy. The redshift of the optical galaxy is z = 0.241, whereas the far IR SED peaks around 350 µm (see Fig. 22). If AGS4 was a dusty star-forming region on the outskirts of 8923, this infrared SED would suggest an abnormally cold dust temperature. It is therefore more probable that AGS4 is not part of ID CANDELS 8923, and is a dusty distant galaxy. The fuzzy emission in the H-band HST image, exactly centered at the position of the ALMA detection (see Fig. 21) has not led to any detection in the CANDELS catalog. In the V-band HST images, only ID CANDELS 8923 is present, seen to the South-East of the position of the ALMA detection (indicated by a white cross). No emission is visible at the exact position of the ALMA detection. In the z-band, a barely visible detection appears extremely close to the center of the image.

The second clue is the detection of a galaxy with redshift z = 3.76 in the FourStar galaxy evolution survey, 0 16 from the ALMA detection. This redshift is much more consistent with the peak of the IR SED. The ZFOURGE survey is efficient at detecting galaxies with redshifts between 1 and 4 by using a K s -band detection image (instead of H-band as used for the CANDELS survey), and also due to the high spectral resolution (λ/∆λ ≈ 10) of the medium-bandwidth filters which provide fine sampling of the Balmer/4000 Å spectral break at these redshifts (Tomczak et al. 2016). Furthermore, the stellar mass derived in the ZFOURGE catalog (10 10.50 M compared with 10 7.64 M in the CANDELS catalog) is more consistent with the expected mass of galaxies detected by ALMA. Indeed as shown in this paper, and as already shown by Dunlop et al. (2017), ALMA tends to reveal the most massive dusty galaxies.

The third piece of evidence is the presence, in the Spitzer-CANDELS catalog (Ashby et al. 2015), of a galaxy detected with the IRAC filers only 0 1 from our ALMA detection. This IRAC galaxy has a magnitude of 22.51 at 3.6 µm, measured within an aperture of 2 4 radius.

We also note that Rujopakarn et al. ( 2016) detect a radio galaxy at S /N ≈ 17 only 55 mas from the center of the ALMA detection shown in Fig. 21 (the positional accuracy of this VLA image is 40 mas). Additionally, AGS4 is detected in two of the three Chandra bands: 0.5-7.0 keV (full band; FB) and 0.5-2.0 keV (soft band; SB), but not at 2-7 keV (hard band; HB) from the 7 Ms Chandra observations of the GOODS-South field. The integrated X-ray flux is only 6.86 × 10 40 erg s -1 , but this galaxy is classified as an AGN in the 7 Ms catalog.

The detection of a local galaxy at this position has been largely documented (e.g., Hsu et al. 2014;Skelton et al. 2014;Santini et al. 2015). In contrast, some studies present the galaxy Feldmann et al. 2006), at z = 2.92. These determinations of high redshift by independent studies support the existence of a distant galaxy at this position.

Although close, the two sources (ID CANDELS 8923 and 8923b) were successfully de-blended using two light-profile models, determined by fitting the HST H-band image with Galfit. The two sources were then fit simultaneously using these two models on all of the available images, fixing the profile to that observed in the H band. The SEDs of these two galaxies are shown in Fig. 23, in blue for the HST galaxy and in orange for the ALMA galaxy, together with the photometric redshift probability distribution for AGS4. The redshifts were estimated using EAZY. For the blue HST galaxy we found z = 0.09 +0.06 -0.07 , in good agreement with that found by Skelton et al. (2014). On the other hand, the redshift found for AGS4 is slightly higher than 2018). The SED of AGS17 (bottom panel), which has no known redshift, is simply presented with an interpolation between the observed flux densities to illustrate that it peaks around 400 µm. This peak is inconsistent with the redshifts of the two optical sources with ID CANDELS 4414 (z = 1.85) and 4436 (z = 0.92) in ZFOURGE, with z AGS4 = 4.32 +0.25 -0.21 . However, we can also see a secondary peak in the redshift probability distribution, at the position of the ZFOURGE redshift. As the Balmer break is well established in the K-band, we consider that the redshift determination (z AGS4 = 4.32 +0.25 -0.21 ) is robust and we adopt this redshift for AGS4. The stellar mass of the ALMA galaxy was then computed with FAST (Kriek et al. 2009), and we found 10 11.45±0.2 M (probably slightly overestimated due to the presence of an AGN, suggested by a flux excess in the IRAC bands). The IR SED of this galaxy is shown in Fig. 22. For the first time, thanks to ALMA, we can argue that there exists, at this position, not one but two galaxies, close to each other on the line of sight.

AGS11

AGS11 is detected at 1.1 mm with a flux of 1.4 mJy (S /N ∼ 8) without any counterpart in the deep HST image. However, the galaxy is also detected by IRAC, confirming the existence of a galaxy at this position. A galaxy was recently found, for the first time, in the ZFOURGE catalog at 0 18 from the center of the ALMA position. This galaxy was not detected directly in the A152, page 22 of 26 This HST-dark galaxy falls in a projected overdensity on the sky, consisting of sources in the redshift range 3.42 ≤ z ≤ 3.56 and brighter than K s < 24.9 (Forrest et al. 2017). This density has been computed by Forrest et al. (2017) using the 7th nearest-neighbor technique (Papovich et al. 2010). This overdensity, centered at RA = 53.08 • , Dec = -27.85 • , extends beyond approximately 1.8 Mpc.

The redshift derived in the ZFOURGE catalog is z = 4.82, making it the farthest galaxy detected in this blind survey. However, we remain cautious regarding this redshift, as this entry has been flagged in the ZFOURGE catalog (use = 0) due to the S/N of this galaxy (4.7) being below the limit defining galaxies with good photometry (S /N ≥ 5). This galaxy is the only galaxy in our catalog flagged in the ZFOURGE catalog. For this reason, we represent it with an empty circle Fig. 19. AGS11 has not been detected in the 7 Ms Chandra survey.

The stellar mass, derived in the ZFOURGE catalog, 3.55 × 10 10 M , is consistent with the masses of all of the other ALMA galaxies found in this survey. What is particularly interesting in the multiwavelength images of this galaxy is that AGS11 is detectable only by ALMA and in the IRAC-bands (in non-stacked images). Outside of these wavelengths, no emission is detectable.

AGS15

AGS15 is at a distance of 0 59 from its possible HST counterpart (ID CANDELS 3818) after astrometric correction, corresponding to a physical distance of 4.33 kpc. This is the largest HST-ALMA offset in our entire catalog. The IRAC position, in contrast, matches much more closely with the ALMA posi-tion, with an offset of only 0 14. The stellar mass of the optical galaxy, given by the ZFOURGE catalog (7.24 × 10 9 M ) would have made AGS15 a galaxy lying far from the median stellar mass (1.1 × 10 11 M ) of our survey. The redshift of ID CANDELS 3818 (z = 3.46) is nevertheless consistent with the other redshifts found in this study.

AGS17

AGS17 is a close neighbor (0 27) of ID CANDELS 4414 (z = 1.85). AGS17 is one of the three galaxies detected by Hodge et al. (2013) at 870 µm in the ALMA field of view (along with AGS8 and AGS15 previously discussed). The counterpart of AGS17 was attributed to ID CANDELS 4414 by Wiklind et al. (2014) with an offset between the ALMA detection and the corresponding F160W object of 0 32. Again, there are indications that the identification may be false: the peak of the IR SED is ∼400 µm (see Fig. 22), suggesting a more distant galaxy. To be detected with the flux densities reported in Table 4, a galaxy at z = 1.85 would have an extraordinarily high star formation rate (∼820 ± 240 M yr -1 ), using the IR SEDs of Schreiber et al. (2018). If truly associated with the CANDELS counterpart, this galaxy would be an extreme starburst with an SFR 59 ± 17 times greater than the SFR MS . Galaxies with these properties cannot be ruled out, as galaxies with much higher star formation rates (and offsets from the main sequence) have already been observed (e.g., Pope et al. 2005;Fu et al. 2013). However, such objects are relatively rare. In addition, the stellar mass of ID CANDELS 4414 (10 10 M ) is inconsistent with the trend of the other detections (more than one order of magnitude below the median stellar mass of our catalog).

Another galaxy (ID CANDELS 4436) is relatively close (0 57) to the ALMA detection. The position of the ALMA detection, which is between ID CANDELS 4414 and ID CANDELS 4436, could be the signature of a major merger occurring between these two galaxies. The emission observed by ALMA could result in this case from the heating of the dust caused by the interaction of these two galaxies, but the redshift determination of 0.92 +0.04 -0.18 by Le PHARE (Arnouts et al. 1999;Ilbert et al. 2006) dismisses this hypothesis.

After subtraction of the 2 galaxies close on the line of sight (ID CANDELS 4414 and 4436) in the HAWK-I image, a diffuse source is revealed (half-light radius = 1 55 ± 0 12, sersic index = 1.0). Lower resolution ALMA observations would be needed in order to correctly measure the total submm flux of this extended source.

We also note the position of the IRAC source, located only 0 06 from the ALMA detection.

Discussion

Of the total 23 detections in this survey, seven do not show an HST H-band counterpart. This lack of counterpart could arise from an occultation of the optical counterpart by a foreground galaxy, faint emission at optical wavelengths, or a spurious ALMA detection.

For the four galaxies previously discussed (AGS4, AGS11, AGS15 and AGS17), we observe a signal with IRAC at 3.6 µm and 4.5 µm, despite the limiting sensitivity of IRAC (26 AB mag at 3 σ for both 3.6 and 4.5 µm; Ashby et al. 2015) being lower than HST-WFC3 (28.16 AB mag at 5σ for F160W; Guo et al. 2013) in the respective images. Furthermore, two of the galaxies (AGS15 and AGS17) have already been detected at submillimeter wavelengths (870 µm) by Hodge et al. (2013).

A152, page 23 of 26 A&A 620, A152 (2018) The other three galaxies (AGS14, AGS16 and AGS19) are not detected at any other wavelength hence there is a high probability that they are spurious. This number is in good agreement with the expected number of spurious sources for our sample (4 ± 2).

Figure 5 gives us a glimpse into how sources can be falsely associated with an HST galaxy. When the offset correction is applied, the three galaxies shown with magenta lines move further away from the center position (∆δ = 0, ∆α = 0), rather than closer to it. Another source also appears to show this behavior: AGS20, seen in the lower left quadrant of Fig. 5. The ALMA detection of AGS20 seems to be clearly offset from an HST galaxy, similar to AGS4. To ensure that there is not a more distant counterpart for AGS20 obscured by the HST source, we performed the same analysis as described in Sect. 7 and illustrated in Fig. 23. The result of the decomposition suggests that the ALMA and HST sources are either two components of the same galaxy or two galaxies merging at this position. A spectroscopic analysis of AGS20 would allow for a distinction between these two possibilities.

The IRAC detections seem to be particularly useful to confirm the existence of a source. In the main catalog, except for the three galaxies that we consider as spurious, all others are also detected in the IRAC filters.

In conclusion, we have detected 20% HST-dark galaxies (4 out of 20 robust detections) with a counterpart confirmed at least by IRAC. This proportion may depend in a manner that we cannot address here on the depth of the optical and millimeter images. Knowing that these HST-dark galaxies are dust, hence metal, rich they are likely progenitors of the most massive galaxies seen at z = 0, hence potentially hosted by massive groups or clusters of galaxies. Two of these HST-dark galaxies have a tentative redshift of z = 4.82 and z = 3.76, we therefore expect these galaxies to be located on average within z ∼ 4-5. These two galaxies are already massive (10 10.55 M and 10 10.50 M respectively), suggesting that this population of galaxies is particularly interesting for understanding massive galaxy formation during the first billion years after the Big Bang. Spectroscopy with the JWST NIRSpec instrument will permit very sensitive spectroscopic detection of Hα emission at z < 6.6, and hence an important new tool to measure redshifts of these HST-dark galaxies. GOODS-South will undoubtedly be a venue for extensive JWST spectroscopy, including Guaranteed Time Observations. Spectral scan observations with ALMA can also be a powerful tool to determine the distances, and hence physical properties, of this intriguing population of HST-dark galaxies.

Summary and conclusions

The GOODS-ALMA survey covers an area of 69 arcmin 2 matching the deepest HST-WFC3 coverage of the GOODS-South field at 1.1 mm and at a native resolution of ∼0 24. We used a 0 60 tapered mosaic due to the large number of independent beams at the native resolution. A comparison of the HST source positions with existing catalogs such as Pan-STARRS allowed us to correct the HST astrometry of the GOODS-South field from both a global and local offset (equivalent to a distortion map, see also Dickinson et al., in prep.). We found a median offset between the HST and ALMA images of -96 ± 113 mas in right ascension, α, and 261 ± 125 mas in declination, δ. The main conclusions from our study are listed below. 1. 20 galaxies brighter than 0.7 mJy at 1.1 mm. We detect in total 20 sources above a detection threshold that guarantees an 80% purity (less than 20% chance to be spurious). Among these 20 galaxies (with an S /N > 4.8), we expect 4 ± 2 spurious galaxies from the analysis of the inverted map and we identify 3 probably spurious detections with no HST nor Spitzer-IRAC counterpart, consistent with the expected number of spurious galaxies. An additional three sources with HST counterparts are detected either at high significance in the higher resolution map, or with different detectionalgorithm parameters ensuring a purity greater than 80%.

Hence we identify in total 20 robust detections. 2. Pushing further in redshift the blind detection of massive galaxies with ALMA. The sources exhibit flux densities ranging from 0.6 to 2 mJy, have a median redshift (and rms) of z = 2.92 ± 0.20 and stellar mass of M = (1.1 ± 0.4) × 10 11 M . By comparison with deeper but smaller ALMA extragalactic surveys (Aravena et al. 2016;Dunlop et al. 2017;González-López et al. 2017;Ueda et al. 2018), our redshift distribution is shifted to higher values even though our survey is shallower. This is due to the low surface density of massive, metal hence dust-rich, galaxies at high redshifts. The size of the ALMA survey is therefore a key parameter to detect high redshift galaxies. 3. 20% HST-dark galaxies. The detection criteria of this main catalog allowed us to identify sources with no HST counterparts. Out of the 20 galaxies listed above, and excluding the three candidate spurious detections, we identified four optically-dark or HST-dark galaxies with the request of 80% purity and with a Spitzer-IRAC counterpart at 3.6 µm and 4.5 µm, confirming the existence of a galaxy at the position of the ALMA detection. It is not the first time that such HST-dark sources have been found using e.g., infrared color selections (H-dropouts, see e.g., Wang et al. 2016), but their identification in an unbiased survey at the depth of ALMA in the millimeter range allows us to determine that 20% of the ALMA sources detected at 1.1mm above ∼0.7 mJy are HSTdark (4/20 sources in the main catalog). Two of these sources are detected in the near-infrared in the ZFOURGE catalog, with a photometric redshift of z phot = 4.32 (derived in this study; AGS4, also detected in the radio with VLA) and 4.82 (AGS11). The other two sources (AGS15 & AGS17) were detected with the LABOCA ECDFS Submillimeter Survey (LESS) at 870 µm and with ALMA after a follow-up at the same wavelength, confirming that they were not the result of source blending (Hodge et al. 2013). 4. Exceptionally high AGN fraction. We found a high proportion of AGNs in our ALMA 1.1 mm sample with 40% (8 out of 20 robust detections) detected in the 7 Msec Chandra Xray survey of GOODS-South in the 0.5-7.0 keV band with a X-luminosity greater than 10 43 erg s -1 . Limiting our analysis to the ALMA sources with a redshift and stellar mass determination, we found that 50% of the ALMA sources located in a well-defined stellar mass (M > 3 × 10 10 M ) -redshift (z ∼ 1.8-4.5) range host an AGN as compared to only 14% for the galaxies located within the same zone but undetected by ALMA. This excess AGN contribution may be due to the fact that the ALMA galaxies are preferentially in a starburst mode due to our detection limit -hence possibly experiencing a merger -or/and that the high-resolution of ALMA favors unresolved, hence compact, sources knowing that the mechanism that leads to such compact star-formation may also trigger an AGN. 5. Alleviating the degeneracy of the bright end of the ALMA counts. The differential and cumulative number counts of A152, page 24 of 26 our 20 primary detections allowed us to partly alleviate the degeneracy observed above 1 mJy beam -1 in previous (sub)millimeter studies. We show that ∼15% of the extragalactic background light is resolved into individual sources at 0.75 mJy. By extrapolation, ∼50% of the EBL is resolved at 0.1 mJy.

Introduction

The formation and evolution of the most massive galaxies (M > 5×10 10 M ) at redshifts z > 2 is still largely debated. Their observed number density exceeds theoretical expectations assuming typical dark matter to stellar mass ratios (Steinhardt et al. 2016). The downsizing of galaxy formation challenges theoretical models which match either the low or high mass end but are unable to match both ends (e.g., Fontanot et al. 2009). The presence of a population of massive passive galaxies at z ∼2 with compact stellar surface densities challenges searches for their progenitors (van der Wel et al. 2014).

Since infrared (IR) wavelengths contribute to approximately half of the total Extragalactic Background Light (EBL; e.g., Dole et al. 2006), the study of dust-enshrouded star-formation in distant galaxies is an important tool to progress in our understanding of the evolution of massive galaxies. The first submillimeter extragalactic surveys (Smail et al. 1997;Barger et al. 1998;Hughes et al. 1998) performed with the Submillimetre Common-User Bolometer Array (SCUBA; Holland et al. 1999) on the James Clerk Maxwell Telescope (JCMT) have revealed a population of high redshift galaxies that are massive, highly obscured and have high star formation rates (SFRs). Recent observations using the Atacama Large Millimetre/submillimetre Array (ALMA), which provides a resolution more than an order of magnitude higher than SCUBA, have since refined our understanding of galaxy evolution by securing the identification of optical counterparts and allowing us to detect not only extreme galaxies (galaxies with particularly high star formation rates, e.g., starburst or lensed galaxies), but also "normal" galaxies that are secularly forming stars.

This paper extends our previous analysis (Franco et al. 2018, hereafter F18) of a deep continuum 1.1mm survey with ALMA over an area of 69 arcmin 2 . This survey is located in the Great Observatories Origins Deep Survey-South (GOODS-South) at E-mail: maximilien.franco@cea.fr a location covered with the deepest integrations in the H-band with the HST-WFC3 camera. In F18, we limited our analysis to the blind detection of ALMA sources without considering prior information at other wavelengths. Due to the large number of independent beams in the high-resolution ALMA image, we were limited to the 4.8-σ detection limit. Here we extend the detection limit to 3.5-σ by cross-matching the ALMA detections with catalogs in the near and mid-infrared. The need for a good astrometric calibration led us to introduce an improved correction for the astrometry of the HST image of the GOODS-South field (hereafter GOODS-S). This paper is organized as follows: in §2, we present the data used. In §3, we describe the astrometric correction to be applied to HST positions to align them with those of ALMA. We give the astrometric correction to be applied for all galaxies in the GOODS-South field present in the Guo et al. (2013) catalog, provided as an external link. In §4, we present the criteria and methods used to select the sample of galaxies which constitutes a Supplementary Catalog to the Main Catalog presented in F18. In §5, we present the properties of the galaxies of the Supplementary Catalog, including two optically-dark galaxies. Finally, in §6, we perform a comparative analysis of the distribution of stellar masses, redshifts, and sizes between the sample of galaxies presented in this paper and in F18 and discuss the implications on the nature of the ALMA sources.

Throughout this paper, we adopt a spatially flat ΛCDM cosmological model with H 0 = 70 kms -1 Mpc -1 , Ω m = 0.3 and Ω Λ = 0.7. We assume a Salpeter (Salpeter 1955) Initial Mass Function (IMF). We use the conversion factor of M (Salpeter 1955 IMF) = 1.7 × M (Chabrier 2003 IMF). All magnitudes are quoted in the AB system (Oke & Gunn 1983).

Article number, page 1 of 16 A&A proofs: manuscript no. main_these

Data

ALMA data

This paper uses the 1.1mm photometric survey obtained with the Atacama Large Millimeter/Submillimeter Array (ALMA) between August and September 2016 (Project ID: 2015.1.00543.S; PI: D. Elbaz). The survey performed using band 6 covers an effective area of 69 arcmin 2 matching the deepest HST/WFC3 Hband part of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS; Grogin et al. 2011, Koekemoer et al. 2011, PIs: S. Faber, H. Ferguson), in the Great Observatories Origins Deep Survey-South (GOODS-South). It is centered at α = 3 h 32 m 30.0 s , δ = -27 • 48 00 (J2000). The original 0 . 2 angular resolution was tapered with a homogeneous and circular synthesized beam of 0 . 60 Full-Width Half Maximum (FWHM; hereafter 0 . 60-mosaic). The sensitivity of the 0 . 60mosaic varies within the six slices of the survey around a median value of RMS 0.18 mJy beam -1 .

Additional data

IRAC catalog

We use the Spitzer-Cosmic Assembly Near-Infrared Deep Extragalactic Survey (S-CANDELS; Ashby et al. 2015) catalog of galaxies detected at 3.6 and 4.5 µm with the Infrared Array Camera (IRAC; Fazio et al. 2004) aboard the Spitzer Space Telescope (Werner et al. 2004). The catalog (Ashby et al. 2015) -hereafter S-CANDELS catalog -that reaches a 5-σ depth of 26.5 mag (AB) includes 2627 galaxies in the GOODS-ALMA field, i.e. about 38 sources.arcmin -2 .

HST H-band catalog

The GOODS-ALMA area covers the deepest H-band part of the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS; Grogin et al. 2011) field (central one-third of the field). The point source catalog reaches a 5-σ depth of 28.16 mag (AB) in the H 160 filter (measured within a fixed aperture of 0 . 17; Guo et al. 2013). The surface density of galaxies detected at 1.6 µm with the Wide Field Camera 3 / infrared channel (WFC3/IR) within the GOODS-ALMA field is about 233 sources.arcmin -2 .

Near-infrared K s -band catalog

We use the 2.2 µm catalog described in Straatman et al. (2016) that uses an ultradeep image resulting from the combination of multiple observations in the K and K s bands from: (i) the Very Large Telescope (VLT), which combines the images of GOODS-S done with the Infrared Spectrometer and array camera (ISAAC; Moorwood et al. (1999)) in the K s -band (Retzlaff et al. 2010) with the High Acuity Wide filed /K-band imager (Hawk-I; Kissler-Patig et al. 2008) image in the K-band (Fontana et al. 2014), (ii) the 6.5m Magellan Baade Telescope combining the K s -band image from the FourStar Galaxy Evolution Survey (ZFOURGE, PI: I. Labbé) using the FourStar near-infrared Camera (Persson et al. 2013) with the K-band image using the Persson's Auxillary Nasmyth infrared camera (PANIC; Martini et al. 2004) in the HUDF (PI: I. Labbé), (iii) the Canada-France-Hawaii Telescope (CFHT), with the K band image done with the wide-field infrared camera (WIRCam; Puget et al. (2004) as part of the Taiwan ECDFS Near Infrared Survey (TENIS; Hsieh et al. 2012).

The 5-σ point-source detection threshold in this ultradeep K s image reaches a magnitude between 26.2 and 26.5, which leads to an average galaxy surface density of about 168 sources.arcmin -2 .

Radio catalog

A radio image that encompasses the GOODS-ALMA field was observed with the Karl G. Jansky Very Large Array (VLA) at a frequency of 3 GHz (10 cm) and an angular resolution of ∼0 . 3 for a total of 177 hours (configurations A, B, & C; PI: W. Rujopakarn). Down to the average depth of the radio catalog within the GOODS-ALMA region of RMS = 2.1 µJy.beam -1 , the average surface density of radio sources is about 5 sources.arcmin -2 .

Astrometric correction of the HST image of GOODS-South

We describe in F18 the presence of a systematic offset of ∆RA = -96 ± 113 mas in right ascension, and ∆Dec = 261 ± 25 mas in declination between the ALMA and HST images. This offset, interpreted as a positional shift of the HST image with respect to all other reference frames, is in good agreement with the offset previously discussed in Dunlop et al. (2017) and Rujopakarn et al. (2016). For the GOODS-North field, the coordinates were shifted by approximately 0.3 arcsec, primarily in declination, compared to those of other astrometric reference datasets (Dunlop et al. 2017). However, this correction has not been made to the v2.0 release for GOODS-South, in part because no external astrometric reference data with both suitable absolute accuracy and faint source density (such as the SDSS) were available 1 .

The offset used until now only corrects for the bulk global shift in astrometry but it does not account for the relative error in the astrometric calibration that was introduced in the building of the HST mosaic. In the following, we propose to determine this local correction that behaves like a distortion correction. This correction is important in the present study since we aim at using prior knowledge of existing sources from other wavelengths in order to push the ALMA detection limit to deeper levels.

We take advantage of the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) Data Release 2 (Flewelling et al. 2016). The offset between HST and Pan-STARRS images computed using an ensemble of 375 common detections (see Fig. 1 left panel) is comparable to the one presented in F18: ∆RA = -96±83 mas and ∆Dec = 252±107 mas.

The comparison of the positions of 69 sources in common between our 3 GHz VLA catalog (5σ detections; Rujopakarn et al., in prep.) and Pan-STARRS within a radius of 0 . 6 shows that there is no offset between both images (Fig. 1

middle panel).

To reduce the risk of misidentification, in all the astrometric analysis, we only retained galaxies that had been observed at least twice in the same filter during the Pan-STARRS survey. The average deviations are found to be ∆RA = 0 ± 98 mas and ∆Dec = 12 ± 160 mas.

Similarly, we find no offset between our ALMA sources (both the Main catalog presented in F18 and the supplementary catalog presented in the following) and their VLA counterparts for the 27 galaxies in common between both catalogs (Fig. 1, right panel). The average offset is ∆RA = 3 ± 113 mas and ∆Dec = 16 ± 93 mas well within the expected uncertainties for S/N ∼ 4 sources (Ivison et al. 2007;Hatsukade et al. 2018). For each panel, the histogram of the offsets in RA and DEC is shown as well as a fit with a Gaussian function (orange curve). The position of the peak and the standard deviation of the Gaussian is indicated for each curve. The middle and the right panels show that there are no significant astrometric differences between ALMA and JVLA nor between JVLA and PS1, while The left panel shows the clear shift in both RA and DEC between the positions of 375 sources in common between the Pan-STARRS (PS) and HST images. We measure a systematic offset of ∆RA = -96 ± 83 mas and ∆Dec = 252 ± 107 mas. In addition, a local offset is presented in Fig. 2. Some of these sources come from the supplementary list discussed in the following sections of this work, but since we applied this astrometric correction to the HST sources used as priors in the catalog production, we decided to present the astrometric correction upfront and to illustrate the positions of all our ALMA galaxies in this section.

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The excellent agreement in the astrometry of VLA, ALMA, and Pan-STARRS implies that it is most likely the HST coordinate system that needs to be corrected.

After subtracting this systematic and global offset from the HST data, the residuals offsets present spatially coherent patterns (see Fig. 2). Each arrow represents the median offset between Pan-STARRS and HST positions, for a sliding median containing on average 30 points. This local offset varies with position in the GOODS-South field, and we refer to this as a distortion offset artificially introduced in the mosaicing of the HST data. The absolute value of the distortion offset is lower than the systematic offset, but it is not negligible, and can reach values higher than 0 . 15 at the edge of our GOODS-ALMA sur--0. vey. A possible explanation for this local distortion may come from the process of making the HST maps themselves. Before the projection of the HST image onto the reference grid according to the World Coordinate System (WCS), a geometric distortion was applied using the WFC3 SMOV F606W data alone 2 (Windhorst et al. 2011). This wavelength-independent geometric solution becomes greater for regions near the field edge (Windhorst et al. 2011), where the error on the correction itself also becomes very large. The combined effect of the global offset and distortion offset between the ALMA and HST positions is illustrated in Fig. 3 and listed in Table 1 both before and after applying the global offset of ∆RA = -96±83 mas and ∆Dec = 252±107 mas and the distortion offset. With the exception of two galaxies for which the offset between the ALMA detected position and that of HST is ∼ 0 . 4 (after correction of both the global offset and the distortion offsets, AGS27 and AGS35), all other galaxies have a difference in the two positions of < 0 . 27. The average deviation after correction is -35 mas in RA and 47 mas in DEC for the sample of galaxies selected in this study. (indicated by a magenta cross in Fig. 3). The updated RA and Dec positions derived for all galaxies in the Guo et al. (2013) catalog after the correction of both systematic and local offset are given at https://github.com/maximilienfranco/astrometry/.

ALMA Main and Supplementary catalogs

ALMA Main Catalog

The main ALMA catalog consists of 20 sources detected above 4.8 σ (F18). This catalog was built without any prior assumption from a blind source extraction down to the 4.8 σ-limit using Blobcat (Hales et al. 2012).

2 http://www.stsci.edu/hst/wfc3/idctab_lbn

The detection limit was set to S/N ≥ 4.8 due to the large number of independent beams that leads to spurious detections that become rapidly more numerous than the number of robust detections below this threshold, despite the tapering at 0 . 60. Here the 4.8 σ-limit concerns the central pixel detection threshold (σ p = 4.8) and is associated with a constraint on the adjacent surrounding pixels that are included in the source if they pass a detection threshold of σ f = 2.7. This combination of parameters ensures an 80 % purity where the purity criterion p f is defined as:

p f = N p -N n N p > 0.8 (1)
where N p and N n are the number of positive and negative detections. The negative detections refer to the detections in the inverse map (in other words detections in the continuum map multiplied by -1).

The initial catalog coming out of the blind source extraction contains 23 detections including 3 detections that we flagged as spurious in F18 (marked with an asterisk in the Table 2 of F18). Finding three spurious detections out of 23 detections matches the expected number of spurious sources obtained from the difference between positive and negative peaks above the 4.8 σ level of 4 with a Poissonian uncertainty of ±2. These three sources are the only ALMA detections in the list without any sign of an IRAC counterpart at λ = 3.6 or 4.5 µm (Spitzer/IRAC channels 1 and 2) despite the availability of ultra-deep IRAC data in this field (26.5 AB mag, Ashby et al. 2015). The possibility that these sources are most likely spurious was later on confirmed by Cowie et al. (2018) using a 100 arcmin 2 survey of the field down to an RMS ∼0.56 mJy at 850 µm with SCUBA-2. While none of the three detections that we listed as spurious were detected by SCUBA-2, 17 out of our 20 brightest ALMA sources were detected by Cowie et al. (2018). The remaining 3 sources were either confirmed with ALMA by Cowie et al. (2018) -AGS21 and AGS23 -or lie outside of the SCUBA-2 field of view -AGS22. We note however, that AGS22 is both at the very limit of our detection threshold and that it is the only galaxy of our list that does not show any IRAC counterpart. In view of the very large number of expected spurious detections at the 3.5σ limit that we plan to reach in the present paper, we will adopt the strategy to limit ourselves to the most secure ALMA detections, which exhibit a clear IRAC counterpart. As a result, we will limit the original main sample to 19 galaxies only, leaving aside AGS22 for consistency. In the present paper, we propose to use counterparts at other wavelengths to identify robust ALMA detections below the 4.8σ limit of the Main Catalog described in Sect. 4.1. This approach is similar in philosophy to a prior source extraction approach, except that we start from the ALMA blind source extraction at a lower threshold and then only keep sources with counterparts already identified in the near and mid infrared. We start with the list of sources detected with the same algorithm than the Main Catalog but push it down to the σ p = 3.5 limit. A total of 1077 sources are detected down to this threshold, most of which are spurious simply due to the large number of independent beams (more than one million in the 0 . 60 tapered map). Indeed the inverse map exhibits an equivalently large, even Fig. 5. Distance between ALMA positions and the closest IRAC galaxy listed in the S-CANDELS catalog for the sources presented in F18, reddashed line, for the supplementary catalog, gray and for all the 3.5σ detections. We also represented the JVLA counterparts (at 3GHz) with a black solid line and for the all the ALMA 3.5σ detections with both IRAC and a JVLA counterpart between 0 . 3 and 0 . 7 from the ALMA detections have been selected.

larger, number of detections of 1157. The number of detections at this level obviously depends on noise fluctuations but does not preclude the existence of real positive sources. Hence we cannot rely on Eq. 1 of F18 to calculate the probability that a source is real from a purely blind detection approach. We observed in F18 that all the ALMA robust detections of the Main Catalog present an IRAC counterpart, hence we start by imposing the requirement that all candidate detections exhibit an IRAC counterpart. We note that this criterion may lead us to reject real ALMA sources without any IRAC counterpart with the possible consequence of biasing our sample towards the most massive galaxies, but this is for the sake of the robustness of the sources. ALMA sources without any IRAC counterpart may well exist (see e.g., Williams et al. 2019) and would be particularly interesting to analyse, but this is out of the scope of the present paper, since including sources without IRAC counterparts would imply including a significant number of hazardous sources in the sample.

In the process of cross-matching the ALMA and IRAC images, we identified several cases of IRAC sources that were present in the IRAC image but were not listed in the S-CANDELS catalog (see Sect. 2.2.1). These sources were systematically located close to one or several brighter IRAC sources. We therefore implemented a new source extraction for those sources taking care of modeling the neighboring sources to proceed to a clean de-blending of the IRAC sources. This allowed us to determine the S/N ratio of those sources and only keep real detections. In most cases, those sources exhibited a counterpart in either the H and K s band catalogs (described in Sect. 2.2.2,2.2.3). This led us to extend our counterpart search to the H and K s bands that we will use as priors to identify candidate IRAC sources that may have been missed in the original S-CANDELS catalog.

We choose the cross-matching radius between the positions of the ALMA detections and the IRAC, H and K band catalogs to be equal to the value of the largest FWHM. It is equal to 0 . 60, the FWHM of the tapered 1.1mm ALMA image, for the cross-match with the CANDELS H-band and ZFOURGE Kband catalogs, and equal to 1 . 95 for the cross-match with the IRAC channel 1 (3.6 µm) catalog (FWHM IRAC = 1 . 95 at 3.6 µm, FWHM IRAC = 2 . 05 at 4.5 µm). Before performing this crossmatching, we apply the astrometric correction to the CANDELS and ZFOURGE catalogs which use the HST reference frame, as described in Sect. 3.

A total of 204 sources detected with ALMA above 3.5σ at 1.1 mm have a counterpart in at least one of the three catalogs (see Fig. 4). In comparison, there are 182 detections above 3.5-σ that also fulfill these criteria in the inverse image. We recall that we used the H and K-band counterparts as priors to search for IRAC sources that may have been missed in the S-CANDELS catalog due to the presence of a bright neighbor.

We note that 84 % (16 out of 19 sources) of the ALMA sources in the Main Catalog described in F18 have an IRAC counterpart closer than 0 . 3 (red dashed line in Fig. 5). Since our goal is not here to include all possible ALMA sources but to limit the Supplementary Catalog to the most robust candidates, we decided to impose a more stringent constraint on the association with IRAC counterparts by keeping as robust candidates those within a distance of 0 . 3. In total, 8 ALMA sources detected between 3.5σ and 4.8σ fulfill this criterion. This close association between ALMA and IRAC may be due in part to the fact that the FWHM of the IRAC images is limited by the pixel size rather than the diffraction limit, hence position accuracies may actually be better determined than the 1 . 95 FWHM of IRAC.

Looking at the remaining three sources in the Main Catalog, we noticed another interesting characteristics. They are all closer than 0 . 7 from their IRAC counterpart and nearly all exhibit a radio counterpart as well (2 out of 3). In fact, out of the 19 sources in the Main Catalog, 16 hence again 84 % exhibit a radio counterpart. We therefore chose to list in the Supplementary Catalog the sources that have both an IRAC and a radio counterpart closer than 0 . 7. This extra condition adds an extra 6 ALMA sources detected between 3.5σ and 4.8σ.

In total, we end up with a list of 14 sources which fulfill the criteria of having an IRAC counterpart either (i) closer than 0 . 3 or (ii) closer than 0 . 7 but associated with a radio counterpart in the 3 GHz catalog.

It is possible that using these criteria does not allow us to detect all "real" ALMA detections with a S/N > 3.5 but these conservative criteria ensure a high purity rate. We performed Monte Carlo simulation to estimate the probability that an ALMA detection lies randomly close to a galaxy listed in the S-CANDELS catalog. We randomly define a position within GOODS-South and then measure the distance to its closest IRAC neighbour using the source positions listed in Ashby et al. (2015) for IRAC sources with S/N > 5 We repeat this procedure 100 000 times. This method gives results comparable to the one presented in ?. The distance from the nearest IRAC galaxies, within a radius of 1 . 95 is given Table 1. In our supplementary catalog, for the farthest source of an IRAC source (0 . 64), the percentage of a random IRAC association is 1.36 %. With the exception of one other source, the other detections have a probability of random IRAC association ≤ 1%.

We checked whether deeper surveys covering parts of the GOODS-S field could be used to validate or invalidate those ALMA Supplementary Catalog sources. The HUDF (Dunlop et al. 2017) and ASAGAO (Hatsukade et al. 2018) surveys reach a depth of RMS 35µJy at 1.3mm and RMS 6 µ Jy at 1.2 mm respectively. Using the same scaling factors as those presented in F18, these depths convert to RMS 52 µJy and RMS 79 µJy respectively at the wavelength of 1.1mm of the present GOODS-ALMA survey. Only three ALMA 1.1mm sources from the Supplementary Catalog fall in the area covered by these deeper surveys and all of them were detected and listed in the associated catalogs (see Fig. 8). The sources AGS29 and AGS35 from our Supplementary Catalog were both detected within the ASAGAO survey and listed as the sources 18 and 26 respectively (Hatsukade et al. 2018). The source AGS38 falls within the HUDF survey and is listed as UDF16 (Dunlop et al. 2017). Hence our independent identification of sources down to the 3.5-σ level did not bring any spurious source without any counterpart in deeper ALMA surveys, instead all 3 sources in these deeper images are confirmed.

Supplementary catalog: optically dark galaxies

As discussed above, we searched for potential IRAC sources that were present in the IRAC images but missed in the S-CANDELS catalog because of the presence of a bright IRAC neighbor. Start- ing from the H and K-band images and catalogs, we identified two such sources, AGS24 and AGS25. Both are detected in the K-band, but neither of these two sources has been detected by the HST even in the 1.6 µm H-band (down to the 5σ limiting depth of H = 28 AB), hence they are HST-dark like 4 sources listed in F18 and as also discussed in Wang et al. e.g., 2016;Elbaz et al. e.g., 2018;Schreiber et al. e.g., 2018;Yamaguchi et al. e.g., 2019.

The source AGS24 exhibits extended IRAC emission that is 0 . 36 away from the ALMA position. This is slightly larger than the 0 . 3 criterion but the source is also detected in the radio at 6 GHz (3.7σ) and 3 GHz (5.7σ). The S/N of this source is higher in the 0 . 29 mosaic than in the 0 . 60 tapered image, which suggests that it is particularly compact at 1.1 mm. This galaxy will be presented in detail in Zhou et al. (in prep), where a stellar mass and photometric redshift are estimated to be z ∼ 3.5 and M = 1.82 +0. 27 -0.50 ×10 11 M . The source AGS25 is 0 . 1 away from its K-band counterpart in the ZFOURGE catalog (after applying the astrometric correction to the position of the ZFOURGE source), the source ID ZFOURGE = 11353 with a magnitude K = 25.9 AB shown by a circle in Fig. 6. This source is not listed in the CANDELS catalog Guo et al. (2013), nor in the S-CANDELS catalog Ashby et al. (2015). It is marginally detected in radio at 5 and 10 cm with a S/N ratio close to 3. AGS25 is close (3 ) to a massive galaxy listed in CANDELS, ID CANDELS = 8067 with a stellar mass of M = 5.6×10 10 M at a redshift of z spec = 1.038). ID CANDELS = 8067 is the bright neighbor that explains the absence of AGS25 in S-CANDELS. We subtracted it from the IRAC image by modeling a Sérsic profile with GALFIT Peng et al. (2010) and measured an IRAC flux density of 0.81±0.19 mJy (see Fig. 6). The IRAC source is 0 . 28 away from the ALMA position of AGS25.

Since the ALMA source is only 0 . 1 away from the ZFOURGE source ID ZFOURGE = 11353, we use the stellar mass and redshift from the ZFOURGE catalog for this source. The characteristics of this galaxy make it particularly interesting, with z AGS 25 = 4.66 +0.25 -0.26 and M ,AGS 25 = 2.0×10 10 M . These properties are similar to those of the Main Cata-Article number, page 6 of 16 log source AGS11, which is also an HST-dark galaxy, with z AGS 11 = 4.83 +0.82 -0.76 and M ,AGS 11 = 2.8×10 10 M . We note that among the 4 HST-dark galaxies for which we were able to determine a mass and redshift, there appear to be two distinct trends. Galaxies (AGS4 and AGS24) are among the most massive of all active UVJ galaxies detected in the region covered by the ALMA survey. AGS4 has a stellar mass M = 2.81 +1. 65 -1.03 ×10 11 M . In other words, it is the most massive galaxy at 4 < z < 5 in our catalogs. AGS24 has a stellar mass M = 1.82 +0. 27 -0.50 ×10 11 M . The other two HST-dark galaxies are of intermediate stellar mass, but with a redshift higher than 4.5.

In total, we end up with a list of 16 sources in the Supplementary Catalog including the two HST-dark sources AGS24 and AGS25 which exhibit the strongest S/N ratio of the catalog. Their properties are listed in Table 1 andTable 2 If we compare the nature of the counterparts of ALMA detections above 3.5-σ in the image and the inverse image, we can see a difference that strengthens the solidity of the 16 sources of the Supplementary Catalog. There are 62 and 45 detections above 3.5-σ in the ALMA image that have a counterpart in the K-band of the ZFOURGE catalog in the image and inverse image respectively. The stellar mass distributions of both samples are represented by dashed black and green lines for the image and inverse image respectively in Fig. 7. Both histograms show the same behavior at stellar masses below 10 10 M but there are nearly no galaxies above this mass threshold in the inverse image while there is a second bump in the histogram of the sources in the real image. Massive galaxies being rarer than low mass ones, the probability to get an association with such galaxy is lower and the fact that there is a second bump at high stellar masses in the real image suggests that these may be real. The Supplementary Catalog histogram shown in filled grey matches very nicely this second bump of massive galaxies. We recall that we did not impose any criterion of brightness or stellar mass in the selection of the Supplementary Catalog but only distances to IRAC, K-band and radio sources. If we limit ourselves to the galaxies above a stellar mass of 10 10 M , we can see that the number of sources in the Supplementary Catalog is close to the difference between the image and inverse image.

In the sample of cross-matched galaxies from the positive image, 21/62 galaxies (∼ 34 %) have a stellar mass greater than 10 10 M , compared with only 2/45 galaxies (∼4 %) in the inverse image (see Fig. 7). A Kolmogorov-Smirnov (KS) test on these data gives a p-value of 3.9×10 -3 between these two samples, meaning that the likelihood that the two samples were drawn from the same distribution is extremely low. When we remove the sample of 16 galaxies listed in Table 1, the two samples become more similar. The p-value from a KS test then reaches 0.71. This means that once the galaxies in our study have been removed, the detections that remain have as high a probability of originating from the same parent sample as the inverse image detections, so that they are no longer statistically different from noise.

This suggests that not only the Supplementary Catalog is robust but also that there is little margin for an extra population of real sources that we would have missed.

Catalog

The positions of the ALMA sources listed in the Main and Supplementary catalogs are shown in Fig. 8 where they can be compared to the locations of other ALMA surveys. The postagestamp images of the sources are shown in Appendix A.1.

Redshifts and stellar masses

Except for the two HST-dark galaxies, AGS24 and AGS25 (discussed in Sect. 4.2.2), all sources listed in the ALMA Supplementary Catalog have been given a photometric redshift by the CANDELS (Guo et al. 2013) and ZFOURGE (Straatman et al. 2016) teams. The two sources of photometric redshifts listed in Col. [START_REF] Dowell | HerMES: Candidate high-redshift galaxies discovered with Herschel/SPIRE[END_REF] and Col.( 6) of Table 2 are in excellent agreement (see Fig. 9-left). Excluding AGS35 (whose redshift given in the ZFOURGE catalog, z = 9.48 is much higher than that given by the CANDELS catalog, z = 2.99), the average of |z HST -z ZFOURGE | /(1 + (z HST +z ZFOURGE )/2) for the galaxies that have redshifts in both catalogs is 0.03.

A total of 38 % of the galaxies in the Supplementary Catalog (6/16) have been assigned a spectroscopic redshift:

-AGS26: z spec = 1.619 determined with VLT/FORS2 (Vanzella et al. 2008). -AGS29: z spec = 1.117 from the VIMOS VLT Deep Survey (Le Fèvre et al. 2013). -AGS30: z spec = 0.65 from the HST/ACS slitless grism spectroscopy of the PEARS program (Ferreras et al. 2009). -AGS37: z spec = 1.956 determined using the Spitzer Infrared Spectrograph (Wuyts et al. 2009;Fadda et al. 2010) and confirmed with the 3D-HST survey (Momcheva et al. 2016). -AGS38: z spec = 1.314 determined with VLT/FORS2 (Vanzella et al. 2008).

We note that two additional spectroscopic redshifts have been determined for galaxies in the Main Catalog since the publication of F18. 1. Details of the positional differences between ALMA and HST-WFC3 for our catalog of galaxies identified in the 1.1mm-continuum map. Columns: (1) Source ID; ( 2), ( 3) Coordinates of the detections in the ALMA image (J2000); ( 4), ( 5) Positions of HST-WFC3 H-band counterparts when applicable from Guo et al. (2013), ( 6), (7) Distances between the ALMA and HST source positions before (Dec∆ HS T 1 ) and after (∆ HS T 2 ) applying both the systematic and local offset correction presented in Sect. 3; ( 8), [START_REF] Williams | The progenitors of the compact early-type galaxies at high redshift[END_REF] Offset to be applied to the HST source positions, which includes both the global systematic offset and the local offset; [START_REF] Huang | Four IRAC sources with an extremely red H -[3.6] color: passive or dusty galaxies at z > 4.5?[END_REF] AGS35, for the reasons mentioned above). They were multiplied by a factor 1.7 to scale them from the Chabrier IMF to a Salpeter IMF. Both catalogs provide gobally consistent stellar masses with no systematic offset, the median of the ratio M ,CANDELS /M ,ZFOURGE = 1.06 (see Fig. 9-right).

Flux and size measurements

Flux densities of the Supplementary Catalog sources were measured by fitting the light profiles with a circular Gaussian in the uv-plane using uvmodelfit in CASA (McMullin et al. 2007). Due to the low S/N (3.5 < S/N < 4.8), we have opted a circular Gaussian rather than an asymmetric Gaussian, in order to limit the number of free parameters. We use the formula given by Martí-Vidal et al. (2012) as in F18 to determine the minimum size that can be reliably measured in the uv-plane as a function of the S/N ratio of the source for an interferometer :

θ min 0.88 θ beam √ S/N (2)
We use the S/N of the tapered map at 0 . 60 and θ beam = 0 . 60. Galaxies for which the circular Gaussian fit in the uv-plane give a size (FWHM) smaller than θ beam , the size limit given by Eq. 2, we set the size of the galaxy to θ beam and use the peak flux density measured on the direct image. This choice is expected to lead to slightly underestimated flux densities since it implies that sources are assumed to be point-like while the typical size measured for distant ALMA galaxies is on average close to 0 . 3 (Simpson et al. 2015a;Ikarashi et al. 2017;Elbaz et al. 2018). Assuming a point-like source for a real size extension of 0 . In this paper, we will take, with the exception of AGS36 which has an inconsistent redshift (z AGS 37,ZFOURGE = 9.47 and for which we will take the data from the CANDELS catalog), the redshifts and stellar masses by the ZFOURGE catalog. Flux uvmodelfit / Flux peak Fig. 10. Ratio between the flux extracted using uvmodelfit in CASA and the peak flux as a function of the size of the galaxy for the supplementary catalog. When the measured size is below the reliable size measurement limit (see Eq. 2), we consider the size given by Eq. 2 as an upper limit. The horizontal solid line indicates flux uvmodelfit = peak flux. The dotted lines show a 15 percent deviation from this equality. For galaxies larger than 0 . 25 (vertical dotted line), the approximation of a point source is no longer valid, and we assume the flux value derived from uvmodelfit for these galaxies.

values having in mind that they may be lower by about 20 %. Using the measurements coming out of uvmodelfit would lead to larger uncertainties for those sources with no reliable size measurement.

For galaxies whose sizes measured using uvmodelfit are larger than this limit (see Fig. 10), we keep the size given by uvmodelfit. For these galaxies, the peak flux approximation is no longer valid and we keep the integrated flux given by uvmodelfit. The flux density of each galaxy, as well as its uncertainty, are listed in Table 2. The sizes measured by uvmodelfit, the detection limit derived from the Eq. 2 and the size of the galaxies are given Table 3.

In order to check whether our flux density measurements were underestimated by a large factor, we computed the expected ALMA flux density that those sources would have if they had et al. 2007;Rodighiero et al. 2011;Elbaz et al. 2011). Since a large fraction of the ALMA sources are actually starbursting and above the MS, this assumption only provides a rough estimate of a lower-limit to the ALMA flux densities. We used the infrared spectral energy distributions (IR SED) from the library presented in Schreiber et al. (2018), with the stellar masses and redshifts listed in Table 1 as input parameters. The measured, F ALMA , and predicted, F S ED , flux densities exhibit a ratio F ALMA /F S ED ranging from 0.73 to 5.2 with a median (average) of 2.4 (2.7) suggesting that about 50 % of the galaxies of the Supplementary Catalog fall within the factor 2 dispersion of the MS, the remaining half being in a starburst phase. None of the measured flux densities fall more than 25 % below the predicted MS ALMA flux density, which suggests that our flux density measurements are probably not largely underestimated.

6.

Comparison of the properties of the ALMA galaxies from the Main and Supplementary catalogs 6.1. Redshifts The redshifts of the Supplementary Catalog covers a wider range (z = 0. 65 -5.36) than the sources of the Main Catalog (z = 1.95 -4.82). Galaxies with a redshift greater than z = 4.5 represented 5 % of the Main Catalog (1/19) and they make 19 % of the Supplementary Catalog (3/16, see Fig. 12). On the other extreme, none of the Main Catalog sources were detected below z = 1.9 whereas 38 % (6/16) of the sources in the Supplementary Catalog are found in this lower redshift range. Despite these differences, the median redshifts of both catalogs are similar, z = 2.70 and 2.56 for the Main and Supplementary catalogs, respectively, showing that there is no systematic shift in redshift between both catalogs but a wider dynamic range for the Supplementary Catalog. This median redshift is also similar to that of Stach et al. (2019), who derive a median redshift of 2.61 ± 0.09. We found no correlation between redshift and flux density of the Supplementary Catalog sources.

Stellar Masses

All galaxies detected in GOODS-ALMA have a stellar mass greater than M = 2×10 10 M . The median stellar mass of galaxies from the Supplementary Catalog, M Supp = 6.6×10 10 M , is half that from galaxies in the Main Catalog, M Main = 1.1 ×10 11 M . Hence by pushing down the ALMA detection limit using IRAC priors, we have reached more normal galaxies, with less extreme stellar masses, and extended the redshift range of the ALMA sources.

We can now compare the galaxies detected by GOODS-ALMA, combining the Main and Supplementary catalogs, to their parent sample of distant star-forming galaxies taken from the ZFOURGE catalog after selecting only the UVJ active galaxies (Williams et al. 2009, using the same definition as in F18, see Fig. 12).

GOODS-ALMA detects nearly half (46%, 6/13) of the most massive star-forming galaxies with log 10 (M /M ) = 11-12 in the range 2 < z < 2.5. Pushing further in redshift to 2.5 < z < 3, GOODS-ALMA also sees nearly half of the star-forming galaxies with log 10 (M /M ) = 10. 7-11 (44%, 7/16). At even further redshifts, 3 < z < 4, GOODS-ALMA detects 38% (3/8) of the most massive galaxies (log 10 (M /M ) = 11-12).

In total, GOODS-ALMA detects about 30 % (11/37) of the most massive star-forming galaxies with a redshift 2 < z < 4 (log 10 (M /M ) = 11 -12).

Sizes

The sizes of the sources of the Main and Supplementary catalogs were derived by fitting a circular Gaussian in the uv-plane using uvmodelfit in CASA. We find that by pushing down the detection limit to 3.5-σ using IRAC priors, we have been able to identify galaxies with nearly twice larger ALMA sizes. The median ALMA 1.1mm FWHM of the galaxies in the Supplementary Catalog is indeed 0 . 32 as compared to 0 . 18 for the galaxies in the Main Catalog. When accounting for the redshift of the sources, we find that the physical circularized half-light radius of the new sources in the present Supplementary Catalog (R 1/2 = FWHM/2) is 1.3 kpc as compared to only 0.65 kpc for the Main Catalog. If we take into account the fact that the Supplementary sources exhibit stellar masses that are half of those of source in the Main catalog, this implies that by pushing down the ALMA detection limit using priors, we were able to identify lower stellar mass galaxies in which dust-enshrouded starformation extends over twice larger sizes.

In Fig. 13, we show the cumulative fraction of sources with a major axis below a given size for the Main (red) and Supplementary (grey) catalogs. This figure clearly shows that the galaxies detected in the Main catalog are generally more compact than those in the Supplementary catalog: 80% of the galaxies in the Main Catalog have a FWHM below 0 . 24, whereas in the Supplementary Catalog, 80% the sources have a size above 0 . 27 arcsec. The size below which 80 % of the galaxies in the Supplementary Catalog are found is twice larger with a FWHM of 0 . 49.

This shows that while the projected sizes of dust-enshrouded star-formation probed by ALMA are globally small for massive and distant galaxies, the new sources that we present here in the Supplementary Catalog do not extend the sample to much lower flux densities but to sources with a wider extension of the dust emission. This explains in part why these sources were not detected in the Main Catalog. Although their integrated flux densities may be equal (and sometimes higher) than sources in the Main Catalog, this flux is diluted into several beams and therefore drops below the detection limit for the central beam.

We recall that this increase in the ALMA sizes measured in the Supplementary Catalog remains such that globally the ALMA emission extends over much smaller sizes than their Hband sizes, confirming that the ALMA sources are particularly compact at 1.1 mm (e.g., Chen et al. 2015;[START_REF] Simpson | The SCUBA-2 Cosmology Legacy Survey: ALMA Resolves the Bright-end of the Sub-millimeter Number Counts[END_REF]Rujopakarn et al. 2016;Elbaz et al. 2018;Calistro Rivera et al. 2018, see also Franco et al., in prep).

How complete is the Main plus Supplementary catalog ?

The average noise in the GOODS-ALMA image is RMS=0.182 mJy, hence the 3.5-σ limit of the Supplementary Catalog converts into a detection limit of about 0.64 mJy. We note that since the RMS of the noise varies across the image, because it is subdivided in 6 slices taken at different epochs, sources may be detected below 0.64mJy (a source was detected at 0.55mJy).

The various studies that have carried out millimetric counts (e.g., Hatsukade et al. 2013;Oteo et al. 2016;Aravena et al. 2016;Umehata et al. 2017;Fujimoto et al. 2017;Dunlop et al. 2017;Franco et al. 2018;Hatsukade et al. 2018) allow us to es-Fig. 13. Cumulative fraction of sources with a FWHM below a given size for the main (red) and the supplementary catalog (gray). These sizes are computed by fitting the ALMA detections with a circular Gaussian in the uv-plane using uvmodelfit in CASA. The shaded areas correspond to the integration of the individual uncertainties of the sizes of each detection. timate an expected galaxy surface density that varies between 2000 and 3500 galaxies.deg 2 above 0.65 mJy at 1.1 mm. Over the size of 69.5 arcmin 2 of the GOODS-ALMA survey, this amounts to an estimated number of sources ranging between 39 and 48. In comparison, we have now extended the number of detections in GOODS-ALMA to 35 galaxies. This number is not far from the expected one, especially when one accounts for cosmic variance, and suggests that the present sample may be more than 70 % complete above 0.65 mJy.

Conclusion

Using prior information at 3.6 and 4.5 µm from IRAC (combined with deep HST H-band and ground-based K s-images), we were able to explore the presence of galaxies detected at 1.1mm with ALMA down to the 3.5-σ limit. This was done despite the extremely large number of independent beams in the ALMA image even after tapering from 0 . 29 to 0 . 6.

In order to avoid introducing spurious associations, we restricted the new sample to ALMA detections with either an IRAC counterpart closer than 0 . 3 or closer than 0 . 7 but with a radio counterpart as well. In two cases, we used the K-band Article number, page 12 of 16 M. Franco et al.: GOODS-ALMA: II. Using IRAC priors to probe fainter millimeter galaxies image to deconvolve IRAC sources that were missed by previous studies because of their close proximity to bright IRAC neighbors. These two galaxies do not exhibit any counterpart in the HST images, hence they are HST-dark, but both present a radio counterpart. In total we find 16 galaxies in the Supplementary Catalog that bring the total sample of GOODS-ALMA 1.1mm sources to 35 galaxies. This number is between 70 and 90 % of the predicted number of galaxies expected to be detected at 1.1 mm above 0.65 mJy as derived from existing millimeter number counts. We now detect in GOODS-ALMA between a third and half of the most massive star-forming galaxies (log 10 (M /M ) = 11 -12) depending on the redshift range within 2 < z < 4.

The redshift range of the Supplementary Catalog covers a wider dynamic range (z = 0. 65 -5.36) than the sources of the Main Catalog (z = 1.95 -4.82), with no systematic shift in the median redshift of z 2.6. The typical physical size of the new sources in the present Supplementary Catalog (1.3 kpc) is twice larger than that of the Main Catalog sources (0.65 kpc). The lower surface brightness of these sources explains partly why they were not detected in the Main Catalog. Hence, pushing down the ALMA detection limit using IRAC priors allowed us to reach galaxies with half the stellar mass of the Main Catalog (median stellar mass M = 6.6×10 10 M ) in which dustenshrouded star-formation extends over twice larger sizes. However, this increase in the ALMA sizes is not large enough to question the fact that the ALMA emission globally extends over much smaller sizes than the H-band light, confirming that the ALMA sources are particularly compact at 1.1 mm.

Finally, we used a comparison of nearly 400 galaxies in common between HST and Pan-STARRS in the GOODS-ALMA field to show that the astrometry of the HST image does not only suffer from a global astrometric shift, as already discussed in previous papers, but also from local shifts that draw the equivalent of a distortion map that was artificially introduced in the process of building the mosaic of the GOODS-South HST image. We present a solution to correct for this distortion and use this correction in our identification of counterparts. We note that in some cases, the absence of this correction led previous studies to attribute the wrong counterpart to ALMA detections. This will be discussed in more detail in a paper in preparation. Our current knowledge of cosmic star-formation history during the first two billion years (corresponding to redshift z > 3) is mainly based on galaxies identified in rest-frame ultraviolet light 1 . However, this population of galaxies is known to under-represent the most massive galaxies, which have rich dust content and/or old stellar populations. This raises the questions of the true abundance of massive galaxies and the star-formation-rate density in the early Universe. Although several massive galaxies that are invisible in the ultraviolet have recently been confirmed at early epochs 2-4 , most of them are extreme starburst galaxies with star-formation rates exceeding 1,000 solar masses per year, suggesting that they are unlikely to represent the bulk population of massive galaxies. Here we report submillimetre (wavelength 870 micrometres) detections of 39 massive star-forming galaxies at z > 3, which are unseen in the spectral region from the deepest ultraviolet to the near-infrared. With a space density of about 2 × 10 -5 per cubic megaparsec (two orders of magnitude higher than extreme starbursts 5 ) and starformation rates of 200 solar masses per year, these galaxies represent the bulk population of massive galaxies that has been missed from previous surveys. They contribute a total star-formation-rate density ten times larger than that of equivalently massive ultraviolet-bright galaxies at z > 3. Residing in the most massive dark matter haloes at their redshifts, they are probably the progenitors of the largest present-day galaxies in massive groups and clusters. Such a high abundance of massive and dusty galaxies in the early Universe challenges our understanding of massive-galaxy formation. Observations of galaxies across cosmic time have revealed that the more massive galaxies have assembled their stellar masses at earlier epochs, with a substantial population of massive ellipticals already in place at redshifts of about 6-8 3-4. The early assembly of these massive galaxies has posed serious challenges to current galaxy formation theories. Understanding their formation processes requires studies of their progenitors formed at even higher redshifts. However, most currently known high-redshift galaxies, including mainly Lyman-break galaxies (LBGs) and a few extreme starbursts, are found inadequate to account for the large population of these early formed ellipticals, owing to either low stellar masses and star-formation rates, SFRs (for LBGs 9 ), or low space densities (for the extreme starbursts). This suggests that the main progenitors of massive galaxies at z > 3 remain to be found. Identification of these currently missing massive galaxies is key to our understanding of both massive-galaxy formation and the cosmic SFR density in the early Universe.

The main targets of this study are a population of galaxies that are Spitzer/Infrared Array Camera (IRAC)-bright (see below for nomenclature) yet undetected in even the deepest near-infrared (NIR: H-band) imaging with the Hubble Space Telescope (HST), that is, H-dropouts. (Throughout this Letter we use the short form 'Telescope/Instrument' to represent usage of a particular instrument on a particular telescope.)

In total, we have identified 63 H-dropouts with IRAC 4.5-μm magnitude, [4.5], less than 24 mag, within a total survey area of approximately 600 arcmin 2 in deep CANDELS fields with a typical depth of H > 27 mag (5σ) (Fig. 1, Extended Data Table 1, Methods). Although previous studies have shown that these bright and red IRAC sources are promising candidates for massive galaxies at 10,11 z > 3, confirming their nature has been difficult so far owing to the limited sample size, the poor resolution of Spitzer and the lack of multiwavelength information. Here we explore their nature with high-resolution, 870-μm continuum imaging with the Atacama Large Millimeter/ submillimeter Array (ALMA). With only 1.8 min of integration per object, 39 of them (detection rates of 62%) are detected down to an integrated flux of 0.6 mJy (4σ, Extended Data Fig. 1, Extended Data Table 2). Their 870-μm fluxes range from 0.6 mJy to 8 mJy, with a median of S 870μm = 1.6 mJy (Extended Data Fig. 2). Hence most of them are fainter than the 2-mJy confusion limit of the single dish instruments that discovered submillimetre galaxies (SMGs) and much fainter than most SMGs studied until now with typical 12 S 870μm ≳ 4 mJy. The sky density of these ALMA-detected H-dropouts is approximately 5.3 × 10 2 deg -2 after correction for incompleteness (Methods), two orders of magnitude higher than Herschel/SPIRE-selected extreme starbursts (with SFR ≳ 1,000M ⊙ yr -1 ; M ⊙ , solar mass) 3,5 .

The ALMA detections confirm unambiguously that most of the H-dropouts are dusty star-forming galaxies at high redshifts, consistent with their admittedly uncertain photometric redshifts-from optical spectral energy distribution (SED) fitting-with median redshift z me- dian = 4 (Extended Data Fig. 3). Further insights into their properties are obtained from the stacked infrared (IR) SED of the 39 ALMAdetected H-dropouts from MIPS 24 μm up to ALMA 870 μm. The stacked SED peaks between the observations at 350 μm and at 500 μm (Extended Data Fig. 3), consistent with being at z ≈ 4. With a median stellar mass of M * ≈ 10 10.6 M ⊙ and a characteristic IR luminosity (over 8-1,000 μm) of L IR = (2.2 ± 0.3) × 10 12 L ⊙ (L ⊙ , solar luminosity) derived from the stacked SED, these ALMA-detected H-dropouts are fully consistent with being normal massive star-forming galaxies at 13 z = 4 (Fig. 2). Moreover, the ALMA detections also provide crucial constrains on the redshift of individual galaxies. Combined with SCUBA-2 450-μm and VLA 3-GHz data, the majority of the ALMAdetected H-dropouts exhibit red S 870μm /S 450μm and S 1.4GHz /S 870μm colours that are suggestive of redshifts of z > 3 (Extended Data Fig. 4). Similarly, the non-detections at 24 μm (5σ detection limit of 20 μJy) for most of the sources implies red S 870μm /S 24μm colours that are also consistent with z > 3 assuming typical SED templates 14 . We hence conclude that whereas the estimated redshifts for individual galaxies exhibit a large uncertainty, all the available data point to the ALMA-detected H-dropouts being massive, dusty star-forming galaxies at z > 3.

For the remaining about 40% of H-dropouts that are not detected with ALMA, photometric redshift estimates based on their optical Q1 Q2 Q3 Q4 Q5 Q6 Q7

1 Institute of Astronomy, Graduate School of Science, The University of Tokyo, Tokyo, Japan. 2 AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, Gif-sur-Yvette, France. 3 National Astronomical Observatory of Japan, Mitaka, Tokyo, Japan. 4 Leiden Observatory, Leiden University, Leiden, The Netherlands. 5 Department of Physics, University of Oxford, Oxford, UK. 6 Research Center for the Early Universe, Graduate School of Science, The University of Tokyo, Tokyo, Japan. 7 Department of Physics, Anhui Normal University, Wuhu, China. 8 Department of Physics, Ludwig-Maximilians-Universität, München, Germany. 9 National Astronomical Observatories of China, Chinese Academy of Sciences, Beijing, China. 10 Academia Sinica Institute of Astronomy and Astrophysics, Taipei, Taiwan. *e-mail: twang.nju@gmail.com N A T U R E | www.nature.com/nature

Letter reSeArCH

SEDs suggest a similar redshift distribution to that of ALMA-detected ones, with z median = 3.8 (Extended Data Fig. 2). Their stacked ALMA 870-μm image yields a 6σ detection with S 870μm = 0.24 ± 0.04 mJy, approximately 8 times lower than that of ALMA-detected ones, suggesting lower specific SFRs compared to ALMA-detected ones, which is also confirmed by a full fitting of the stacked optical-to-IR SEDs (Extended Data Fig. 5).

Spectroscopic confirmation of H-dropouts has been so far limited to a few sources, which are all found at z > 3. Most of these confirmed cases are extreme SMGs with S 870μm ≳ 10 mJy, for example 2 , HDF-850 at z = 5.18. An H-dropout galaxy with submillimetre flux similar to that of our sample (S 744μm = 2.3 ± 0.1 mJy) has been recently confirmed 15 to be at z = 3.709: it was discovered serendipitously near a quiescent galaxy at the same redshift 6 . By targeting three H-dropouts in our sample that show significant excess (>4σ, Methods) in Subaru medium bands in the optical (about 3,500-6,000 Å) with VLT/ X-SHOOTER, we have successfully detected Lyman-α for two of them and confirmed their redshifts to be z > 3 (z = 3.097 and z = 5.113, Extended Data Fig. 6). These spectroscopic redshifts (z spec ) are in good agreement with their photometric redshift (z phot ) based on optical SED fitting, with σ ≈ .

-/ + 0 1

z z z ( ) (1 )

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Having established that most of the H-dropouts are massive galaxies at z > 3, we now derive their contribution to the cosmic SFR density and stellar mass function. Whereas populations of similarly red galaxies are known to exist at lower redshifts 16 , these largely overlap with the stellar-mass-limited sample used to estimate the SFR density at z < 3. Assuming that the intrinsic IR SED of the ALMA-detected H-dropouts is the same as the SED derived from stacking, the SFR density of ALMA-detected H-dropouts (in M ⊙ yr -1 Mpc -3 ) reaches about 2.9, 2.1 and 0.9 at z = 4, 5 and 6, respectively, or approximately 1.6 × 10 -3 M ⊙ yr -1 Mpc -3 when averaged over the three bins (Fig. 3). This corresponds to about 10% of the SFR density from LBGs at similar redshifts 17 . However, if we focus only on LBGs with masses similar to those of H-dropouts with M * > 10 10.3 M ⊙ , the SFR densities of H-dropouts are one to two orders of magnitude higher, demonstrating that H-dropouts dominate the SFR density in massive galaxies. This dominance is further reflected in the stellar mass functions, as shown in Fig. 3. The fraction of H-dropouts becomes progressively higher at higher masses. At M * ≳ 10 10.5 M ⊙ , the number density of H-dropouts surpasses that of LBGs. Moreover, if we also include galaxies detected in H-band but which show similar red colours (H -[4.5] > 2.5 mag, Extended Data Fig. 7) 8,11 , they make up more than 80% of the most massive galaxies at z > 4. Taken together, these results suggest that the majority of the most massive galaxies at z > 3 have indeed been missed from the LBG selection, and are optically dark.

To put the H-dropouts in the context of the cosmic evolution of massive galaxies, we probe their clustering properties through their cross-correlation with H-detected galaxies at 3.5 < z < 5.5 from the CANDELS survey in the same three fields (Extended Data Fig. 8, Methods). The derived galaxy bias, that is, the relationship between the spatial distribution of galaxies and the underlying dark matter density field, for the H-dropouts is b = 8.4 ± 1.5, corresponding to a dark matter halo mass of M h ≈ 10 13 ± 0.3 h -1 M ⊙ at z = 4 (Fig. 4, Methods). This halo mass of H-dropouts is consistent with them being progenitors of the most massive quiescent galaxies at z = 2-3, as well as progenitors of today's ellipticals that reside in the central region of massive groups and clusters.

The discovery and confirmation of these H-dropouts as massive galaxies at z ≈ 3-6 alleviates greatly the tension between the small number of massive LBGs at z > 3 and the rapid emergence of massive (and quiescent) galaxies at z ≈ 2-3. Assuming an average redshift of z ≈ 4 and SFR ≈ 220M ⊙ yr -1 , these H-dropouts will grow in stellar mass by 1.3 × 10 11 M ⊙ before z ≈ 3. Their number density, n ≈ 2 × 10 -5 Mpc -3 , is also comparable to that of the most massive, quiescent galaxies at z ≈ 3 with 18 M * > 10 11 M ⊙ . The early formation of such a large number of massive, dusty galaxies is unexpected with Red open circles, the total contribution of red galaxies, including both H-dropouts and those non-H-dropouts that have similar red colours (H -[4.5] > 2.5 mag) selected from ZFOURGE at 3.5 < z < 6.5. Q8 4-5 (ref. 26 ) and massive passive galaxies ('Passive galaxies'; purple squares) with M * > 10 10.5 M ⊙ at z = 2-3 (ref. 27 ).

Error bars, 1σ estimated from Poisson statistics. Filled dark-blue and light-blue triangles denote massive and more typical (L * ) LBGs with UV magnitudes of M UV ≈ -22 and M UV ≈ -20.5, respectively. Dotted lines, the corresponding galaxy bias for fixed halo mass (labelled) at different redshifts 28 ; dashed line, the evolutionary track 29 for galaxies with the same galaxy bias as H-dropouts. The descendants of H-dropouts are consistent with massive ellipticals at z ≈ 2-3 and today's most massive galaxies residing in massive groups and clusters.

N A T U R E | www.nature.com/nature

Letter reSeArCH current semi-analytical models 19 , which underestimate their density by one to two orders of magnitude (Fig. 3). Similarly, a deficit of such galaxies is also present in hydrodynamic simulations, which contain no such galaxies at z > 3 in mock deep fields (about 23.5 arcmin 2 , from the Illustris Project 20 ). Moreover, even considering LBGs alone, the number of massive galaxies already appears too large when compared to the number of massive haloes at z > 4 predicted 21 by our current understanding of galaxy evolution in the Lambda Cold Dark Matter (LCDM) framework. Together, this unexpected large abundance of massive galaxies in the early Universe suggests that our understanding of massive-galaxy formation may require substantial revision. Spectroscopic follow-up of the whole population of H-dropouts would be key to providing further insights into this question, which calls for mid-infrared spectroscopy with James Webb Space Telescope in the near future.

Methods

Here we give details of the multi-wavelength observations and the determination of physical properties of sample galaxies. Throughout we adopt a Chabrier initial mass function 30 and the concordance cosmology with matter density parameter Ω M = 0.3, dark energy density parameter Ω Λ = 0.7 and Hubble constant H 0 = 70 km s -1 Mpc -1 . All magnitudes are in the AB system. Observations. Selection of H-dropouts and incompleteness correction. We have cross-matched the F160W-selected catalogue from the three CANDELS fields (Table 1) with an IRAC 3.6-μm and 4.5-μm-selected catalogue 31 from the SEDS survey. The SEDS survey covers the three fields of H-dropouts to a depth of 26 AB mag (3σ) at both 3.6 μm and 4.5 μm and is 80% complete down to [4.5] ≈ 24 mag. We first matched sources with [4.5] < 24 mag in the SEDS catalogue to the F160Wselected catalogue and identified those without H-band counterparts within a 2″ radius (corresponding roughly to the point spread function (PSF) size of IRAC 3.6 μm and 4.5 μm observations). This 4.5-μm magnitude cut was applied to enable sufficient colour range to identify extremely red objects while keeping a complete 4.5-μm-selected sample. We then visually inspected the IRAC images and excluded sources whose flux is contaminated by bright neighbours as well as those falling on the edge of the F160W image. With knowledge of their positions, some of these H-dropouts are marginally detected in the F160W band but exhibit extended profiles and are unidentifiable as real sources without that prior knowledge. This left us 63 sources with 2 of them serendipitously detected in previous band-7 continuum observations with ALMA.

The criterion of no HST counterparts within 2″ radius ensures a clean selection of H-dropouts with reliable constraints of IRAC fluxes. However, given the high density of HST sources in these deep fields, the chance probability of an IRAC-HST coincidence (with distance <2″) is non-negligible. This means that we may have missed some H-dropouts simply because of the presence of a random HST source falling within the 2″ search radius of the IRAC source. To correct for this effect, we calculate the completeness of this selection approach, which is defined at a given position as the probability of finding zero galaxies in the 2″ radius, p(n = 0) = exp(-Nπr 2 ), with N representing the surface density of HST sources and r the searching radius. Averaging over the three CANDELS fields yields N = 0.05 arcsec -2 , implying p(n = 0) = 0.53. This suggests that while our approach yields a clean selection of H-dropouts, roughly half of the true H-dropouts have been missed simply due to chance superposition of sources, which needs to be corrected. In fact, this completeness correction is consistent with recent findings from a blind ALMA survey, which reveals four H-dropouts (with [4.5] < 24 mag) that were not picked up by our approach within an area of one-third of the GOODS-South field 32,33 , in comparison to 12 sources selected by our approach in the whole GOODS-South field. Among these four sources, three have at least one HST counterpart within 2″ (with the remaining one absent from our IRAC catalogue, which is shallower than the one used in ref. 32 ), which is inconsistent with being the right counterpart of the ALMA emission based on the redshift and other physical properties. Albeit with small number statistics, this implies a completeness of our searching approach of about 57%, consistent with our estimated value. In addition to this correction, we also need to correct for the incompleteness of the IRAC imaging from the SEDS survey, which ranges from 93% at [4.5] = 22 mag to 75%-80% at [4.5] = 24 mag in the three fields. Combining the two corrections, a factor of 2 to 2.4 has been applied to the number density (and to the SFR and stellar mass density) of H-dropouts, depending on their IRAC 4.5-μm magnitudes. Multiwavelength photometry. In each field, we gathered mosaics in a large number of bands, including all the images used to build the 3DHST 34 and ZFOURGE 22 catalogues. All our galaxies therefore had rich and deep photometry from the UV to the NIR, reaching typical 5σ depths (AB) of 27 in u to i, 26 in z to H, and 25 in Ks. We provide below full details of the mosaics used.

For GOODS-South, we used VLT/VIMOS images in the U and R bands 35 , ESO/WFI images in the U, U38, B, V, R and I bands from GaBoDS 36 , a CTIO/ MOSAIC image in the z band from MUSYC 37 , Subaru images in 15 medium bands from MUSYC 38 , Hubble images in the F395W, F606W, F775W, F8514W, F850LP, F105W, F125W and F160W bands from GOODS and CANDELS programmes 39-41 , VLT/ISAAC images in the J, H and Ks bands 42 , CFHT/WIRCam images in the J and Ks bands from TENIS 43 , Magellan/FOURSTAR images in the J1, J2, J3, Hs, Hl and Ks bands from ZFOURGE 22 , a VLT/HawK-I image in the Ks band from HUGS 44 , and Spitzer IRAC images from SEDS 31 .

For UDS, we used a CFHT/Megacam image in the u band produced by the 3DHST team 34 , Subaru images in the B, V, R, i and z bands 45 , Hubble images in the F606W, F814W, F125W, F140W and F160W bands from the CANDELS and 3DHST programmes 41,46 , UKIRT/WFCAM images in the J, H and K bands from UKIDSS 47 , Magellan/FOURSTAR images in the J1, J2, J3, Hs, Hl and Ks bands from ZFOURGE 22 , VLT/HawK-I images in the Y and Ks bands from HUGS 44 , and Spitzer IRAC images from SEDS 31 and SpUDS (PI: J. Dunlop).

For COSMOS, we used CFHT/Megacam images in the u and i bands from CFHTLS 48 , Subaru images in the B, g, V, r, i and z bands as well as 10 medium bands 49 , Hubble images in the F606W, F814W, F125W, F140W and F160W bands from the CANDELS and 3DHST programmes 41,46 , CFHT/WIRCam images in the H and Ks bands 50 , Magellan/FOURSTAR images in the J1, J2, J3, Hs, Hl and Ks bands from ZFOURGE 22 , VISTA/VIRCAM images in the Y, J, H and Ks bands from UltraVISTA DR3 51 , and Spitzer IRAC images from SEDS 31 and S-COSMOS 52 .

The photometry was obtained with a procedure very similar to that previously used in deep surveys 22,46 , which we summarize here. Fluxes in UV to NIR were extracted on re-gridded and PSF-matched images in fixed apertures of 2″ diameter. Because of the broader PSF in Spitzer images, fluxes in the IRAC bands were extracted separately, with a 3″ aperture and without PSF matching. The asymmetric IRAC PSF was rotated to match the telescope roll angle for each field. Before extracting the fluxes, all the neighbouring sources within a 10″ radius were subtracted from the images. This was done by identifying the sources from a stacked detection image, and using the HST F160W profile of each source as a model. These models were convolved by the PSF of each image, where they were fitted simultaneously using a linear solver. Most often the dropouts were not found in the stacked detection image, and were therefore modelled as point sources at the coordinates of their IRAC centroid during the de-blending stage. Once the flux was extracted, additional 'sky' apertures were placed randomly around each dropout. The median flux in these sky apertures was subtracted from the dropout's flux, to eliminate any remaining background signal, while the standard deviation of these fluxes was used as flux uncertainty. Last, fluxes and uncertainties were aperture-corrected using the matched PSF's light curve, assuming point-like morphology. ALMA observations and data reduction. Our ALMA band-7 continuum observations of H-dropouts were performed during January and July 2016. The observations were centred on the IRAC positions with a spectral set-up placed around a central frequency of 343.5 GHz. Although we asked for 0.7″-resolution observations for all the three fields, only the CANDLES-COSMOS field was observed as requested, yielding a synthesis beam of 0.6″ × 1″. The other two fields were observed at 0.2″-0.3″ resolution. The integration time was roughly 1.8 min per object with a total observing time of ~2 h. We reduced the data using the CASA pipeline (version 4.3.1). To reach an homogeneous angular resolution, we tapered the baselines for these two fields to an angular resolution of 0.6″. This resolution corresponds to ~4 kpc at z = 4, compared to typical sizes of ~2 kpc for SMGs 53 .

We measured the total flux of all our targets directly in the (u,v) plane using the uvmodellfit procedure from the CASA pipeline. The sources were modelled with a circular Gaussian profile of variable total flux, centroid, width, axis ratio and position angle. 39 H-dropouts were detected at S/N > 4 with S 870μm > 0.6 mJy, including two galaxies that were serendipitously detected in a previous ALMA programme 54 targeting H-detected z ≈ 4 galaxies, which reached a similar depth as this observation. The positions of the 870-μm emission as measured from ALMA are in good agreement with IRAC, with ΔRA = 0.081″ ± 0.128″ and ΔDec. = -0.13″ ± 0.16″. SCUBA-2 450-μm and VLA observations. One of the three H-dropout fields, CANDELS-COSMOS, is covered by deep SCUBA-2 450-μm and 870-μm observations from the STUDIES survey 55 . Previous observations with JCMT/SCUBA-2 of the same region 56-58 have also been combined to produce an extremely deep 450-μm image and a confusion-limited 850-μm image. The instrumental noise at 450 μm and 850 μm at the deepest regions reach ~0.65 mJy and ~0.1 mJy, respectively.

The SCUBA-2 450-μm and 850-μm fluxes for H-dropouts are measured at the position of the IRAC 3.6-μm and 4.5-μm emission with the prior-based PSFfitting code FASTPHOT 59 . We further restrict all the extracted fluxes to be positive with bounded value least-square minimization. During the fit we included all the MIPS 24-μm and VLA detections as priors to perform source extraction. The VLA 3 GHz observation in COSMOS 60 reaches a r.m.s. of 2.3 μJy per beam at an angular resolution of 0.75″, which is deep enough to put useful constraints on their redshifts. The flux measurement for H-dropouts in the far-infrared suffers minimum source confusion due to our selection criterion (no close neighbours within a 2″ radius). A comparison of 870-μm fluxes measured by ALMA and SCUBA-2 yields excellent agreement with a median value of S ALMA /S SCUBA-2 = 1.05. X-SHOOTER spectra. In the COSMOS field, deep medium band images in the optical were obtained with the Subaru telescope 49 . We visually inspected these images at the location of each dropout in our sample and found three galaxies with flux excesses in one of these images, with a significance above 4σ. Examples are shown in Extended Data Fig. 6. Such flux excess can be interpreted as coming from a bright emission line 61 . For these three dropouts, the line could be identified as Lyα at z = 5.0, 3.2 and 4.1, respectively. Even though H-dropouts are typically very obscured, Lyα may still be detected through un-obscured sight lines, or by scattering 62 . Judging from the spatial offsets of about 1″ we observed between this optical flux excess and the Spitzer-IRAC or ALMA emission, scattering appears to be the most plausible explanation.

Extended Data Fig. 3 | Stacked far-infrared SED of ALMA-detected H-dropouts. The stacked IR SED is derived by median stacking of the Spitzer/24 μm, Herschel/100 μm, 160 μm, 250 μm, 350 μm, 500 μm, and ALMA 870 μm images of the 39 H-dropouts detected with ALMA. The measured fluxes from the stacked images and the predicted fluxes from the best-fit model (solid line) are shown with the large and small open circles, respectively. Error bars (1σ) on the stacked SED are obtained from either bootstrapping or from the statistics of the residual map (whichever is largest, as described and validated elsewhere 24 ). For the ALMA photometry, the error bar is the formal error on the mean ALMA flux, and is smaller than the data point on this figure. The stacked images are shown in the row of insets at the top, which are linked to their corresponding stacked photometric points by grey arrows. The inset histogram shows the photometric redshift distribution of the H-dropouts based on opticalto-NIR SED fitting, which shows a median redshift (dotted line) of z ≈ 4. The infrared luminosity L IR and dust temperature T dust are derived from the best-fit SED at z = 4, the average redshift of the sample, using an empirical IR SED library calibrated on galaxies at 0 < z < 4 (ref. 13 ). The uncertainty on the infrared luminosity (ΔL IR ) accounts for uncertainty on the photometry and on the dust temperature, but not on the mean redshift of the sample.

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Extended Data Fig. 4 | Photometric redshifts of H-dropouts. a, b, S 870μm /S 450μm (a) and S 1.4GHz /S 870μm (b) colours versus redshift for ALMA-detected H-dropouts in CANDELS-COSMOS; c, comparison between redshifts derived from optical SEDs and from S 870μm /S 450μm colours. a, The redshifts are photometric redshifts derived from opticalto-NIR SED fitting except for the two sources denoted in cyan squares, which are spectroscopic redshifts derived from X-SHOOTER spectra. The S 870μm /S 450μm colour for galaxies undetected at 450 μm (S/N < 2, open circles) are shown with their lower limits (using the 4σ upper limits at 450 μm). One of the spectroscopically confirmed galaxies with z spec = 3.097 is only marginally detected with S 870μm = 0.4 ± 0.1 mJy, below our conservative detection limit, but we also include it here for illustration. The lines (see key) denote expected colour evolution of different SED templates as a function of redshift, including the stacked IR SED of the H-dropouts. We note that the S 870μm /S 450μm colour for both spectroscopically confirmed sources are consistent with the average SED of ALESS z = 4 SMGs. A few previously spectroscopically confirmed bright SMGs at z > 5 are shown by purple squares 3,72,73 . b, A 3σ upper limit of 7 μJy is assigned to non-detections, which are shown with open circles. The dotted and dashed lines denote the relation between S 1.4GHz /S 870μm and redshift for IR SEDs with spectral index in the submillimetre region of 3 (M82-like) and 3.5 (Arp220-like), respectively, as shown in ref. 74 . The same relation for the stacked IR SED of H-dropouts is also shown (orange line). c, Comparison between submillimetre redshifts (z FIR ), derived on the basis of their S 870μm /S 450μm colour and their stacked IR SED (orange line in the left panel), and redshifts derived from optical SED fitting (z OPT ) for sources detected at both 450 μm and 870 μm. The cyan square denotes the source that is spectroscopically confirmed. Despite their large dispersion, both methods suggest that most of the H-dropouts are indeed at z > 3.

Extended Data

FIGURE 1 . 1 :

 11 FIGURE 1.1: "Radial velocities, corrected for solar motion, are plotted against distances estimated from involved stars and mean luminosities of nebulae in a cluster. The black discs and full line represent the solution for solar motion using the nebulae individually; the circles and broken line represent the solution combining the nebulae into groups; the cross represents the mean velocity corresponding to the mean distance of 22 nebulae whose distances could not be estimated individually".Figure and citation from Hubble (1929).

  FIGURE 1.1: "Radial velocities, corrected for solar motion, are plotted against distances estimated from involved stars and mean luminosities of nebulae in a cluster. The black discs and full line represent the solution for solar motion using the nebulae individually; the circles and broken line represent the solution combining the nebulae into groups; the cross represents the mean velocity corresponding to the mean distance of 22 nebulae whose distances could not be estimated individually".Figure and citation from Hubble (1929).

FIGURE 1 . 2 :

 12 FIGURE 1.2: Left panel: Lookback time as a function of the redshift, black curve as well as the cosmic scale factor a(t), gray curve. Right panel: different distances used in comsmology (comoving distance with the solid line, luminosity distance with the dotted line, angular distance with the dashed line, lookback distance with the dot-dashed line) as a function of the redshift.

FIGURE 1 . 7 :

 17 FIGURE 1.7: Illustration of the Schmidt-Kennicutt law by[START_REF] Bigiel | The Star Formation Law in Nearby Galaxies on Sub-Kpc Scales[END_REF] showing the evolution of the SFR density as a function of the total gas surface density. In addition, the three distinctly different regimes (indicated by the vertical lines) of the star-formation law are also shown. Figure from[START_REF] Bigiel | The Star Formation Law in Nearby Galaxies on Sub-Kpc Scales[END_REF].

FIGURE 1 . 8 :

 18 FIGURE 1.8: Double-Gaussian decomposition (main-sequence, MS, and starburst, SB, activity) of the sSFR distribution at fixed M * > 10 10 M for galaxies at z ∼ 2. Figure from Sargent et al. (2012).

FIGURE 1 . 9 :

 19 FIGURE 1.9: Evolution of the surface brightness as a function of the Sérsic index (from 0.25 to 4). n = 0.5 corresponds to a Gaussian profile while n=1 and n = 4 correspond to exponential and de Vancouleurs profiles respectively. The surface brightness and the radius are given in arbitrary units.

FIGURE 1 . 13 :

 113 FIGURE 1.13: Luminosity distance as a function of redshift adopting a spatially flat ΛCDM cosmological model with H0 = 70 kms -1 Mpc -1 , Ωm = 0.7 and ΩΛ = 0.3. For comparison, the function f(z) = A×(1+z) α with α = 1.5, 2 and 3 has been scaled to fit the luminosity distance.

FIGURE 1 . 14 :

 114 FIGURE 1.14: Evolution of the flux of a galaxy (given in arbitrary units) as a function of the redshift, through different filters, Spitzer-MIPS at 24 µm, Herschel-PACS, at 160 µm, Herschel-SPIRE at 250, 350, and 500 µm, ALMA band 6 and band 7 at 870 µm and 1mm and VLA at 5cm. The effect of the strong negative k-correction, which is clearly visible at (sub)millimeter wavelengths, disappears at radio wavelengths.

FIGURE 1 . 16 :

 116 FIGURE 1.16: Example of the spectral energy distribution for AGS1. The solid black line represents the best fit which can be decomposed by the IR dust contribution (brown line), a stellar component uncorrected for dust attenuation (dark blue line), synchrotron emission (brown line) and the AGN contribution (orange line). In addition, we show the best fit of a modified black body, with β = 1.5 (light blue line). The corrected UV emission is also shown in green. The bottom panel shows the residuals: (observation -model)/observation.

  FIGURE 1.17: Observed radio-far infrared spectrum of M82. The measurements (black dots) were made by[START_REF] Klein | Radio continuum observations of M82[END_REF] and[START_REF] Carlstrom | H II regions in M82 -High-resolution millimeter continuum observations[END_REF]. The synchrotron emission (dot-dashed line), the free-free emission (dashed line), the dust component (dotted line) and the sum of the SED (solid line) are shown as a function of the frequency. For M82, the synchrotron emission is dominant for frequencies below 30GHz, while the dust is dominant for frequencies higher than 200 GHz. Between these two frequencies, the free-free emission is higher than the two other components. Figure from: Condon (1992).

FIGURE 1 . 18 :

 118 FIGURE 1.18: Blackbody emission spectrum, according to Planck's law as a function of wavelength at different temperatures. According to Wien's Law, the peak emission wavelength of a body depends on its temperature. The warmer the body is, the more it will emit at higher frequencies, and the colder it is, the lower wavelength its peak emission will be. That is why "cold" stars with temperatures ∼ 3000-5000 K emit in the near-infrared, and why we use millimeter wavelengths to study 20 -50K dust emission.

  The central part of the Cosmic Evolution Survey (COSMOS, Scoville et al. 2007) centered at RA=150.116321 • , DEC +2.200973. -UKIDSS-Ultra Deep Survey (UDS; Lawrence et al. 2007; Cirasuolo et al. 2007), centered at RA = 4.406250 • , DEC = -5.2000000 • -The Extended Groth Strip (EGS; Davis et al. 2007, centered at RA = 214.825000 • , DEC = +52.825000 • -The Great Observatories Origins Deep Survey (GOODS; Dickinson and GOODS Legacy Team 2001; Giavalisco et al. 2004). The GOODS program is divided into two fields, one in the northern part of the sky (GOODS-North) centered at RA = 189.228621 • , DEC = +62.238572 • , the other in the southern part (GOODS-South), centered at RA = 53.122751 • , DEC = -27.805089 • .

FIGURE 3 . 2 :

 32 FIGURE 3.2: Relative sizes of some of the main large surveys. The yellow rectangles indicate the five CANDELS fields overlaid on a cosmological N-body simulation performed within the MultiDark project (see http://www.multidark.org/MultiDark/) viewed at z = 2. Figure from Madau and Dickinson (2014).

FIGURE 3 . 4 :

 34 FIGURE 3.4: Graphical representation of the sensitivity of the filters used as a function of wavelength. The points are color-coded as a function of the instruments while the sizes of the points are proportional to the size of the beam.

FIGURE 3 . 5 :

 35 FIGURE 3.5: 10'× 6.8' ALMA 1.1mm survey (0.128 mJy-rms; blue rectangle) overlaid on HST-WFC3 coverage (greyscale) and matching the deep CANDELS WFC3 region. Green contours: GOODS-Herschel ultra deep survey spaced with 40% intervals starting from a 100 µm rms of 0.17 mJy in the center. Red square : 4 arcmin 2 ALMA HUDF 1.3mm survey (PI Dunlop). Pink polygon: HST-ACS borders. Our ALMA coverage extends over an effective area of 69 arcmin 2 within the GOODS-South field (Fig. 4.3), centred at α = 3 h 32 m 30.0 s , δ = -27 • 48 00 (J2000; 2015.1.00543.S; PI: D. Elbaz). To cover this ∼ 10 × 7 region (comoving scale of 15.1 Mpc × 10.5 Mpc at z = 2), we designed a 846-pointing mosaic, each pointing being separated by 0.8 times the antenna Half Power Beam Width (i.e. HPBW ∼ 23 3).

FIGURE 3 . 6 :

 36 FIGURE 3.6: uv-coverage of one of the 846 ALMA pointings constituting this survey. We show the uv-coverage for one pointing, left panel as well as for all 846 pointings, right panel. This uv-coverage allows us to perform the source detection in the dirty map.

FIGURE 3 . 7 :

 37 FIGURE 3.7: Antenna position during our survey. ALMA was in C40-5 configuration with a minimum baseline of 16.7 m and a maximum baseline of ∼1200 m.

FIGURE 3 . 8 :

 38 FIGURE 3.8: Spectral visualizer set with the parameters of our survey. The Local Oscillator (LO1) frequency is shown with a yellow line at the middle of the image at a frequency of 264.9 GHz. The bandwidth of the four spectral windows at 255.9 GHz, 257.9 GHz, 271.9 GHz and 273.9 GHz are represented with blue line within the sideband in yellow. The atmospheric transmission curve is also display in gray.

FIGURE 3 . 9 :

 39 FIGURE 3.9: Left panel: illustration of a detection in the stacked continuum map, bottom part while the detection is displayed in a random channel in the top part. Middle panel: visualization of the spectrum of the detection. Right panel: illustration of the stacking process, to produce the image in the continuum. All the individual channels are summed together to produce the continuum map.

FIGURE 3 . 10 :

 310 FIGURE 3.10: 3D representation of the clean beam (left panel) and dirty beam (right panel).The projection of these beams according to each of the dimensions is also represented. Because the clean and the dirty beam are very similar and in order to prevent any bias generated by the CLEAN process, we decided to work with the dirty map.

  FIGURE 3.11

FIGURE 3 . 13 :

 313 FIGURE 3.13: Distribution of the 846 pointings composing the GOODS-ALMA image according to a hexagon configuration. Each pointing has an antenna Half Power Beam width ∼ 23.3" and are separated by 0.8 times the HPBW.

7 NFIGURE 3 . 15 :

 7315 FIGURE 3.15: Distribution of flux density of the signal map at two different resolution 0.29" in the left panel and 0.60" in the right panel. While the S/N distribution is practically Gaussian, except at high SN, for detections (see Fig.4.1, the pixel distribution is not Gaussian at low or high signal.

FIGURE 3 . 16 :

 316 FIGURE 3.16: Noise map for the image tapered at 0.6", created by σ clipping method. With the exception of slice B, which has a higher average noise than the others (224 µJy), the average noise of the other slices is between 164 and 186 µJy (see Table3.6. The edge of the noise map does not benefit from the overlapping of several pointings and has a higher noise level than the rest of the map. In the analysis of the image tapered at 0.6", areas located on the edge and having a noise greater than 0.3 mJy.beam -1 will not be taken into account.

FIGURE 3 . 17 :

 317 FIGURE 3.17: Example of two sources AGS18 on the top line and AGS3 on the bottom line at different resolutions. From left to right, untapered image, image tapered at 0.29", 0.60" and 1". The color scale has been fixed to better visualize the effects of tapering. The beam size is indicated for each resolution with a dotted black line. AGS18 is the most extended source of our main catalog (see Sect. 4.3) while AGS3 is the most compact source.

FIGURE 4 . 3 :

 43 FIGURE 4.3: ALMA 1.1 mm image tapered at 0 . 60. The white circles have a diameter of 4 arcseconds and indicate the positions of the galaxies listed in Table 4.1. Black contours show the different slices (labelled A to F) used to compose the homogeneous 1.1 mm coverage, with a median RMS-noise of 0.18 mJy per beam. Blue lines show the limits of the HST/ACS field and green lines indicate the HST-WFC3 deep region. The cyan contour represents the limit of the Dunlop et al. (2017) survey covering all the Hubble Ultra Deep Field region. All of the ALMA-survey field is encompassed by the Chandra Deep Field-South.

FIGURE 4 . 5 :

 45 FIGURE 4.5: Postage stamps of 1.8 × 1.8 arcsec. ALMA contours(4, 4.5 then 5 to 10-σ with a step of 1-σ) at 1.1mm (white lines) are overlaid on F160W HST/WFC3 images. The images are centered on the ALMA detections. The shape of the synthesized beam is given in the bottom left corner. Astrometry corrections described in Sect. 4.5 have been applied to the HST images. In some cases (AGS1, AGS3, AGS6, AGS13, AGS21 for example), the position of the dust radiation matches that of the stellar emission; in other cases, (AGS4, AGS17 for example), a displacement appears between both two wavelengths. Finally, in some cases (AGS11, AGS14, AGS16, and AGS19) there are no optical counterparts. We will discuss the possible explanations for this in Sect.7.3.

FIGURE 4 . 7 :

 47 FIGURE 4.7: ALMA 1.1 mm continuum maps for the 23 detections tapered at 0.60 arcsec. Each 3 . 5 × 3 . 5 image is centered on the position of the ALMA detection. Cyan double crosses show sources from the GOODS-S CANDELS catalog. White circles show sources from the ZFOURGE catalog. Blue circles show common sources from both optical catalogs (sources with an angular separation lower than 0 . 4). The shape of the synthesized beam is given in the bottom left corner.

FIGURE 4 . 8 :

 48 FIGURE 4.8: East-west profile of the PSFs corresponding to the six different parallel slices composing the ALMA image in the 0 . 60-mosaic (see Fig. 4.3).

FIGURE 4 . 9 :

 49 FIGURE 4.9: Comparison between the stacked PSF (black solid line) and the stack of the 23 ALMA-detections (black dashed line) in the 0 . 60-mosaic. As each slice has a specific PSF, we stack the PSF corresponding to the position of each detection. The fluxes of each detection have been normalized, so that the brightest sources do not skew the results. Fluxes of the PSF and ALMA detections are normalized to 1. Flux profiles are taken across the East-west direction. The result is consistent with unresolved or marginally resolved sources at this resolution. The insert in the top-right corner shows the same procedure for the 15 sources detected in the 0 . 29-mosaic (see Table4.2).

FIGURE 4 .

 4 FIGURE 4.10: 10 × 10 postage stamps, centered on the galaxy detections. Left to right: the source in the 0 . 60-mosaic map, and the residuals obtained after PSF, Gaussian and Sérsic flux fitting. The residuals are very similar between the three different extraction methods. Only the 6 brightest galaxies are shown.

FIGURE 4 . 11 :

 411 FIGURE 4.11: Size distribution histogram for the 20 robust detections. These sizes are computed by fitting the ALMA detections with a circular Gaussian in the uv-plane using uvmodelfit in CASA. 85% of the sources exhibit a FWHM smaller than 0 . 25.

FIGURE 4 . 12 :

 412 FIGURE 4.12: Redshift distributions (photometric or spectroscopic) for millimetre-selected galaxies. The blue solid line shows the redshift distribution of our ALMA GOODS-South blind survey. The green dashed line shows the Hubble Ultra Deep Field Survey redshift distribution(Dunlop et al., 2017), the black dash-dotted line shows the ASPECS sample(Aravena et al., 2016), the red dotted line shows the ALMA Frontier Fields Survey(González-López et al., 2017) and the yellow dotted line shows the ASAGAO survey(Ueda et al., 2018). Short coloured lines at the top of the figure indicate the median redshifts for these four studies.

FIGURE 4 .

 4 FIGURE 4.13: Size-depth plan for the contiguous ALMA surveys color-coded by the median redshift. We represented the Hubble Ultra Deep Field Survey(Dunlop et al., 2017), the pilot-ASPECS sample(Aravena et al., 2016), the ALMA Frontier Fields Survey (González-López et al., 2017), the ASAGAO survey(Hatsukade et al., 2018) and this work. For this work, we also include the sample of galaxies describes in Chapter6 (which has a lower median redshift than the sample presented in this chapter).

FIGURE

  FIGURE 4.14: Stellar mass versus redshift for the galaxies detected in our ALMA GOODS-South blind survey (red points). For comparison, the distribution of all of the galaxies, listed in the ZFOURGE catalog, in the same field of view is given in blue. Only UVJ active galaxies are shown. The two HST-dark galaxies for which we have estimated a photometric redshift (AGS4 and AGS11) are represented by open circles. The redshift of AGS11 is however uncertain. The green dashed line shows the position that would be occupied by a typical star-forming galaxylying on the median of the SFR-M star-formation main sequence (MS) -that would produce a 1.1mm flux density equal to our average detection limit of 0.88 mJy (4.8-σ) using the Spectral Energy Distribution (SED) library ofSchreiber et al. (2018a). The dotted line illustrates the position of galaxies 3 times above the MS using the appropriate SEDs from the same library. Galaxies hosting an AGN that are undetected or detected by ALMA are identified with black dotes and yellow stars respectively. Inside the black dashed rectangle, 50% of the galaxies detected by ALMA host an AGN, while only 14% of the UVJ active galaxies undetected by ALMA host an AGN.

5 65 4. 6 66 4. 7

 5656667 Astrometric correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Identification of counterparts . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass and redshift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.8 AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

FIGURE 5 . 1 :

 51 FIGURE 5.1: Schematic Spectral Energy Distributions for the Cosmic Microwave Background (CMB), the Cosmic Infrared Background (CIB) and the Cosmic Optical Background (COB). For each panel, the brightness is given in units of nW m -2 sr -1 . Figure fromDole et al. (2006).

FIGURE 5 . 2 :

 52 FIGURE 5.2: Differential number counts at 70µm, 100µm, 160µm, 250µm, 350µm, 500µm, 850µm, and 1.1 mm plotted with Euclidean-normalized units. The shaded regions represent the 1σ uncertainties. Figure from[START_REF] Casey | Dusty star-forming galaxies at high redshift[END_REF].

5. 4 .

 4 (Sub)millimeter surveys over contiguous areas of the sky 85

FIGURE 5 . 3 :FIGURE 5 . 4 :

 5354 FIGURE 5.3: Size-depth plan for some of the main (sub)millimeter surveys with 850µm¡ λ < 3 mm . The dots represent the following surveys:Hughes et al. (1998);Barger et al. (1998);[START_REF] Eales | The Canada-UK Deep Submillimeter Survey: First Submillimeter Images, the Source Counts, and Resolution of the Background[END_REF][START_REF] Eales | The Canada-UK Deep Submillimeter Survey. IV. The Survey of the 14 Hour Field[END_REF];[START_REF] Bertoldi | Three highredshift millimeter sources and their radio and near-infrared identifications[END_REF];Scott et al. (2002);[START_REF] Chapter | Faint Submillimeter Counts from Deep 850 Micron Observations of the Lensing Clusters A370, A851, and A[END_REF];[START_REF] Webb | The Canada-UK Deep Submillimeter Survey. VI. The 3 Hour Field[END_REF];[START_REF] Mortier | The SCUBA Half-Degree Extragalactic Survey -I. Survey motivation, design and data processing[END_REF]; Coppin et al. (2006); Perera et al. (2008); Weiß et al. (2009); Hatsukade et al. (2011); Staguhn et al. (2014); Hatsukade et al. (2016); Walter et al. (2016); Dunlop et al. (2017); Umehata et al. (2017); González-López et al. (2017); Geach et al. (2017); Umehata et al. (2018); Hatsukade et al. (2018); Franco et al. (2018); González-López et al. (2019a) as well as the future NIKA2 Cosmological Legacy Survey (NIKA2 GT-LP -N2CLS, PI : G. Lagache, A. Beelen, N. Ponthieu). The dots color-coded followingthe instruments used. The size of the dots correspond to the size of the beam. The black outer line means that the survey covers a lensed area. This list of surveys is not exhaustive. We point out that to date, the GOODS-ALMA survey is the largest (sub)millimeter survey without confusion issues.

FIGURE 5 . 5 :

 55 FIGURE 5.5: Cumulative number of positive (red histogram) and negative (blue histogram) detections as a function of the σp. The red and blue dashed lines use the best fit parameters of the Eq. 5.6 for the positive and negative distribution respectively.

4

 4

  A = (-7.58 ± 1.31) × 10 5 , B = -1.55 ± 0.02, C = (1.51 ± 0.25) × 10 6 for the positive histogram and A = (-1.9 ± 0.5) × 10 6 , B = -1.46 ± 0.02, C = 3.80 ± 0.91 × 10 6 for the negative histogram.

FIGURE 5 . 7 :

 57 FIGURE 5.7: Effective area as a function of flux density, where a source with a given flux can be detected with an SN > 4.8 σ. 90 percent of the survey area reaches a sensitivity of at least 1.06 mJy.beam -1 .

FIGURE 5 . 10 :

 510 FIGURE 5.10: Process of creation and injection of artificial sources. Top left: Gaussian shape sampled accounting to pixel size; Top middle: PSF of the slice considered; Top right: convolution of the Gaussian by the PSF. Bottom left: Gaussian noise; Bottom middle: the flux is smoothened by a Gaussian kernel so that it is no longer random pixel by pixel but correlated as in our image. Bottom right: addition of the source (Gaussian shape) convolved with the PSF and the correlated noise. The integrated flux of the injected source is 1mJy, i.e., S/N = 5.5 (the cuts of the image are normalized to the source).

FIGURE 5 . 11 :

 511 FIGURE 5.11: Example of detection test according to the intrinsic size of the injected source and its integrated flux, for the left column, for a point-like source, for the middle column for a source with an FWHM of 0.5" and for the right column for an FWHM of 0.8". To better analyze the effects of size on detection, for a run, at each given flux, the sources were injected at the same positions when we vary the size. Detections at a threshold of 4.8σ, corresponding to the detection threshold of our survey are indicated by a yellow circle. To ensure that these completion tests are done in exactly the same way as for the creation of our catalog, we used the same code, Blobcat for the source detection.

Fig. 5 .

 5 Fig. 5.12 shows the resulting completeness as a function of input flux, for different FWHM Gaussian sizes convolved by the PSF and injected into the map.

FIGURE 5 . 12 :

 512 FIGURE 5.12: Median source detection completeness for simulated point-like and Gaussian galaxies as a function of integrated flux, for different FWHMs (see figure's legend). The shaded regions correspond to the standard deviation of 100 runs, each containing 300 simulated sources.

  ); Scott et al. (2012); Karim et al. (2013); Hatsukade et al. (2013); Ono et al. (2014); Simpson et al. (2015b); Oteo et al. (2016); Carniani et al. (2015); Hatsukade et al. (2016); Aravena et al. (2016); Fujimoto et al. (2016); Umehata et al. (2017); Geach et al. (2017); Dunlop et al. (

6. 3 .-FIGURE 6 . 1 :

 361 FIGURE 6.1: Left: offset between Pan-STARRS and HST; Middle: offset between JVLA and Pan-STARRS; Right: offset between JVLA and ALMA. For each panel, the histogram of the offsets in RA and DEC is shown as well as a fit with a Gaussian function (orange curve). The position of the peak and the standard deviation of the Gaussian is indicated for each curve. The middle and the right panels show that there are no significant astrometric differences between ALMA and JVLA nor between JVLA and PS1, while The left panel shows the clear shift in both RA and DEC between the positions of 375 sources in common between the Pan-STARRS (PS) and HST images. We measure a systematic offset of ∆RA = -96 ± 83 mas and ∆Dec = 252 ± 107 mas. In addition, a local offset is presented in Fig.6.2.

FIGURE 6 . 2 :

 62 FIGURE 6.2: Difference between HST and Pan-STARRS position after subtraction of the median offset value. Each arrow represents a sliding median including in average 15 points, with an overlap of 60 percent between neighboring arrows. The blue line defines the area encompassing the GOODS-ALMA survey.

FIGURE 6 . 6 :

 66 FIGURE 6.6: IRAC 3.6µm map (17 × 17 ) image is centred on the position of the ALMA detection. We show the image before (left pannel) and after (right pannel) the subtraction with GALFIT of the source IDZF OU RGE = 11024 located to the Northeast of the detection and which masks the emission of the source located at the ALMA position. After subtraction we can see an emission located in the central position which suggest that the source is not present inAshby et al. (2015) only because of blending. Cyan double crosses show sources from the GOODS-S CANDELS catalog. White circles show sources from the ZFOURGE catalog. Blue circles show common sources from both optical catalogs (i.e. sources with an angular separation lower than 0 4).

FIGURE 6 . 8 :FIGURE 6 . 9 :

 6869 FIGURE 6.8: ALMA 1.1 mm image tapered at 0 60. The white circles have a diameter of 4 arcseconds and indicate the positions of the galaxies listed in Table 6.1. Black contours show the different slices (labeled A to F) used to construct the homogeneous 1.1 mm coverage, with a median RMS = 0.18 mJy.beam -1 . Blue lines show the limits of the HST/ACS field and green lines indicate the HST-WFC3 deep region. The cyan contours represent the limit of the Dunlop et al. (2017) survey covering all of the Hubble Ultra Deep Field region, the yellow contours show the ASAGAO survey(Hatsukade et al., 2018), while the purple contours show the ASPECS Pilot survey(Walter et al., 2016), the pink contours show the ASPECS Large Program(Decarli et al., 2019). The Chandra Deep Field-South encompasses all of the ALMA-survey field.

FIGURE 6 . 11 :

 611 FIGURE 6.11: Underestimation of the flux when asuming a point-like source instead of the real size of the galaxy. For example, a source with an intrinsec FWHM of 0 3 will be underestimated of 20%.

FIGURE

  FIGURE 6.13: Cumulative fraction of sources with a FWHM below a given size for the main (red) and the supplementary catalog (gray). These sizes are computed by fitting the ALMA detections with a circular Gaussian in the uv-plane using uvmodelfit in CASA. The shaded areas correspond to the integration of the individual uncertainties of the sizes of each detection.

FIGURE 6 . 14 :

 614 FIGURE 6.14: Postage-stamp (10 × 10 arcseconds), centred on the position of the ALMA detection at different wavelengths. From left to right : HST-WFC3 (a verifier (F814W, F160W), ZFOURGE (Ks), Spitzer-IRAC channel 1 (3.6 µm), Spitzer-MIPS (24µm), ALMA band 6 (1.1mm), VLA (5 and 10 cm). Blank images mean that the source is out of the field of view of the instrument. The white cross indicates the position of the ALMA detection.

FIGURE 6

 6 FIGURE 6.15: (continued)

FIGURE 6

 6 FIGURE 6.16: (continued)

FIGURE 7 . 1 :

 71 FIGURE 7.1: Figure from Smail et al. (1997). Observation at 850 µm of the fields A370, left panel and Cl 2244-02, right panel.

FIGURE 7 . 2 :

 72 FIGURE 7.2: Postage stamps of 10 × 10 arcsec from HST-WFC3 at 0.606 µm to VLA at 5cm, for the four optically-dark galaxies discussed in Sect. 7.3. For the two ALMA images at 1.1 mm, those marked by 1 correspond to the non-tapered images, those marked by 2 correspond to the 0 . 60mosaic images. The Ks-band thumbnail comes from the super-deep detection image described in Sect. 3.3. All images are centered on the ALMA detection. We indicate with white arrows the position of the previously associated HST counterpart.

FIGURE 7 . 3 :

 73 FIGURE 7.3: Spectral energy distributions of AGS4 and IDCANDELS 8923. Aperture photometry allows the separation between the local galaxy detected by HST (blue, and indicated by a white arrow in Fig.7.2, IDCANDELS 8923) and the distant galaxy detected by ALMA (orange). The top panel shows the photometric redshift probability distribution of AGS4. As the Balmer break is well established in the K-band, we consider that this redshift determination is robust, and we adopt the derived redshift zAGS4 = 4.32+0.25 -0.21 and stellar mass (10 11.45±0.2 M ) values for AGS4.

FIGURE 7 . 4 :

 74 FIGURE 7.4: Postage stamps (18"×18") centered at the position of AGS4 (white cross). The top line shows the original image while the bottom line shows the image after the sources located near AGS4 have been removed using Galfit. The extracted fluxes were used to fit the spectral energy distributions of Fig. 7.3 .

FIGURE 7 . 5 :

 75 FIGURE 7.5: Spectral energy distribution (SED) of AGS4. The flux densities from 100 to 500 µm are from GOODS-Herschel(Elbaz et al., 2011). AGS4 (z = 4.32, see Sect. 7.3) is fitted with the model ofSchreiber et al. (2018a).

FIGURE 7 . 6 :

 76 FIGURE 7.6: Left panel: Postage stamp of 1.8 × 1.8 arcsec centered at the position of AGS11. ALMA contours (4, 4.5, 5 σ) at 1.1mm (white lines) are overlaid on F160W HST/WFC3 images. Right panel: Postage stamp of 9 × 9 arcsec showing the ALMA contours (white), IRAC 3.6µm contours (red) overlaid on IRAC channel 1 image.

FIGURE 7 . 7 :

 77 FIGURE 7.7: Spectral energy distribution of AGS17. The flux densities from 100 to 500 µm are from GOODS-Herschel(Elbaz et al., 2011). The SED of AGS17 (bottom), which has no known redshift, is simply presented with an interpolation between the observed flux densities to illustrate that it peaks around 400 µm. This peak is inconsistent with the redshifts of the two optical sources with IDCANDELS 4414 (z = 1.85) and 4436 (z = 0.92).

FIGURE 7 . 8 :

 78 FIGURE 7.8: Postage stamps of 5×5 arcsec from HST-WFC3 at 0.606µm to VLA at 5cm, for AGS24. The biggest red circle shows the position of AGS24. Figure from Zhou et al., in prep.

FIGURE 7 . 9 :

 79 FIGURE 7.9: Top: Photometric redshift probability distribution function derived by EAzY(Brammer et al., 2008). Below: SED fitting using the technique described in Sect.7.3.1. Figure from Zhou et al., in prep.

FIGURE 7 . 10 :

 710 FIGURE 7.10: IRAC 3.6µm (18 × 18 ) image centred on the position of the ALMA detection. We show the image before (left pannel) and after (right pannel) the subtraction with GALFIT of the source IDZF OU RGE = 11024 located to the Northeast of the detection and which masks the emission of the source located at the ALMA position. After subtraction we can see an emission located in the central position which suggest that the source is not present inAshby et al. (2015) only because of blending. Cyan double crosses show sources from the GOODS-S CANDELS catalog. White circles show sources from the ZFOURGE catalog. Blue circles show common sources from both optical catalogs (i.e. sources with an angular separation lower than 0 . 4).

FIGURE 7 . 11 :

 711 FIGURE 7.11: Right panel: 1.8 × 1.8 arcsec postage stamps centered at the position of the ALMA detection. The ALMA contour (4 and 4.5σ), in white are superimposed to an HST H-band image.Left panel: The two possible source, at the position of the HST detection and at the position of the ALMA detection were then fit simultaneously using these two light-profile models (using Galfit) on all of the available images, fixing the profile to that observed in the H-band. The redshift probability density of the "ALMA" galaxy is represented at the top of the panel.ALMA HST redshift 2.61+0.32 -0.34

FIGURE 7 . 12 :FIGURE 7 . 13 :

 712713 FIGURE 7.12: IRAC 3.6 µm (red contours, 3. µJy to 30. µJy in steps of 3.0 µJy) and ALMA 1.1mm (white contours, 4, 4.5 then 5 to 10-σ in steps of 1-σ) overlaid on 8 . × 8 . HST H-band images. The position of the previously associated HST counterpart is shown by a cyan circle.

  characterize a population of extreme [OIII] + Hβ emitting galaxies tracing an overdensity with 3.42 < z spec <3.478 at RA = 53.08 • , Dec = -27.85 • covering approximately 1.8 Mpc in size.

FIGURE 7 . 14 :

 714 FIGURE 7.14: Projected density map of the 366 galaxies with 3.42 ≤ z ≤ 3.57 with the GOODS-ALMA field. The red star shows AGS24 while the yellow stars indicate three other optically dark galaxies, AGS11, AGS15, and AGS17. Two other galaxies, listed in the main catalog, AGS1, and AGS5 with the same redshift range are shown with the green dots. The red circle has a radius of 50 corresponding at a physical radius of 400kpc at z = 3.5. Figure fromZhou et al., in prep.

FIGURE 7 . 15 :FIGURE 7 . 16 :

 715716 FIGURE 7.15: Spectral energy distribution of AGS11 in units of F λ , left panel and νFν , right panel. The balmer break may have been misidentified which would allow a redshift z ∼ 3.5. (Figure from: http://zfourge.tamu.edu/).

7. 6 .FIGURE 7 . 17 :

 6717 FIGURE 7.17: Left panel: Contribution of the ASAGAO sources to the cosmic star-formation rate density. The contribution of the two secure optically dark galaxies is shown with the red solid line while the additional contribution of the three less secure sources are shown with the red dashed-line. Figures from Yamaguchi et al. (2019a), left panel and Williams et al. (2019), right panel

FIGURE 7 . 18 :

 718 FIGURE 7.18: Left panel: Current cosmic star formation rate density based on LBGs at z > 4 (black solid line and blue triangle). The contribution of the massive H-dropout (red dots), ALESS SMGSs (purple pentagons), H-dropout in semi-analytical models (orange squares) as well as the massive LBGs (M * > 10 10.3 M ; based on dust-corrected UV) are shown in this image. Right panel: Fraction of massive galaxies, in number, that are either detected as LBGs or H-dropouts for galaxies with 3.5 < z < 6.5. Figures from:[START_REF] Wang | A dominant population of optically invisible massive galaxies in the early Universe[END_REF]

  /IRAC a loyal ally for HST-dark galaxies identification . . . . . . . . . 141 7.5 The HST-dark galaxy as an overdensity tracer . . . . . . . . . . . . . . . . . . 144 7.6 Implications of HST-dark galaxies in cosmic density of star-formation . . . . 147 7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

2 .

 2 Publicly available at http://cschreib.github.io/s17-irlib/

FIGURE 8 . 1 :

 81 FIGURE 8.1: Example of spectral energy distribution for AGS1. The solid black line represents the best fit, which can be decomposed into the IR dust contribution (brown line), a stellar component uncorrected for dust attenuation (dark blue line), synchrotron emission (brown line) and the AGN contribution (orange line). In addition, we show the best fit of a modified black body, with β = 1.5 (light blue line). The corrected UV emission is also shown in green. The bottom panel shows the residuals: (observation -model)/observation. The 34 other SEDs are given at the end of this chapter.

FIGURE 8 . 2 :

 82 FIGURE 8.2: Evolution of the dust temperature as a function of IR luminosity (left panel) and redshift (right panel). The ALMA detections are shown in red. By comparison, we also plot the temperatures of all the galaxies within GOODS-ALMA, color-coded by redshift (left panel) or IR luminosity (right panel). We show the sliding median (and the 1σ error) in black.

FIGURE 8 . 4 :

 84 FIGURE 8.4: Location of our ALMA detected galaxies in the SFR-M * plane. The SFRIR of these galaxies have been used. Galaxies with Herschel counterparts are color-coded as a function of the fgas. The other galaxies are represented by grey dots. We measured the distance to the MS using Eq. 9 from Schreiber et al. (2015) and its dispersion is 0.3 dex. We have rescaled all of the SFRs by multiplying by SFRMS(z)/SFRMS(z = 2.6), in order to maintain their relative positions with respect to the main sequence.

  Fig. 8.4 we compare the position of the ALMA detected galaxies with the[START_REF] Meurer | Dust Absorption and the Ultraviolet Luminosity Density at z ˜3 as Calibrated by Local Starburst Galaxies[END_REF];Calzetti et al. (2000);[START_REF] Reddy | The MOSDEF Survey: Measurements of Balmer Decrements and the Dust Attenuation Curve at Redshifts z ˜1.4-2.6[END_REF] relation.

FIGURE 8 . 5 :

 85 FIGURE 8.5: IRX-β relation for the ALMA detected galaxies. The black solid and dashed lines represent the SMC extinction curves fromCalzetti et al. (2000) and[START_REF] Pettini | Infrared Observations of Nebular Emission Lines from Galaxies at Z ˜= 3[END_REF] respectively. For comparison, all of the galaxies in the GOODS-South field for which this value has been derived are also shown, color-coded by redshift.

FIGURE 8 . 6 :

 86 FIGURE 8.6: qF IR as a function of redshift for the galaxies detected in GOODS-ALMA by both ALMA (at 1.1mm) and the VLA (at 3 GHz). The ALMA-detected galaxies are color-coded as a function of SFR. The Magnelli et al. (2015) and Delhaize et al. (2017) evolutionary trends and the local relation from Yun et al. (2001) are also shown for comparison. The shaded areas represent the ±1σ uncertainty on qF IR.

. 25 ) 8 . 3 .FIGURE 8 . 7 :

 258387 FIGURE 8.7: Evolution of the molecular gas fraction (fgas) and the gas depletion timescale (τ dep ) as a function of the distance to the main sequence of star-forming galaxies (RSB = SFR/SFRMS) (RSB = SFR/SFRMS), for the main and supplementary catalog of galaxies detected by ALMA in the GOODS-ALMA field. The solid blue line shows the relation obtained by[START_REF] Tacconi | PHIBSS: Unified Scaling Relations of Gas Depletion Time and Molecular Gas Fractions[END_REF] for the median redshift and stellar mass of our sample (z med =2.69, M * ,med =8.52 × 10 10 M ). The dispersion is obtained by Monte-Carlo simulations. In order to compare the gas fractions of all of the galaxies in our sample, we have rescaled our gas fractions according to the median redshift and the stellar mass of our sample.

FIGURE 8 . 8 :

 88 FIGURE 8.8: Evolution of the distance to the main sequence of star-forming galaxies (RSB = SFR/SFRMS, left panel) and the molecular gas fraction (fgas, right panel) as a function of the stellar mass. The best fit, given by Eq. 8.26, is shown by the gray shaded region .

FIGURE 8 . 9 :

 89 FIGURE 8.9: Left panel: H-band size-mass plane for the galaxies located in the GOODS-South field for which sizes have been measured in van derWel et al. (2014). The density of the UVJ active galaxies (with 2 < z < 4) in the GOODS-ALMA field is represented by the blue hexagons. The blue and red lines represent the trends of active and passive galaxies respectively, while the dashed lines give the scatter on these relations. The ALMA-detected galaxies are shown with black squares and the AGNs are marked with blue stars. Right panel: ALM A size-mass plane for the ALMA detected galaxies. For comparison, the trends for active and passive galaxies are also shown. We indicate the compactness criterion described in Eq. 8.28 to visualize which galaxies are compact in H-band.

FIGURE 8 . 10 :

 810 FIGURE 8.10: Depletion time as a function of the ΣSF R, color-coded according to the distance to the main sequence. The solid and dashed lines are the fit to the sliding median and its 68% scatter respectively.

FIGURE

  FIGURE 8.11: Optical to radio Spectral Energy Distributions created using the CIGALE code, for the main catalog galaxies. The UV and optical photometry is from the ZFOURGE catalog, the infrared measurements come from the Herschel catalog. The radio data at 5 cm is fromRujopakarn et al. (2016). The green (dark blue) lines fit the attenuated (unattenuated) stellar emission. The brown lines fit the dust emission and the purple fits the radio emission. The black is the sum of all emission components. The blue line shows the MBB fit. The lower panel shows the residuals between the observations and the model.

FIGURE 8 .

 8 FIGURE 8.12: (continued).

FIGURE 10 . 1 :

 101 FIGURE 10.1: ALMA 1.1 mm image of the map combined high-and low-resolution images, tapered at 1.5" and cleaned.

FIGURE 10 . 2 :

 102 FIGURE 10.2: Cumulative number of positive (red histogram) and negative (blue histogram) detections as a function of σp (at fixed σ f = 2.7), in units of σ f in the combined map. For comparison, the distribution of negative and positive sources in the 0.6" map is also shown with red and blue lines.

FIGURE 10 . 3 :

 103 FIGURE 10.3: Visualization of the 2494 pointings comprising the image created by combining the HUDF (Dunlop et al., 2017), ASAGAO Hatsukade et al. (2018) and GOODS-ALMA Franco et al. (2018) surveys. The 45 pointings from the HUDF are shown in red, the 1602 pointings from ASAGAO are shown in yellow and the 847 pointings from GOODS-ALMA are shown in purple.

FIGURE 10 . 5 :

 105 FIGURE 10.5: Left panel: HST/H-band image of the galaxy. The seven major clumps are shown with (dashed for less certain redshifts, solid for more secure redshifts) color circles. The CAN-DELS ID Guo et al. (2013), the redshifts (photmetric or spectroscopic) and the stellar masses (Chabrier IMF) are shown for each galaxy. Right panel: Simulation representing the gas within all the galaxy (∼20kpc). Image from Frederic Bournaud.

FIGURE 10 . 6 :

 106 FIGURE 10.6: Left panel: RGB (F814W, F125W, F160W) color image of the studied galaxy (image from: http://zfourge.tamu.edu/). Middle panel: ALMA 1.1mm (white) contours (2-3σ) overlaid on HST H-band images. Right panel: Spectral Energy Distribution (SED) of the galaxy using the SED fitting code CIGALE[START_REF] Noll | Analysis of galaxy spectral energy distributions from far-UV to far-IR with CIGALE: studying a SINGS test sample[END_REF] and the photometry from the ZFOURGE catalog(Straatman et al., 2016).

FIGURE 10 . 8 :

 108 FIGURE 10.8: Distribution of the number of clumps detected by a clump finding algorithm (see Fig. 10.7) as a function of the ratio of the Mgas contained in a clump (psf size, left panel; full clump, right panel) over the total Mgas of the disk. This distribution was performed on a mock catalog of galaxies simulating compact galaxies (blue distribution, less compact, orange distribution, and intermediate, green distribution). The cumulative proportion of the mass of gas contained in all detectable clumps in the galaxy is shown in the insert at the top of the figure.

  David Elbaz; Corentin Schreiber; Roger Leiton; Tao Wang; Mark Dickinson; Emanuele Daddi; Laure Ciesla; Luwenjia Zhou; Wiphu Rujopakarn CO

Figure 1 :

 1 Figure 1: Left: Postage stamps of 10 × 10 arcsec from HST-WFC3 at 0.606 µm to VLA at 5cm for AGS4 Top right: IRAC 3.6 µm (red contours) and ALMA 1.1mm (white contours) overlaid on 8.3" × 8.3" HST H-band images. The position of the previously associated HST counterpart is shown by a cyan circle. Bottom right: Postage stamps of 10 × 10 arcsec from HST -WFC3 at 0.606 µm to VLA at 5cm for AGS24

Figure 2 :

 2 Figure 2: Spectral energy distributions of GS8 (left panel ) and AGS4 (right panel ) . Aperture photometry allows the separation between the local galaxy detected by the HST (blue, and indicated by a white arrow in Fig. 1, ID CAN DELS 8923) and the distant galaxy detected by ALMA (orange).The top panels show the photometric redshift probability distributions for the two ALMA galaxies.

Figure 3 :

 3 Figure 3: Position of CO transitions and CI lines as a function of z and observed frequency in band 4, used here for the spectral z search for the HST-dark galaxies.

  MNRAS 429, 3047 • Daddi+15, A&A 577, 46 • Dunlop+17, MNRAS 466, 861 • Elbaz+18, ArXiv e-prints • Franco+18, ArXiv e-prints • Fujimoto+16, ApJS 222, 1 • Guo+13, ApJS 207, 24 • Grogin+11, ApJS 197, 35 • Rujopakarn+16, ApJ 833, 12 • Schreiber, Elbaz+18, A&A 609, 30 • Skelton+15, ApJS 2414, 24 • Straatman+16, ApJ 830, 51 • Tan+13, ApJ 776, 24

Fig. 1 .

 1 Fig. 1. ALMA 1.1 mm image tapered at 0 60. The white circles have a diameter of 4 arcseconds and indicate the positions of the galaxies listed in Table 3. Black contours show the different slices (labeled A-F) used to compose the homogeneous 1.1 mm coverage, with a median rmsnoise of 0.18 mJy per beam. Blue lines show the limits of the HST/ACS field and green lines indicate the HST-WFC3 deep region. The cyan contour represents the limit of the Dunlop et al. (2017) survey covering all the Hubble Ultra Deep Field region. All of the ALMA-survey field is encompassed by the Chandra deep field-South.

Fig. 2 .

 2 Fig. 2. uv-coverage of one of the 846 ALMA pointings constituting this survey. This uv-coverage allows us to perform the source detection in the dirty map.

Fig. 3 .

 3 Fig.3. Histogram of pixels of the S/N map, where pixels with noise >0.3 mJy beam -1 have been removed. The red dashed line is the best Gaussian fit. The green dashed line is indicative and shows where the pixel brightness distribution moves away from the Gaussian fit. This is also the 4.2σ level corresponding to a peak flux of 0.76 mJy for a typical noise per beam of 0.18 mJy. The solid black line corresponds to our peak threshold of 4.8σ (0.86 mJy).

Fig. 4 .

 4 Fig. 4. Cumulative number of positive (red histogram) and negative (blue histogram) detections as a function of the σ p (at a fixed σ f , left panel) and σ f (at a fixed σ p , right panel) in units of σ. Solid black line represents the purity criterion p c define by Eq. (1), green dashed-line represents the percentage of positive detection with HST-WFC3 counterpart p HST and magenta dashed-line represents the percentage of positive detection with ZFOURGE counterpart p ZFOURGE . Gray dashed-lines show the thresholds σ p = 4.8σ and σ f = 2.7σ and the 80% purity limit.

1 )

 1 IDs of the sources as shown in Fig.1. The sources are sorted by S/N. * indicates galaxies that are most likely spurious (not detected at any other wavelength); (2) redshifts from the ZFOURGE catalog. Spectroscopic redshifts are shown with three decimal places. As AGS6 is not listed in the ZFOURGE catalog, we used the redshift computed byDunlop et al. (2017); (3) S/N of the detections in the 0 60 mosaic (except for AGS21). This S/N is computed using the flux from Blobcat and is corrected for peak bias; (4) peak fluxes measured using Blobcat in the 0 60-mosaic image before de-boosting correction;[START_REF] Dowell | HerMES: Candidate high-redshift galaxies discovered with Herschel/SPIRE[END_REF] deboosting factor;[START_REF] Glazebrook | A massive, quiescent galaxy at a redshift of 3.717[END_REF] fluxes measured by PSF-fitting with Galfit in the 0 60-mosaic image before de-boosting correction;(7) stellar masses from the ZFOURGE catalog; (

Fig. 6 .

 6 Fig. 6. Postage stamps of 1.8 × 1.8 arcsec. ALMA contours (4, 4.5 then 5-10-σ with a step of 1-σ) at 1.1 mm (white lines) are overlaid on F160WHST/WFC3 images. The images are centered on the ALMA detections. The shape of the synthesized beam is given in the bottom left corner. Astrometry corrections described in Sect. 4.3 have been applied to the HST images. In some cases (AGS1, AGS3, AGS6, AGS13, AGS21 for example), the position of the dust radiation matches that of the stellar emission; in other cases, (AGS4, AGS17 for example), a displacement appears between both two wavelengths. Finally, in some cases (AGS11, AGS14, AGS16, and AGS19) there are no optical counterparts. We will discuss the possible explanations for this in Sect. 7.

26 A&A

 26 Fig. 6. Postage stamps of 1.8 × 1.8 arcsec. ALMA contours (4, 4.5 then 5-10-σ with a step of 1-σ) at 1.1 mm (white lines) are overlaid on F160WHST/WFC3 images. The images are centered on the ALMA detections. The shape of the synthesized beam is given in the bottom left corner. Astrometry corrections described in Sect. 4.3 have been applied to the HST images. In some cases (AGS1, AGS3, AGS6, AGS13, AGS21 for example), the position of the dust radiation matches that of the stellar emission; in other cases, (AGS4, AGS17 for example), a displacement appears between both two wavelengths. Finally, in some cases (AGS11, AGS14, AGS16, and AGS19) there are no optical counterparts. We will discuss the possible explanations for this in Sect. 7.

Fig. 8 .

 8 Fig. 8. ALMA 1.1 mm continuum maps for the 23 detections tapered at 0.60 arcsec. Each 3 5×3 5 image is centered on the position of the ALMA detection. Cyan double crosses show sources from the GOODS-S CANDELS catalog. White circles show sources from the ZFOURGE catalog.Blue circles show common sources from both optical catalogs (sources with an angular separation lower than 0 4). The shape of the synthesized beam is given in the bottom left corner.

Fig. 9 .

 9 Fig. 9. East-west profile of the PSFs corresponding to the six different parallel slices composing the ALMA image in the 0 60-mosaic (see Fig. 1).

Fig. 10 .

 10 Fig. 10. Comparison between the stacked PSF (black solid line) and the stack of the 23 ALMA-detections (black dashed line) in the 0 60mosaic. As each slice has a specific PSF, we stack the PSF corresponding to the position of each detection. The fluxes of each detection have been normalized, so that the brightest sources do not skew the results. Fluxes of the PSF and ALMA detections are normalized to 1. Flux profiles are taken across the East-west direction. The result is consistent with unresolved or marginally resolved sources at this resolution. The insert in the top-right corner shows the same procedure for the 15 sources detected in the 0 29-mosaic (see Table3).

Fig. 11 .Fig. 12 .

 1112 Fig. 11. 10 × 10 postage stamps, centered on the galaxy detections. Left to right: source in the 0 60-mosaic map, and residuals obtained after PSF, Gaussian and Sersic flux fitting. The residuals are very similar between the three different extraction methods. Only the 6 brightest galaxies are shown.

Fig. 13 .

 13 Fig. 13. Median source detection completeness for simulated point-like and Gaussian galaxies as a function of integrated flux, for different FWHMs (see figure's legend). The shaded regions correspond to the standard deviation of 100 runs, each containing 300 simulated sources.

Fig. 14 .

 14 Fig. 14. Effective area as a function of flux density, where a source with a given flux can be detected with an S /N > 4.8σ. Ninety percent of the survey area reaches a sensitivity of at least 1.06 mJy beam -1 .

Fig. 15 .

 15 Fig.[START_REF] Schreiber | Jekyll & Hyde: quiescence and extreme obscuration in a pair of massive galaxies 1.5 Gyr after the Big Bang[END_REF]. Flux boosting as a function of measured S/N estimated from simulations. The median of the boosting is shown by a solid red line. The 1σ confidence intervals (dashed red lines) are overplotted. The solid black horizontal line corresponds to F out = F in (see text for details). We used the same set of simulations that we used for the completeness analysis.

Fig. 16 .

 16 Fig.[START_REF] Riguccini | The composite nature of Dust-Obscured Galaxies (DOGs) at z ~ 2-3 in the COSMOS field -I. A far-infrared view[END_REF]. 1.1-mm cumulative (left panel) and differential (right panel) number counts derived using the corrections described in Sect. 5.4, for the sources detected at >4.8σ in the main catalog. AGS19 is located at a position where the noise is artificially low, and has therefore not been taken into account. Previous (sub)millimeter cumulative number counts are also shown(Lindner et al. 2011; Scott et al. 2012; Karim et al. 2013; Hatsukade et al. 2013 Hatsukade et al. , 2016;; Ono et al. 2014;[START_REF] Simpson | The SCUBA-2 Cosmology Legacy Survey: ALMA Resolves the Bright-end of the Sub-millimeter Number Counts[END_REF] Oteo et al. 2016; Carniani et al. 2015; Aravena et al. 2016; Fujimoto et al. 2016; Umehata et al. 2017; Geach et al. 2017; Dunlop et al. 2017). The different fluxes are scaled to 1.1 mm flux densities using S 1.1 mm /S 1.2 mm = 1.29, S 1.1 mm /S 1.3 mm = 1.48, S 1.1 mm /S 870 µm = 0.56. From the Umehata et al. (2017) study, we used only sources which do not have z = 3.09, (which means we are excluding the protocluster members). Results from single-dish surveys are shown with unfilled pentagon markers and are only indicative, they are not considered for model fitting. The gray curve shows the best-fit Schechter function (with 1-σ) uncertainties, the red curve shows the best-fit DPL function (with 1-σ).

  Fig.[START_REF] Riguccini | The composite nature of Dust-Obscured Galaxies (DOGs) at z ~ 2-3 in the COSMOS field -I. A far-infrared view[END_REF]. 1.1-mm cumulative (left panel) and differential (right panel) number counts derived using the corrections described in Sect. 5.4, for the sources detected at >4.8σ in the main catalog. AGS19 is located at a position where the noise is artificially low, and has therefore not been taken into account. Previous (sub)millimeter cumulative number counts are also shown(Lindner et al. 2011; Scott et al. 2012; Karim et al. 2013; Hatsukade et al. 2013 Hatsukade et al. , 2016;; Ono et al. 2014;[START_REF] Simpson | The SCUBA-2 Cosmology Legacy Survey: ALMA Resolves the Bright-end of the Sub-millimeter Number Counts[END_REF] Oteo et al. 2016; Carniani et al. 2015; Aravena et al. 2016; Fujimoto et al. 2016; Umehata et al. 2017; Geach et al. 2017; Dunlop et al. 2017). The different fluxes are scaled to 1.1 mm flux densities using S 1.1 mm /S 1.2 mm = 1.29, S 1.1 mm /S 1.3 mm = 1.48, S 1.1 mm /S 870 µm = 0.56. From the Umehata et al. (2017) study, we used only sources which do not have z = 3.09, (which means we are excluding the protocluster members). Results from single-dish surveys are shown with unfilled pentagon markers and are only indicative, they are not considered for model fitting. The gray curve shows the best-fit Schechter function (with 1-σ) uncertainties, the red curve shows the best-fit DPL function (with 1-σ).

Fig. 18 .

 18 Fig.[START_REF] Straatman | A substantial population of massive quiescent galaxies at z ~ 4 from ZFOURGE[END_REF]. Redshift distributions (photometric or spectroscopic) for millimeter-selected galaxies. The blue solid line shows the redshift distribution of our ALMA GOODS-South blind survey. The green dashed line shows the Hubble Ultra Deep Field Survey redshift distribution(Dunlop et al. 2017), the black dash-dotted line shows the ASPECS sample(Aravena et al. 2016), the red dotted line shows the ALMA Frontier Fields survey(González-López et al. 2017) and the yellow dotted line shows the ASAGAO survey(Ueda et al. 2018). Short colored lines at the top of the figure indicate the median redshifts for these four studies.

  Fig.[START_REF] Henriques | Galaxy formation in the Planck cosmology -I. Matching the observed evolution of star formation rates, colours and stellar masses[END_REF]. Stellar mass versus redshift for the galaxies detected in our ALMA GOODS-South blind survey (red points). For comparison, the distribution of all of the galaxies, listed in the ZFOURGE catalog, in the same field of view is given in blue. Only UVJ active galaxies are shown. The two HST-dark galaxies for which we have redshifts (AGS4 and AGS11) are represented by open circles. The redshift of AGS11 is however uncertain. The green dashed line shows the position that would be occupied by a typical star-forming galaxy -lying on the median of the SFR-M star-formation main sequence (MS) -that would produce a 1.1 mm flux density equal to our average detection limit of 0.88 mJy (4.8-σ) using the spectral energy distribution (SED) library ofSchreiber et al. (2018). The dotted line illustrates the position of galaxies 3 times above the MS using the appropriate SEDs from the same library. Galaxies hosting an AGN that are undetected or detected by ALMA are identified with black dots and yellow stars respectively. Inside the black dashed rectangle, 50% of the galaxies detected by ALMA host an AGN, while only 14% of the UVJ active galaxies undetected by ALMA host an AGN.

Fig. 20 .

 20 Fig. 20. IRAC 3.6 µm (red contours, 3 µJy-30 µJy in steps of 3.0 µJy) and ALMA 1.1 mm (white contours, 4, 4.5 then 5 to 10-σ in steps of 1-σ) overlaid on 8 3 × 8 3 HST H-band images. The position of the previously associated HST counterpart is shown by a cyan circle.

Fig. 21 .

 21 Fig. 21. Postage stamps of 10 × 10 arcsec from HST-WFC3 at 0.606 µm to VLA at 5 cm, for the four optically-dark galaxies discussed in Sect. 7. For the two ALMA images at 1.1 mm, those marked by 1 correspond to the non-tapered images, those marked by 2 correspond to the 0 60mosaic images. The K s -band thumbnail comes from the super-deep detection image described in Sect. 2.4.1. All images are centered on the ALMA detection. We indicate with white arrows the position of the previously associated HST counterpart.

Fig. 22 .

 22 Fig. 22. Spectral energy distributions (SED) of the two optically-dark galaxies AGS4 and AGS17. The flux densities from 100 to 500 µm are from GOODS-Herschel Elbaz et al. (2011). AGS4 (top) (z = 4.32, see Sect. 7) is fitted with the model of Schreiber et al. (2018). The SED of AGS17 (bottom panel), which has no known redshift, is simply presented with an interpolation between the observed flux densities to illustrate that it peaks around 400 µm. This peak is inconsistent with the redshifts of the two optical sources with ID CANDELS 4414 (z = 1.85) and 4436 (z = 0.92)

Fig. 23 .

 23 Fig. 23. Spectral energy distributions of AGS4 and ID CANDELS 8923. Aperture photometry allows the separation between the local galaxy detected by HST (blue, and indicated by a white arrow in Fig. 21, ID CANDELS 8923) and the distant galaxy detected by ALMA (orange).The top panel shows the photometric redshift probability distribution of AGS4. As the Balmer break is well established in the K-band, we consider that this redshift determination is robust, and we adopt the derived redshift z AGS4 = 4.32+0.25 -0.21 and stellar mass (10 11.45±0.2 M ) values for AGS4.

Fig. 1 .

 1 Fig.1. Left: offset between Pan-STARRS and HST; Middle: offset between JVLA and Pan-STARRS; Right: offset between JVLA and ALMA. For each panel, the histogram of the offsets in RA and DEC is shown as well as a fit with a Gaussian function (orange curve). The position of the peak and the standard deviation of the Gaussian is indicated for each curve. The middle and the right panels show that there are no significant astrometric differences between ALMA and JVLA nor between JVLA and PS1, while The left panel shows the clear shift in both RA and DEC between the positions of 375 sources in common between the Pan-STARRS (PS) and HST images. We measure a systematic offset of ∆RA = -96 ± 83 mas and ∆Dec = 252 ± 107 mas. In addition, a local offset is presented in Fig.2.

Fig. 2 .

 2 Fig. 2. Difference between HST and Pan-STARRS position after subtraction of the median offset value. Each arrow represents a sliding median including on average 15 points, with an overlap of 60 percent between neighboring arrows. The blue line defines the area encompassing the GOODS-ALMA survey.

Fig. 6 .

 6 Fig. 6. IRAC 3.6µm map (17 × 17 ) image centred on the position of the ALMA detection. We show the image before (left panel) and after (right panel) the subtraction with GALFIT of the bright source ID ZFOURGE = 11024 (ID CANDELS = 8067) located to the Northeast of the detection and which masks the emission of the source located at the ALMA position. After subtraction we can see emission located in the central position which suggests that the source is not present in Ashby et al. (2015) only because of blending. Green double crosses show sources from the GOODS-S CANDELS catalog. White circles show sources from the ZFOURGE catalog. Blue circles show common sources from both optical catalogs (i.e. sources with an angular separation lower than 0 . 4).

Fig. 7 .

 7 Fig.7. Stellar mass distribution for the sources that were cross-matched between the ZFOURGE catalog and the image (black contours) or the inverse image (green contours). The sample galaxies selected in this study are shown in grey.

  .

4. 3 .

 3 Consistency test of the Supplementary Catalog: stellar mass distribution

  -AGS36: z spec = 0.646 from the Arizona CDFS Environment Survey (ACES), spectroscopic redshift survey of the Chandra Deep Field South (CDFS) using IMACS on the Magellan-Baade telescope (Cooper et al. 2012) and confirmed by the VIMOS VLT Deep Survey (Le Fèvre et al. 2013).

Fig. 8 .

 8 Fig. 8. ALMA 1.1 mm image tapered at 0 . 60. The white circles have a diameter of 4 arcseconds and indicate the positions of the galaxies listed in Table 1. Black contours show the different slices (labeled A to F) used to construct the homogeneous 1.1 mm coverage, with a median RMS = 0.18 mJy.beam -1 . Blue lines show the limits of the HST/ACS field and green lines indicate the HST-WFC3 deep region. The cyan contours represent the limit of the Dunlop et al. (2017) survey covering all of the Hubble Ultra Deep Field region, the yellow contours show the ASAGAO survey (Hatsukade et al. 2018), while the purple contours show the ASPECS Pilot survey (Walter et al. 2016), the pink contours show the ASPECS Large Program (Decarli et al. 2019). The Chandra Deep Field-South encompasses all of the ALMA-survey field.

Fig. 9 .

 9 Fig.9. Comparison of redshift (left panel) and stellar mass (right panel) from the CANDELS and the ZFOURGE catalogs. Solid black lines represent z ZFOURGE = z CANDELS . The galaxies presented in F18 (main catalog) are shown in red, while the galaxies presented in this paper are shown in gray. Black squares indicate spectroscopic redshifts. The stellar mass has been scaled from a Chabrier IMF to a Salpeter IMF by applying a factor of 1.7 in the ZFOURGE catalog. In this paper, we will take, with the exception of AGS36 which has an inconsistent redshift (z AGS 37,ZFOURGE = 9.47 and for which we will take the data from the CANDELS catalog), the redshifts and stellar masses by the ZFOURGE catalog.

Fig. 11 .

 11 Fig. 11. Underestimation of the flux when asuming a point-like source instead of the real size of the galaxy. For example, a source with an intrinsic FWHM of 0 . 3 will be underestimated by 20%.

  Fig. A.2. (continued)

Fig. 1 |

 1 Fig. 1 | Example images and SEDs of H-dropouts. Top three rows, images of five H-dropouts obtained in three different spectral bands-HST/ F160W (top row), IRAC 4.5 μm (second row) and ALMA 870 μm (third row). The H-dropouts, named in the top row, were selected randomly from the parent sample, with all but the last one (COS-27392) detected with ALMA. Each image is 12″ × 12″; see scale bar in bottom right image. Bottom row, the measured UV-to-NIR SED (squares) and best-fit stellar population synthesis models (red lines). S λ , differential flux per unit wavelength. The error bars are 1σ. The filled and open squares indicate photometric points with measured signal-to-noise ratio (S/N) above and below 3, respectively.

Fig. 2 |

 2 Fig. 2 | Stellar masses and SFRs of H-dropouts. The red filled and open circles represent respectively the ALMA-detected and the ALMA-undetected H-dropouts. For comparison, a sample of LBGs at z = 4-6 from the ZFOURGE survey22 and bright z > 3 SMGs (S 870μm > 4.2 mJy) from the ALESS survey are also shown23 . The stellar masses for the ALESS SMGs are reduced by 0.3 dex to account for the systematic differences caused by the different methods used in mass estimation. The grey solid and dashed lines indicate respectively the star-forming main sequence (MS) at z = 4 and its 1σ scatter24 . The SFRs for ALMA-detected H-dropouts are derived from the 870-μm fluxes assuming their intrinsic far-infrared SED resembles that of the stacked one. Error bars are 1σ. The SFRs for ALMA-undetected H-dropouts are derived from optical SED fitting with an additional constraint of SFR > 1M ⊙ yr -1 , for which error bars represent the 16th and 84th percentiles of the distribution obtained in the Monte Carlo simulations (Methods), the same as that for stellar mass estimates.

Fig. 3 |

 3 Fig. 3 | Contribution of H-dropouts to the cosmic SFR density and the stellar mass function. a, Plot of cosmic star-formation-rate density, ψ, versus redshift z. The black line indicates the current known total cosmic star-formation history, which is based on LBGs at z ≳ 4 (' All LBGs' , blue open triangles17 ). Red filled circles ('Massive H-dropouts'), ALMAdetected H-dropouts with M * > 10 10.3 M ⊙ . Purple filled pentagons, the ALESS SMGs (S 870μm > 4.2 mJy)12 , whose contribution to the SFR density peaks at z ≈ 2.5. Blue filled triangles ('Massive LBGs'), the SFR density (based on dust-corrected UV) for the brightest/massive LBGs with M * > 10 10.3 M ⊙ , based on the latest determination of the UV luminosity

Fig. 4 |

 4 Fig.4| Clustering properties and halo masses of H-dropouts. Shown is the galaxy bias of ALMA-detected H-dropouts (red star) and its comparison to other populations, including the brightest LBGs ('Massive LBGs'; blue triangles) at z ≈ 4-5 (ref.26 ) and massive passive galaxies ('Passive galaxies'; purple squares) with M * > 10 10.5 M ⊙ at z = 2-3 (ref.27 ). Error bars, 1σ estimated from Poisson statistics. Filled dark-blue and light-blue triangles denote massive and more typical (L * ) LBGs with UV magnitudes of M UV ≈ -22 and M UV ≈ -20.5, respectively. Dotted lines, the corresponding galaxy bias for fixed halo mass (labelled) at different redshifts28 ; dashed line, the evolutionary track29 for galaxies with the same galaxy bias as H-dropouts. The descendants of H-dropouts are consistent with massive ellipticals at z ≈ 2-3 and today's most massive galaxies residing in massive groups and clusters.

Fig. 6 |

 6 X-SHOOTER spectra of two spectroscopically confirmed H-dropouts. The two galaxies (with IDs 25363 and 32932) are shown on separate rows. Left, main panel, the observed spectra are shown as black solid lines and blue shading, with uncertainties shown in the background as a grey shaded area. The best emission line model for Lyα is shown in red, and the centroid of the line is indicated with a vertical dotted line. The 2D spectrum is shown on the top, aligned with the 1D spectrum. Right, smoothed cutouts of the galaxies as observed in the Subaru medium band (IB738) where Lyα was detected. The X-SHOOTER slit is shown in blue, Spitzer-IRAC contours are shown in yellow, and ALMA contours are shown in red. The second galaxy (with ID = 32932) is only marginally detected, with S 870μm = 0.4 ± 0.1 mJy. The centroid of each dropout (determined from the IRAC image) is shown as a white cross.Letter reSeArCHExtended Data Fig.7| H -[4.5] colour versus stellar mass for massive galaxies at 3.5 < z < 6.5. Galaxies selected from the ZFOURGE catalogue (left, 3.5 < z < 4.5; right, 4.5 < z < 6.5) with HST/F160W detections (H > 27 mag) are shown in green while the H-dropouts selected in the same fields are shown in red. The H -[4.5] colour of the H-dropouts are shown by their lower limit assuming H > 26.5 mag (5σ). Quiescent and star-forming galaxies are shown by open and filled circles, respectively. Quiescent H-dropouts are defined as those undetected with ALMA while quiescent ZFOURGE galaxies are defined by their sSFR (based on SED fitting) with sSFR < 0.3 Gyr -1 and no MIPS 24-μm detections 8 .

Table 3 .

 3 2.

	IRAC	PACS	SPIRE	SUBARU	WFI	FourStar	WFC3	ACS	VIMOS	MIPS		10 3
												10 2
												10 1	wavelength [µm]
												FWHM ["]	0.1	0.5	1	5	10	10 0
	30	28	26	24	22	20	18	16	14	12
						Magnitude (AB)

  Measurement of the average of the rms (red line) and the median of the rms (blue line) according to the size of the measured area. The grey areas represent the standard deviation of the measurement. The size of the chosen area is 100 pixels. This corresponds to the smallest possible area (which takes better into account the spatial variations of the noise map) for which the rms stops increasing. The rms map converges to the typical value of the noise in the ALMA map while taking into account the local variation of noise

	3.6. Noise map									51
		0.250								mean
		0.225								median
	rms [mJy/beam]	0.125 0.150 0.175 0.200
		0.100
		0.075	0	50	100	150	200	250	300	350	400
						size box [px]
	FIGURE 3.14:

TABLE 3 . 4 :

 34 Quantification of the effect of the change the size of the selected area on the average and median noise when creating the noise map.

3 h 32 m 10.00 s 20.00 s 30.00 s 40.00 s 50.00 s RA (J2000)

TABLE 3 . 6 :

 36 Summary of the observations. The slice ID, the date, the number of antennae, the time on target, the total time (time on target + calibration time), the resolution and the 1-σ noise of the slice are given.

	CHAPTER 4
	CREATION OF THE ALMA SOURCE CATALOG

Contents 3.1 Historical context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2 CANDELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3 Multi-wavelength coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.4 Survey presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.5 Mosaic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.6 Noise map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

  3.

		0.5 0.6	HST (1.6 m) inside HUDF HST (1.6 m) outside HUDF IRAC (3.6 m)
	p (X < d cl )	0.3 0.4
		0.2
		0.1
		0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Distance to the closest galaxy (d cl ) ["] 0.0
	FIGURE 4.6: Probability of a randomly selected position in the area defined by this survey to
	have at least one

Table 4 .

 4 2).

	AGS1 PSF	Gaussian Sersic	AGS2 PSF	Gaussian Sersic
	AGS3 PSF	Gaussian Sersic	AGS4 PSF	Gaussian Sersic
	AGS5 PSF	Gaussian Sersic	AGS6 PSF	Gaussian Sersic

z∼2

(Barro et al. 2013; Williams et al. 2014; van der Wel et al. 2014; Kocevski et al. 2017

, see also

Elbaz et al. 2018

).

TABLE 5 .

 5 Number of entries per bin for cumulative number counts; (4) Centre of the flux density bin; (5) Differential number counts; (6) Number of entries per bin for differential number counts. Flux density bins, ∆logSν = 0.20 dex wide for differential number counts. The uncertainties are computed by Monte-Carlo simulations, added in quadrature to the Poisson uncertainties.

	)

1: Number counts at 1.1mm derived from > 4.8 σ detections (main catalog). Columns: (1) Flux Density; (2) Cumulative number counts; (3)

TABLE 5 .

 5 2: Best-fit parameters for the cumulative and differential number counts for a double power law function (Eq. 5.19) and a Schechter function (Eq. 5.20).

		N 0	S 0	α	β
		10 2 deg -2	mJy
		Cumulative number counts
	DPL Schechter	2.8±0.2 14.3 +1.4 -2.3 Differential number counts 4.4 +0.3 -0.5 8.45 +0.28 -1.07 2.0 ± 0.3 -1.38±0.05	1.68±0.02
	Schechter 35.2 +4.6 -10.8	1.6 +0.3 -0.4	-1.99±0.07

[START_REF] Henriques | Galaxy formation in the Planck cosmology -I. Matching the observed evolution of star formation rates, colours and stellar masses[END_REF]

. We use a least squares method with

  Beforehand, we previously removed from the image the sources that had been detected Chapter 4 . For example, in the "direct" image, 6 galaxies are only detected in Ksband, 26 only in H-band, 113 only with IRAC. 31 are detected in the ultra-deep Ks and H-band but are not present the S-CANDELS catalog, 3 source are in common between H-band image Distance between ALMA detection and the closest IRAC galaxy listed in the S-CANDELS catalog for the sources presented Chapter 4, red-dashed line, for the supplementary catalog, gray and for the all the 3.5σ detection. We also represented the JVLA counterparts (at 3GHz) with a black solid line. All the ALMA 3.5σ detections with both IRAC and JVLA counterpart between 0.3 and 0.7" from the ALMA detection have been selected.

	10		Total Main cat
			0.6	Before correction After correction	Supp. cat JVLA
	#	5	0.4
			0.2
	∆δ ["]		0.0
	6 Inverse image -0.4 4 0 31 4 10 Deep combined K s (2.2µm) -0.2 0.0 0.2 ∆α ["] Spitzer/IRAC (3.6µm) 0.4 113 34 HST/WFC3-H (1.6µm) 113 Spitzer/IRAC (3.6µm) FIGURE 6.4: Number of sources cross-matched between the ALMA 3.5σ detection and the 0.6 -0.6 -0.4 -0.2 6 0 26 31 3 25 Deep combined K s (2.2µm) HST/WFC3-H (1.6µm) Image 99 Spitzer/IRAC (3.6µm) 6 0 26 31 3 25 Deep combined K s (2.2µm) HST/WFC3-H (1.6µm) Image ZFOURGE (Straatman et al., 2016), CANDELS (Guo et al., 2013) and S-CANDELS (Ashby et al., 2015) catalog in the image (left panel) and in the inverse image (right panel), within a radius of 0.6" for the ZFOURGE and CANDELS catalogs and 1.95" with the S-CANDELS catalog Ashby 0.4 0.6 Distance IRAC-ALMA [arcsec] 0 et al. (2015). 0.2 FIGURE 6.5:

FIGURE 6.3:

Positional offset (RAHST -RA ALMA , DECHST -DEC ALMA ) between HST and ALMA, before (red crosses) and after (blue crosses) the correction of both a global systematic offset and a local distortion offset. The black dashed circle corresponds to the cross-matching limit radius of 0 . 6. The grey dashed circles show positional offsets of 0 . 2 and 0 . 4 respectively. The mean offset and the standard deviation are shown by the magenta cross. and Spitzer/IRAC channel 1 image but are not detected in the ultra-deep Ks image and 25, in addition to being detected at 3.5σ with ALMA, are detected in the 3 other wavelengths.

  Cowie et al. (2018) using a 100 arcmin 2 survey of the field down to an RMS ∼0.56 mJy at 850 µm with SCUBA-2. While none of the three detections that we listed as spurious were detected by SCUBA-2, 17 out of our 20 brightest ALMA sources were detected byCowie et al. (2018). The remaining 3 sources were either confirmed with ALMA byCowie et al. (

  Stellar mass distribution for the sources that were cross-matched between the ZFOURGE catalog and the image (black contours) or the inverse image (green contours). The sample galaxies selected in this study are shown in grey.

	6.4. ALMA Main and Supplementary catalogs		113
		16				Image
		14				Inverse Supp. cat
		12
	\#	8 10
		6
		4
		0 2	7	8	9 log 10 (M ) [M ] 10	11	12
	FIGURE 6.7:
							10 M

TABLE 6 .

 6

1: Details of the positional differences between ALMA and HST-WFC3 for our catalog of galaxies identified in the 1.1mm-continuum map. Columns: (1) Source ID; (

2

), (

3

) Coordinates of the detections in the ALMA image (J2000); (

TABLE 6 .

 6

2: Columns: (1) Source ID; (

  z spec = 0.646 from the Arizona CDFS Environment Survey (ACES), spectroscopic redshift survey of the Chandra Deep Field South (CDFS) using IMACS on the Magellan-Baade telescope(Cooper et al., 2012) and confirmed by the VIMOS VLT Deep Survey (Le

	6.5. Catalog	117
	-AGS36:

TABLE 6 .

 6 3: Table of sizes measured with uvmodelfit and reliable size measurement limit given Martí-Vidal et al. (2012). The last column gives the adopted size: θuvmodelfit if θuvmodelfit > θ lim , θ lim if θuvmodelfit < θ lim .

		1.8
	real /F point-like	1.4 1.6
	F	1.2
		1.0
		0.0	0.2	0.4	0.6	0.8	1.0
				galaxy size [arcsec]

  6.6. Comparison of the properties of the ALMA galaxies from the Main and Supplementary catalogs 121

	# ALMA coverage	0 500 1000 1500 2000						All Main cat Supp. cat Main + Supp. cat	2 4 6 8 10 12 14 16 # This work 12 2 4 6 8 10 # This work
		10 11
	M [M ]	10 9 10 10
		10 8	All Main cat				#ALMA/# Total [%]
			Supp. cat Optically dark galaxy			0 20 40 60 80 100
		0 10 7	1	2	3	4	5	6	0	1000	2000
					redshift				# ALMA coverage
		FIGURE 6

TABLE 7 .

 7

1: Redshift, stellar mass and dust attenuation for the ALMA detection as well as for the HST-detection.

TABLE 7 .

 7 2: The probability of an HST or IRAC random association (RaA) between the ALMA detection and the closest HST and IRAC galaxies (seeFig. 4.6) for the 4 HST-Dark galaxies discussed in Sect.7.3.

	Chapter 7. HST-dark galaxies

TABLE 8 . 1 :

 81 Parameters used in the SED fitting procedures by CIGALE.

TABLE 8 .

 8

2: Derived properties of the GOODS-ALMA sources. Columns: (1) Source name; (2) LIR derived from SED fitting (3), SFRtot = SFRIR + SFRUV , (4) RSB = SFR/SFRMS, where SFRMS is the average SFR of MS galaxies following Schreiber et al. (

  -Company et al. (2015a) only provide fragmented information onn them. We cross-matched our sample with the catalog of Huertas-Company et al. (2015a) that estimates the probability of being a spheroid, disk or irregular using the Convolutional Neural Network technique. In addition to the 6 HST-dark galaxies, which, by definition, cannot be categorized, nine other galaxies have H-band fluxes too faint to be classified (F160W > 24.5 AB mag). This leaves only 20 of our galaxies that are present in this catalog. We use the simplified classification proposed in Huertas-Company et al. (2015b):

-pure bulges: f sph > 2/3 AND f disk < 2/3 AND f irr < 1/10; -pure disks: f sph < 2/3 AND f disk > 2/3 AND f irr < 1/10; -disk+sph: f sph > 2/3 AND f disk > 2/3 AND f irr < 1/10; -irregular disks: f disk > 2/3 AND f sph < 2/3 AND f irr > 1/10; -irregulars/mergers: f disk < 2/3 AND f sph < 2/3 AND f irr > 1/10.

TABLE 8 .

 8

3: Column (1) ALMA ID. Column (2) visual morphology from HST-WFC3 H-band: single/isolated galaxy (S), merger (M) and undefined (U). Column (3) FWHM measured from uvmodelfit in CASA. Column (4) ΣSF R. Column (5)τ dep ( = Mgas/SFR), in Myr.

•

  Wang, Elbaz+16, ApJ 816, 84 This science goal contains the scan in band 4, with 4 tunings aligned to the highest frequency observable in the band.

											SG-1
								2018.1.01079.S
	SG : 1	of 1	Dark-HST band 4	Band 4
	Science Goal Parameters
		Ang.Res.	LAS	Requested RMS	RMS Bandwidth	Rep.Freq.	Cont. RMS	Cont. Bandwidth	Poln.Prod.	Non-standard mode
		0.8000"		1.0"	200 µJy, 17 mK	399.745 km/s, 200 MHz	149.992000 GHz	17.455 µJy, 1.5 mK	25.797 GHz	XX,YY	Yes
	Use of 12m Array (43 antennas)
	t_total(all configs)	t_science(C43-3)	t_total()	Imaged area	#12m pointing	12m Mosaic spacing	H P B W	t_per_point	Data Vol	Avg. Data Rate
		10.0 h		3.8 h		0.0 h	12.9 "	6		offset	38.8 "	580.0 s	73.6 GB	2.5 MB/s
	Use of ACA 7m Array (10 antennas) and TP Array
		t_total(ACA)	t_total(7m)	t_total(TP)	Imaged area	#7m pointing	7m Mosaic spacing	H P B W	t_per_point	Data Vol	Avg. Data Rate
	Spectral Scan Setup
		Start Frequency		END Frequency	Bandwidth	Resolution	Vel. Bandwidth	Vel. Resolution	Res. El. per FWHM	R M S
		137.100 GHz		162.800 GHz	1.875 GHz	7.813 MHz	3748 km/s	15.615 km/s	25.6	198.24 µJy, 16.8 mK
	6 Targets						Expected Source Properties
									Peak Flux	S N R	Linewidth	R M S (over 1/3 linewidth)	linewidth / bandwidth used for sensitivity	Pol.	Pol. S N R
								Line	1.10 mJy	3.2	400 km/s 343.25 µJy, 29.1 ...	1.00	80.0%	2.6
	No.	Target	Ra,Dec ( ICRS )	V,def,frame --OR--z	Continuum 120.00 uJy	6.9	50.0%	3.4
	1 1-GS8		03:32:46, -27:51:20	929356.62 km/s,lsrk,OPTICAL	Dynamic range (cont flux/line rms): 0.6
	2 2-AGS11		03:32:26, -27:52:08 1049273.60 km/s,lsrk,OPTICAL	Spectral scan tunings (frequencies on Sky)
	3 3-AGS4		03:32:34, -27:49:40	629564.16 km/s,lsrk,OPTICAL
	4 4-AGS15		03:32:17, -27:52:33	899377.37 km/s,lsrk,OPTICAL	Tuning		Spw1(GHz)	Spw2(GHz)	Spw3(GHz)	Spw4(GHz)
	5 5-AGS17		03:32:19, -27:52:14	224844.34 km/s,lsrk,RADIO	1		138.030625	139.733750	150.030625	151.733750
	6 6-AGS24		03:32:20, -27:50:24	224844.34 km/s,lsrk,RADIO	2		141.436875	143.140000	153.436875	155.140000
								3		144.843125	146.546250	156.843125	158.546250
								4		148.249375	149.952500	160.249375	161.952500

Table 1 .

 1 Summary of the observations.

	A152, page 3 of 26

  .082738 -27.866577 53.082705 -27.866567 0.11 0.19 0.124 -0.225 0.03 AGS8 15261 18282 53.020356 -27.779905 53.020297 -27.779829 0.33 0.03 0.159 -0.275 0.20 AGS9 12016 15639 53.092844 -27.801330 53.092807 -27.801208 0.45 0.16 0.100 -0.276 0.18 AGS10 16972 19833 53.082118 -27.767299 53.081957 -27.767202 0.62 0.39 0.128 -0.300 0..092365 -27.826829 53.092381 -27.826828 0.05 0.29 0.116 -0.247 0.18 AGS21 6905 10152 53.070274 -27.845586 53.070230 -27.845533 0.24 0.06 0.143 -0.249 0.07 AGS22 28952 -53.108695 -27.848332 53.108576 -27.848242 0.50 0.29 0.106 -0.226 -AGS23 10954 14543 53.086623 -27.810272 53.086532 -27.810217 0.35 0.19 0.111 -0.263 0.16

	ID ID CLS ID ZF RA ALMA deg (1) (2) (3) (4)	Dec ALMA deg (5)	RA HST deg (6)	Dec HST deg (7)	∆ HST1 ∆ HST2 (∆α) HST (∆δ) HST ∆ IRAC arcsec arcsec arcsec arcsec arcsec (8) (9) (10) (11) (12)
	AGS1 14876 17856 53.118815 -27.782889 53.118790 -27.782818 0.27 0.03 0.091 -0.278 0.16 AGS2 7139 10316 53.063867 -27.843792 53.063831 -27.843655 0.51 0.23 0.163 -0.269 0.04 AGS3 9834 13086 53.148839 -27.821192 53.148827 -27.821121 0.26 0.06 0.099 -0.262 0.10 AGS4 8923b 12333 53.142778 -27.827888 53.142844 -27.827890 0.21 0.40 0.087 -0.264 0.09 AGS5 20765 23898 53.158392 -27.733607 53.158345 -27.733485 0.46 0.13 0.087 -0.329 0.26 AGS6 15669 -53.183458 -27.776654 53.183449 -27.776584 0.26 0.03 0.054 -0.267 0.40 AGS7 4854 7867 5340 AGS11 -7589 53.108818 -27.869055 ------0.12 AGS12 15876 18701 53.160634 -27.776273 53.160594 -27.776129 0.53 0.28 0.076 -0.242 0.51 AGS13 16274 19033 53.131122 -27.773194 53.131080 -27.773108 0.34 0.05 0.087 -0.291 0.14 AGS14 --53.223156 -27.826771 -------AGS15 3818b 6755 53.074847 -27.875880 53.074755 -27.875976 0.45 0.57 0.125 -0.195 0.12 1 AGS16 --53.039724 -27.784557 -------AGS17 4414b 6964 53.079374 -27.870770 53.079327 -27.870781 0.16 0.27 0.122 -0.231 0.06 AGS18 15639 18645 53.181355 -27.777544 53.181364 -27.777501 0.16 0.12 0.043 -0.256 0.10 AGS19 --53.108041 -27.813610 -------AGS20 9089 12416 53

Notes. Columns: (1) Source ID; (

Table 3 .

 3 Details of the final sample of sources detected in the ALMA GOODS-South continuum map, from the primary catalog in the main part of the table and from the supplementary catalog below the solid line (seeSects. 4.1 and 4.2).

	ID (1)	z (2) (3) S /N	S Blobcat peak mJy (4)	f deboost S Galfit PSF mJy (5) (6)	log 10 M 0 60 0 29 M (7) (8) (9)	S 6 GHz µJy (10)	L X /10 42 erg s -1 (11)	ID sub(mm) (12)
	AGS1 2.309 11.26 1.90 ± 0.20 1.03 1.99 ± 0.15 11.05 AGS2 2.918 10.47 1.99 ± 0.22 1.03 2.13 ± 0.15 10.90 AGS3 2.582 9.68 1.84 ± 0.21 1.03 2.19 ± 0.15 11.33 AGS4 4.32 9.66 1.72 ± 0.20 1.03 1.69 ± 0.18 11.45 AGS5 3.46 8.95 1.56 ± 0.19 1.03 1.40 ± 0.18 11.13 AGS6 3.00 7.63 1.27 ± 0.18 1.05 1.26 ± 0.16 10.93 AGS7 3.29 7.26 1.15 ± 0.17 1.05 1.20 ± 0.13 11.43 AGS8 1.95 7.10 1.43 ± 0.22 1.05 1.98 ± 0.20 11.53 AGS9 3.847 6.19 1.25 ± 0.21 1.05 1.39 ± 0.17 10.70 AGS10 2.41 6.10 0.88 ± 0.15 1.06 1.04 ± 0.13 11.32 AGS11 4.82 5.71 1.34 ± 0.25 1.08 1.58 ± 0.22 10.55 AGS12 2.543 5.42 0.93 ± 0.18 1.10 1.13 ± 0.15 10.72 AGS13 2.225 5.41 0.78 ± 0.15 1.10 0.47 ± 0.14 11.40 AGS14* -5.30 0.86 ± 0.17 1.10 1.17 ± 0.15 -AGS15 -5.22 0.80 ± 0.16 1.11 0.64 ± 0.15 -AGS16* -5.05 0.82 ± 0.17 1.12 0.99 ± 0.17 -AGS17 -5.01 0.93 ± 0.19 † 1.14 1.37 ± 0.18 -AGS18 2.794 4.93 0.85 ± 0.18 † 1.15 0.79 ± 0.15 11.01 AGS19* -4.83 0.69 ± 0.15 1.16 0.72 ± 0.13 -AGS20 2.73 4.81 1.11 ± 0.24 1.16 1.18 ± 0.23 10.76 AGS21 3.76 5.83 0.64 ± 0.11 1.07 0.88 ± 0.19 10.63 AGS22 -4.90 1.05 ± 0.22 1.15 1.26 ± 0.22 -AGS23 2.36 4.68 0.98 ± 0.21 1.19 1.05 ± 0.	1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1	1 18.38 ± 0.71 1.93 1 -51.31 1 19.84 ± 0.93 34.54 1 8.64 ± 0.77 10.39 1 14.32 ± 1.05 37.40 1 9.02 ± 0.57 83.30 1 -24.00 1 -3.46 1 14.65 ± 1.12 -1 -2.80 1 --1 12.65 ± 0.55 4.53 UDF3, C1, ASA8 GS6, ASA1 GS5, ASA2 UDF1, ASA3 LESS18 0 22.52 ± 0.81 13.88 ASA12 0 --1 --LESS34 0 --0 --LESS10 0 6.21 ± 0.57 -UDF2, ASA6 0 --1 12.79 ± 1.40 4.02 1 -19.68 0 --

  at 1.3 mm, C indicates the ALMA Spectroscopic Survey in the Hubble Ultra Deep Field (ASPECS) at 1.2 mm (Aravena et al. 2016), LESS indicates data at 870 µm presented in Hodge et al. (2013), GS indicates data at 870 µm presented in Elbaz et al. (2018), ASA indicates the ALMA 26 arcmin 2

  , a dust temperature T d = 35 K (e.g.Chapman et al. 2005;

				A&A 620, A152 (2018)
						10 8
		10 6				10 7
		10 5				10 6
	N(>S) [deg 2 ]	10 2 10 1 10 0 10 1 10 2 10 3 10 4	10 1 Flux S 1.1mm [mJy] 10 0 Double Power Law Schechter This work Dunlop+18 (1.3mm) Hatsukade+16 (1.1mm) Hatsukade+13 (1.3mm) Fujimoto+16 (1.2mm) Umehata+16 (1.1mm) Aravena+16 (1.2mm) Oteo+15 (1.2mm) Karim+13 (870 m) Simpson+15 (870 m) Scott+12 (1.1mm) Lindner+11 (1.2mm) Geach+17 (850 m)	10 1	] dN/dS [mJy 1 deg 2	10 2 10 0 10 1 10 2 10 3 10 4 10 5	10 1 Bethermin+17 Schechter This work Hatsukade+16 (1.1mm) Flux S 1.1mm [mJy] 10 0 Fujimoto+16 (1.2mm) Umehata+16 (1.1mm) Ono+14 (1.2mm) Carniani+15 (1.1mm) Karim+13 (870 m) Scott+12 (1.1mm) Lindner+11 (1.2mm) Geach+17 (850 m)	10 1
								A152, page 15 of 26

Table 4 .

 4 Number counts at 1.1 mm derived from >4.8σ detections (main catalog).

	S ν mJy (1)	N(>S ν ) deg -2 (2)	N cum (3)	S ν mJy mJy -1 deg -2 dN/dS ν (4) (5)	N diff (6)
	0.70 2772 +1776 -2641 0.88 950 +575 -775 1.11 524 +530 -188 1.40 327 +277 -124 1.76 209 +178 -119	19 13 11 7 4	0.80 8257 +26 121 -8023 1.27 1028 +6547 -638 2.01 327 +148 -160	7 6 6
	Notes. Columns: (1) flux density; (2) cumulative number counts; (3) number of entries per bin for cumulative number counts; (4) cen-
	ter of the flux density bin; (5) differential number counts; (6) num-
	ber of entries per bin for differential number counts. Flux density bins,
	∆ log S ν = 0.20 dex wide for differential number counts. The uncertain-
	ties are computed by Monte-Carlo simulations, added in quadrature to
	the Poisson uncertainties.

  Resolved 1.1 mm EBL computed from the best-fit Schechter function to the differential number counts. The green, red, purple and brown lines are from the number counts estimated by Fujimoto et al. (2016), Ono et al. (2014), Hatsukade et al. (2016), and Carniani et al.

					A&A 620, A152 (2018)
					]
	Resolved Fraction [%]	10 100	10 2 This work Flux Density [mJy] 10 1 Fujimoto+16 Ono+14 Hatsukade+16 Carniani+15	10 0	1 10 Integrated Flux density [Jy deg 2
	Fig. 17.
					,
					A152, page 17 of 26

  Positional offset (RA HS T -RA ALMA , DEC HS T -DEC ALMA ) between HST and ALMA, before (red crosses) and after (blue crosses) the correction of both a global systematic offset and a local distortion offset. The black dashed circle corresponds to the cross-matching limit radius of 0 . 6. The grey dashed circles show positional offsets of 0 . 2 and 0 . 4 respectively. The mean offset and the standard deviation are shown by the magenta cross.

			Before correction
		0.6	After correction
		0.4
		0.2
	∆δ ["]	0.0
	-0.2
	-0.4
	-0.6
			0.6	0.4	0.2	0.0 ∆α ["]	-0.2	-0.4	6
	Fig. 3.

  Article number, page 4 of 16 M.Franco et al.: GOODS-ALMA: II. Using IRAC priors to probe fainter millimeter galaxies Number of sources cross-matched between the ALMA 3.5σ detection and the ZFOURGE(Straatman et al. 2016), CANDELS(Guo et al. 2013) and S-CANDELS(Ashby et al. 2015) catalogs in the image (left panel) and in the inverse image (right panel), within a radius of 0 . 60 for the ZFOURGE and CANDELS catalogs and 1 . 95 with the S-CANDELS catalogAshby et al. (2015). Beforehand, we previously removed from the image the sources that had been detected in F18. For example, in the "direct" image, 6 galaxies are only detected in K s -band, 26 only in H-band, 113 only with IRAC. 31 are detected in the ultra-deep K s and H-band but are not present the S-CANDELS catalog, 3 source are in common between the H-band image and the Spitzer/IRAC channel 1 image but are not detected in the ultra-deep K s image and 25, in addition to being detected at 3.5σ with ALMA, are detected in the 3 other wavelengths.

		Image Image			Inverse image
			Spitzer/IRAC (3.6µm) Spitzer/IRAC (3.6µm)				Spitzer/IRAC (3.6µm)
	Deep combined K s (2.2µm) Deep combined K s (2.2µm)	6 6	Deep combined K s (2.2µm)	4
		0 0			0
	31 31	25 25	113 113	31	10	4	99
	26 26	3 3	34
	HST/WFC3-H (1.6µm) HST/WFC3-H (1.6µm)		HST/WFC3-H (1.6µm)
	0 5 10 Fig. 4. 0.2 #	0.4	0.6 Total Main cat Supp. cat JVLA
	Distance IRAC-ALMA [arcsec]

  Dec HS T ∆ HS T 1 ∆ HS T 2 (∆α) HS T (∆δ) HS T

				A&A proofs: manuscript no. main_these
	ID (1)	RA ALMA deg (2)	Dec ALMA deg (3)	RA HS T deg (4)	deg (5)	arcsec arcsec (6) (7)	arcsec (8)	arcsec (9)	∆ IRAC arcsec (10)	%RAa % (11)
	AGS24 53.087178 -27.840217 AGS25 53.183710 -27.836515 AGS26 53.157229 -27.833468 53.157238 -27.833446 ... ... ... ... AGS27 53.069132 -27.807155 53.068992 -27.807169 AGS28 53.224467 -27.817214 53.224476 -27.817151 AGS29 53.202362 -27.826284 53.202340 -27.826190 AGS30 53.168097 -27.832632 53.168025 -27.832509 AGS31 53.068906 -27.879739 53.068851 -27.879698 AGS32 53.111595 -27.767860 53.111564 -27.767771 AGS33 53.049749 -27.771007 53.049662 -27.770929 AGS34 53.105431 -27.830749 53.105466 -27.830650 AGS35 53.181971 -27.814127 53.181989 -27.814120 AGS36 53.153025 -27.735192 53.152971 -27.735114 AGS37 53.071752 -27.843712 53.071694 -27.843631 AGS38 53.176650 -27.785435 53.176577 -27.785446 AGS39 53.091634 -27.853413 53.091606 -27.853342	... ... 0.09 0.45 0.23 0.35 0.50 0.23 0.34 0.40 0.37 0.06 0.33 0.34 0.24 0.27	... ... 0.18 0.44 0.06 0.11 0.27 0.07 0.04 0.13 0.24 0.25 0.11 0.04 0.33 0.04	... ... 0.075 0.151 0.029 0.065 0.074 0.120 0.099 0.148 0.096 0.073 0.068 0.149 0.068 0.122	... ... -0.232 -0.279 -0.231 -0.226 -0.215 -0.194 -0.280 -0.310 -0.232 -0.241 -0.298 -0.273 -0.240 -0.228	... ... 0.305 0.643 0.086 0.585 0.261 0.133 0.136 0.206 0.234 0.118 0.370 0.009 0.402 0.114	... ... 0.33 1.38 0.03 1.14 0.24 0.07 0.07 0.14 0.19 0.05 0.47 0.00 0.55 0.05
	Table
										Article number, page 7 of 16

  Distance from the closest IRAC galaxy; (11) IRAC random association (RaA) between the ALMA detection and the closest IRAC galaxy.

	ID ALMA ID CLS (1) (2)	ID ZF (3)	ID S -CLS (4)	z CLS (5)	z ZF (6)	z sp (7)	S/N (8)	Flux mJy (9)	log 10 (M * ) M (10)	S 3GHz µJy (11)
	AGS24	...

Table 3 .

 3 Table of sizes measured with uvmodelfit and reliable size measurement limit given by Martí-Vidal et al. (2012). The last column gives the adopted size: θ uvmodelfit if θ uvmodelfit > θ lim , θ lim if θ uvmodelfit < θ lim .

	ID	θ uvmodelfit	θ lim	θ final
	AGS24 AGS25 AGS26 AGS27 AGS28 AGS29 AGS30 AGS31 AGS32 AGS33 AGS34 AGS35 AGS36 AGS37 AGS38 AGS39	0.06 0.12 0.30 0.54 0.50 ... ... ... 0.33 0.51 ... 0.45 0.23 0.28 0.32 0.25	0.27 0.27 0.25 0.25 0.25 0.30 0.27 0.54 0.26 0.50 0.28 0.28 0.26 0.26 0.27 0.27 0.27 0.33 0.27 0.51 0.27 0.27 0.27 0.45 0.28 0.28 0.28 0.28 0.28 0.32 0.28 0.28

  ). Red filled circles ('Massive H-dropouts'), ALMAdetected H-dropouts with M * > 10 10.3 M ⊙ . Purple filled pentagons, the ALESS SMGs (S 870μm > 4.2 mJy)12 , whose contribution to the SFR density peaks at z ≈ 2.5. Blue filled triangles ('Massive LBGs'), the SFR density (based on dust-corrected UV) for the brightest/massive LBGs with M * > 10 10.3 M ⊙ , based on the latest determination of the UV luminosity functions25 . Filled orange squares, the SFR density from H-dropouts ([4.5] < 24 mag and H -[4.5] > 2.5 mag) in semi-analytical models19 , which are identified from a K-selected mock catalogue (K < 27 mag) from a total area of 75.36 deg 2 . Error bars, s.d. assuming Poisson statistics. b, Number fraction of massive galaxies that are detected either as LBGs (blue filled triangles) or as H-dropouts (including both ALMA-detected and ALMA-undetected ones; red filled circles) averaged over z = 3.5-6.5.

It is not really a photograph as we understand it, it was made using a "stellar pantograver"[START_REF] Roberts | the Stellar pantograver[END_REF] which engraves the image of a glass plate directly onto copper plate[START_REF] James | DR Isaac Roberts (1829-1904) and his observatories[END_REF].

In this thesis, we will try to parameterize a relationship that similarly links the (Σ IR ) to the star formation efficiency of a galaxy.

A star of 10 solar masses will produce light equivalent to 4000 solar luminosities. Massive stars therefore dominate in brightness, while low mass stars dominate the total mass of a galaxy.

The near-infrared emission of an AGN is most often associated with type I AGN[START_REF] Burtscher | Obscuration in active galactic nuclei: near-infrared luminosity relations and dust colors[END_REF].

For more specific needs, we also used LePhare, Eazy, FAST, etc.

Publicly available at http://cschreib.github.io/s17-irlib/

https://www.spacetelescope.org/news/heic1315/ 3.2. CANDELS

The sampling theorem is often called Nyquist-Shannon sampling theorem but similar results had been demonstrated independently by[START_REF] Whittaker | Xviii.-on the functions which are represented by the expansions of the interpolation-theory[END_REF];[START_REF] Kotelnikov | On the carrying capacity of the ether and wire in telecommunications[END_REF];[START_REF] Raabe | Untersuchungen an der wechselzeitigen Mehrfachübertragung (Multiplexübertragung)[END_REF];[START_REF] Gabor | Gaia Data Release 1. Summary of the astrometric, photometric, and survey properties[END_REF];[START_REF] Someya | Waveform Transmission[END_REF].

The Beam Area is given by A beam = 2 × π × σ 2 . For a 2-D gaussian, FWHM = 2σ 2ln[START_REF] Walter | The intense starburst HDF 850.1 in a galaxy overdensity at z ≈ 5.2 in the Hubble Deep Field[END_REF]. By combining these two equations, we obtain the formula set out above.

Chapter 5. Number counts

https://archive.stsci.edu/pub/hlsp/goods/v2/h goods v2.0 rdm.html

http://www.stsci.edu/hst/wfc3/idctab lbn

As a reminder, all the stellar masses given in this manuscript have been converted into aSalpeter (1955) IMF.

FAST++: https://github.com/cschreib/fastpp

Publicly available at http://cigale.lam.fr

+ log 10 (O/H) = 8.90 + 0.37m -0.14s -0.19m 2 + 0.12ms -0.054s2 (8.7)

https://archive.stsci.edu/pub/hlsp/goods/v2/h_goods_v2.0_rdm.html

© The Author(s), under exclusive licence to Springer Nature Limited 2019N A T U R E | www.nature.com/nature

Remerciements

Acknowledgements. We wish to thank Ivo Labbé for sharing with us the IRAC/GREATS images and Bahram Mobasher for sharing the spectroscopic redshift of AGS4 with us. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2015.1.00543.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. RD and NN gratefully acknowledge the support provided by the BASAL Center for Astrophysics and Associated Technologies (CATA) through grant PFB-06 Etapa II. Support for BM was provided by the DFG priority program 1573 "The physics of the interstellar medium". DMA thanks the Science and Technology Facilities Council (STFC) for support from grant ST/L00075X/1. WR is supported by JSPS KAKENHI Grant Number JP15K17604, Thailand Research Fund/Office of the Higher Education Commission Grant Number MRG6080294, and Chulalongkorn University's CUniverse. NN acknowledges funding from Fondecyt 1171506.

8. Acknowledgements R.D. gratefully acknowledges support from the Chilean Centro de Excelencia en Astrofísica y Tecnologías Afines (CATA) BASAL grant AFB-17000. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2015.1.00543.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. Acknowledgements This paper makes use of the following ALMA data: ADS/ JAO.ALMA 2015.1.01495.S and ADS/JAO.ALMA 2013.1.01292.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC, ASIAA (Taiwan) and KASI (South Korea), in cooperation with Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. This Letter makes use of JCMT data from programmes M16AL006, MJLSC91, M11BH11A, M12AH11A and M12BH21A. T.W. acknowledges support by NAOJ ALMA scientific research grant no. 2017-06B, JSPS Grant-in-Aid for Scientific Research (S) JP17H06130, and funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 312725 (ASTRODEEP). X.S. acknowledges support by NSFC 11573001 and National Basic Research Program 2015CB857005. C.-F.L. and W.-H.W. were supported by Ministry of Science and Technology of Taiwan grant 105-2112-M-001-029-MY3.

franceculture.fr/emissions/la-methode-scientifique/galaxies-noires-cest-pas-//irfu.cea.fr/dap/en/Phocea/Vie_des_labos/Ast/ast.php?t=actu&id_ast=4567 3. http://www.cea.fr/drf/Pages/Actualites/En-direct-des-labos/2019/il-etait-une-fois-deux-galaxies-

Data availability

Source data for the ALMA 870-μm imaging are available through the ALMA archive. Optical-to-infrared imaging for all the galaxies in the sample are also publicly available through the HST and Spitzer data archives. The other data that support the plots within this Letter and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The codes used to reduce ALMA and X-SHOOTER data are publicly available. The codes used to model the optical-to-infrared SEDs, and to stack the optical and infrared images, are accessible through github (https://github.com/cschreib).

-AGS6, previously reported at z = 3.00, has been observed by the ALMA Spectroscopic Survey Large Program (ASPECS-LP; Decarli et al. 2019) in the Hubble Ultra-Deep Field, giving a z spec = 2.698 from the transition of CO at 93.51 GHz. This spectroscopic redshift confirms the redshift also found by MUSE, at the same position (Boogaard et al. 2019).

-AGS18, previously reported at z = 2.794, has also been observed in the ASPECS-LP survey, giving a z spec = 2.696 from the transition of CO at 93.51 GHz. This spectroscopic redshift again confirms the one found by MUSE at the same position Boogaard et al. (2019).

In the following, we will adopt for each source (i) the spectroscopic redshift when available, otherwise (ii) the photometric redshift from the ZFOURGE catalog (except for AGS35 for which we use the CANDELS redshift). These redshifts are given in Table 2.

We note that the redshift range of the Supplementary Catalog covers a wider dynamic range than the sources of the Main Catalog including two low redshift sources (z ∼ 0.6), with no equivalent in the Main Catalog. These two sources will be discussed in detail in a following paper.

The stellar masses of the Main and Supplementary catalogs have been chosen from the ZFOURGE catalog (except

# This work

All Main cat Supp. cat Main + Supp. cat Fig. 12. Stellar mass as a function of redshift for the galaxies detected in F18 (red points) and in this work (gray points). For comparison, the distribution of all the galaxies, listed in the ZFOURGE catalog, in the same field of view is given in blue. Only UVJ active galaxies are shown.

For each bin of redshift (z = 0.5) and stellar mass (log 10 (M /M ) = 0.5), with a yellow shade, the fraction of sources detected by ALMA compares to the UVJ active galaxies in GOODS-ALMA. The optically dark galaxies for which redshifts and masses have been derived are represented by open circles. The upper panel shows the compared distribution of redshift between all the UVJ active galaxies in GOODS-ALMA and the ALMA-detected galaxies while the right panel shows the stellar mass distribution. The median of the redshift and of the stellar mass are shown in these two panels. The median redshift is 2.56 for the galaxies presented in this paper, compared to 2.70 in F18, while the median stellar mass is 6.7×10 10 M in this study, compared to 1.1×10 Article number, page 14 of 16

Letter reSeArCH

We thus followed up these objects with VLT/X-SHOOTER to confirm the presence of an emission line. Each dropout was observed in May 2018 in the UVB and VIS arms for 50 min in stare mode (no nodding), split over three exposures. The 2D spectra were reduced using the standard pipeline, and 1D spectra were produced by fitting a Gaussian profile to each spectral slice. Uncertainties were controlled by computing the standard deviation of spectral elements in regions without sky lines; we found that the 1D uncertainty spectrum had to be rescaled upwards by a factor of 1.27 to match the observed noise.

We then searched for emission lines in the spectra, considering only the wavelength range covered by the Subaru medium band in which the flux excess was previously identified. The result of this search is displayed in Extended Data Fig. 6. We found a 10σ detection at 0.498 μm for dropout 32932, corresponding to z spec = 3.0971 ± 0.0002, and a more marginal but still significant 4.3σ detection at 0.739 μm for dropout 25363, corresponding to = . -.

+ .

z 5 113 spec 0 005 0 001 . Because our search space is tightly limited by the Subaru passband, the latter only has a 0.4% chance of being spurious, and we therefore consider it a reliable detection. The third dropout showed no significant line emission above 2σ. Lyman-break galaxy selection. In order to compare the properties of H-dropouts and LBGs 63 , we have selected LBGs using the ZFOURGE catalogues in the same three CANDELS fields 22 . The advantage of the ZFOURGE catalogue is that it is essentially a K s -band-selected catalogue, for which the deep K s -band data provide critical constraints on the redshift and stellar mass estimates at z > 4. We select our z = 4-6 LBG galaxy sample using the selection criterion in ref. 64 . Owing to the lack of B-band data from HST, the z ≈ 4 LBG sample is limited to the GOODS-South field only, while the z ≈ 5 and z ≈ 6 LBG samples include galaxies from all three fields. To enable a clean selection of galaxies with reliable flux density measurements, we have further limited the selection to galaxies with use = 1 as recommended 22 . This reduces the effective area to 132.2 arcmin 2 , 139.2 arcmin 2 and 135.6 arcmin 2 for GOODS-South, COSMOS and UDS field, respectively. To identify total SFR density from massive LBGs with M * > 10 10.3 M ⊙ , we used the latest determination 25 of the UV luminosity function at z ≈ 4-6. Taking into account variations in the M * -M UV relation, this mass cut corresponds to M UV < [-21.55, -22.04, -22.27] at z = [START_REF] Marrone | Galaxy growth in a massive halo in the first billion years of cosmic history[END_REF][START_REF] Dowell | HerMES: Candidate high-redshift galaxies discovered with Herschel/SPIRE[END_REF][START_REF] Glazebrook | A massive, quiescent galaxy at a redshift of 3.717[END_REF], respectively. We then derive the dust-corrected SFR for these brightest UV-selected galaxies following the approach in ref. 17 . Determination of physical properties. Stacked optical SEDs. To produce the stacked optical SEDs, we took the fluxes of each galaxy in our photometric catalogue and normalized them by their respective IRAC 4.5-μm flux. We then computed the mean flux in each band, using inverse variance weighting, and finally multiplied the resulting stacked fluxes by the average 4.5-μm flux of the stacked sample. In the stack, we combined bands that have similar effective wavelengths, even though the true passbands could be slightly different; for example we stacked together all the Ks bands from UKIDSS, UltraVISTA, FOURSTAR, WIRCam and ISAAC into a single Ks band. The uncertainties on the stacked fluxes were derived by formally combining the uncertainties of each stacked galaxy. We note that, since we obtained our photometry using fixed-size apertures, this method is strictly equivalent to stacking the images. Photometric redshift and stellar mass determination. Using the aforementioned multiwavelength photometry, including bands with formal non-detections, photometric redshifts were computed with EAzY 65 using the full set of template SEDs, that is, including the 'old-and-dusty' template and the 'extreme emission line' template. The prior on the observed magnitudes was not used. Using these redshifts, we then ran FAST 66 to estimate the stellar masses. We assumed a delayed exponentially declining star-formation history, with a range of ages and exponential timescales. Dust attenuation was modelled with the prescription of ref. 67 , allowing A V up to 6 mag. Metallicity was fixed to solar during the fitting. We also used the infrared luminosities inferred from the ALMA fluxes to further constrain the fits. This was implemented as follows. From the stacked Herschel SED (see Fig. 3), we measured the mean dust temperature of our sample: T dust = 36.7 ± 2.1 K. On the basis of Herschel and ALMA observations of z > 2 galaxies 13 , we expect a typical scatter of 5 K around the average temperature at any given redshift. Assuming this distribution of temperatures holds for the dropouts, we generated probability distributions for L IR using a Monte Carlo procedure: the measured ALMA flux was randomly perturbed with Gaussian noise of amplitude set by the flux uncertainty, and the dust temperature was drawn from a Gaussian distribution centred on 36.7 K and with a width of 5 K; the resulting dust SED was then used to extrapolate L IR from the ALMA measurement. For galaxies whose ALMA flux has S/N < 2, the resulting probability distribution of L IR was close to Gaussian, while for the detections the probability distribution was close to log-normal. We modelled these two regimes accordingly in the fit, by assuming either Gaussian noise on L IR or log 10 (L IR ), respectively. The observed infrared luminosity was then compared to the modelled value, which we computed as the difference of bolometric luminosity before and after applying dust attenuation. This resulted in an additional contribution to the χ 2 , which was then used for standard model selection.

Uncertainties on the photometric redshifts were derived from the 16th and 84th percentiles of the probability distribution produced by EAzY. This accounts for uncertainty on the photometry as well as on the model galaxy templates. Uncertainties on the derived physical parameters, including the stellar mass, were derived using Monte Carlo simulations, where the observed photometry was randomly perturbed with Gaussian noise of amplitude determined by the estimated photometric uncertainties. This was repeated 200 times. The error bars on physical parameters were then derived from the 16th and 84th percentiles of the distribution of the values obtained in the Monte Carlo simulations. For each fit, the redshift was left free to vary within the 68% confidence interval reported by the photometric redshift code. Therefore the resulting error bars account for uncertainties on the photometry and on the redshift. Clustering measurements. Because the number of H-dropouts is small, we calculate the two-point angular cross-correlation function (CCF, ω) with a much larger population of galaxies sharing the same cosmic volume (redshifts) in order θ θ

where θ, HG, HR, GR and RR are respectively angular separation, pair counts of H-dropout-galaxy, H-dropout-random, galaxy-random and random-random. The 'random' galaxy sample is created within the same CANDELS footprint as the H-dropouts (we exclude HUDF in the GOODS-S field because of its much deeper integration than other regions). The uncertainties of the CCF are estimated as:

We then fit the derived CCF with a power-law model:

where A ω is the correlation amplitude, β is the power-law index fixed to 0.8, and IC is the integral constraint. The integral constraint is an offset due to the clustering measurement over the limited area, and is calculated by:

The derived correlation amplitude can be converted to 3D correlation length r 0 by the Limber equation 69 modified by ref. 70 for the cross-correlation.

The correlation length is related to galaxy bias b, such that

where σ 8,gal is a galaxy fluctuation, γ = 1 + β, and σ 8 (z) is the amplitude of the dark matter fluctuation 71 on the scale of - h 8 Mpc 1 . The halo mass is then derived from the estimated galaxy bias 28 .

Author contributions T.W., C.S. and D.E. conceived the work, and led the analysis and interpretation. T.W. proposed and carried out ALMA observations, reduced the ALMA data, measured SCUBA-2 fluxes and performed full SED fitting, and authored the majority of the text. C.S. conducted multiwavelength photometry and SED fitting, and carried out VLT/X-SHOOTER observations and data reduction. Y. Yoshimura performed the clustering analysis. C.-F.L., W.-H.W. and X.S. contributed to the 450-μm photometry. K.K., Y. Yamaguchi, M.F., M.P. and J.H. contributed to the overall interpretation of the results and various aspects of the analysis.

Competing interests

The authors declare no competing interests.

Additional information

Correspondence and requests for materials should be addressed to T.W. Peer review information Nature thanks Asantha Cooray and Joaquin Vieira for their contribution to the peer review of this work. Reprints and permissions information is available at http://www.nature.com/ reprints.

Letter reSeArCH

Q9

Letter reSeArCH extended data table 1 | survey depths for each field

First, second and third lines show data from the three CANDELS fields, GOODS-S, UDS and COSMOS, respectively. WFC3/F160W data are in units of magnitude.

extended data table 2 | Physical properties of h-dropouts

In column 4, [4.5] indicates 4.5-μm magnitude.