L Capitanio
email: letizia.capitanio@obspm.fr

R Lallement

J L Vergely

M Elyajouri

A Monreal-Ibero

Three-dimensional mapping of the local interstellar medium with composite data

Keywords: metadata preparation and hierarchical inversion, 12, 2 Hierarchical inversion for EVEN and ODD sub sets, 13 ISM: lines and bands -ISM: dust, extinction -Line: profiles

The Interstellar Medium (ISM) represents a small fraction of the Milky Way baryonic matter ( typically 10% ), but it plays a fundamental role because it governs the galactic evolution and its structure. Understanding this evolution requires the knowledge of its various phases, their physical parameters, temperatures, pressures, their compositions in ionised, atomic, and molecular gas as well as in dust grains, to better characterise their dynamical, physical and chemical interactions. Most of the ISM gaseous constituents have been identified through their emission or absorption characteristics, however, despite decades of efforts a category of interstellar absorptions, the "diffuse interstellar bands" (or DIBs), still has no counterpart in absorbing species. More specifically, an increasing number of these hundreds of weak optical and infrared bands is found to have internal structures that correspond to large organic molecules, but at the exception of the C60+ fullerene cation none of these molecular carriers has been identified yet. Moreover, nothing is clearly established about the life cycle of the DIB carriers, neither their formation, nor evolution or destruction. Because DIBs may represent a large fraction of the organic matter, it is mandatory to understand their role during star and planet formation, in particular their interactions with other species and grains, and this requires measurements of their distributions and preferential sites. Large surveys from ground or space have started to provide such statistical information on their spatial distribution and links with the other constituents. In particular, a serendipitously favourable situation is the presence of a DIB (with central wavelength 862 nm) within the spectral interval of the Radial Velocity Spectrometer (RVS), one of the instruments of the ESA Gaia astrometric mission. Thanks to the numerous stellar spectra that are currently (and will be) recorded with the RVS, one may expect the construction of a very large catalog of measurements of this DIB, and the first part of the work presented in this document is directly related to the construction of this future catalog and its potential use. More specifically, I have attempted to answer the following questions:

-How many DIB measurements can be potentially reliably extracted from the RVS spectra of individual stars? -What will be the characteristics of this sample of targets? -What kind of limitations will have this DIB survey? -What range of distances will be potentially explored?

To answer these questions, I have developed a profile fitting code adapted to the Gaia DIB and to the RVS instrument. I have applied this adjustment code to a large series of synthetic RVS spectra obtained from the simulator GOG developed for the RVS, for different stellar types, star magnitudes and extinction IVMapping improvements: building and testing a full 3D hierarchical method

11 Principle of the hierarchical method 141 11.

ranges, and I have merged the results with the statistics derived from the Gaia Universe Model Snapshot (GUMS), a Milky Way model adapted to the Gaia instrumental performances. The resulting information on the characteristics of the targets that are adapted to DIB measurements as well as their numbers is presented.

The second part of this thesis has been related to the three-dimensional (3D) mapping of the ISM, a goal motivated by the increasing number of large photometric stellar surveys as well as the availability of the Gaia parallax distances. In particular, I have focused on the potential use of DIBs for the mapping, here motivated by the advent of large spectroscopic surveys and the Gaia DIB catalog. Can we use these absorptions to chart the ISM? What are the advantages and disadvantages of such a choice? How to optimise the use of the catalogs of spectra, in particular the catalog of RVS spectra which will be available with the Gaia DR3 (or DR4)? To answer these questions I have followed several paths. In ran parallel inversions of two extinction and DIB datasets for the same target stars, both data derived from the SDSS/APOGEE survey, and compared the distributions. I made the first tomography based on composite data, both extinctions and DIBs and showed this is a viable way. The resulting map has been used by GEPI colleagues during a photometric calibration of the G band Gaia, a calibration they in turn used for the production of additional extinction estimates. I ran the inversion of all data to produce improved 3D maps. In both cases of mapping from extinction or DIB measurements, one encounters the same difficulty associated with the use of massive datasets. The full 3D tomographic inversion technique in this case requires an unrealistically large computing time. I have developed a technique called "hierarchical tomographic technique", an iterative inversion using the previous step 3D distribution as a prior for the next inversion, and where each new step corresponds to an increased spatial resolution in reduced volumes that depend on the target distribution density. I have applied this technique to a new catalog of 30 millions of extinction measurements based on Gaia and 2MASS. Preliminarily to this development I have tested the used of an arbitrary, complex 3D prior distribution for the inversion based on Pan-STARRS extinction results. Finally, I used high resolution ground-based stellar spectra to extracted through profile-fitting radial velocities and columns of IS absorbing species in several specific regions and participated to the first step of a "kinematic" 3D map of the ISM based on these data, radio emission and 3D dust maps.

Abstract

Le milieu interstellaire (MIS) représente une fraction mineure de la matière baryonique de la Voie Lactée (environ 10%), mais joue un rôle fondamental parce qu'il gouverne l'evolution de la Galaxie en contenu et structure. Comprendre cette évolution nécessite la connaissance de ses diverses phases, ses paramètres physiques, température, pression, sa composition dans le gas ionisé, atomique et moléculaire, et de la même façon dans les grains de poussière, pour mieux caractériser ses interactions dynamiques, physiques et chimiques. La majorité des constituants du MIS ont été identifiés grace à leurs émissions ou absorptions, mais une catégorie d'absorptions interstellaires, les "bandes interstellaires diffuses" (DIBs), n'ont pas encore de particules identifiées comme responsables des absorptions, malgré des dizaines d'années dédiées à leur étude. Un nombre de plus en plus élevé de bandes parmi les centaines détectés des en optique et infrarouge présente des profils spectraux qui correspondent à des larges molecules organiques, mais aucune molécule nà été encore identifiée, hormis le cation du fullerene C60+. Rien n'est vraiment établi sur le cycle de vie des porteurs de DIBs, ni leur formation ni leur évolution et destruction. Comme les DIBs pourraient représenter une large fraction de la matière organique, il est fondamental de comprendre leur rôle dans la formation stellaire et planétaire, en particulier leur interaction avec les autres espèces et les grains; pour atteindre cet objectif il est nécessaire de mesurer leur distribution et leurs sites préférentiels. Les grands relevés sol soit spatiaux ont commencé à apporter des informations statistiques sur la distribution spatiale des porteurs de DIBs et aussi sur leurs liens avec d'autres constituants. Par un heureux hasard, une DIB dont la longueur d'onde centrale est 862 nm est présente dans l'intervalle spectroscopique du Radial Velocity Spectrometer (RVS), un des instruments de la mission astrométrique Gaia de l'ESA. Grace aux spectres stellaires en cours de mesure avec le RVS, on s'attend à obtenir un large catalogue de mesures de DIBs et la première partie de ma thèse est directement relié à la construction de ce futur catalogue et son usage potentiel. Plus précisément, j'ai exploré les questions suivantes:

-combien des mesures de DIB seront potentiellement extraites des spectres RVS individuelles?

-quelles caractéristiques aura cet échantillonnage de DIB? -quelles limitations aura cette survey des DIB? -quel range des distances pourra être exploré? Pour répondre à ces questions, j'ai développé un code de profile fitting adapté à la DIB "Gaia" et à l'instrument RVS. J'ai appliqué ce code à une large série de spectres stellaires synthétiques RVS obtenus avec le simulateur GOG développé expressément pour le RVS, pour différents types stellaires, 6 magnitudes et intervalles d'extinction. J'ai comparé les résultats avec des statistiques dérivées du Gaia Universe Model Snapshot (GUMS), un modèle de la Voie Lactée adapté aux performances instrumentales GAIA. Les informations sur les caractéristiques des étoiles cibles ont été adaptées aux mesures de la DIB. Je présente dans la thèse une estimation des DIB mesurables pour chaque ensemble de paramètres stellaires et observationels simulés, en fonction de la qualité de l'ajustement. La second partie de la thèse concerne les cartes en trois dimensions du MIS, un objectif motivé par l'augmentation des grands relevés photométriques et spectroscopiques stellaires, et par la disponibilité des parallaxes Gaia. En particulier, j'ai commencé à étudier l'usage potentiel des DIBs pour la cartographie. Peut-on utiliser ces absorptions pour cartographier l'ISM? Quels sont les avantages et désavantages de ce choix? Comment optimiser l'usage des catalogues des spectres, en particulier le catalogue des spectres du RVS qui seront disponibles avec la DR3 (ou DR4) Gaia? Pour répondre à ces questions j'ai suivi différents chemins. J'ai fait tourner en parallèle des programmes d'inversions des données des extinctions et des DIBs pour les mêmes cibles stellaires, les deux dérivés du relevé SDSS/APOGEE et comparés les distributions inversées obtenues. J'ai fait la première tomographie basée sur des données composites, extinctions et DIBs et j'ai montré que c'est praticable. La carte résultante a été utilisé par des collègues du GEPI pour aider à la calibration photométrique de la bande G de Gaia, une calibration qu'ils ont utilisée pour la production de l'estimation de nouvelles extinctions supplémentaires. Ces extinctions ont été utilisés ensuite pour produire et améliorer les cartes 3D. Dans tous les cas, cartes d'extinction ou mesures des DIBs, on rencontre les mêmes difficultés associées aux des dataset massives. La technique de l'inversion du 3D tomographic dans ce cas demande un temps de calcul non realiste. J'ai développé une technique appelée "technique tomographique hiérarchique", une inversion itérative qui utilise la distribution 3D de l'étape précédente comme prior pour l'inversion suivante, et où chaque étape nouvelle correspond à une résolution spatiale plus grande. J'ai appliqué cette technique aux nouveau catalogue de 30 millions des mesures d'extinction basé sur Gaia et 2MASS. Comme préliminaire à ce développement, j'ai testé un prior complexe dérivé des profils d'extinction obtenus à partir de Pan-STARRS. Finalement, j'ai utilisé des spectres à haute résolution stellaire obtenus au sol pour extraire soit les vitesses soit la colonne des matériaux interstellaires absorbants avec un programme de profile-fitting et j'ai participé aux premiers étapes d'une carte cinématique 3D du MIS basée sur ces données, sur les émissions radio CO et les cartes 3D des poussières.

In memory of Giulio Regeni TRUTH FOR GIULIO REGENI.

Contents

V Full-sky hierarchical method applied to Gaia DR2 extinctions 173

VII Conclusion 233

18

Thesis context

Chapter 1

Interstellar Medium general properties

Interstellar Medium environments

The interstellar medium is an astronomical object with variable characteristics, but it can be defined as non-homogeneous mixture of gas-phase baryonic matter, dust, cosmic rays (interstellar matter) and magnetic field and radiation (electromagnetic field). It is not simply an environment where stars float, but the physical processes that occur create, with stars, the galactic ecology.

The mass of the Milky Way is 10-15% composed of interstellar matteratomic gas, molecular gas, dust -, concentrated on the disk, with small structures highly fractal and non-homogeneous; 50% of the interstellar matter is organised into cloudy structures, which occupy ∼1-2% of the interstellar volume [START_REF] Karttunen | Fundamental astronomy[END_REF][START_REF] Ferrière | The interstellar environment of our galaxy[END_REF]. Clouds structures could be classified as dark, cold and translucent clouds and matter in more diffuse interstellar medium is in warm gas, warm ionised gas or ionised gas. Different clouds propriety are summarised in Tab 1.1.

I present here a general description of the interstellar medium components and in Chapter 1.2 I am going to describe the measurement techniques.

Component

Temperature [K] [START_REF] Ferrière | The interstellar environment of our galaxy[END_REF].

Dust

Dust is the solid component in interstellar matter, composed in amorphous or regular crystals of carbon, silicon, ice and others impurities -depending on the environment and the dynamical time of formation. There are some space missions which have collected directly interstellar dust grains in our Solar System, most recent Cassini Mission [START_REF] Altobelli | Flux and composition of interstellar dust at Saturn from Cassinis Cosmic Dust Analyzer[END_REF], but only noncharged or larger particles can enter in the heliosphere. Dust is very important for stellar cycle, because dust coagulation is the beginning for the gravitational contraction in dark clouds. Dust origin is not completely understood, but there are many identified formation environments: outer atmospheres of red giants and supergiants, and planetary nebula, but also in the ISM itself there are favourable condition for formation, as in the high density clouds.

From the observations, astronomers have deduced the distribution of the size of the interstellar dust grains. Usually dust grains are described as ranging in size from nanometers to micrometrics, but the steps of coagulation from micrometers and planetary objects (kilometre) are still unknown. Macromolecules like polycyclic aromatic hydrocarbons (PAHs), which have nano-metric dimensions, are considered as components of the dust, because they could represent the pre-coagulation steps in ISM. In the Milky Way, the dust is concentrated in the galactic disc, with a scale height of ∼ 120 pc (Kos et al., 2014).

Physical processes involving dust and light are:

• absorption and re-emission: the photon energy is transformed into heat, which is then re-radiated at the infrared wavelengths corresponding to the temperature of the grains particles

• scattering: light trajectory is changed, therefore the intensity on the original direction is reduced

Gas phases

Gas is the main component of interstellar medium, but it is more elusive because it can be measure only by spectrometric observations, see Chapter 1.2. Hydrogen in different states -H, H + and H 2 -is the main component (70%), followed by He (28%) and the other elements (2%). Heavy elements are measured as significantly less abundant than in the Sun and other stars of population I; since the global composition in the interstellar medium would be regular, the interpretation is that heavy elements are embedded in the dust grains, so they can no longer be measured in the absorption lines. Many atoms are ionised in the interstellar space, because the density of interstellar matter is very low and free electrons cannot be easily captured; so ionisation states due to the UV radiation from stars or cosmic rays do not come back easily at the neutral state.

Atomic gas Atomic gas structures have wide variety depending on the physical conditions. Atomic hydrogen is observed in UV band with Lymanα absorption (n=2, 121.6 nm) and in radio band with the hyperfine suppressed transition at 21 cm. The H + regions usually are ionised by the UV radiation, and we measure them in the star formation regions or in OB complexes.

INTERSTELLAR MEDIUM ENVIRONMENTS

The most common metals C, O, N are depleted by a factor 1.2-3, while other as Mg, Si and Fe have a 10 -100 depletion factor in comparison to the stars, so they are supposed to be in dust grains, but it is difficult to measure directly the dust composition.

Molecular gas Molecular gas has different states, from simply bi-atomic gas (i.e: H 2 , CO, CH) to more complex poly-atomic molecules. Bi-atomic hydrogen forms by recombination of atomic hydrogen, having dust grains as chemical catalysts. They can be stable only isolated from UV and in sufficiently cold environment, because of the their molecular inner energy, to avoid collisional dissociation; for these reasons their environment are the cores of darks clouds.

Thanks to the ease in measurement, it is the CO emission -in equilibrium with the cosmic rays heating -which provides us the observed temperature, estimated 10-20 K, but probably lower in denser cores.

Molecular gas, measured in dark clouds, is confined in Milky Way disk as inferred from different studies. The total mass is estimated as 1.3-2.5 10 9 solar mass [START_REF] Ferrière | The interstellar environment of our galaxy[END_REF].

Molecular gas structures are hierarchically organised in interstellar medium, with different scales from tens to few tenths of parsec. Larger structures have lower density as ∼ 100 -1000cm -3 , smaller ones can contain billions of molecules per cubic centimetre.

Diffuse Interstellar Bands

Special absorptions from interstellar medium are Diffuse Interstellar Bands (DIB) -an example is shown in Fig. 1.1. There are a few hundreds of large absorptions in optical bands and some tens in the infrared band [START_REF] Hobbs | A Catalog of Diffuse Interstellar Bands in the Spectrum of HD 204827[END_REF], but new DIBs are going to be discovered thanks to the ESO Diffuse Interstellar Bands Large Exploration Survey (EDIBLES) [START_REF] Cox | The ESO Diffuse Interstellar Bands Large Exploration Survey (EDIBLES) . I. Project description, survey sample, and quality assessment[END_REF]. Their carriers are not identified, but for the most solid theories they are macroorganic molecules [START_REF] Jones | The evolution of amorphous hydrocarbons in the ISM: dust modelling from a new vantage point[END_REF][START_REF] Jones | Dust evolution, a global view: III. Core/mantle grains, organic nano-globules, comets and surface chemistry[END_REF]. Sometimes we use the acronym DIBs both for the absorptions and for the unknown carriers: in this manuscript I will refer to DIB only for absorptions.

In the last few decades, some near infrared DIB carriers have been partially identified, such as the fullerene C 60 + [START_REF] Foing | Detection of two interstellar absorption bands coincident with spectral features of C 60 +[END_REF], and these have been confirmed in the laboratory experiments in gas phase [START_REF] Campbell | Laboratory confirmation of C 60 + as the carrier of two diffuse interstellar bands[END_REF]. This detection suggests that PAHs (Poli Aromatic Hydrocarbons) could be good candidates for DIBs carriers and in general for interstellar medium environmental (van der [START_REF] Van Der Zwet | Polycyclic aromatic hydrocarbons and the diffuse interstellar bands[END_REF][START_REF] Salama | Assessment of the Polycyclic Aromatic Hydrocarbon-Diffuse Interstellar Band Proposal[END_REF].

DIB carriers have different regimes; for example there is a basic categorisation that distinguishes DIBs in irradiated regions an (σ -type) and others (ζ -type). The discriminator factor is the ratio between the Equivalent Width (EW) of the DIB at 5797 Åand 5780 Å. Lines of sight with lower ratio values are classified as σ -type, while those with a high ratio are considered ζ -type, [START_REF] Cami | Diffuse Interstellar Bands in single clouds: new families and constraints on the carriers[END_REF][START_REF] Maíz Apellániz | The little-studied cluster Berkeley 90. II. The foreground ISM[END_REF].

DISTANCE -LIMITED INTERSTELLAR MEASUREMENTS

19 measured rotation is additionally depending on the column of electrons.

• the radio synchrotron emission from relativistic electrons. In this case the measured rotation is additionally depending on the column of cosmic-ray electrons. To obtain the magnetic field from this emission it is mandatory to break the degeneracy with the spectrum of cosmic-ray electrons [START_REF] Rockstroh | A new determination of the local interstellar electron spectrum from the radio background[END_REF].

Cosmic rays

The cosmic rays are energetic particles, composed by protons, 10% alpha particles, 1% heavier nuclei, 2% electrons, and smaller amounts of positrons and antiprotons [START_REF] Blandford | Particle acceleration at astrophysical shocks: A theory of cosmic ray origin[END_REF]. The supernova explosions are supposed to be the main source of cosmic rays, as recently confirmed by measurements of the Fermi satellite, but other mechanisms are also proposed because the only supernovae are not enough to account for all energy ranges, as for example ejections from active galactic nuclei. Measurements of these particles were very important for the development of the Standard Model of particle physics, for example muons, pions and positrons were identified using cosmic rays showers. The low energy part of the cosmic rays (on the order of hundred of MeV or lower) is very important since it is responsible for most of the interstellar gas ionization in the dense molecular cores. Since the ionised fraction of the gas is the only one to be coupled to the magnetic field, and the field plays an essential role during the cloud collapse, low energy cosmic rays are an important actor in star formation. Along the Galactic plane there is an approximate equipartition between the gas thermal pressure, the magnetic pressure and the total cosmic rays pressure. The fraction of pressure associated with the cosmic rays increases with the distance from the Galactic mid-plane due to their escape to the halo.

Distance -limited interstellar measurements

The interstellar medium is widely observed thanks to the lack of light, because, with the exception of some emissions in the infrared and radio bands, the main effect of dust and atomic/molecular gas is the disappearance of photons emitted by stellar sources. It is fundamental to identify and quantify the matter that -laying between the source and the observer -affects the light in the path to the observer. This is the basic characteristic of the measurements used for the interstellar medium maps, because knowing the spatial segment where the light has been modified it is possible to obtain the position of the agents responsible for the modification, that is the ISM.

Extinction and reddening

Considering the space from a bright source to the observer completely empty, the difference from the real brightness of a source to the observed one is due only by distance from the source and the observer:

M -m = 5 log d 10pc
(1.1)

CHAPTER 1. INTERSTELLAR MEDIUM GENERAL PROPERTIES

But when the space is not empty, the interstellar medium modifies the light flux. The processes that take place between dust grains and light are essentially absorption and diffusion; these two processes subtract photons from the lines of sight. Absorption is followed by temperature-dependent re-emission, but since the photon is re-emitted in a random direction, there is a net light loss on the line of sight. The dispersion is very efficient from grains with dimension similar to the optical wavelength and it is the main cause of photon loss. In theory, gas diffusion could also contribute to light-subtraction, but it is not an efficient process, since the density is too low to have a high impact [START_REF] Karttunen | Fundamental astronomy[END_REF].

As consequence, taking in account the presence of dust, the difference between emitted and observed magnitude is increased by a factor A > 0, that is the extinction due to the medium.

M -m = 5 • log d 10pc + A(d) (1.2)
Scattering efficiency is size-grain depending, thus A is not a constant, but extinction is stronger for shorter wavelength, producing in optical bands the so called reddening. For this reason in optical band more distant stars seem to have a (B -V) index higher than the intrinsic for their own stellar type.

E(B -V ) = (B -V ) observed -(B -V ) intrinsic (1.3)
or more general for two bands:

E(B 1 -B 2 ) = (B 1 -B 2 ) observed -(B 1 -B 2 ) intrinsic (1.4)
The empirical law connects the E(B -V) -called excess of colour in V bandwith extinction in optical band, Av, and it is usually expressed as a proportion:

R V = Av E(B -V ) ≈ 3.1 (1.5)
Important studies of this relationship were done for different bands, to describe R λ -the milestone is the [START_REF] Cardelli | The relationship between infrared, optical, and ultraviolet extinction[END_REF] empirical extinction law. Next studies modified this law, and in the last years there are was important improvement in this branch thanks to Planck Collaboration et al. (2014) dust map results, which show important variability of the relationship at different latitude.

Measurements of the extinction curve show some features (Fig 1 .2), the most famous one is the UV -bump, whose origin is still under investigation [START_REF] Gavilan | Polyaromatic disordered carbon grains as carriers of the UV bump: Far-UV to mid-IR spectroscopy of laboratory analogs[END_REF][START_REF] Berruto | Laser-Induced Skyrmion Writing and Erasing in an Ultrafast Cryo-Lorentz Transmission Electron Microscope[END_REF] and probably depends on peculiar components or grains dimension.

The proportion between extinction (or excess of colour) and dust column is possible only supposing strong hypothesis about the dust nature, shape and dimension. It is presumed a general uniformity in dust composition and reaction at the scattering, but it is always true that extinction us always correlated with dust presence.

Extinction changes for directions and distances, depending on the dust concentration in the line of sight: for example dense dust clouds in the Galactic centre direction produce an optical extinction index of 30 mag, which makes impossible direct observations in the optical band.

distances, but the absorption law depends on the photon energy and the cross section of the dust grains. Measuring the degradation for two different wavelengths and knowing the emitted spectral curve of the star, we can resolve the degeneracy:

E(λ 1 , λ 2 ) = C R 0 (k λ1 (r) -k λ2 (r))ρ(r)dr (1.8)
As far as we cannot resolve the dust density and proprieties degeneracy in Eq 1.7, the excess of colour becomes:

E(λ 1 , λ 2 ) = C R 0 θ λ1,λ2 (r)dr
(1.9) with θ λ1,λ2 (r) a global variable for differential opacity, expressed in magnitude per pc units. Observed E(λ 1 , λ 2 ) is a variable which depends only on the distance from the source and the opacity, it means that it contains the information about the global presence of matter on the line of sight, but it not depends on the matter distribution along the line of sight.

Atomic and molecular absorptions

The gas does not produce a generic light extinction on one band, but we can observe it by their absorption lines in UV and optical range. The central position of the absorption line (frequency ν or wavelength λ) depends on the type of particles present in the gas; the shape and depth of a line depends on the physical characteristics of the global medium, i.e. temperature and optical depth. If we schematise the interstellar medium as a gas composed by homogeneous clouds, the cross-section between atoms and light is constant and the optical depth is proportional to the cross-section, σ ν , and the number of absorbers:

τ ν = σ ν N (1.10)
So, it could be sufficient to measure the absorption curve:

φ(ν) = σ ν m e c πe 2 f (1.11)
where m e is the electron mass, c is the speed of light and f is the oscillator strength specific for each absorption.

An absorption line can be schematised as three different regimes, depending on the number of encountered particles: optical thin, saturated regime, damped regime. An empirical quantity used as physical units is the Equivalent Widht (EW), the width of a rectangle below the normalised spectrum having the same surface as the one comprised between the line profile and the continuum. The curve that describes the variation of EW depending on the optical depth is called the curve of growth. For various regimes, the curve follows various functions:

• Optical thin regime: the Equivalent Width is proportional to the number of absorber particles

The equation 1.12 needs special attentions, because it is valid only in case of parallaxes measured without uncertainty. Since the measured parallaxes in the astronomic catalogs have associated errors, the distance determination is more complicated [START_REF] Bibliography Bailer-Jones | Estimating Distances from Parallaxes[END_REF]. In particular, using the simpler transformation:

d min (pc) = 1 π + σ π and d max (pc) = 1 π -σ π
we pass from a gaussian and symmetric probability distribution in the parallaxes errors space to an asimmetric distribution in the real distance space. Moreover, some negative parallaxes belong to the catalogs, but they are not outlier, but they contain statistical information about distances, but if we apply the transformation, we get a nonsense negative distance. Rejecting all the negative parallaxes add some bias in the used sample. Since these problems are more and more important for distant objects with parallaxes errors larger then 20%, and we use for our analysis only objects with distances with small errors, in this thesis I widely applied the naif transformation.

Available catalogs for parallaxes

For parallaxes, main catalogs come from Hipparcos and Gaia astrometric missions -see Chapter 3.1 for more detailed description of the Gaia mission.

Hipparcos This European mission was launched in August 1989, and it observed sky for 3.5 years, until March 1993. Hipparcos catalog contains 118 218 stars, but comparing the Hipparcos measurement to others previous less precise catalog, the Tycho Catalogue of 1 058 332 stars and Tycho 2 Catalogue of 2 539 913 stars were finally compiled. Last catalog was released in 2007, Hipparcos 2 [START_REF] Van Leeuwen | Validation of the new Hipparcos reduction[END_REF].

Gaia DR1 Gaia DR1 was available in 2016 September and it is based on the TGAS catalog (Arenou et al., 2017a). Parallaxes for ∼ 2 millions objects were available, therefore it was not a complete survey and it contains some bias. This release missed some objects in very dense regions -above 400 000 sources per square degree -where only brighter objects were observed; many bright stars with magnitude G < 7 were lost in DR1 and also objects near brighter objects could be missing. Colour dependent and spatially correlated systematic errors occurs at the level of ±0.2 mas.

Gaia DR2 Since 2017 April, second data release is available, improving the first one in several critical points. The completeness in this case is respected for sources in G = (12;7) interval, but brighter stars and objects near bright sources are still partially lost. Denser regions have always some selections in magnitude, in particular the magnitude limit of Gaia DR2 is as bright as G = 18. More than 1 billion of parallaxes are now published, with associated uncertainties. These errors are known to be underestimated for G>16 source by a factor of 10% and for G<12 by a factor of 30%. Some systematic are present depending on celestial position, magnitude and colour, and [START_REF] Arenou | Gaia Data Release 2: Catalogue validation[END_REF] estimated them to be lower than 0.1 mas.

Photometric distances

The photometric distances are based on some presupposition about the stellar type and the extinction. Basically they are based on the Eq 1.2, and there are many strategy to determine the absolute magnitude M and extinction A. A calibration for M can be done by standard candles as RR Lyrae, Cepheids or Red Clump stars. Extinction can be estimated at the same time that distance or A(d) could be assumed as know, for example extracted from the 3D maps.

Photometric estimations are all model depent, at different levels, and they benefit from independent distances measurements at nearer distances, as trigonometric parallaxes.

Red Clump technique -APOGEE/Gaia calibration In the post-main sequence area on HR diagram, the Giant Branch, the Red Clump stars have temperature between 4500 K and 5300 K; they are characterised by a low mass He-burning core and usually higher metallicity than the Horizontal Branch. Since all stars have the helium flash at the same mass of the degenerated helium core (0.5 solar masses), their luminosity does not vary a lot with metallicity, temperature or radius: they can be used as standard candles in the Milky Way [START_REF] Girardi | Red Clump Stars[END_REF].

During my thesis we collaborated with Ruiz-Dern and Danielski to improve the Gaia photometric calibrations, with a virtuous iterative exchange between extinction maps and distance -extinction couples estimated from stellar catalogs [START_REF] Danielski | The empirical Gaia G-band extinction coefficient[END_REF][START_REF] Ruiz-Dern | Empirical photometric calibration of the Gaia red clump: Colours, effective temperature, and absolute magnitude[END_REF].

Standard Candles -Maser

Standard Candles are in general emitting points with regular luminosity, thus the observed luminosity depends only by the distance and the interstellar medium medium. For the ISM maps, we use point-like emissions which are directly related to the dense clouds, the Maser sources.

Maser (Microwave Amplification by Stimulated Emission of Radiation) is a particular kind of emitted, coherent and monochromatic light; it occurs in population inversion, when en excited state contains more atoms then the ground state. Typically the excited state is metastable, with a long average life, so spontaneous emissions are negligible and this gives rise to coherence.

In the interstellar medium there are some molecular clouds where it is measured a maser emissions from OH molecules, H 2 O and SiO; since they are very small regions (5-10 AU), we can consider point-like sources. They are generally in HII regions, or near Mira variables or some supergiant stars. The positions of the Maser sources can be used directly to identify the spiral arms, star formation regions and molecular clouds, because they are associated with short-lived objects and this means that they do not move away from the formation site. [START_REF] Lépine | The Dynamical Origin of the Local Arm and the Sun's Trapped Orbit[END_REF]. The Sun is is (0,0), the x axis is the Galactic Center direction, distance units are in parsec.

Chapter 2

Mapping the Interstellar Medium

Mapping the spatial distribution of objects in the Universe is the oldest and main objective of astronomy. The ISM is diffuse matter and its volumes are not well defined, there are different types of plasma that require different techniques of observation. The mapping of diffuse matter is complicated, and often involves the measurement of starlight.

Three-dimensional (3D) maps of the Galactic interstellar matter (ISM) are useful in several ways. First, they provide observations to be compared with evolutionary models of the interstellar matter under the action of stellar winds and supernovae. Such models (see e.g. de Avillez et al. ( 2015)) will help explaining star-ISM feedback processes that are not yet well understood.

They are also useful for evolutionary models of Milky Way stellar populations. Evolutionary models require measurements of the spatial distribution of massive amounts of stars as well as their dynamical, physical and chemical properties, all quantities currently provided by the ESA satellite Gaia (Gaia Collaboration et al., 2016a,b) and ground-based surveys. In this context, threedimensional (3D) maps of the Galactic interstellar dust are an additional and mandatory tool since they allow de-reddening of stellar spectra and suppression of degeneracies between star temperature and dust reddening on the one hand, and, on the other hand, since they may shed important additional light on the star formation through the inter-play between star and interstellar matter. Fortunately, Gaia parallaxes and Gaia photometric data complemented by ground-based photometric data allow the construction of the required IS dust maps in parallel with the stellar studies.

Finally, 3D ISM maps are a general tool for various purposes: studies of foreground, background or environment for specific Galactic objects, modelling of photon or high energy particle propagation, estimates of integrated Galactic foregrounds, and finally, as also mentioned above, of particular importance today in the context of Gaia, calibration for the reddening of the Milky Way objects.

Existing interstellar medium mapping techniques

There are two main categories of maps: 2D maps, which describe the distribution on the projection of the celestial sphere, and 3D maps, which try to assign

CHAPTER 2. MAPPING THE INTERSTELLAR MEDIUM

to each of them not only the position on the sky, but also the distance from Earth.

2D maps

2D maps could be based on absorption or emission, in particular from the thermal emission of dust particles. The advantage for this kind of maps is that for each line of sight the emission directly measures the total amount of dust, and therefore the total extinction, without a distance -limitation. Schlegel et al. (1998) published an extinction map based on DIRBE and IRAS/ISSA, with an accurate remotion of noising light from zodiacal radiation and point sources. It is a far-infrared map, with data from 100 to 240 µm. To make the extinction map, they suppose a standard reddening law, and they use the elliptical galaxies as calibration for the reddening corresponding to the 100 µm emission. Their observational range is dominated by the emission from the biggest grains that are in thermal equilibrium with the local radiation field.

More recently, Planck Collaboration et al. ( 2014) provides emission 2D maps, with a similar extraction technique. For the interstellar medium science, this map discovered large structures in the emissivity spectral index of the dust β without relationship with known stellar structures.

3D maps

In this section, several 3D mapping methods are described with the categorisation of [START_REF] Sale | Galactic 3D extinction maps[END_REF]. More or less every map is based on a stellar catalog, with stellar positions, on the sky and distance, and probe for interstellar matter. As said in Chapter 1.2, there are essentially two distance -limited measurements: extinction, linked with dust grains, and absorptions, that measure the gas components. A 3D map could also be based both on extinctions (at different bands) and the absorbed lines. Generally, the ion, atomic or bi-atomic lines were used for the local maps, because they reach rapidly the saturation regime, where the Equivalent Width (EW) is not proportional to the matter quantity, therefore it is useless for mapping. These maps evolved a lot passing from an handful of line of sight to some thousands [START_REF] Vladilo | The distribution of the local interstellar medium derived from MG II column densities towards seven cool stars[END_REF]van Loon et al., 2013;Vergely et al., 2010a). The DIB absorptions are more interesting for the larger scale mapping because they never reach the saturated regime, and their EW is always proportional to the absorbers column, and the DIBs were used both for local ISM [START_REF] Van Loon | Probing the Local Bubble with Diffuse Interstellar Bands (DIBs)[END_REF] and larger galactic environment (Zasowski et al., 2015).

Independently from the matter probe, there are three main techniques to chart interstellar medium in Milky Way: voxelised methods, model-based maps and gridless methods.

• Voxelised methods are for example used by Green et al. (2015): they divide the 2D sky in "pixels", for each pixel they assign bins at various distances. Globally, bins at the same direction on the sky form a voxel. In each voxel, they evaluate the extinction curve in different bins, to match individual observations or statistical variability along the voxel. These methods produce maps with high coherence in single bins on 2D sky, but each bins is independent and the results are maps with unnaturally CHAPTER 2. MAPPING THE INTERSTELLAR MEDIUM elongated pencils. An example of this method applied using a different probe is the Zasowski et al. (2015), where the chosen feature to describe interstellar medium is a DIB absorption in APOGEE spectra.

• Model-based methods produces a synthetic stellar population in the modelled map of interstellar medium, to reproduce the observed population (Marshall et al., 2006). The similarity with the voxelised method is the use of an tessellation approach. They are actually pseudo-three dimensional maps, because they evaluate the extinction at different lines of sight, but there is not a correlation between to adjacent directions.

The consequence of a non-correlation between adjacent directions is a fragmentary map, with strong gradients which are not realistic for the interstellar medium physics, as it is remarkable in Fig 2 .2. In the top) panel there is a zoom in the Green map for the solar neighbour, where the interstellar medium seems to have non-natural segmented shapes; in the other hand, their map has a high precision on the sky -bottom panel.

• Gridless methods do not use a first guess of specific grid-distribution for the interstellar matter. They use information on stellar position and distances, and extinction for single lines of sight, but also the correlation in orthogonal directions. Light measured from two neighbour points in the space must pass through similar environments, and it means that the inferred map has to take in account not only the information for each line of sight, but also the reciprocal position between the sources. It is un under-estimated problem, because it guesses to determined extinction value for all points (infinite) in a given volume, using finite extinction estimations.

A possible technique is to describe the correlation between the different points in the volume as an analytical function. For these techniques, the advantages are more physical structures; unfortunately these methods are very slow and they cannot be used for very large volumes, because of the calculation time. First maps with this technique were done by Vergely et al. (2001), but recently other groups start to use similar approach.

In particular promising mapping technique are developed by Sale and Magorrian (2014a) and Rezaei Kh. et al. (2016).

In this thesis, I apply the gridless method from Vergely and I adapted it at new data and larger stellar catalogs, in preparation at the final Gaia catalog.

Known 3D Structures

Thank to previous maps, we yet know some important ISM structure in Milky Way. The interstellar medium is concentred on the galactic disk, it reproduces the same large stellar structures. In particular, depending on the charted volumes in the maps, large structures or local ISM are well investigated.

Large structures

From measured distances of emitting regions and the 21 cm radio emissions, Milky Way is schematised as a spiral double barred galaxy (Georgelin and CHAPTER 2. MAPPING [START_REF] Georgelin | The spiral structure of our Galaxy determined from H II regions[END_REF][START_REF] Dame | The Milky Way in Molecular Clouds: A New Complete CO Survey[END_REF][START_REF] Reid | Trigonometric Parallaxes of High Mass Star Forming Regions: The Structure and Kinematics of the Milky Way[END_REF]. Also maser sources are largely used to locate arms, since they are young objects related to high mass star formation [START_REF] Hou | The observed spiral structure of the Milky Way[END_REF][START_REF] Lépine | The Dynamical Origin of the Local Arm and the Sun's Trapped Orbit[END_REF]. An artistic Milky Way representation is in Fig. 2.3 describe our knowledge about the large structures. Sun is located on the Orion Spur, a small arm between Sagittarius and Perseus, at 8 kpc from the Galactic Centre. Despite all these accurate studies, the arms structure is not yet well determined, and in particular an accurate dust distribution map is not available; Gaia DR2 boosted extinction-based maps, and some examples are now in publication [START_REF] Chen | Three-dimensional interstellar dust reddening maps of the Galactic plane[END_REF][START_REF] Kh | Detection of the Milky Way spiral arms in dust from 3D mapping[END_REF].

Considering the galactic plane as a unlimited plane with uniform gravitational potential, the distribution of matter in a cylinder perpendicular to the plane is:

ρ = ρ 0 exp -z H (2.1)
where ρ 0 is the density on the plane, z the distance to the plane and H is the so-called "scale height". Moving away from the disk, the scale height varies for different interstellar medium components, as reported in Tab 2.1. These variabilities are due to their origins environments, their preferable locations and their resistibility in different environments.

Local Bubble, Local ISM

The Sun sets in a hot and diffuse interstellar medium cavity, called Local Bubble, located in the Orion Spur and at ∼8.5 kpc from the galactic centre. In the Local Bubble plasma has a kinematic temperature of million of degrees, and it is delimitated by a ring of denser environment. The total size depends on the explaination, but in general it occurs for ∼100 pc on the galactic plane and hundreds of parsec in a vertical chimney through the disk. Using atomic absorptions, three dimensional maps have been done for fifteen years (Vergely et al., 2001;Welsh et al., 2010;[START_REF] Vergely | Spatial distribution of interstellar dust in the Sun's vicinity. Comparison with neutral sodium-bearing gas[END_REF], then also through light extinction (Lallement et al., 2014) and different optical DIBs [START_REF] Van Loon | Probing the Local Bubble with Diffuse Interstellar Bands (DIBs)[END_REF]. The Bubble is surrounded from neutral gas clouds, with some tunnels in direction l = 70 • and l = 250 • , in direction of the radio emission source GSH238+00+09 (Lallement et al., 2014). In tilted by ∼20 • from the galactic plane. Since the Local Bubble and the Gould belt has a similar inclination, it could mean a common origin mechanism. The local environment origins are largely unknown, many possible mechanisms were been evaluated -from supernovae series to interaction between a super cloud and spiral arm -and a accurate 3D mapping can strengthen or exclude some hypothesis.

For the local astronomy this environment is objects of investigations, because its small dense structures and their kinematics impact on the interstellar dust and the few comets which arrives in the Solar System and penetrate heliosphere.

Chapter 3

Used observational surveys

The Gaia Mission

Gaia is a ESA space mission, launched on 2013 December 19, arrived in L2 one month later and at the moment in operative state. Scanning the full sky for a minimum of 5 years, it is a global astrometric mission, whose main goal is to measure position, parallax and proper motion for at least 10 9 sources, to describe Milky Way three dimensional structures. It is measuring some tens million stars with distance accuracy better than 1%, and hundreds million around 10%.

To achieve this scientific objective, Gaia has three instruments: astrometric, photometric and spectrometric.

Data realises are scheduled 1 and they provide (short list):

• First release: 14 September 2016. Positions (α, δ) and G magnitudes only for sources with acceptable formal standard errors on positions; the five-parameter astrometric solution -positions, parallaxes, and proper motions -for stars in common between the Tycho-2 and Gaia is contained in Gaia DR1; positions and G magnitudes for some thousands of quasars;

• Second release: 25 April 2018. The five-parameters astrometric solution -positions on the sky (α, δ), parallaxes, and proper motions -for more than 1.3 billion sources, in the magnitude limit G = (3, 21); median radial velocities for ∼>7.2 million stars with a mean G magnitude between about 4 and 13;

Gaia instruments

There are three scientific instruments on the Gaia satellite; the most important instrument for the goal mission is the one dedicated at the astrometric measurements, and it is based on the global astrometry concept than in Hipparcos intruments. The photometric instrument is composed by two low resolution fused-silica prisms -called Blu and Red Photometer-, which disperse all the light entering the field of view. The Blu Photometer and Red Photometer operate respectively in the wavelength range 330-680 nm and 640-1050 nm [START_REF] Carrasco | Gaia Data Release 1. Principles of the photometric calibration of the G band[END_REF]. It permits to roughly determinate stellar proprieties as temperature, mass and composition for all stars in catalogue. Third instrument was coinceved to be dedicated at the stellar velocity measurements:

Radial Velocity Spectrometer (RVS) is an integral spectrograph that disperses all the light entering in its field of view (∼ 2.5 × 1.6deg 2 ). Its resolving power is R = λ δλ = 11500. As its name suggests, the main aim is the measurement of radial velocities, to describe the kinematics in Milky Way. Radial velocities are crucial to study the kinematical and dynamical evolution of the Milky Way and they are needed to correct the astrometry from the perspective accelerations [START_REF] Katz | Spectroscopic survey of the Galaxy with Gaia-I. Design and performance of the Radial Velocity Spectrometer[END_REF]. Moreover, thanks to the multi-epoch measurements, it will be possible to identify and characterise not-single systems. Because of scattered light and other non-conformity, the precision is actually 15 km s -1 at the V limiting magnitude of 15.2 for GV2 stars and of 11.3 for B1V stars.

The RVS range between [848-874] nm was chosen because of the presence of the Ca II doublet; all the stellar lines will be used to determinate stellar intrinsic parameters as temperature, gravity, metallicity and obviously the observational parameters as radial velocity and rotation velocity.

Broad scientific yield from the RVS measurements, here I list some examples: kinematics of the globular cluster could constrain the MW accretion history, general kinematics is a fondamental measure to determine the Dark Matter distribution, as it is inferred principally from kinematical considerations; also the disk kinematic needs to be studied to separate thin and thick disk behaviours, for example velocity structures with peculiar velocities could be old small merges debris; the metallicity determination is fundamental to built a realist evolution model. RVS shall discover and help the classification of the poor stars, the fossil stars which could represent the Population III and which are the most important constrain for the Big Bang nucleogenesis rate, in particular the helium abundances [START_REF] Wilkinson | Spectroscopic survey of the Galaxy with Gaia-II. The expected science yield from the Radial Velocity Spectrometer[END_REF].

Gaia for the interstellar medium astronomy

Gaia catalogues provide 1.5 and a half billion precise parallaxes, and extinction for a subset of targets; basically, extinctions will be estimated from photometry and spectrometry, using excess of colour as a proxy for extinction. For the subsample of the whole catalogue also measured by the RVS, stars will associate magnitude, parallax, temperature and metallicity; in those cases the distanceextinction pairs will have high precision, because it will possible to disentangle the reddening due to the temperature, the metallicity and the dust. In DR2 there is a first extinction catalogue, but it is strongly conditioned by the fact

THE GAIA MISSION

that Gaia spectra are not yet available and reddening measurements are based only on Red/Blue photometric filters.

In addiction to extinction estimations, from RVS spectra, it will possible directly measure an interstellar medium absorption -the Gaia Diffuse Interstellar Band (Gaia DIB).

Gaia DIB Gaia DIB is a small DIB absorption, centred at 862.0 nm; the DIB is rather in the middle of the spectral range of Gaia-RVS. Only a small part of the RVS spectra will be usable for the extraction of the DIB, because of the high SNR required for the extraction. In addition, the closest objects, with apparently higher magnitudes, have less interstellar absorption, while the more distant objects for which the DIB is deeper and easier to measure, have lower apparent magnitudes and therefore a lower SNR. One of the objectives of my thesis is to develop a fit technique adapted to RVS spectra and predict the order of magnitude of the measurable DIB; these issues are investigated in Part II.

The Gaia DIB was studied and characterised by [START_REF] Munari | The diffuse interstellar band at 8620 Å: A good reddening tracer for GAIA[END_REF]. This study is based on 37 observations at the Asiago Echelle spectrograph and describes its empirical law for correlation with excess of colour:

E B-V = 2.69EW Å (3.1)
but Munari him-self proposed that this law should be:

E B-V = α(l, b, D)EW (3.2)
because the exact slope depends on the interstellar medium proprieties, and it is a good ansatz its variation for different Galactic structures. Puspitarini et al. (2015) did an accurate fit for the 862 nm DIB for 64 stellar targets in CoRot field l = 212.9 • and b = -2 • of Gaia-ESO Survey (GES), founding an α proportion value is 2.3, compatible with the Munari value of 2.69. Since the spectra in Puspitarini are all concentrated in the same line of sight, the Munari estimation for the proportion is more safe. They empirically extracted the DIB shape, using the technique for DIBs shapes profiling described in [START_REF] Chen | Automated Extraction of DIBs from Cool Star Spectra[END_REF].

Variations of the DIB shape or the extinction/EW proportion are a strong constraint for the identification of DIB carriers, as well as understanding the different positions for the different carriers of DIB and grains of dust. A map of the Gaia DIB was still drawn from Kos et al. (2014) up to 3 kpc from the Sun; based on 500,000 spectra from the Radial Velocity Experiment (RAVE), they mapped a pseudo 3D map of the DIBs and independently of extinction. They estimated the distance-extinction pairs using Bayesian techniques, while the 862 nm DIBs were detected after combining different RAVE spectra to obtain an SNR ratio of ∼300. The maximum distance of their points from the galactic plane is 1.5 kpc and 40 • at galactic latitude, for operational reasons. The map, in Fig 3 .1, is composed of bins at different distances, with variable altitude on the plane, so all information on the z directions are compressed into 2 points, for the North and South hemispheres. Despite its distance and direction limits, this first map shows very similar behaviour when comparing the extinction and equivalent widths of the DIB, but the height of the DIB

SDSS/APOGEE

The Sloan Digital Sky Survey is a large survey using a 2.5-m wide-angle optical telescope at Apache Point Observatory in New Mexico, United States. The Apache Point Observatory Galactic Evolution Experiment (APOGEE) is a high-resolution and high signal-to-noise infrared spectroscopy survey in the 44 CHAPTER 3. USED OBSERVATIONAL SURVEYS Chapter 4

This thesis project

My thesis is developed in a period of large surveys and strives to prepare tools to map in the most efficient way the huge amount of data Gaia will provide. In particular, I am interested to use the excess of colour and DIB absorptions from the Gaia catalogs to improve the 3D maps. In practice my project follows two main branches:

Gaia DIB: tools for efficient Gaia-DIB profile-fitting and estimate of expected results The first issue is to estimate how many DIBs will be measurable with the Gaia spectra. To make this prevision, I simulate the DIB extraction in synthetic spectra in the RVS band, with wide variation in stellar types, magnitudes and extinctions; then I code a specific fit profile for the Gaia DIB, adapted to the simulated Gaia RVS spectra. For each synthetic spectrum, I estimate how many objects of that type will be observed by the RVS, using a Milky Way simulation. In this way, it is possible to estimate how many objects will have a good DIB fit. This work is presented in Part II.

Three dimensional maps: improvement of techniques adapted to future massive datasets The gridless techniques are not adapted to chart large volumes or to manage massive target catalogs. In preparation to the large surveys, it is fundamental to understand how to use in the most efficient way all the available data. I test for the first time a tomographic inversion using different types of input data, that is individual DIBs absorptions, individual photometric extinctions and statistical interstellar medium 3D maps based on extinction in groups of stars. The maps were used to help the Gaia photometry to calibrate the Gaia photometry and, in return, new additional extinction measurements were obtained from the new calibrations, that were subsequently inverted to produce better 3D maps. I propose also a way to estimate uncertainties of quantities in the maps (see Part III). I developed a new method to invert data into a 3D map with reduction of the computational time, called "hierarchical technique", which reduces the calculation time without actually changing the map precision, because the map resolution is now directly the best resolution achievable at each point in space, and depends on the volume density of the stellar targets (Part IV). This technique was applied to 30 million of stellar targets from the DR2 Gaia, with positive results -Part V.

CHAPTER 4. THIS THESIS PROJECT

New developments using 3D maps Moreover, other astronomical informations are available from the 3D maps: in Part VI I investigated the comparison between DIBs carriers and dust distribution on the one hand, and developed a first 3D-kinematic map on the other hand. As the organic matter in interstellar medium seems to be largely in DIBs carriers [START_REF] Snow | Diffuse Interstellar Bands: Past and Present[END_REF], it is important to identify these molecules, their origins and distributions; the APOGEE DR14 provides a large database of distance -extinction couples and spectra from which the λ ∼ 1.527µm DIBs were extracted by my colleague Meriem Elyajouri. I produced two maps from the same stellar target using only photometrical extinctions and then only extinctions estimated from the DIBs absorptions. As the future Gaia DIBs will be measured with high precision, similar maps will be done and comparisons between the distributions of different DIBs will constrain the DIB preferred environments and as consequence the life cycle of the carriers.

To understand the evolution and the reciprocal relationships between the clouds, it is important to assign specific velocities to the interstellar medium clouds. I did this exercise in the Taurus region, based on various observational constraints: potassium absorptions in optical bands, CO emissions in radio bands and extinction 3D maps.

To resume, the scientific project was both how to extract the DIBs and how to use them, to be prepared to the challenge of Gaia data exploitation and to be ready and armed with the appropriate technical tools.

Chapter 5

Simulated analyses of Gaia RVS spectra

In 2021, 150 000 millions of RVS spectra should be available to the community. This number applies to combined spectra from all visits to the same target (about 35 visits per star in average) and it is mainly due to the fact that only targets with G(RVS) <16 are retained on board for RVS spectroscopy1 (G(RVS) is the target magnitude in the RVS spectral domain).

As already mentioned in the introduction, the Gaia RVS wavelength domain contains a weak diffuse interstellar band (DIB) centered at ∼862 nm, commonly called the Gaia DIB. Its response to the extinction was first studied by [START_REF] Munari | The diffuse interstellar band at 8620 Å: A good reddening tracer for GAIA[END_REF] thanks to the spectra from the RAVE survey, and later by [START_REF] Chen | Automated Extraction of DIBs from Cool Star Spectra[END_REF] and Puspitarini et al. (2015) based on ESO/VLT spectra with the FLAMES-GIRAFFE spectrograph. The DIB spectral profile (shape) has been first derived by [START_REF] Chen | Automated Extraction of DIBs from Cool Star Spectra[END_REF] and later confirmed by Puspitarini et al. (2015) using GES data (see Chapter 3.1 for an introduction). The normalised shape used in the following analysis is represented in Fig 5 .3.

What we want to estimate is how many spectra will be useful for the extraction of the DIB and what kind of precision will be achieved for these spectra. Preliminary and very crude estimates had been done prior to the commissioning of the instrument, but much more precise predictions can be done after this phase and after the first results. Unfortunately, the unexpected straylight, discovered after the launch, affects primarily the RVS, and expectations in terms of signal and DIB extraction are lower than initially hoped.

The two main difficulties of the DIB measurements are associated with the relative weakness of the DIB and the subsequent requirement for a high signal to noise, and the need to disentangle stellar features and DIB absorption. Examples of stellar spectra recorded by the RVS are shown in Fig. 5.1 for stellar types varying from M to early B stars. As can be see, stellar lines strongly vary with the star temperature and one needs to possess accurate models for all types in order to obtain a good adjustment. The target stars of Fig. 5.1 are all very bright and close. Note that for such targets, the extinction is very low and no detectable absorption is expected, as it is indeed the case.

An example of 862 nm DIB observed from the ground for a reddened star is displayed in Fig. 5 The stellar lines must be very precisely modelled and adapted to all types if we wants to extract the diffuse interstellar band from the data.

the Gaia-ESO Survey at the VLT and was recorded with FLAMES/GIRAFFE with a resolution R=17,000, i.e. on the same order than the RVS resolution of 11,500. The DIB depth amounts to several percents and corresponds to the target color excess E(B-V) on the order of 0.7 (A V ∼ 2, note in all along our study we assume that A V ∝ E(B-V).). This shows how accurate must be stellar models if we want to extract such DIBs. Fortunately, no telluric emissions or absorptions will contaminate the spectra in the case of the RVS, at variance with the ground spectrum (see caption).

In the frame of the preparation of the Gaia data analysis and catalogues, the Gaia Data Processing and Analysis Consortium (DPAC) has prepared a set of simulators, and I used two of them to perform my estimations: the Gaia Object Generator (GOG) and the Gaia Universe Model (GUM).

First, I simulated a very large set of RVS spectra, using the Gaia Object Generator (GOG) [START_REF] Luri | Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator[END_REF] . GOG can simulate RVS spectra as they are expected at the end of the mission (final mission spectra), and takes into account a large number of observational properties for the simulated object, in addition to the star properties themselves. It provides also an assigned uncertienties for each simulated pixel, based on the target's light and all instrumental effects. In the simulation it is possible to vary the position on the sky, the distance, and the radial velocity.

Second, I developed a pipeline for the DIB profile fitting, adapted to varying stellar types, extinction and magnitude.

CHAPTER 5. SIMULATED ANALYSES OF GAIA RVS SPECTRA

Preliminary estimate of upper limits on DIB measurements

If we assume that the stellar spectrum is completely flat, i.e. there are no stellar features at all (equivalently, if we assume that each stellar spectrum is perfectly known), and in addition that the DIB shape is constant, it is possible to estimate what is the achievable maximum G (RVS) magnitude for which the DIB can be extracted; we can estimate that for any DIB depth or equivalently any extinction A V if we assume the DIB-A V proportionally from the above formula. The key point for this estimate is the relationship between the stellar magnitude in the RVS wavelength range and the S/N. This SNR-G(RVS) relationship has been well calibrated and is available in numerical form from the Gaia website; it is shown in Fig. 5.4. It corresponds to end-of-nominal mission performances, and the average total number of visits to a given star.

We did a simulation using simply a Gaussian noise (for a series of S/N values) and a superimposed DIB, whose Equivalent Width (EW) corresponds to three extinction levels A V =1, 3, and 6 mag. For the DIB we used the normalised DIB spectral profile shown in Fig 5 .3. We assume an exact proportionality between the DIB EW and the reddening, according to the [START_REF] Munari | The diffuse interstellar band at 8620 Å: A good reddening tracer for GAIA[END_REF] law E (B-V ) = 2.69 × Equivalent Width(Å). The fitting function is made of a flat continuum (equal to unity) and a DIB profile, whose position and depth are free parameters. The error on the DIB EW is estimated in two ways:

1) with a bootstrap-type method: 100 different noise patterns are generated and for each one a fit is performed. The average solution and its standard deviation are taken as EW and σ(EW)

2) using an approximate simple formula based on the S/N (SNR), the number of pixels defining the DIB (N) and the wavelength interval for each pixel δ(λ) (assumed to be constant over the spectrum) δ(EW ) EW ≃ δ(λ) • (N ) • 1/SN Rr. Fig. 5.5 shows the resulting relative error on the equivalent width σ(EW )/EW as a function of G(RVS) for the three A V values. The two methods give slightly different results, as expected, however they can be considered as consistent for only an estimation. The figure can be used to guess which upper limit on the G(RVS) magnitude is compatible with a DIB detection for different quality criteria: e.g. a relative error of 50% is achievable for G(RVS) < 12, 13.2, 14 for A V =1, 3 and 6 mag respectively. Or, a relative error of 20% is achievable for G(RVS) < 11, 12.2, 13.5 for the same A V values of 1, 3 and 6 mag.

The actual DIB extractions will be evidently more difficult due to the stellar features, and will depend on the quality of the stellar models. As already found for DIBs observed from ground, the most difficult stellar types are not the same for all DIBs since the detection difficulty depends on the DIB width: schematically, stellar lines either much narrow or on the contrary much wider that the DIBs allow a better detection than stellar features with widths on the same order as the DIB width. This is the reason why nothing can replace a simulation for each type, and this is done in the next section.

Simulation of RVS spectra with the GOG tool

The RVS spectra are not publicly available yet and are expected for the third data release (DR3). The Gaia DPAC members work on the data, but they are not allowed to communicate any data before the release. For this reason, I used only simulated data.

The GOG simulates realistic RVS spectra, in particular it simulates their associated noise, that is modelled using all the knowledge about its various sources: errors linked with the instrument characteristics and errors due to the stellar input flux.

The GOG simulator was not initially conceived with Gaia DIB absorptions, however one of the free parameters in a GOG simulation is the extinction which affects the spectra. This allowed C. Babusiaux from GEPI (with help of P. Sartoretti an N. Leclerc) to briefly test the inclusion of an additional absorption proportional to the extinction in one of the GOG versions. Thanks to the collaboration with Carine Babusiaux, I could make use of such a simulation.

The simulation uses the normalised DIB spectral profile shown in Fig 5 .3. This initial profile corresponds to a reddening of reference. In all the study we assume that the DIB shape is unchanged and that there is an exact proportionality between the DIB equivalent width (EW) and the reddening, according to the [START_REF] Munari | The diffuse interstellar band at 8620 Å: A good reddening tracer for GAIA[END_REF] law:

E (B-V ) = 2.69 × Equivalent Width(Å)
Because the DIB is shallow, we are always far from the saturation for the absorption and in this case it is well known that multiplying the EW by a coefficient α is equivalent to elevate the DIB normalised profile D(λ) at the power α. Therefore, the amount of reddening is very simply proportional to the coefficient α.

-

E (B-V ) → α x E (B-V )
(5.1)

- EW → α x EW (5.2) - D(λ) → D(λ) α (5.3)

Grid of parameters for the simulated spectra

Each simulated spectrum is specific of a set of parameters Π.

-Four stellar atmosphere parameters -effective temperature, gravity, metallicity and rotational velocity -The extinction (or equivalently the reddening).

-The star absolute magnitude Π = [T, log(g), [Fe/H], vsini; visual extinction, absolute magnitude V]

It may seem surprising to vary the absolute magnitude of the star and not the distance from the star (and equivalently the visual magnitude and the flux). However this is motivated by practical reasons. Keeping the distance fixed

GRID OF PARAMETERS FOR THE SIMULATED SPECTRA

55

and varying the absolute magnitude (even if the magnitudes are unrealistic) produces variable fluxes in an equivalent way. There are some small changes in the RVS response to the same stellar light depending on the location of the star in the sky, however their effects are much smaller than the uncertainties in our final estimates and I did not vary the position on the sky. For practical reasons we used a fixed distance d= 91.69 pc and a fixed direction -α= 249.68 • and δ= -16.2 • -, however these values are not important in our study.

The simulation table is a squared grid. It contains non-existing stellar types, however those will be eliminated later. The grid is the following: 3500,4500,5500,6500,7500,8500,10000,15000,20000,25000,30000;

• Temperature [K]:
• Log(g): 1.01, 1. 61, 2.21, 2.81, 3.40, 4.01, 4.61;

• [Fe/H]: -3.0, -2.5, -2.0, -1.5, -1.0, -0.5, 0.0, 0.5, 1.0;

• vsini [km/s]: 0.0, 5.0, 10.0, 50.0, 99.0;

• mean absolute V [mag]: -1.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0; 0.6, 1.2, 1.8, 2.4, 3.0 , 3.6, 4.2, 4.8, 5.4;

• A V [mag]: 0.0 ,
As we will see in the Chapter 7, the above range of parameters corresponds to G RV S > 9 mag, but magnitudes below 9 correspond to high SNR and for such spectra the DIB will always be accurately measured. The number of spectra for stars with G RV S > 9 are estimated as ∼700 000, to be add to our following results for fainter targets.

It is also possible with GOG to simulate the RVS spectra as they would be in the absence of photon noise, and we will also use this capability (see next section). Fig. 5.6 shows an example of GOG simulated spectra for the same stellar type, including the GOG simulated noise and in absence of any noise.

The inclusion of the DIB is illustrated in Fig 5 .7. The figure displays a series of GOG simulated spectra that corresponds to the same stellar parameters and mean absolute V magnitude, but a variable extinction, and therefore a variable corresponding DIB. The extinction varies from A V =0 to A V =5.4 and allows to estimate the S/N required to extract DIBs of various strengths. It shows that the detection will crucially depend on both the signal and the amount of extinction. An advantage is that faint stars are generally more distant and more reddened for a given direction close to the galactic plane, i.e. a weak signal corresponds to a stronger DIB (in average and, again, for the same direction).

GOG is not remodelling a new theoretical spectrum for each input, but it is based on a very extended library of pre-computed stellar models for grids of parameters. For computational reasons, it does not interpolate between them, instead it searches for the stellar type (equivalently the set of parameters) that corresponds the most closely to the required parameter values. As a consequence, GOG does not exactly provide us with a an output spectrum that corresponds exactly to the set of parameters entered in input, but to the closest set. However, in some cases, the combination entered in input is too far from all the parameter sets of the database and there is no solution, a situation that corresponds to very rare stellar types. For this reason, the output from GOG consisted of 381 900 spectra from the 450 450 required.

temperature.

-Vrad is the star radial velocity -The parameter vsini (stellar rotation velocity) controls the stellar line broadening and the parameter ǫ the atmospheric limb darkening.

-The use of a linear continuum has proven to be adequate. A flat continuum is not fully adapted since the extinction reduces the flux differently as a function of the wavelength (the reddening). Indeed, allowing for a slope gives slightly better results than the absence of slope.

The fit parameters (ensemble φ) are finally: α , β, vsini, ǫ, the radial velocity, the continuum slope m and its intercept q. Since there are no doppler shifts associated with the star radial velocity in the simulated data, and no variability of the location of the DIB absorption there should be not be any variability of this parameter. However Doppler shifts will evidently exist in real Gaia spectra. For this reason I kept the radial velocity as a variable parameter, but as expected the adjusted value was always close to zero. In future our simulations will be extended to the case of variable DIB Doppler shifts and variable stellar radial velocity.

I coded the adjustment program in Python language. The convergence to the best-fit solution is based on a classical non-linear least squares criterion, using the open -packages scipy.optimize.curve_fit and PyAstronomy.

Choice of initial parameters

We must fit enter initial guesses for the parameters, a set φ 0 .

-Our input α 0 value is the input A V , used to simulate the spectra. We justify this choice by the fact that an estimate of the extinction will be available based on photometry (as is already the case, work in progress or published work of [START_REF] Chen | Three-dimensional interstellar dust reddening maps of the Galactic plane[END_REF]). We impose lower and upper limits to this parameter and used the values -0.1 and 20; I have chosen in purpose an unrealistic negative value to avoid a bias around zero.

-The parameters m and q are very important because they define the continuum, that must be realistic in order to avoid secondary minimum of the χ 2 . I imposed for the initial gradient m 0 =0 and for the y-intercepta 0 as the maximum value of the simulated flux in the spectral interval used for the fit.

-β 0 is equal to 1 and corresponds to the case of a perfect stellar model -vsini 0 is the input vsini, used to simulated the spectra. This is justified by the fact that vsini will be deduced from the width of the stellar lines.

-ǫ 0 is taken equal to 0.5, a median value between the limits for this parameter (0,1).

-There are not Doppler effects associated to a radial velocity in these simulated spectra, since Vrad=0, but they will exist in real Gaia spectra. For this reason I inserted its influence in the fit function as already discussed, but fitted values were compatible with zero.

α parameter is the most important because is directly connected with the DIB absorption and the fitted A V .

Spectral interval used for the adjustment The adjustment was not done along all the whole RVS spectral interval, but in a smaller region, between 860.6 and 863.6 nm. I have chosen these limits after some tests because it provides equivalent results for a shorter computation time, as illustrated in one typical case shown in Fig 5 .8. The figure displays adjustments to the same spectrum but using two different spectral intervals; in the top panel the fit is done on the entire RVS band and in the bottom panel on the shorter interval. It can be seen from the top panel that the model reproduces very well the spectra over the whole RVS interval, and that our assumption of a linear continuum is acceptable, even for the entire interval. On the other hand, here, as in other cases, the fit results for the fit in the complete interval are generally not closer to the input values than for the fit in the limited region. E.g. α = A V f it is 0.93±0.10 mag for the entire interval and α = A V f it is 1.06±0.17 mag in the smaller interval, while the input extinction is 1.2 mag. The fit on the complete interval being not significantly better but slower, I decided to use the smaller interval.

In Fig 5.9,5.11 and 5.12 are shown some example of fits. Fig 5.9 shows two stellar spectra corresponding to the same stellar parameters and the same absolute V magnitude, but with different extinctions Av -respectively 5.6 mag and 0 mag. The extinction changes both the flux level and the DIB depth. The fitted α value is indicated on the figure. 12 are examples of fit for one cold and one hot star. In the second case the stellar model is almost featureless in the fit region, this is the case for most stellar types above ∼ 8000 K.

Chapter 6

Gaia Universe Model Snapshot

Gaia Universe Model Snapshot: generalities

The Gaia Universe Model Snapshot (GUM) is a simulation of the Milky Way objects, developed at the Besancon observatory, see [START_REF] Robin | Gaia Universe model snapshot. A statistical analysis of the expected contents of the Gaia catalogue[END_REF]. This simulation was done to produce a useful tool to make predictions and to prepare the production and exploitation of the Gaia catalogues. It is based on the fully developed Besancon model of Milky Way stellar populations, which among other qualities has the advantage of being self-consistent from the dynamical point of view.

The model distinguishes four different stellar populations: the thick disk, the thin disk, the stellar halo and the bulge. White dwarfs are computed separately. All the objects are seen through a three-dimensional extinction model, based on Drimmel and Marshall dust maps -at very large and large distances respectively.

Using a very complex modelling [START_REF] Robin | A synthetic view on structure and evolution of the Milky Way[END_REF]) that I will briefly present in the following paragraph, they computed the number of stars for any given age, stellar type and parameters, absolute magnitude, and how they are distributed all around the Galaxy. In their model the Sun is assumed to be at 8.5 kpc from the Galactic center and 15 pc above the plane. A series of Monte Carlo drawings are performed, knowing the expected density for each stellar type.

Apparent magnitudes and star colours as seen at the Sun are computed star by star following the luminosity in wavelength intervals along the path from the star to the Sun, in repsonse to the reddening due to the encountered dust. Astrometry and kinematics are calculated for the different stellar populations and for different ages using several initial velocity dispersions and velocity dispersion gradients. At the end of the entire process a simulated catalog is produced, including both intrinsic and observable stellar parameters, the star positions and each interstellar extinction.

GUM simulations are publicly available. I used one of the GUM simulations available under the form of twelve files, corresponding to Healpix decompositions. These files are in the HDF5 format and huge (up to 350 MO), therefore I did not concatenate them and worked on them always individually.

I used in this study the last version of November 2017. Galactic objects are simulated using the BGM model, which provides stellar parameters, distribu- that are actually in the GUMs. This includes both stellar and observational parameters, since I want to quantify the fits results. To do so, I looked in each GUM HDF5 file (UM) parts for the parameters I varied in GOG. For example I'm interested in variation in extinction but not in radial velocity because I did not vary this value in GOG simulations. Hereafter are listed the intervals for the varied parameters (the sign ... means regularly spaced intervals similar to the previous one), and, for the twelve HDF5 files, the numbers of objects in the file that have the corresponding characteristics. Temperature:

• 3500 K= (3000 : 4000)

• 4500 K= (4000 : 5000)

• ...

• 25000 K= (22500 : 27500)

• 30000 K= (27500 : 33500) Gravity:

• 1.01 = (0.7 : 1.3)

• 1.61 = (1.3 : 1.9)

• ...

• 4.01 = (3.7 : 4.3)

• 4.61 = (4.3 : 4.9)

[Fe/H]:

• -3.0= (-3.2 : -2.8)

CHAPTER 6. GAIA UNIVERSE MODEL SNAPSHOT

Condition on magnitude How many in GUM 2.5< 3 < 3.5 522 3.5 < 4 < 4.5 1853 4.5 < 5 < 5.5 6239 5.5 < 6 < 6.5 20094 6.5 < 7 < 7.5 58955 7.5 < 8 < 8.5 166722 8.5 < 9 < 9.5 437047 9.5 < 10 < 10.5 1102757 10.5 < 11 < 11.5 2702765 11.5 < 12 < 12.5 6428939 12.5 < 13 < 13.5 14549599 13.5 < 14 < 14.5 31270207 14.5 <15 26757289 Table 6.5 -How many stars in our bins of magnitude.

Chapter 7

DIB measurements with the RVS: a global estimate

My goal is to establish an estimate of the total number of DIB measurements of reasonable quality we can expect from the RVS instrument. To do so we will use our results for the GOG simulated and fitted spectra for each parameter set:

Π = [T, log(g), [Fe/H], vsini; visual extinction, absolute magnitude V] = [π, absolute magnitude V]
and consider that they are representative of what would be obtained for all the GUM stars with the same parameter set.

First of all, we recall that varying the absolute magnitude V, as we did, does not correspond to real variable physical conditions, because we know that the absolute value is intrinsic for each stellar type: we used the variability of the number entered in GOG for the absolute magnitude V as a way to vary the apparent magnitude instead of varying the distance. The extinction also contributes at the apparent magnitude variation, because for the same simulated absolute magnitude V, a stronger extinction results in a lower luminosity (higher apparent magnitude). In Chapter 5 the Figure 5.9 shows an example of the influence of the extinction for two simulations with the same absolute magnitude, i.e. the mean absolute V is 4.0 for the two spectra, but the extinction changes the total flux, and as a consequence the magnitude in the RVS spectra interval.

After all the calibration phases, the fluxes measured with the RVS instrument are associated with a specific magnitude, called G (RVS). G (RVS) depends on the incoming stellar flux but also from the instrument it-self, because it is an operational magnitude [START_REF] Recio-Blanco | Stellar parametrization from Gaia RVS spectra[END_REF].

From the GUMs, I extracted the total number of objects in 6D boxes, using as Σ parameters, effective temperature, gravity, metallicity, rotational velocity, extinction and magnitude G (RVS). It means that we have disentangled for the GUMs counts the influence of the extinction and the magnitude.

The idea is to understand for each spectrum with parameter set Π i simulated with GOG, how many similar objects are in GUMs in a corresponding Σ j interval. The GOG interval is centred in temperature, gravity, metallicity, vsini and extinction as for the Π GOG simulations, but when converting into I tested two ways to derive the G (RVS) magnitude for each i-spectrum. Both are based at some level on the simple idea to derive the noise as the difference between the GOG simulated spectrum and the fitted model, and find the standard deviation (or SNR) in the residuals. To do so we have to assume that the model is excellent, but this is the case in our simulations.

The first method uses each fit and computes the standard deviation in the fit residuals (i.e., in the spectral interval used for the fit), then transforms this estimate of noise into a SNR by dividing by the median flux in the fit interval SN R = median model_f lux standard_deviation_of _noise and in a last step converts the obtained SNR into a G (RVS) magnitude, by applying the formula 7.1 derived from the Gaia calibration. In this way each spectrum has a G (RVS) magnitude calculated in the fit interval, with its-own SNR, depending on the fit.

For the second technique, we use a series of test spectra to build a law connecting the flux level in the GOG simulation to the magnitude G (RVS). Seven spectra were selected as test -shown in Fig 7 .2; they have same π parameters T = 10 000 K, log(g) = 4.01, [Fe/H] = -0.5, vsini = 10 km/s, A V = 0.0, and different mean absolute magnitudes V = (4,5,6,7,8,9,10). As they have not extinction, I used directly the synthetic spectra without noise and with the simulated noise to calculated the standard deviation of the noise on the whole spectra.

This time, I derived the SNR on the entire spectrum:

SN R = max model_f lux standard_deviation_of _noise For the seven spectra I calculated their SNRs and then the corresponding magnitudes G (RVS) (again from the general law described above). In used this list of seven flux values and magnitudes G (RVS) to establish a fluxmagnitude G (RVS) relationship, a relationship that can be applied to all median flux values in the i-spectra of GOG. In short, instead of using fit results, and independently of the fits, we transform the flux in the GOG spectrum into a SNR, then into a G (RVS).

Comparing the results for the two approaches, as shown in Fig 7 .3, it is evident that the first method has a large dispersion at small magnitudes, but globally they give comparable results. Our simulated spectra cover very well the range between G (RVS) (9 : 16), with only some spectra at lower and higher magnitude. The RVS catalogue will be published with also ∼ 700 000 objects with magnitude G (RVS) lower than 9, which are not part of our simulation; as we have already said, for those objects the DIB will be accurately measured in all cases. On the other side, as the SNR is very low for objects with magnitude G (RVS) higher than 15, the loss of objects in that range does not change our estimate.

Estimates of DIB measurements from RVS spectra

Having the magnitude G (RVS) for each i-spectrum from the GOG simulations, it is possible to connect to each simulated spectrum the number of correspond-

CHAPTER 7. DIB MEASUREMENTS WITH THE RVS: A GLOBAL ESTIMATE

Table 7.1 -Numbers of stars satisfying to the different criteria associated to the fit: the two estimates correspond to the two methods used to derive the magnitude G (RVS) for each GOG simulated spectrum. data-model adjustment such as those we simulated is able to reproduce the input value A V . I translate this requirement into our first condition COND:

Av input ∩ (Av f itted ± 2error f it )
a condition that must be apply to the λ intervals for each π set. Testing for this condition is interesting since it gives us some insight on the conditions of reliability of the fitting method, however it will not be reproduced at the time of real data analysis, because we will not know the real extinction; on the other hand, extinction measurements will be available, based on photometry and distances, and testing this condition provides us with some limits on future comparisons between photometric extinctions and DIB absorptions.

Other requirements correspond to a limitation on the uncertainty on A v (fitted) (COND1,COND2,COND3 respectively:

• for spectra with a Av f it < 1 only fits with an associated absolute error on the α parameter in the fit respectively < 0.5 / 0.3 / 0.15 mag will be acceptable

• for spectra with a Av f it > 1 only fits with associated relative error on the α parameter in the fit respectively < 50% / 30% / 15% are acceptable These criteria are the most useful since they predict the numbers of potential fits with limited uncertenties, i.e. the numbers of objects in a final DIB catalog. Tab 7.1 contains the total number of objects estimated in this way for the whole set of GOG simulated spectra, using the four different criteria COND 1,2,3,4. Since we can associate to the GOG spectra two different estimated magnitudes G (RVS), we end up with two different estimates of the numbers of objects, because different limiting magnitudes correspond to different limits for the integration. However, it can be seen that the order of magnitude of the two estimates is very similar.

Table 7.1 shows that DIB extractions using good stellar models and with relative errors better than 30% should be achievable for an unprecedented number of objects, on the order of 1.3 millions. Since the ∼ 700 000 objects with magnitude lower than 9 mag G (RVS) will have a very high SNR, they will be used for the DIB measures, despite their absorption will be probably very small, the number of objects with a good DIB measure associate will be on the order of 2 millions. Statistics on the extinction I also binned the results for extinctions intervals, in order to understand to which range of extinctions our fit applies. In Fig 7 .8 is shown the estimated number of detections for different extinctions ranges; higher extinctions correspond objects because the magnitudes become too high. Our global count in this case is similar for conditions COND1 and COND2, we see that we will measure accurately the DIBs in those rare case of both sufficient SNR and high extinction. Results are summarised in Tab 7.2.

ESTIMATES OF DIB MEASUREMENTS FROM RVS SPECTRA 81

Statistics on the distances I have binned the results in intervals of distances. The results are shown in Tab 7.3. It is clear that at least 40% -50% will be closer than 1 kpc for COND1 -COND2 which is not surprising. On the other hand, interestingly, hundreds of targets beyond 1 kpc will participated at the detection and even than 1 hundred thousand more distant than 5 kpc with DIB detected at better than 30% (COND2).

Possible influence of GOG simulation on our count [START_REF] Luri | Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator[END_REF] investigated the difference between the input and output parameter sets for the GOG simulator, using for comparison the Gaia Universe Model (GUM) as a source of all stellar types and magnitudes. They found a good agreement in most cases, as can be seen in Fig 7 .9. E.g., in the case of temperature, the GOG library contains temperatures between 850 and 102 000 K, and the maximum difference between input and output values is 640K, with a mean difference of 390K. Therefore, since our temperature grid has intervals of 1000K, we can consider that this parameter is well simulated. On the other hand, there is a significant spread of metallicity output values for a given input value, especially around [Fe/H]=0. Our input metallicity grid has bins of 0.5 dex for a total range -6.5:+4.6, and the average input-output difference is 0.57 dex. Since we have used a perfect "stellar model" for the fit, the fit results for the extinction have not trends for the metallicity: for this reason the possible

Part III

Mapping improvements in the context of the full 3D tomographic technique

Chapter 8

Description of the full 3D tomographic inversion technique

Inversion: basic principles

In a milestone work, Tarantola and Valette (1982) formulated a general solution for generalised non-linear inverse problems which, among many projects in other fields, inspired earlier work on inversion of distance-limited columns of interstellar matter (Vergely et al., 2001[START_REF] Vergely | Spatial distribution of interstellar dust in the Sun's vicinity. Comparison with neutral sodium-bearing gas[END_REF]Lallement et al., 2014) as well as the inversions presented in this thesis.

In direct (or forward) modelling, one uses a theoretical relationship g and a set of model parameters p to compute the modelled values d f of some measurable quantities. In most cases, the modelled data d f are subsequently compared to the actual measurements d and some method is used to tune the parameters p in order to minimise the discrepancies between model and data.

-

d f = g • (p), (8.1) - d f ←→ d, (8.2)
-Tune parameters (p) back to (1)

(8.3)
where d are a set of measurements, g is the operator which expresses the mathematical model of the physical system (usually non-linear) and d f are the modelled data. Forward modelling has the advantage of some control on the parameters and estimates of the source of uncertainties: since the predicted values from a forward model usually are not exactly like the measures and this deviation is the combination of measurements errors and imperfections in model, such imperfections can be quantified. Forward modelling is the most common way to model measurements and is widely used.

In inverse problems (as opposed to direct ones) one uses values of measured quantities d and a theoretical relationship g to derive information on the values of a set of parameters p.

- (d), (8.4) -+theoretical relationship d = g •(p) (8.5) - → (p) (8.6)

CHAPTER 8. DESCRIPTION OF THE FULL 3D TOMOGRAPHIC INVERSION TECHNIQUE

Due to the lack of direct control on the parameters, non-uniqueness of the solution (i.e. different sets of parameters correspond to identical measurements) is more difficult to resolve in the case of inverse problems. More generally, it is crucial for inverse problems to be well posed, with existing, unique and stable solutions. In many inverse problems one wants to reconstruct a analytical function in the parameter space with only a finite number of measures and the solution is not unique; in order to prevent an ill posed problem one has to impose some regularisation. This is the case for ISM tomography in the actual state of measurements, a situation characterise by a very strong underdetermination. The regularisation may have diverse forms, generally a priori information on the parameters (p 0 ) and smoothness of the solution through a covariance function linking neighbouring points C (both will be used in the ISM tomography).

Tarantola and Valette have shown that when all informations can be described by Gaussian probabilities the solution of the inversion can always be obtained trough a least squares formalism. In the linear case, the solution can be computed explicitly (as in the very simple example given below) and in the non linear case it can be reached in an iterative way. Here we give only the general form of the iterative solution as taken from Tarantola formulation:

p k+1 = p k + (G T k • C -1 d0d0 • G k + C -1 p0p0 ) -1 • (G T k • C -1 d0d0 • (d 0 -g(p k )) -C -1 p0p0 • (p k -p 0 )
)(8.7) A least squares criterion and a threshold for the χ 2 decrease rate rule the end of the interations. In the 3D tomography of Vergely et al. (2001) and subsequent work, the relationship is a an integral in the 3D distribution of interstellar matter and this iterative solution must be used.

Illustration in (very) simple cases

To illustrate the difficulties encountered in the reversal, let's start with a very simple situation: 5 girls return from a day of shopping during a period of discount. They all bought clothes but spent different amounts of money, respectively 100, 200, 300, 1000 and 2000 euros. The problem is to estimate how many clothes each bought (and then the prices of the various clothes). The problem is highly indeterminate if you only have this information, however there are several additional statistical information:

• in the same shopping area the prices of the dresses remain very similar, but can strongly depart from one shopping area to the other.

• the first three girls shopped all three in the same area, the two others in another area. (These first two conditions can be seen as a regularisation based on spatial smoothing) -

• in average a girl buys two dresses during the discount period, sometimes one or three, rarely four (and rarely zero). This third condition corresponds to some "a priori", favoured value.

With this additional information, you can exclude high prices in the first area and low prices in the second, otherwise the number of dresses would be

ILLUSTRATION IN (VERY) SIMPLE CASES

89 too high or too low and lower than one. In the first area, since prices must be similar, you can quickly converge to 100 euros per dress and to a solution of 1, 2 and 3 dresses purchased by the first three girls. In the second area, the most likely solution is one and two dresses, with a price of 1000 euros per dress. There are other solutions, although much less likely.

The following second example is used to clarify how the choices of the additional information may influence the inversion. Here one wants to estimate the values of a function f(x) for a continuous set of x values within a given interval for x (between 0 and 1). The data are the measured values d i for 10 values of x i (i=1,10) and the associated measurement uncertainties (blue circles and bars in the figure). The problem is again strongly underdetermined but there is some additional information: first, one assumes that the solution can not depart strongly from a prior value y 0 and that the dispersion around the prior is on the order of σ. Second, there is a regularization under the form of smoothing, i.e., for two values of x, x a and x b separated by a distance x b -x a on the order or smaller than a given smoothing length ξ, then y a = f(x a ) and y b =f(x b ) must be very similar. More specifically, there is a non-null covariance between such points and there is a correlation length ξ along the x axis that defines the smoothing scale. Following these two conditions, let's assume that the covariance function C has the following form:

C(x a , x b ) = σ 2 exp(- 1 2 (x a -x b ) 2 ξ 2 ) (8.8)
which means a variance σ and a correlation length ξ. For this one-dimensional, linear case with an extremely simple relationship G i (x)=δ(x i -x) (i=1,10) (where δ is the delta function) and a covariance function C the solution for the inversion becomes:

y(x) = y 0 (x) + Σ i Σ j C y0y0 (x, x i ) • (S -1 ) ij • (y j 0 -d 0 (x j )) (8.9)
where

S ij = C ij d0d0 + C y0y0 (x i , x j ) (8.10)
Figure 8.1 (top panel) shows the computed solution for the Gaussian kernel of equation 8.8 with ξ=0.05 and σ=1, a constant prior y 0 equal to 2 and the 10 shown data points. For clarity σ and ξ are shown by vertical and horizontal segments. The standard error be computed in this case from the a posteriori covariance function (see Tarantola and Valette for the formulation). One can see that far from the data the standard error tends to reach the standard error on the prior value.

The role of the correlation length in the covariance function is illustrated in the middle and bottom panels of figure 8.1. For unrealistically large ξ values (0.3 in the figure) the smoothing is so spatially extended that the solution always departs from the data confidence intervals. On the contrary, in case of a too narrow correlation length (here 0.01), i.e. a length narrower than the mean interval between two consecutive data point abscissae x, the solution is unrealistically close to the exact data values and too rapidly forced to the prior value even at short distance from the data points (the inversion is over-fitted). Therefore, the choice of the kernel is closely associated with the distribution of the data points, and governs the spatial variation of the distribution. This is true here in one-D, but also in 3D, and as we will see in the inversion of INVERSION TECHNIQUE columns of interstellar matter the kernel ξ must be chosen according to the mean distance between two target stars, and will govern the minimum size of the recovered structures. One can easily deduce that, ideally, the size of the kernel should correspond approximately to the dimensions of the interstellar medium structures in 3D space. A wide kernel will permit only large structures and miss smaller ones, a too narrow kernel will produce unrealistic, small structures. As we will see, the choice of a double kernel will allow to better reconstruct both diffuse and compact structures, but it remains that a fractal structure is extremely difficult to reconstruct by inversion.

The role of the variance σ on the prior is illustrated in the middle and bottom panels of figure 8.2. For unrealistically large (respectively low) σ values (2.5 then 0.05 in the figure) the errors on the the solutions outside the data points are over-(respectively under-) estimated. One can see σ as a factor governing the global dynamical range, with small (respectively high) σ values associated with a low (respectively high) dynamical range around the prior. Finally, the choice of the prior level value itself (not illustrated here) is also important and obvious. Here a value of 2 is simply chosen close to the average of the data for the ten data points.

Interstellar medium tomographic inversion

In the case of the ISM full 3D tomography:

• Instead of a one-dimensional problem, data and parameters are in 3D

and the parameters p one wants to derive are the values of the volume density of matter (grains, atoms or molecules) at series of points in 3D space.

• The data d are the integrated columns of interstellar matter, dust grains or molecules that are measured in the lines of sights toward as many as possible target stars. These columns are derived from extinction (for the dust grains) or absorption lines or bands (for gaseous species). Therefore, instead of the simple inverse function y i of the illustrative example, where f (x) must approach the measured value y i for N points, here the theoretical relationship d f = g • (p) is the equality between these measurements d and the integrals within the 3D distribution of grains or molecules along the corresponding sightlines (the parameters p one wants to derive.

• Following previous work, a double kernel is preferred to the unique Gaussian kernel.

• Instead of a constant the prior is an analytically computed 3D distribution fro the parameters, or, as described in Chapter 10, a numerically computed distribution.

Inversion Algorithm

Except for cases presented as DIB inversion, see Chapter 16, the tomography described here uses measured values of excess colour in a series of lines of sight to reconstruct a three-dimensional distribution of dust opacity, i.

INVERSION ALGORITHM

93 absorption line or band inversion is straightforward since it is equivalent to replacing dust grains by atoms or molecules. Note that the actual computed physical quantity at a point P is the reddening per unit distance subjected by the stellar light when it crosses P (e.g. a quantity expressed in mag pc -1 ). This quantity is proportional to the number of nano-micrometric dust grains encountered by the photons per unit traveled distance, and, therefore, to the local volume density of these dust grains.

For each star i at distance R i and Galactic coordinates l i , b i , its excess of colour can be expressed as the integral along the line of sight between the Sun and the star of the optical thickness per unit distance, expressed as the product of a constant and a quantity θ proportional to the volume density of grains and an absorption coefficient:

E i = R 0 dτ dr dr = C R 0 θ(r)dV (r) = C R 0 θ(r)sin(b)cos(b)dldbdr (8.11)
As in the 1D example above, the inversion is regularised by additional assumptions. The main one is that two points in space that are very close to each other can not have extremely different densities of matter (the smoothing assumption). The second is that the solution is as close to a prior distribution as permitted by the constraints from the data.

The inversion algorithm was developed from Jean-Luc Vergely then further developed and maintained thanks to the STILISM project. This software is a FORTRAN programme. The main programme input is the set of measurements along a series of lines of sight, i.e. their directions in the sky -in galactic coordinates (l, b), the distances to the targets (in parsec) and associated relative errors, the excesses of colour between B and V standard bands (in in magnitude) and absolute errors on the excess of colour.

Algorithm is fed by different parameters:

Prior distribution : parameters in the case of an analytical prior distribution The initial inversion code uses as a prior a quasi-homogeneous distribution that depends only on the distance to the galactic plane, i.e. it is independent of the location of the projection onto the plane. The prior interstellar medium density is assumed to decrease exponentially as a function of the height above/below the plane z with a height scale H.

ρ = ρ 0 exp -(z -z 0 ) H (8.12)
In practice the input H parameter is deliberately over-estimated in comparison with the measured height scale. There are operational reasons for that, as explained in Vergely et al. (2010a). An higher height scale allows a better inversion of the small structures at hight latitude/distance from the plane and better results were obtained when charting the Local Bubble, which has a very low opacity. As a result, the two parameters are:

• ρ 0 , density on the Galactic plane

• H, the prior height scale INVERSION TECHNIQUE

Prior distribution: case of a non-homogeneous prior distribution defined everywhere in the 3D space For the first time during my thesis I ran new inversions using a non-analytical prior distribution. The main goal is to allow the mapping of regions with low numbers of targets, and the basic principle is to build a preliminary map at very low spatial resolution that covers all the space (including target-poor regions and that is subsequently used as a prior for subsequent inversions at better resolution and restricted to regions that possess more targets. This will be detailed in the next sections and Parts III and IV.

Two types of such prior distributions were used:

• prior based on completely different data, i.e. not the data to invert

• prior based on an inversion made in a previous step, during an iterative process

Parameters controlling the regularization: spatial smoothing and dynamics: The covariance function C controls the relationship between the densities in two neighbouring points, therefore the size of the structures through the kernel parameter ξ, and the allowed dispersion around the prior for all data points, therefore the dynamical range of the structures, through the parameter σ. It may take various forms. Two different autocorrelation function f(ξ) are accepted in the code:

C 1 (x) = σ ξ0 2 cosh(-x ξ0 ) + σ ξ1 2 exp -x 2 ξ 1 (8.13)
and:

C 2 (x) = σ ξ0 2 exp -|x| ξ 0 + σ ξ1 2 exp -|x| ξ 1 (8.14)
The choice of an appropriate kernel is very difficult, especially in 3D, since it is related to the interplay between the distribution of the targets and the characteristic sizes of the structures (the dust clouds). It is much more difficult for an irregular dataset, which is the case here: the distribution of the targets in space is far from homogeneous, instead the number of targets per unit volume decreases with distance from the Sun (observational selection for fainter sources), and with distance from the galactic plane (the stellar distribution is concentrated close to the plane). On the other hand, the sizes of the dust clouds vary from fractions of parsecs to tens, even hundreds of parsecs.

For all the presented inversions I used always the C 1 function. It has the advantage of allowing the representation of relatively compact and small clouds (through the Gaussian term) and more extended and much less contrasted clouds (through the cosh -1 term. The first type (resp. the second) corresponds to dense (resp more diffuse) entities.

Whatever the quality of the kernel, the decrease of target density at increasing distances from the Sun implies that a unique kernel can not describe correctly nearby and distant regions. This is certainly one of the most difficult problem from the point of view of the algorithm. A part of this thesis work has been devoted to the search for a solution to this problem. This is discussed in Chapter 11. INVERSION TECHNIQUE

• target star longitude and latitude

• target star distance and associated relative error on this distance

• target star color excess and associated uncertainty Stars with very uncertain distance or very uncertain colour excess do not bring useful constraints and may increase the computation time in a useless manner. A selection is made on the distance relative error.

Moreover, in order to be conservative in case the smaller error considered for the excess of colour is of 0.01 mag. For input points with associated excess of colour error lower than 0.01, this the value used in the inversion.

Parameters controlling the computation and treatment of outliers

The central part of the code is the computation (by blocks) of a very big matrix representing the mutual influences of all points in space that are constrained by the data. To do so, all sightlines with a known colour excess are discretised into distance bins that will enter the matrix. One parameter, called resolution, defines the size of the distance bins. It is chosen to be close to the integration step for the sightline reddening in Eq 8.11. For points in space that are very distant one can obviously neglect their mutual influence. For this purpose, two parameters control the thresholds for the distance between two points beyond which their mutual influence is not computed. One parameter applies to the computation of the matrix linking the observed lines of sight and the second to the computation of the final density in each point in space.

Finally, a special treatment of the outliers has been implemented in the latest version of the program. Starting with the third iteration, errors bars on the colour excess for lines of sights that are highly discrepant from the solution are multiplied by a factor of three, and this is done foe each subsequent iteration. Tests made by J.L. Vergely have shown that this eliminates data points with unrealistic measurements.

The convergence criterion is based on the relative decrease of the χ 2 . When it becomes lower than 0.01 the iterations are stopped. This happens in general for between 5 and 10 iterations. The maximum number of iteration is modifiable, but in this thesis I always use 10.

Parameter choices

As we have more than twenty parameters, it is not trivial to tune them in a proper way. In general, for the prior parameters I used the same than in Lallement et al. (2014), i.e. ρ = 0.00025 mag/pc and height scale = 200 pc. The final distribution was calculated with voxels of 5pc 3 , in a global MW region of 4000×4000×600 pc 3 , otherwise it is specified. The other parameters will be specified for each inversion.

Specific difficulties of full 3D inversions

3D mapping is complex, and each technique has its own advantages and shortcomings. The full 3D inversion has several critical points. They are intrinsic to the technique and the used algorithm. In the following chapters I will present

SPECIFIC DIFFICULTIES OF FULL 3D INVERSIONS

97

several improvements that I have made using different strategies with the aim of limiting the effects of two main problems discussed below.

Non-uniformity of target distribution in 3D space

Ideal inversions are those based on a homogeneous spatial distribution of sightline constaints, which would here imply a uniform volume density of target stars, with similar errors in distance and reddening. Since we invert distancelimited quantities, we already said that it is (by far) not the case, due to dimming of starlight with distance and rarefaction of targets out of the plane. In addition, every survey has its observational selection biases. For all these reasons, it is obvious that the target distribution is non homogeneous. As explained above the targets' spatial distribution in the inversion is fundamental regarding the choice of an appropriate kernel. A reasonable choice of kernels takes in account the Nyquist-Shannon criterion, and it affects the maps reliability: in not well-constrained areas (usually far from the Sun) the inversion tends to "invent" structures that are based on too few data and not reliable. Our available inversion code don't allows us to use different kernels at different distances, which implies that a kernel appropriate in the inner regions will no longer be appropriate at large distances and vice versa.

Computational time

In the new era of big surveys, the main practical problem of full 3D tomographic inversions becomes the computational time. This is illustrated by the following test. I made use of the CPU time of different inversions based on increasing number of targets, and I fitted how this number influences the time. Our fit shows that the general trend is :

CP U T ime[s] = a(target number) 2 + b(target number) + c (8.15) with a, b, c = [ 6e-03, 5e-17, 1e-20].
The CPU time is related not only with the number of targets, but also with the integration step and the pixel resolution for the final distribution. The pixel resolution for the final 3D distribution influences only the very last step of the inversion after the convergence is reached, and is not so important. The integration steps influences every iteration, but for a given target it does not increase if the target distance does not increase. Finally, the number of targets is the main factor governing the CPU. One can see from Fig. 8.4 that it increases roughly as the square of the target number.

One of the main goals of my thesis has been to test a new method allowing to avoid the unsurmountable increase of computational time linked to the existing code. This need for a new technique is especially motivated by the availability of massive Gaia data. With the current techniques, even 10 5 objects are feasible.

Chapter 9

Mapping improvements: using APOGEE DIBs as additional data

The improvements and tests on full 3D mapping in this thesis work have as start point the map performed in 2014 (Lallement et al., 2014). This map is very accurate in the solar vicinity, but it is much less precise beyond a few hundreds parsecs (say, ∼ 400 pc). This map was based on ∼ 24000 lines of sight, whose distances were determined for ∼ 20% from the Hipparcos parallaxes and the rest based on photometry. Stellar targets for this map were concentrated in the first 200 pc from the Sun, because of the difficulty to have good estimations beyond the first matter wall (targets are too faint and thus absent from catalogues).

With the goal of extending and improving the map at longer distances, I started using for the mapping the absorptions derived from APOGEE DIBs. APOGEE DIB measurements have a strong advantage: being measured in the H-band, where extinction is less important than in the optical, they allow to probe denser, more opaque clouds with more distant targets.

Description of APOGEE DIB data

We used results of APOGEE DR12 (Alam et al., 2015, DR12); in addition to the ∼ 160000 science targets, APOGEE also recorded a sample of ∼ 17000 spectra of hot calibration stars, used for telluric line elimination (called Telluric Standard Stars, TSSs). These are bright sources with H-band magnitudes ranging from 5.5 to 11 (Zasowski et al., 2013). For such hot stars the DIB extraction could be much simpler and precise than for cool stars, due to the absence of stellar features.

APOGEE data are very high quality stellar spectra, from which precise atmospheric stellar parameters were obtained; consequently target distances and estimated colour excess have become very accurate, because they are based on both spectroscopy and photometry as well as on carefully adjusted theoretical stellar spectra, especially since the latest Data Release and the use of the Cannon software. However, this is true only for the cooler scientific targets and not for the calibration stars (the TSSs). For the TSSs, stellar theoretical spectra are not appropriate and there are no distance-extinction estimates based on the spectro-photometry. This is why we had to make use of parallax 99 distances and retain targets possessing a parallaxes. At the time of this work, only Gaia DR1 data were available, i.e., only targets belonging to the Tycho catalog could have a Gaia parallax. The Gaia DR1 was published with data collected in the first year of observation, and to assign a parallax estimation they used the previous Tycho measures. I explain briefly the spectra fit and selection of targets, but for details, I refer at the accompanying paper [START_REF] Capitanio | Three-dimensional mapping of the local interstellar medium with composite data[END_REF].

DIBs profile fitting

The series of the 25 409 APOGEE DR12 spectra of targets belonging to the Tycho catalog were analysed to determine the presence or absence of a detectable DIB at 1527.3 nm and measure its equivalent width. The methodology and the technique applied to the TSSs spectra is described in Elyajouri et al. (2016).

Among the 25 000 star spectra analysed, only the best spectra were selected, excluding target stars for which the stellar models were not suitable, for which S/N was too low or if there were too many telluric line residuals, following the criteria exposed in Tab 9.1; this filtering selected 9913 spectra.

Inclusion of DIB data addiction to colour excess data

After crossmatch with the targets of the Gaia DR1 catalogue [START_REF] Arenou | Gaia Data Release 1. Catalogue validation[END_REF] I could obtain a catalogue of 7800 stars with Gaia distances and well measured DIBs. I subsequently filtered to eliminate stellar targets with fractal error on distances larger than 33%: 4886 targets were finally used for the inversion. DIB equivalent widths were converted into extinction then into excess of colour using the relationship established by Zasowski et al. (2015):

EW = 0.102 A 1.01 V Å (9.1)
and the ratio and Mathis, 1979). DIB absorptions are not produced by dust grains, as does the extinction, but the carriers are probably large molecules in the gas phase. Therefore, they trace IS matter but not exactly the same kind and they are not exactly proportional to the extinction. To take into account the dispersion around the average relationship, I assigned to the excess of colour derived from DIBs an error of 50% that comes in addition to the uncertainty associated with the fit.

R V = A V /E(B -V ) = 3.1 (Savage

New inversions

Using Gaia DR1 parallaxes

Before merging DIBs and colour excess data, I ran a preliminary inversion without DIBs, but using the newly published Gaia DR1 (TGAS) parallaxes.

Starting with the Lallement catalog of 23444 targets available for inversion, I searched for targets possessing a a Gaia DR1 parallax (Arenou et al., 2017a) and found ∼ 80% of them in this case; I replaced the photometric or Hipparcos parallaxes-derived distances by these Gaia DR1 distances, when available.

Because the Gaia parallaxes have smaller errors compared to the Hipparcos or photometry distances, and because for our inversion only stars with distance errors smaller than 33% are finally retained, the new catalog available for an inversion is slightly different from the one used by Lallement et al. (2014).

The result of the new inversion with the same technique as in Lallement et al. (2014) is illustrated in Fig 9 .3. The figure shows the distribution of dust in the Galactic plane. We note that the use of Gaia DR1 distances introduces several modifications, as expected, and they are explained in the paper [START_REF] Capitanio | Three-dimensional mapping of the local interstellar medium with composite data[END_REF]; the main change on the galactic plane is seen in the first quadrant at longitudes on the order of 70-80 • where the absorbing matter is now found at larger distances, beyond 600 pc. We knew that in this region the inversion was potentially incorrect due to strong oscillations during the iterations. The new distance is in better agreement with the radial profiles found by Green et al. (2015).

Merging color excess and DIB measurements

The second inversion is an attempt, the first of its kind, to run inversions based on composite data. The DIB catalog converted into colour excess described above corresponds to significantly different characteristics of the lines of sight.

For the colour excess catalog the stellar median distance was 219 pc, while for APOGEE stars the average distance is 724 pc. This means that we augmented the previous catalog with 20% of new targets with much larger distances.

As shown in Fig. 9.3, after the combination of photometric and DIB-based excess of colour values, the new inverted map reveals in the Galactic Plane several important changes in the distant regions in the anti-center directions. This is due to the fact that 14% of the APOGEE targets are closer than 20 pc from the galactic plane and to their large distances, as said above. The absence of changes in the fourth quadrant is simply explained by the absence of new APOGEE stellar targets in this area (the APOGEE observing site is in the Northern hemisphere). Local Bubble has not changed much, because there are a lot of old data in the first 200 pc, and the added data are consistent with the previous ones: for this reason the inversion leads to stable results in the nearest regions.

More details can be found in [START_REF] Capitanio | Three-dimensional mapping of the local interstellar medium with composite data[END_REF] (published article inserted in this document). .

Chapter 10

Using the Pan-STARRS -based extinction radial profiles for 3D dust map and a prior 3D distribution

In this chapter we describe two different ways of using the highly detailed extinction mapping recently performed by Green et al. (2015). Both exercises correspond to attempts of improving our 3D dust maps. The first attempt is the extraction of several extinction-distance pairs from the Green et al. (2015) extinction radial profiles, in a large number of directions. After combination with the Galactic coordinates of the direction, these pairs are considered as virtual targets to be added to our database and treated in the same way.

The second attempt is the construction of a 3D prior distribution based on actual measurements, here Pan-STARRS, at variance with the previously used, analytical prior. This second prior will also be based on the Pan-STARRS reddening radial profiles.

Introducing to Pan-STARRS based map of reddening radial profiles

The Green et al. (2015) map is based on Pan-STARRS and 2MASS photometry, and the derived classifications, stellar distances and reddenings for ∼ 800 millions of Pan-STARRS targets; Green et al. ( 2014) developed a statistical method to derive from this dataset the extinction radial profile along all lines of sight accessible with the survey at high angular resolution. To do so, they work solid angle by solid angle, i.e. for a given central direction they select all the targets that are contained within a small solid angle around this direction. Based on their photometric distance and reddening they construct the best fit, monotonously increasing reddening profile along the radial direction. The resulting map of radial profiles is available at the website http://argonaut.skymaps.info/. It is possible to download the complete map or to access at the information choosing the line of sight. There are some fullyprepared query forms in Python to download large amounts of data. The map has a variable but always very high angular resolution, ranging from 3.40 to 106 CHAPTER 10. USING THE PAN-STARRS -BASED EXTINCTION RADIAL PROFILES FOR 3D DUST MAP AND A PRIOR 3D DISTRIBUTION 13.70 arcmin, however the bins of distance moduli (i.e. a logarithmic scale for the distance) correspond to a distance-dependent distance resolution of 25%, i.e. very broad radial distance bins, especially at large distance.

Because of their statistical technique, there are some well explained limitations in excess of colour reliability at different lines of sight. In pixels corresponding to a very low number of objects -as in the case of shorter distancestheir statistics fail because they do not have enough information. For the more distant pixels the problem is still the decrease in the number of objects that leads to insufficient information, but also the observational distortion, because the more distant stars observed are usually close to the limit of magnitude of the investigation and are favoured targets weakly reddened. They use a very refined technique to determine where their determination of the reddening is reliable, and the distance without a good reliability are well indicated for each line of sight.

The Pan-STARRS radial profiles, as said above, have low accuracy and reliability at small distances, and the reliability area starts at distances on the order of 300 pc. This fact entails that there is a complementarity between our 3D maps that are the most precise at small distances and the Pan-STARRS profiles and this complementarity has motivated the attempts described in the next sections.

Pan-STARRS extinction radial profiles as sources of additional color excess data

A 3D inversion is alimented by a large series of distance -excess of colour pairs, and such pairs usually come from individual stars for which distances and reddenings are simultaneously estimated. The Pan-STARRS extinction radial profiles are also initially based on a large number of targets used in conjunction, but for each direction the resulting profile is a statistical result. Still, it is a series of distance modulus-extinction pairs, and our idea has been to consider each point of the profile, i.e. each one of these pairs as a potential virtual target star having the same distance and the same excess of colour value. As mentioned above, it provides a possibility to extend and improve our mapping because it has information at further distances and because the spatial distribution of the additional targets is uniform. Green et al. (2015) provides the extinction, with its standard deviation, for all distance moduli between 4 and 19 with a distance modulus (DM) step of 0.5. after transformation of DM in parsecs using the relationship:

d[pc] = 10 (0.2•DM +1) (10.1)
we can realise the non-uniformity in distances and the bin widths, with 5 bins over 600 pc between 400 and 1000 pc (DM 8-10) and with 5 bins over 1500 pc between 1000 pc and 2512 pc (DM 10-12). The set of reliability flags shows that the most reliable data start at about 400 pc. Since we need additional targets over 500 pc, in this sense, the Pan-STARRS may enormously help.

Data selection:

PAN-STARRS EXTINCTION RADIAL PROFILES AS SOURCES OF ADDITIONAL COLOR EXCESS DATA 107

• For each line of sight several extinction curves are given, based on different star subsamples. I did not use the samples but only the profile marked "Best Fit", with its corresponding error.

• Lines of sight were selected with one degree steps in Galactic longitude and latitude.

• We retained only the parts of the profiles in the reliability zone, using the given flag.

• To be conservative in our choice, we selected only data with relative error on the excess of colour less than 0.3. This criterion strongly reduces the imported data.

• For our 3D inversion, we only use data with distances to the galactic plane lower than 600 pc. We retained Pan-STARRS data that fulfil this criterion.

• For each line of sight I have selected a maximum of three points chosen to be in the flat areas of the reddening profile, because they are the regions in which the different samples are in good agreement, and as consequence also the "Best Fit" curve is more reliable.

• My selection has only excess of colour that grows monotonically.

• The most distant point is taken into account only if the difference between the second and third point is less than 20% because for the inversion code, a too important gradient is a source of errors and elongated structures that we want to avoid.

After this selection, I retained only virtual stellar targets closer than 2500 pc.

These selection criteria could seem too strict, but anyway the inversion cannot manage more than ∼ 70000 points, and it takes a lot of computational time. The strategy was to select only the more useful virtual stars.

In

Inversion based on real and virtual stars

A new inversion has been attempted for a total number of 69 707 distanceexcess of colour couples, with only 22 900 points from the initial catalogue, the rest being Pan-STARRS virtual stars. The spatial distribution of all the targets is shown in Fig 10 .3 with different colours for the Lallement et al. (2014) and my Pan-STARRS selection. Most of the improvement is in the sampling of distances and increase of distance range. An arbitrary error of 5% was assigned to the distance of the virtual Pan-STARRS targets. As prescribed by Green et al. (2015), we corrected the reddening taken from the Pan-STARRS website by a factor 0.88.

The resulted map is damaged by an artefact in the anticenter direction (see Fig. 10.4), and we still have not completely understood the origin. Given the distribution of the spurious voxels along a sphere centered on a point in space without any particular characteristics, very likely one of the elements of the matrix of mutual influences has a false value, maybe due to a problem during the transmission of one of the files during its computation. Since the artefact affects a limited region only, and the computational time for such a direct inversion is very large (1 month and 26 days), we did not perform a second run.

CHAPTER 10. USING THE PAN-STARRS -BASED EXTINCTION RADIAL PROFILES FOR 3D DUST MAP AND A PRIOR 3D DISTRIBUTION

Fig 10.4 shows the Galactic plane distribution from the new inversion and how it compares with the inverted distribution without the virtual stars. There are some new structures in the new map, especially at large distances, as expected, for example a second rank of massive clouds is mapped. On the other hand, some of the structures in the third quadrant are more compact, a sign of improved realism.

When comparing some vertical cuts through the distribution, - of information at large distance, while towards l = 160 • the most important changes are in the nearest 800 pc and then the exponential prior dominates.

Again, we emphasise that this inversion has a much lower angular resolution than the original Green et al. (2015) map, due to our selection of directions and because tour 3D inversion can not reproduce very small structures. Also, the sizes of the distant structures are large, since the initial distance bins are wide and have increasing spacing. However, we derive from these comparison that this is a potential technique of combining different datasets.

Prior based on Pan-STARRS extinction map

Another possible use of the Pan-STARRS extinction map is the derivation of a large scale 3D prior distribution for our 3D inversions. The prior distribution is very important in inversion processes as it controls how the medium should be described where there is no information from the data, and it is especially fundamental in 3D inversions that are generally intrinsically under-constrained. For those reasons, it is important to choose the most realistic one. Moreover, a realistic prior facilitates the convergence towards the best-fit solution. I prepared and tested the evolution from an analytically computed prior, namely an exponentially decreasing function of the distance from the galactic plane [START_REF] Chen | Comparison of two different extinction laws with HIPPARCOS observations[END_REF], to a more realistic prior. For our 3D mapping, we need a Using the Pan-STARRS map as a prior does not mean that we make use its high angular resolution, because the inversion can not reproduce structures with a very small size (due to the use of the kernels), but we can better recover the large structures. Moreover, since the Pan-STARRS radial profile distance bins are increasing rapidly with distance, the prior is expected to generate structures at different scales, from the smaller and better defined near the Sun to the wider and largely smoothed for more distant areas.

CHAPTER 10. USING THE PAN-STARRS -BASED EXTINCTION RADIAL PROFILES FOR 3D DUST MAP AND A PRIOR 3D DISTRIBUTION

Building the prior

To build the prior we used all the points for the extinction curves with reliability flag, sampling the sky each 0.5 • in longitude and latitude. I obtained a total sampling of 3 071 230 distance-excess of colour value pairs. As done previously and recommended by Green et al. (2015), I corrected the reddening as they come from the Pan-STARRS website by a factor 0.88.

We used for the first time a hierarchical method to build the new prior. This new technique, devised by J.L. Vergely, allows the users to reconcile reasonable computation time and large number of targets as well as a distance-dependent structure size (from very large structures at large distance to increasingly small

MAPPING RESULTS

113

structures at decreasing distance). It starts with a very low frequency map (structures of 800 pc and a 5 kpc volume), using a dataset of values obtained by averaging data in cells of a size that allows to fulfil the Nyquist-Shannon criterion. This technique will be largely explained in Part IV.

1. The Pan-STARRS reddening data subsample is converted into local opacities by computing the local gradients of the reddening profile ρ 0 :

ρ 0 = δ E(B-V ) /δ R .
2. A spatial scale S of restitution of the opacity is fixed, starting with the (large) scale that can possibly be restored on the whole map. The average opacity is computed in a 3D grid of boxes of size SxSxS by averaging local values of locations contained within each grid cell. Thus, the resulting average opacity is dependent on the scale.

3. Based on these average opacities, maps of smoothed opacities are computed by Bayesian interpolation with a smoothing kernel twice as large as S.

4. We then move on to a scale twice smaller. S/2 x S/2 x S/2 boxes are built and the average opacity is calculated for each box. The dynamics of the average opacity for this set of boxes is stronger. We suppress the boxes that do not fulfil the Nyquist-Shannon criterion for S/2, and usually they are the more distant boxes.

5. A Bayesian interpolation is carried out again with a smaller smoothing kernel and using the previous map as prior.

6. Again, the scale is divided by two and steps 2) and 3) are performed again for this new scale, etc.

New prior

Final Pan-STARRS prior map is a 3D map, with dimension [-3000:3000]

Mapping results

I performed the inversion of the same dataset as in Chapter 9, this time with the Pan-STARRS prior. Fig. 10.6 shows the resulting distribution in the Galactic plane, to be compared with the previous maps. More details can be found in the published article included in this chapter. It is shown that with a more realistic prior, the Bayesian inversion has an improved accuracy and assigns more reliable distances to the interstellar medium structures. The improvement is shown using the 2D Schlegel et al. (1998) map and soft X-ray emission maps. Moreover, we compared the bubbles found in our 3D map and locations of recent supernovae, modelled by Breitschwerdt et al. (2016). The

CHAPTER 10. USING THE PAN-STARRS -BASED EXTINCTION RADIAL PROFILES FOR 3D DUST MAP AND A PRIOR 3D DISTRIBUTION

Maps representation

In this thesis and in different papers, we must represent a 3D map in 2D figures, in particular we are not interested at represent projections, but slices in the 3D, interpolated in the 3D matrix. I usually show for illustration the Galactic plane and some vertical planes, perpendicular at the galactic plane. Actually, for me the Galactic plane is the plane at galactic latitude equal zero. In For this reason, the 3D map is available and for different uses different representations could be more or less appropriated. In this thesis, I try to note everywhere the colour scale, but I prefer the c) and d) representations, because I can identify easily the Local Bubble, cavities and regions where the analytical prior is dominant.

Maps errors

Our excess of colour/pc map contains some errors, in distances positions and fro the reddening/pc values. Uncertainties depend from the error on dataon distances and on reddening values, the positions on the sky are assumed as without errors. Uncertanties' propagation is very complicated by the relationship between prior and data, the reciprocal covariances and additional uncertainties vary because of the bias in observations. Sale and Magorrian (2014b) proposed a technique for calculating errors during the Bayesian inver-10.8. STILISM WEBSITE 117 sion, but this evaluation are too expensive in computational time to be really applied. Without an assigned error it is very difficult to interpret the map, so it is necessary to develop an approach to obtain some estimates of errors. In the strategy I used, I processed separately the errors on distances and excess of colour, even if they are connected in inversion. I did not calculate the errors in the excess of colour/pc value but on the integrated value on the line of sight.

Uncertainty on the clouds' positions

I have assumed that distance errors are directly related to the spatial distribution of the volume of the star targets, and not to the errors assigned to them. Structures cannot be constrained to a better position than is acceptable by the Nquist-Shannon theorem, otherwise the inversion produces variations in the distribution of opacity with a frequency too high in relation to the distribution of data, which should be considered noise. Translated in a very simplified way, if in a certain volume of 10pc 3 I have only 9 star targets, the reversal can not have an accuracy of more than 10 pc at that volume.

I calculate for each point on the map the smallest sphere centred in that point that contains 10 targets -because I don't know the spatial distribution of the sphere, nor the uncertainties of the targets. As our map for the [START_REF] Capitanio | Three-dimensional mapping of the local interstellar medium with composite data[END_REF], it contains 800x800x120 points, and it is based on ∼ 28000 stellar targets, this approach is too expensive in computational time. Another simpler technique is to calculated for each map's point the mean targets' volume density N/pc 3 around this point, using a fixed volume, and the error is the reciprocal value of the mean volume density.

Uncertainty on the excess of colour value in the maps

Because of the fixed kernels and the σ, our reversal tends to smooth the structures and is not flexible enough to recognise the denser clouds. We estimated the error on the total excess of colour on the line of sight simply looking at the difference between excess of colour in input and excess of colour in output. For each point in the map p = (x, y, z), there are considered the N stellar targets closer to p. The difference between the input excess of colour and the output excess of colour is averaged. We will obtain a total cube of error on excess of colour. As the emission maps give a maximum value for the excess of colour, I used the Schlegel et al. (1998) map as maximum value for excess of colour. It is not a statistically true incertitude on the map, but it helps to understand where our maps are more reliable.

STILISM website

In the STILISM project frame, they developed a new website1 where they published the 3D maps inverted during my thesis, and the incertitudes, and it is possible to visualise extinction curves (Fig 10.10) and slices at different inclinations.

PIECEWISE-DEFINED INVERSION

119 but it is a operational choice that I applied also in other cases, as illustrated in Chapter 15 and 16. Since the borders of two original maps do not show any jumps or discontinuities, the total merged map is reliable.

Introduction

Three-dimensional (3D) maps of the nearby and distant Milky Way interstellar medium (ISM) are useful multipurpose tools have been only recently developed at variance with the extremely detailed, multiwavelength 2D emission maps or spectral cubes that have been accumulated over decades. As a matter of fact, a revolution is underway that dramatically changes the situation: photometric, spectrophotometric, and spectroscopic massive stellar surveys have started to provide extinction and absorption data that, coupled with parallax or photometric star distances, bring the third dimension for the ISM, i.e., the distance to the clouds. Thanks to 3D maps of the interstellar matter, structures overlapping on the sky are now converted into distinct clouds distributed at different distances, which will progressively allow emission components to be assigned a well-located production site. Three-dimensional maps or pseudo-3D maps have already been produced based on various kinds of stellar data; that is mainly photometric extinction but also diffuse interstellar bands (DIBs) and spectral lines of gaseous species (Marshall et al. 2006;Vergely et al. 2010;van Loon et al. 2013;Welsh et al. 2010;Lallement et al. 2014;Schlafly et al. 2014;Sale & Magor-rian 2014a;Kos et al. 2014;Schultheis et al. 2014;Zasowski et al. 2015;Green et al. 2015;Schlafly et al. 2015;Rezaei Kh. et al. 2016). Various methods have been used to synthesize the distance-limited data, including full 3D tomographic inversion of individual sightline extinctions (Vergely et al. 2001;Sale & Magorrian 2014b), statistical methods based on photometry, and stellar population synthesis or color-color diagrams; see the Monreal-Ibero & Lallement (2015) proceedings for recent developments in this field. In the coming years, maps of increasing quality are expected thanks to continuing or new stellar surveys, on the one hand, and precise Gaia parallaxes, on the other hand.

Each mapping technique has its advantages and limitations. Statistical methods require large amounts of targets and are appropriate at large distances, while the synthesis of individual line-of-sight data may work closer to the Sun. Near-infrared (NIR) or infrared (IR) surveys allow one to go deeper in cloud opacities compared to optical data but are more difficult to correct for telluric emissions and absorptions. Maps based on DIBs may slightly suffer from the fact that DIB carriers tend to disappear in dense cores of clouds (Lan et al. 2015), thereby potentially reducing the resolution. Nevertheless, there are numerous DIBs and their combinations may become powerful tools Article number, page 1 of 18 A&A proofs: manuscript no. Capitanio2017 to probe the physical state of the encountered media. Whatever the technique, a major difficulty is associated with the decrease with distance of the achievable spatial resolution in the radial direction, due to increasing uncertainties on target distances. Full 3D inversions that combine the radial and ortho-radial information may partly overcome this difficulty provided they are based on massive datasets, however at the price of strongly increased computing time (see, e.g., Sale & Magorrian (2014b)).

We present a first attempt to address these limitations by means of a combination of three different datasets as follows: (i) individual color excess measurements from broad-and narrowband photometry of nearby stars (mostly ≤500pc), (ii) NIR DIB equivalent widths (EWs) measured in individual spectra of more distant stars (500-1500pc), and (iii) color excess measurements at larger distance (up to 3kpc) based on a statistical analysis of multiband photometric data. Our purpose is to test such an association and its potential for improved 3D mapping of nearby or distant ISM. The first two datasets are merged by means of a conversion from DIB strengths to E(B-V) color excesses. A Bayesian inversion is applied to the resulting composite database. The large distance color excess data are used to build a very low-resolution 3D distribution that is subsequently used as the prior distribution in the Bayesian inversion to replace a plane-parallel homogeneous distribution.

Prior to the combination of these different sources, we analyzed the changes that are induced in the inverted 3D maps based on the first color excess dataset alone when Hipparcos or photometric distances are replaced with new Gaia Data Release 1 (DR1) parallax distances (the TGAS catalog), when available.

In section 2 we describe the three datasets used in the inversions. In section 3 we briefly recall the Bayesian technique developed in Vergely et al. (2010) and Lallement et al. (2014) (hereafter LVV) and the changes introduced in the method. We also describe the hierarchical method developed to build the largescale prior distribution. Section 4 describes the 3D map evolution introduced successively using Gaia distances, the addition of the DIB-based data, and finally the large-scale prior map. Section 5 discusses uncertainties and shows comparisons between the resulting final map and other measurements of cloud distances or cavities. Section 6 discusses the results and perspectives of such composite maps.

Data

Individual color excess data

We started with the reddening dataset of ≃22,500 sightlines compiled and inverted by LVV. It comprises four different catalogs that were cross-matched and homogenized; for more details about the stellar types and characteristics of the calibration method for each separate dataset, see Vergely et al. (2010); Cramer (1999); Nordström et al. (2004); Dias et al. (2012). Most target stars are nearby (d≤500pc), cluster data only correspond to larger distances. The four catalogs are complementary in terms of sky coverage. Of the target distances used for the inversion presented in LVV, 75% were photometric. For one-quarter of these distances the Hipparcos distance was preferred. In the four inversions presented here we kept the same error bars on the reddening as those used by LVV. The only difference in the LVV series of targets is the removal of ≃400 targets with photometric distances that had no catalog identifications. The coordinates, brightnesses, estimated distances, and reddening reasonably of these ≃400 targets correspond to those of nearby stars. Therefore, these targets were not excluded for the inversion presented in LVV. However, as we discuss in section 4, after the addition of new, more distant APOGEE targets and the subsequent mapping improvement we realized that for these particular targets the color excesses were significantly above other data in the same area. For this reason, we conservatively excluded the targets. Fig. 1 shows the distribution of the remaining targets over the sky.

As shown in LVV, the distribution of the targets is highly biased toward low reddening regions in the sky. This had strong consequences on the resulting maps; cavities surrounding the Sun were well defined along with the boundaries of the first encountered dense clouds. On the other hand, clouds located behind foreground dense structures were either not mapped or were very poorly mapped.

Measurements of DIBs and DIB-based color excess estimates

Except for the recent identification of ionized fullerenes C + 60 , the carriers of the DIBs are still unknown, and it may seem strange to use absorptions due to unknown species for mapping purposes. However the link between DIB strengths and the columns of interstellar matter is strong and successful DIB-based 3D mapping has now been carried out (see Sect. 1). Up to now such mapping used solely DIBs. At variance with these works, here we attempted to merge color excess data and DIB absorption data and perform a unique inversion of a composite dataset. This requires a conversion of DIB equivalent widths into reddening (or the inverse); because none of the DIBs have been shown to be perfectly correlated with the reddening, such a mixing of color excesses computed in so many different ways-for example, with photometric and spectrometric techniques-is potentially hazardous. On the other hand, initial comparisons between DIB equivalent widths and reddening radial profiles in the same sightlines have demonstrated that their similarity (Puspitarini et al. 2015) and global maps also have strong similarities (Kos et al. 2014). Additionally, it is possible to account for the variable E(B-V)/DIB ratio by increasing error bars on the estimated E(B-V), which we have carried out in this work.

Data

We used the results of the SDSS-III Apache Point Observatory Galactic Evolution Experiment (APOGEE), which is one of the four Sloan Digital Sky Survey III (SDSS-III; Eisenstein et al. 2011;Aihara et al. 2011) experiments. The APOGEE uses a 300-fiber multiobject spectrograph working in the near-infrared (H-band; 1.51-1.70 µm) at high spectral resolution (R∼22 500; [START_REF] Wilson | Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series[END_REF]. Specifically, we downloaded spectra from the SDSS data release1 (DR12; Alam et al. 2015), which provides all the data taken between April 2011 and July 2014. In addition to the ∼160 000 scientific targets selected from the source catalog of the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) and distributed across all Galactic environments, APOGEE contains a sample of ∼17 000 spectra of hot stars, called telluric standard stars (TSSs). The TSSs form the basis for the correction of the telluric absorption lines across all field types (see Zasowski et al. (2013), for a detailed description of the different target classes). These stars are the bluest stars on a given APOGEE plate with a magnitude in the range 5.5 ≤ H ≤ 11 mag and are therefore hot and bright stars with spectra that are most often featureless. The APOGEE products contain the decontaminated spectra and synthetic stellar spectra that provide the main stellar line locations and relative depths and widths. Both were used by Elyajouri et al. (2016) to extract a catalog of λ15273 DIB measurements from 6700 TSS spectra. Further details on the sample can be found in Elyajouri et al. (2016, and references therein). Weaker DIBs have been further studied based on the same TSS spectra (Elyajouri et al. 2017). Here we focus on the strongest 15273 Å DIB with the aim of extracting as many accurate measurements as possible from both scientific targets and TSSs possessing a Gaia parallax.

We analyzed the series of 25 409 DR12 spectra of targets belonging to the Tycho catalog to determine the presence or absence of a detectable DIB at 15273 Å and measure its equivalent width (resp. an upper limit) in case of positive (resp. negative) detection. We took as a starting point the methodology presented by Elyajouri et al. (2016) for TSSs spectra. We kept the same fully automated fitting technique and method of classification but we adapted the fitting constraints to take into account the inclusion of targets cooler than the TSSs. The code was developed using the IGOR PRO environment 2.

Fitting method

We restricted the fit to the spectral range [15 260 -15 280]Å in the vicinity of the DIB. This range is wide enough to ensure an adequate sampling of the neighboring Bracket 19-4 stellar line at 15264.7 Å. We used for the fit the Levenberg-Marquardt algorithm implemented in IGOR PRO2 .

We fit the data to a combination of an adjusted synthetic spectrum, DIB model, and smooth continuum as shown in equa-tion 1. Below we provide information specific to each of the equation variables as follows:

M λ = [S λ ] α × DIB[σ, λ, D] × (1 + [A] × λ), (1)
• [S λ ] α , an adjusted stellar spectrum, where S λ is the stellar model provided by APOGEE. We included the scaling factor α to adjust the model stellar line depths to the data.

• DIB[σ, λ c , D], the DIB shape was modeled as a Gaussian function allowed to vary in strength, depth, and velocity shift with three free parameters associated with its Gaussian RMS width (σ), central wavelength (λ c ), and depth (D).

• (1 + [A] × λ), a 1-degree polynomial function introduced to reproduce the continuum around the DIB as close possible.

An example illustrating our fitting procedure is shown in Figure 2.

Selection criteria and error estimates

Residuals, computed as differences between data and model, were used to obtain three measurements of the standard deviations RA, RB, and RC. To do so, we performed the local fit and a second fit over the whole spectral range covered by APOGEE using the same fit function as that presented in equation 1.

We selected the standard deviations RA, RB, and RC of the fit residuals, as follows:

• RA from the local fit was calculated in a region A = [λ c -10 Å , λ c + 10 Å ] close to the DIB.

• RB was calculated over a spectral range B= [15890-15960] Å, which is free of DIB absorption, strong stellar lines, and telluric residuals.

• RC was obtained from region C= [15200-15250] Å relatively close to the DIB, and is also free of DIB and potentially contaminated by stellar residuals.

These are used for the selection criteria shown in Table 1 and also used below to estimate the uncertainty on the DIB equivalent width. The uncertainty is conservatively estimated based on the following formula:

δ EW = √ 2π σ max(RA, RB, RC), ( 2
)
where σ is the Gaussian RMS width that results from the fit. The quantity max (RA,RB,RC) is the maximum of the three standard deviations.

Table 1 shows the fitting constraints that were used to select our final sample. They are somewhat different from the criteria of Elyajouri et al. (2016). In particular, we no longer used HI 21 cm data to limit the width of the DIB, but we used limits based on the FWHM histograms built in this previous work. Representative examples illustrating our fitting procedure and the various categories are shown in Fig. 2.

Final data selection for the inversion

Equivalent widths and stellar rest-frame wavelengths are determined from the best-fit parameters in each sightline for the 25,000 attempted spectra of targets belonging to the Tycho catalog. We rejected those cases where the fit failed due to low S/N, an inadequate stellar model, or very strong telluric contamination most of the time, and we retained 9913 spectra following the criteria in Table 1. The corresponding targets were crossmatched with the targets of the Gaia DR1 catalog (Arenou et al. 2017) to obtain a catalog of 7800 stars with Gaia distances. We added to the DIB measurement an additional 50% uncertainty to account for the E(B-V)/EW variability associated with the influence of the physical properties of the encountered media. As a matter of fact, from the most neutral to the most ionized media, this ratio may reach a variability factor of three (see, e.g., Elyajouri et al. (2017)). After the additional filtering for our criteria on target distances and distance uncertainties (see Sect 4.1), only 4886 targets were retained for the present inversion. Other targets will become useful after the next Gaia data releases. The number of retained targets is small with respect to the initial number of APOGEE spectra of Tycho stars (less than 20%) and targets from the reddening catalog. Despite the limited number of these retained objects, they are precious since they allow us to probe more reddened regions, in particular to reveal a second or third rank of clouds, something often precluded using the bright targets measurements in the optical. We converted the DIB EW into a color excess using the Zasowski et al. (2015) formula

EW = 0.102 A 1.01 V Å (3)
and the classical average total-to-selective ratio A V /E(B-V)= 3.1 (Savage & Mathis 1979). The relationship established by Zasowski et al. (2015) has been confirmed, by Elyajouri et al. (2016), to be valid locally based on the closer TSSs.

Subsample of Pan-STARRS color excess measurements

Green et al. ( 2015) have used Pan-STARRS and 2MASS photometric measurements toward 800 millions targets to build re-markable 3D dust reddening maps with a very high angular resolution (5-15 arc-minutes) covering distances from ≃300 pc to 4-5 kpc. The publicly available maps contain a quality flag that allows to exclude results at small or large distances that are uncertain because of limitations on the number of targets for geometrical or sensitivity reasons. Both surveys were conducted from the Northern Hemisphere. We used those data to build a low-resolution 3D prior distribution to be used in our Bayesian inversion in replacement of the previous analytical solution corresponding to a homogeneous plane-parallel opacity.

To do this, we downloaded a grid of Pan-STARRS E(B-V) estimates for lines of sight equally spaced every 0.5 degree in Galactic latitude and longitude and for all distances available from the Pan-STARRS online tool, in this way obtaining 3,071,230 pairs of distance and extinction after exclusion of all data points flagged as uncertain. As result of this process, we do not benefit from the very high angular resolution of the maps, however this information would be lost in our approach. In many directions the first 200 pc are flagged because of the limited number of targets available to define the reddening in the very small solid angle chosen for this Green et al. (2015) study. However this is where the present inversion of individual data may be advantageous. The method applied to these Pan-STARRS results is described in Section 3.2.

Inversion techniques

Bayesian inversion of individual sightlines

The Bayesian inversion technique is based on the pioneering work of Tarantola & Valette (1982) and its first developments and applications to the ISM are described in detail in Vergely et al. (2001Vergely et al. ( , 2010)); Welsh et al. (2010); Lallement et al. (2014). Briefly, the inversion optimizes an analytical solution for the 3D opacity distribution through the adjustment of all integrated opacities along the target sightlines to the observed color excess data. Because the solution is strongly under-constrained, it is regularized based on the assumption that the 3D solution is smooth. Opacities ψ at two points (x), (x ′ ) in space follow correlation kernels: here

ψ 1 (x, x ′ ) = exp( -x-x ′ 2 2ξ 2 1 ) and ψ 2 (x, x ′ ) = 1 cosh(-x-x ′ /ξ 2 )
, where the first (resp. second) term represents the compact (resp. diffuse) structures. The correlation distances ξ 1 and ξ 2 , which roughly correspond to the minimum size of the computed structures, are evidently limited by the average distance between the target stars. Here we have chosen ξ 1 =15 pc and ξ 2 =30 pc. As we discuss in the next sections, such kernels are valid in internal regions where the target distribution is the densest. The model variance, which controls the departures from the prior distribution, is σ 1 =0.8 for the first kernel and σ 2 =1.0 for the second (see LVV for its definition). The Tarantola & Valette (1982) formalism allows one to compute the least-squares solution iteratively. For the present maps the convergence is reached in about six iterations. Uncertainties on the reddening and target distance are treated in a combined way (see Vergely et al. (2001)). The distribution is computed in a volume of 4 kpc by 4 kpc along the Galactic plane and 600 pc along the perpendicular direction.

Compared to the method used in Lallement et al. (2014), an additional treatment of outliers was introduced. During each iteration except the first two, in case one measured color excess value is found to be incompatible with the kernels and the surrounding data, its error bar is multiplied by 2. This method has proven to solve for data points that have underestimated er- rors and eliminates oscillations. The Bayesian approach implemented in Vergely et al. (2001) and subsequent works allows us to include an a priori knowledge of the ISM 3D distribution. This prior distribution can in principle be provided by a model that represents the density variations in the Galactic plane by an analytic law or alternatively by a distribution based on external data. The latter case is fully appropriate to our objective of combining different sources of extinction. As a matter of fact, it is possible to produce density maps by successive refinements following integration of data from different sources in a sequential and non-simultaneous manner. The advantage of such an approach is twofold: first, the amount of data to be integrated at each step is reduced, which makes it possible to reduce computation times and, second, it is easier to see the contribution of each set of data.

In this perspective, a new development was introduced in our inversion code. Now, it is possible to use any 3D prior distribution, i.e., we can replace the homogeneous plane-parallel prior that corresponded to an analytical representation (we used an exponential decrease from the Galactic plane) with any arbitrary precomputed distribution. We used this possibility to test a twostep inversion based on two different datasets as described in section 4.3. The construction of the prior distribution is described in the next section.

Large-scale prior distribution based on Pan-STARRS

We used the Green et al. (2015) color excess subsample described in 2.3 to develop a low-resolution opacity model extended to large distances, to be used as a prior for the inversion of individual lines of sight as described above. Because this reddening model is based on photometric measurements of hundreds of millions of objects, the Green et al. (2015) model has a very high angular resolution, whereas the radial resolution is limited by uncertainties on photometric distances. In principle our prior distribution is losing all the details contained in the angular variations, first because we start with a coarse angular sampling of 0.5 deg, and also because our full 3D inversion has a spatial resolution limited by the radial distance uncertainties.

Ideal inversions are based on a homogeneous spatial sampling of targets, i.e., a homogeneous volume density of targets and similar uncertainties on their locations at all distances, which allows us to retrieve structures of the same minimal spatial scale everywhere in space. But for most surveys, including Pan-STARRS, the achievable resolution is dependent on the distance to the Sun, especially owing to distance-dependent uncertainties on the star locations. The sampling of the data in this case does not allow the Nyquist-Shannon criterion to be fulfilled for the same minimal autocorrelation length everywhere; also, some of the energy attributable to high spatial frequencies is likely to be redistributed in low spatial frequencies, especially at large dis-tances or in the radial directions when the sampling is weak. Therefore, we need an approach that allows us to retrieve only the large scales at large distances and all large and small scales at short distances. We implemented a hierarchical approach that allows us to achieve this goal in an iterative way by progressively updating the opacity model. Schematically, we first constructed a low spatial frequency map in a sphere with a large radius (here 5 kpc). In a subsequent step, we estimated spatial frequencies that are higher by a factor of 2, however this time in a smaller sphere (for instance 3 kpc) by removing data at large distances for which the available information does not make it possible to reach these frequencies using the Nyquist-Shannon criterion. The information at large distances is kept under the form of the prior, which is simply the distribution derived from the previous step. This procedure is repeated for increasingly high frequencies until their maxima compatible with the radial sampling (reached at small distances) are obtained. In practice we proceeded as follows:

1. The Pan-STARRS reddening data subsample (see section 2.3) is converted into local opacities ρ 0 through derivation w.r.t. the radial distance R, ρ 0 = δ E(B-V) /δ R . 2. A spatial scale S of restitution of the opacity is fixed, starting with the (large) scale that can possibly be restored on the whole map. The average opacity is computed in a 3D grid of boxes of size SxSxS. The resulting average opacity is thus dependent on the scale. 3. Based on these average opacities, maps of smoothed opacities are computed by Bayesian interpolation with a smoothing kernel twice as large as S. 4. We then move on to a scale twice smaller. S/2 x S/2 x S/2 boxes are built and the average opacity is calculated for each box. The dynamics of the average opacity for this set of boxes is stronger. We suppress the boxes that do not fulfill the Nyquist-Shannon criterion for S/2. 5. A Bayesian interpolation is carried out again with a smaller smoothing kernel and using the previous map as prior. 6. Again, the scale is divided by two and steps 2) and 3) are performed again for this new scale, etc.

A planar cut along the Galactic plane in the resulting 3D prior is shown in Fig. 3. The Sun is at center and Galactic longitude increases counter-clockwise. As expected, far from the Sun we can only restore the very large scales. On the contrary, one can reach scales on the order of 100 pc within the first few hundreds parsecs. Because Pan-STARRS data are recorded from the Northern Hemisphere, the prior in the fourth (bottom-right) quadrant appears homogeneous at large distances from the Sun. This map can be used as a prior in the inversion of the individual lines of sight for which accurate distances are available, with the goal of improving estimates of opacity fluctuations and refining the distance assignment of the structures (see Sect 4.3).

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A&A proofs: manuscript no. Capitanio2017

Inversion of datasets

Inverting pre-and post-Gaia individual color excess data

In order to test the influence of the new Gaia parallax distances we inverted the reddening dataset described in section 2.1 twice with exactly the same method, criteria, and parameters, but with different target distances. The first inversion (A) used the ini-tial Hipparcos+photometric distances and errors as in LVV and the second (B) used Gaia-TGAS distances and associated errors when available, or unchanged values in the absence of Gaia result. Gaia DR1 parallaxes are about 20 times more numerous than Hipparcos parallaxes and about three to four times more accurate. These characteristics will evolve with the next releases, which will contain many more stars and reduced parallax uncer- tainties. As in LVV the prior dust opacity is a plane-parallel homogenous distribution decreasing exponentially from the Galactic plane with a scale height of 200 pc. We also similarly retained for the inversion targets closer to the Galactic plane than 1000 pc and less distant than 2601 pc with relative errors on the distance smaller than 33%. The number of targets retained for the first inversion was 22467 and among these 5106 were assigned their Hipparcos distance, and the rest were photometric. In the second inversion 23444 targets were retained, with about 80% having a Gaia parallax. As the Gaia-DR1 uncertainties were 3-4 times smaller than Hipparcos uncertainties, the number of targets excluded for uncertain distances was significantly reduced. Importantly, the fraction of photometric distances decreased by a factor of four and Gaia distances started to be largely dominant.

The values of the χ 2 per target are computed from the differences between the observed color excesses and the color excesses computed by integration of the model 3D distribution along the target lines of sight. These values are reported in Table 2 for both the prior and final distribution. The value of χ 2 for the prior distribution is significantly higher for the second inversion, reflecting the fact that error bars entering its computation are on average smaller because of the reduced uncertainties on Gaia-DR1 distances, especially by comparison with previous uncertainties on the photometric distances. On the contrary, the final χ 2 is lower despite reduced error bars, demonstrating that the found distribution is more compatible with the new distances than with the previous distances.

Panels a and b (top left and right) in Figure 4 show planar cuts in the two inverted opacity distributions A and B. The plane is parallel to the Galactic plane and contains the Sun. The pre-Gaia inverted distribution is not exactly the same as in LVV because of the removal of some targets and the introduction of the new method to treat outliers (see section 3.1). The difference between the two pre-and post-Gaia distributions is visible: on average the structures are more compact. Some elongated structures diminished owing to the reduction of distance uncertainties, as in the third and fourth quadrants (bottom left and right); some others appeared, which may be due to contradictions between new Gaia distances and the remaining photometric distances. The latter regions will have to be carefully studied once all targets benefit from Gaia parallaxes. The Local Bubble keeps its global shape, but looks slightly more complex owing to the higher compactness of structures. At larger distance the most conspicuous difference appears in the first quadrant, in particular in the Cygnus Rift region. At l≃70 • the Rift is located signifi-cantly farther away in the new inversion, at about 800 pc instead of ≃600 pc, interestingly now in agreement with the Green et al. (2015) distance assignment. We knew that this was a region of strong oscillations in the first inversion; these oscillations have now disappeared. In the second quadrant there are substantial changes and we start to sketch a ring of clouds, more specifically the very large structure located from 100 to 400 pc is decomposed into two smaller structures.

Inversion of combined photometric and DIB-based color excess data

The same inversion code was applied to the merged catalog of photometric and DIB-based reddening estimates (inversion C).

As can be seen in Table 2, the introduction of the APOGEE targets reduces both the initial and final χ 2 per point. The former decrease means that error bars on the DIB-based estimated E(B-V)s are not underestimated. The latter decrease strongly suggests that the APOGEE targets do not introduce contradictory data and their inclusion produces a reasonable solution. In comparing the new Galactic plane cut in Fig 4 and the distribution C at the bottom left with the previous inversion with photometric data alone (distribution B, top right), we can clearly see some changes; these changes are particularly apparent in the second quadrant, where some decoupling or fragmentation of large structures into distinct cloud complexes along with new structures at large distances are visible. Since 14 % of the APOGEE targets are closer than 20 pc from the Galactic plane, are highly concentrated in this quadrant, and are more distant that the LVV targets, it is not surprising to find most changes there. The fourth quadrant does not change because the APOGEE catalog adds targets observed from the Northern Hemisphere. Since it is the first time that such measurements of different types are used, which could trigger incoherence in the inversion, it is mandatory to investigate the observed changes in all areas in order to validate this new technique. Table 2: Evolution of the prior and final χ 2 per line of sight in the four inversions.

in the appearance of new structures, especially at large distances in locations where there was initially no targets.

The Orion region is well suited for comparisons owing to the existence in similar proportions of targets of the two types beyond 150 pc. There are ≃750 lines of sight from the photometric catalog and ≃375 from the APOGEE catalog within the longitude interval l=(208:218 • ). As shown in Fig 9, the two types of targets are spatially well mixed. If the data were not compatible we would observe radially elongated and/or wide structures in the middle map that were absent in the top. Instead, there are no significant changes, which demonstrates that the two datasets trace the same structures. Indeed, the figure shows that the APOGEE data reinforce the dense structures at 500 and 600 pc, at distances poorly covered by targets with photometric measurements.

Another region suited to a further check is the anticenter region. At variance with the Orion area, the LVV targets are concentrated in the first 100 pc, while APOGEE introduces many more distant targets. Fig 10 shows clearly that this addition allows us to map new clouds beyond 300 pc, in particular to transform a unique wide structure at ≃ 450pc into at least three structures located between 300 and 700 pc, confirming that infrared data such as APOGEE add valuable information in areas where stars are already reddened by close clouds. The structures at small distances already seen in the first map (inversion B) remain in the second map but appear more compact with their relative opacities somewhat changed. Because the sightlines to the distant targets cross the nearby clouds, contributing to their mapping, the increased compactness of the foreground structure shows that the new data do not contradict the old data and instead help shape the close clouds.

We finally consider the Cepheus region in the second quadrant (Fig 11). There are several clouds distributed in the same region of the sky, which is a very good test for the inversions. Here, the number of targets in the longitude interval l=(105 • ;115 • ) increases from 390 to 664. It can be seen that the large structure at distances between 200 and 300 pc and at heights above the Galactic plane between 0 and 150 pc is now more clearly decomposed into three cores and an additional fourth cloud just below the Galactic plane at ≃ 300 pc. This last structure below the Galactic plane had apparently been erroneously associated spatially with a more distant and wide structure at 500 pc. As a result of Gaia distances and additional targets, its location has now been better defined. Indeed, the final distribution D (bottom panel of Fig 11 andsection 4.3) confirms this new location. Behind those structures a hole as well as two different more distant clouds are revealed near the Galactic plane. The large structure located at about 400 pc in distribution A, which was derived from only a few targets, is now much better defined and significantly displaced farther away at about 500 pc. This again shows that using infrared data enables the mapping of distributed clouds and holes between them.

Article number, page 9 of 18 A&A proofs: manuscript no. Capitanio2017 Fig. 6: Local cavity boundaries: the distance at which a color excess of 0.015 mag is reached is plotted as a function of rectangular Galactic coordinates. In very weakly reddened directions for which 0.015 mag is not reached within our computation domain, the distance to the domain boundary is plotted after conversion to negative values. This allows us to distinguish between the two cases well. The figure illustrates well the local warp of gas associated with the Gould belt, i.e., more matter at positive latitudes in the Galactic center hemisphere and at negative latitudes in the anticenter hemisphere. It also reveals very clearly the local bubble openings to the halo at about 210-240 • longitude.

Inversion of merged data using the Pan-STARRS-based prior 3D distribution

We performed an additional inversion (inversion D) of the set of LVV+ APOGEE targets, this time replacing the plane-parallel homogeneous prior with the large-scale distribution described in Sect. 3.2, based on Green et al. (2015) results. This allowed us to test our new capacity of using an arbitrary 3D prior distribution.

In the new prior, the smallest structures allowed are 100 pc wide and the kernel sizes for the largest structures are 800 pc.

Table 2 shows that using the new prior has the effect of reducing the initial χ 2 per point significantly and decreasing the final χ 2 too. This means that the data for individual sightlines are, not surprisingly, in better agreement with this more realistic prior. A comparison of panels c and d in Fig. 4 shows the differences introduced by using the new prior in the Galactic plane. As expected, the main variations are at large distance, especially beyond 1 kpc, while closer the changes are very small. The same effects are seen out of the Galactic plane, as shown in , where the bottom panels show the D opacity distribution. There are significant changes far from the Sun and negligible changes closer to the Sun, where the target density is high enough to suppress the influence of the prior. In all cases, it is interesting to see how the nearby structures connect with the distant very low-resolution Pan-STARRS based distribution. This two-step process allows large-scale and smaller-scale structures to coexist in a map, while avoiding an overinterpretation of the data. Other vertical planes drawn every 30 • Galactic longitude are shown in Appendix. These vertical planes give us a general idea of the nearby ISM distribution out of the Galactic plane.

Fig 5 (upper panel) shows the dust opacity in the Galactic plane for the entire computational area 4000pc x 4000 pc. As can be seen in the Figure, at large distances there are co-existing compact structures with the minimum size allowed by the kernels and large-scale structures that mainly result from the Pan-STARRS prior. The small structures however should be considered with caution, as is discussed in the next section.

Bottom panel of Fig 5 shows a zoom in the 1000pc x 1000pc central area. It shows numerous clouds and cavities and that the shape of the so-called Local Bubble is far from simple. It is well known that the interstellar matter within the first hundreds of parsecs is very complex and characterized by the series of clouds forming the Gould belt, a wide structure tilted w.r.t. the Galactic plane by about 20 • (e.g., Perrot & Grenier (2003)). The origin of this structure is still a matter of debate (see, e.g., Lallement (2015) for a recent discussion and suggested origin). Two chimneys connect the Local Bubble to the northern and southern halos forming a hole whose axis is nearly perpendicular to the Gould belt plane; this peculiar structure is illustrated in Fig 6 .  The figure shows for all directions the line-of-sight length that corresponds to an integrated color excess E(B-V)=0.015 magnitude. When the distance required to reach this color excess is larger than the distance to the boundary of the computational volume, such as toward high Galactic latitudes, we used this distance multiplied by -1. The figure shows very clearly the local warp of IS matter as well as the chimneys connecting to the halo. Fig. 7 shows 2D color excesses from inversions A (top map) and D (bottom map), which are computed by integrating local opacities from the Sun to the boundaries of our computational domain; the distance to the Galactic plane is smaller than 300 pc and distances along the X and Y axes are smaller than 2,000 pc. Iso-contours from Schlegel et al. (1998) for E(B-V) = 0.025 mag and E(B-V)=0.32 mag are drawn for comparison. Compared to our previous inversion (A, at top) the structures are more compact for inversion D (at bottom), showing that the data are more consistent and the resolution is improved thanks to Gaia distances and additional data.

Uncertainties and comparison with other 3D measurements

Resolution and errors

Uncertainties on cloud distances and dust columns are strongly dependent on the distance to the Sun due to the combined effect Article number, page 10 of 18 of target space density decrease and target distance uncertainty increase. Additionally, uncertainties vary from one region to the other since databases have strong biases. Theoretically the errors may be calculated for each point in space along with the Bayesian inversion, but this kind of evaluation is very expensive in computation time (Sale & Magorrian (2014b)). On the other hand less precise error estimates for the distance to the structures and the amount of integrated reddening may be obtained by means of simpler approaches. We present these approaches here.

In the frame of a first simple approach we assumed that the error in distance varies as the achievable resolution, i.e., depends on the target space density. We choose as an estimate of the error at each point the size of the smallest sphere around this point that contains at least 10 targets. Another simpler and computationally faster approach is to calculate again in each point the target density ρ (in pc -3 ) in a cube of a given size centered on this point and use (1/ρ) 1/3 as the error estimate. This second technique is less precise because we keep the same volume everywhere in an arbitrary way. The results for the Galactic plane are shown in Fig 13 . The results from both methods are not markedly different and as expected there is a strong increase of the distance uncertainty from the center to the peripheral regions. The error can be compared with a similar estimate by LVV: it can be seen that the addition of the APOGEE targets improves the resolution in a number of regions from the first to third quadrant. The errors on cloud localization owing to uncertainties on the target distances are limited by the use of our threshold (see Sect 4.1).

As already mentioned in LVV, estimating the error on the local dust opacity is meaningless because by principle the clouds have a minimum size and as a consequence the dust is distributed in larger volumes in the model compared to the volumes of the actual, clumpy clouds. This spreading of the opacity in volumes that are wider than the volumes of the actual clouds introduces systematic underestimates of the opacities and integrated reddenings in the cloud cores. As a result, this systematic error is expected to be small for sightlines that do not intercept small, dense cores, but may reach high values in highly reddened regions in case the reddening is generated by one or a few small structures. We come back to this point in Section 6. On the other hand, it is possible to give rough estimates of the errors on the reddening (integrated opacity) that are linked to the dataset, independently of the errors due to the assumed cloud minimum size. To do this, for every point in our 3D map we selected all targets contained in a cube of specific size around the considered point, and for those targets we calculated the mean difference between the data and model color excess. Fig 14 shows the results for the Galactic plane with a cube of 50x50x50 pc 3 ; in case the cube contains less than 10 targets we use a volume of 200x200x200 pc 3 . Uncertainties on distances and color excess will be available on our website and displayed interactively. These authors have mapped the clouds cores with a very high angular resolution, while our inversion produces much wider structures, however it is interesting to use this catalog for a comparison of cloud locations.

In Fig. 9, 12, and the bottom panel of Fig. 11, we superimposed the opacity distribution resulting from our D inversion and the position of the cloud cores identified by Schlafly et al. (2014) with associated error bars on their positions. For the Orion region ( galactic longitude = 212 • ; Fig. 9), these authors found a sequence of clouds distributed from 400 pc to 600 pc, which are distances similar to the structures appearing after the inversion. In the case of Perseus ( galactic longitude = 158 • ; Fig 12), our map also indicates the same distances. In the case of the Cepheus region (galactic longitude =110 • ; Fig. 11) the inversion produces two large, opaque structures above the Galactic plane, the first between 250-300 pc and the second between 700-800 pc. Two groups of high latitude molecular clouds have also been mapped in this region by Schlafly et al. (2014). The closest group is in reasonable agreement with our mapped structures, while the second is at somewhat larger distances. However, in this case our targets are very scarce at high latitude (see upper and middle panels in Fig 11 ) and more data are needed to allow a comparison.

Soft X-ray emitting cavities as signatures of nearby recent supernovae

Following the work of Puspitarini et al. (2014) we searched for cavities in our 3D maps, which can be counterparts of supernova remnants (SNRs) or massive stellar winds. Such cavities are detected through their soft X-ray emission in ROSAT maps. Fig. 15 shows four vertical cuts in the 3D distribution along meridian lines crossing the four ROSAT 3/4 keV bright spots labeled 1 to 4 by Puspitarini et al. (2014). The coordinates of those X-ray spots are l,b = (-30 • , +14 • ), (-18 • , +18 • ), (-5 • , +9 • ), and (-8 • , -10 • ).

In the four cases, we see that at the latitude of the bright spot centers there are cavities surrounded by dense clouds, which is the typical configuration for moderately old SNRs. Moreover, these cavities are not separated from the Sun by opaque clouds, which is a condition for their detection in soft X-rays, since million K gas soft X-rays photons are easily absorbed; more precisely, the cavities must have foreground extinction that is lower than E(B-V)=0.1 to be easily detected. Compared to the previous search using LVV maps, the cavities are now better defined. Interestingly, the two cavities seen in the maps at l,b,d=(-18 • ,+18 • ,125 )), and at similar distances. These authors have used the signature of 60 Fe in deep-sea crusts as a sign of recent (about 2.2 million years ago) explosions of supernovae in the solar neighborhood, and, based on proper motions and ages of the young stellar groups, they computed the most probable present locations of the latest explosions. Given the uncertainties associated with their statistical modeling, the small differences between our cavities 1 and 2 and their results is negligible, and these identifications reinforce their model and the 60 Fe measurements and interpretations.

Article number, page 13 of 18

A&A proofs: manuscript no. Capitanio2017

Conclusions and perspectives

We updated and improved our previous 3D maps of the local interstellar dust, based on the Bayesian inversion of photometrybased color excess measurements, in several ways. Our goal is to analyze the influence of the use of new Gaia parallaxes and to test two additional techniques aimed at providing more accurate 3D maps. First, the merging of photometric color excesses with color excesses estimated from diffuse interstellar band absorptions and, second, the use of a non-homogeneous large-scale prior distribution deduced from massive photometric surveys. The first technique increases the number of sightlines available for the inversion and, in turn, the resolution. The second work aims at testing hierarchical techniques to be used for Gaia photometric data in the future .

-We replaced ≃ 5,100 Hipparcos and ≃ 17,400 photometric distance measurements with ≃ 18,700 new Gaia-DR1 available parallactic distances and ≃ only 4,700 remaining photometric distances. In the resulting maps some elongated structures have been suppressed, which demonstrates that such features were artefacts owing to the lower accuracy of for- -We extracted by means of a dedicated profile-fitting technique a series of ≃ 5,000 equivalent widths of 15273 Å diffuse interstellar bands from SDSS/APOGEE high-resolution spectra of targets possessing a Gaia parallax and converted their equivalent widths into E(B-V) color excesses. We allowed for an additional 50% uncertainty to take into account the absence of a strict proportionality between the DIB EW and the color excess E(B-V). We then performed a new inversion using the combination of the previous reddening data and the DIB-based reddening estimates. In general the APOGEE targets are more distant than the previous stars, which results in more extended maps. We do not find any contradiction between previous and new maps in regions where both types of targets are present in similar numbers. Instead, a number of structures that were broad and had low opacities are assigned more complex shapes and denser cores, which suggests that the DIB-based color excess estimates can enter the Bayesian inversion and be used to get better constraints on the cloud locations. This has important consequences because all spectroscopic surveys provide DIB measurements that may help locate the interstellar clouds, especially if all targets have precise parallax measurements.

-We used a subsample of Green et al. (2015) Pan-STARRS reddening estimates to build a low-resolution 3D map by means of a new hierarchical Bayesian interpolation method. This map is used as a prior during the Bayesian inversion of the individual data instead of a homogeneous distribution. We see that such a prior complements well the low distance map by adding spatially averaged large structures farther away. This means that data from statistical methods applied to massive photometric surveys and also future Gaia data may be used in conjunction with the databases of individual sightline data.

The resulting 3D maps are significantly improved with respect to the previous maps thanks to the use of Gaia parallaxes, the additional DIB database, and the use of a prior. This is demonstrated by the residuals, and especially by the increased compactness of the structures and the disappearance or decrease of some of the elongated artifacts due to contradictory distances (the fingers of god) or lack of targets. Many of these artifacts remain, however, and are expected to disappear when all targets are assigned an accurate distance. In addition, the comparisons with other cloud location assignments and X-ray emitting cavities are encouraging. This shows that future Gaia parallax catalogs should considerably help the 3D mapping by allowing the use of a much larger number of targets. Merging photometric and DIB-based color excess estimates does not reveal any contradictory information and instead improves the maps, especially beyond foreground dense clouds. This opens the perspective of using the massive amounts of DIB data that are expected to be provided from high-resolution spectroscopic surveys. Finally, the use of a Pan-STARRS based prior demonstrates the feasibility of hierarchical methods for the inversion based on different datasets or massive amounts of data.

Our distributions are particularly useful at short distances, as they show how cloud complexes and cavities are spatially organized. In this respect, they are also appropriate tools for comparing with multiwavelength emission data, understanding environments of specific objects, computing particle or photon propagation modeled distributions, and searching for unreddened areas in case of stellar photometric model calibrations. In terms of angular resolution, they cannot compete with the distributions based on massive surveys. Especially, owing to the imposed cloud minimum size, opacities, and integrated reddenings toward the cores of the dense clouds can be strongly underestimated. In such nearby, opaque regions a valid approach may be the combination of both types of information, from high angular resolution maps, on the one hand, and from our 3D structure, on the other. Vertical planar cuts in the 3D distribution are given in Appendix at longitude intervals of 30 • . Our final map is available at stilism.obspm.fr in its entirety and online tools allow one to obtain reddening curves estimated through integration in the 3D opacity distribution along with rough estimates of the uncertainties on distances of the structures and reddening. We plan to update the maps and improve online tools when additional data are included in the inversion.

Principle of the hierarchical method

Theory

As already mentioned, the distribution of targets available for 3D inversion is far from ideally homogeneous due to several limitations and biases, essentially observational constraints inherent to each survey and to stellar types, and, most importantly, magnitude limits. As a consequence of limitations on magnitude, 3D ISM mapping is increasingly under-constrained at increasing distances, and, in turn, a given covariance function can not be appropriate simultaneously at small and large distances: e.g., a distance of correlation of, say, ∼20 pc may be convenient close to the Sun where bright targets are numerous and distant from each other by a distance of this order, but may become totally inappropriate 2 or 3 kpc from the Sun if distances between target stars become significantly larger because only the brightest ones can be observed, as it is the case for the surveys we are currently using. Reciprocally, a distance of correlation on the order of 100 pc will not correspond to an optimal use of the nearby targets and will smooth the nearby structures. The hierarchical method presented below is a possible approach to solve this problem, while keeping the full-3D approach.

The basic idea of the hierarchical method is to perform inversions in an iterative way, and to decrease progressively both the distance of correlation (or structure size) and the volumes containing the targets to be used in the inversion. In the course of this process, at each step with a distance of correlation ξ, all stars located in regions where the mean distance between them is larger than ξ are eliminated from the input target list and as 3D prior, the 3D the result of the previous inversion, i.e. the one performed for a larger ξ and larger volume. Doing so, constraints from the eliminated targets are used only indirectly by means of this prior distribution. In other words, little by little data, which do not add a useful constraint for the attempted structures' dimensions, are deleted.

In parallel, a second important change has been introduced in the frame of the hierarchical method, namely the use of metadata, instead of individual targets. Metadata are obtained by averaging extinctions towards targets contained within a given fractional volume (cell). The size of the cell at each step will be governed by the correlation length used for this step, i.e., first iterations 142 CHAPTER 11. PRINCIPLE OF THE HIERARCHICAL METHOD will use large cells and last iterations small cells, with sizes ultimately converging to the mean distances between targets in the Sun vicinity. An enormous gain is associated to the use of metadata, in the sense that it will considerably reduce the number of lines of sight at each iteration and consequently the computation time. The first iterations will be performed over a large global volume but a small number of large averaging cells, and the latest will use smaller cells but will be done only over a small volume close to the Sun. Such a reduction of the computational time is mandatory at the time of massive surveys and especially Gaia data.

Fig 11 .1 shows the target stars within 20 pc from the Plane: the target stars circled in the top-left corner are isolated, and obviously they cannot provide any useful constraint for structures of size 15 pc 3 , as required by the inversion program for a kernel parameter ξ = 15 pc. The circled targets are only an example, it can be seen that a large fraction of the targets represented (mostly those more than 250 pc away) cannot constrain such small structures.

In this case, we will start inverting only large structures of, say, ∼500 pc characteristic size, and, step by step, we will use the previous inversion results as prior distribution for the following inversion and eliminate the targets in distant regions of space. It means, for a m-step inversion:

• First inversion for structures of size ξ 0 pc using an analytical prior (or any 3D prior with structures larger than ξ 0 )

• For i=1,(m-1) ... Inversion for structures of size ξ i pc, with ξ i < ξ i-1 ...

• Final inversion for the smallest scales ξ m pc

The core of the inversion program itself is not different from the one used for the direct method, but for the hierarchical method, we change the input data, the parameters and the 3D prior at each step. At the end, we get a 3D map with a spatially-variable resolution. Following this procedure, the input dataset that is used at each step is produced from the same initial catalog but with a specific distribution, and it is important to construct metadata with a well-determined information. In case of structure size ξ, we need data distributed within a volume of size at least ξ/2, we need a number of targets sufficient in the cell to obtain a significant average, and we need realistic errors associated with the average distance to the cell and with the averaged extinction in the cell.

Implementation of the hierarchical method

Preparation of intermediate datasets (metadata)

From the total dataset of distance-excess of colour pairs we now have for each inversion step to build a data subset adapted to the chosen covariance length, with all cells containing a minimum number of targets (e.g. 12 in the first example below). These metadata are based on averages of actual data, and their use implies new estimates of the associated uncertainties. As we will see this is the most complex aspect of the whole procedure. 2017): input targets within 20 pc from the Plane are superimposed (black plus signs). Targets like those circled at top left will be eliminated along the hierarchical process, since the target density at their location is too small to contribute to the definition of small structures. They will be taken into account at the first steps only. Colour scale is like 10.9 -panel d)

IMPLEMENTATION OF THE HIERARCHICAL METHOD

The problem of uncertainty estimates for metadata We start with a given cell containing N targets. We replace the N targets by a metastar at an average location l C , b C , D C (generally close to the coordinates and distance of the cell barycentre) and characterised by an average colour excess excess of colour C computed as the mean of the N excess of colour values. It comes to mind to use the dispersion σ(excess of colour ) of excess of colour values among targets within the cell as the uncertainty associated with the metastar mean colour excess. However this is not correct and overestimates the uncertainty. This comes from the fact that in the same way the colour excess excess of colour for any sightline to a target contained in the cell is built over the whole path, i.e. including foreground cells, the information contained in the dispersion corresponds to the entire pathlengths from 0 to D. For this reason, the dispersion on the reddening measurements is the sum of the dispersion generated in the cell and the dispersion generated in front of the cell. As a result, in order to avoid overestimating the errors, we cannot simply use the dispersion among the data σ(excess of colour ), instead we must subtract from this dispersion the variance in the foreground cell that is crossed by the N sightlines. This is the source of complexity, since the variance computed in this way does not only depend on measurement errors, but also on measurements in the region in front of the cell. The general formulation is:

σ = σ C 2 -σ F C 2 + σ C 2 N objectincell (11.1)
where C (cell) refers to the considered cell and FC (ForeGround) refers to the cell just in front of C. N C is the number of objects in the cell. The first (and usually dominant) term is linked to the gradient of variance and the second is the simple statistical error associated with the average over the N targets. The way the uncertainty estimate is made has strong consequences in terms of cell geometries. As a matter of fact, at each step and for each cell one must use the colour excess dispersion in a front cell that is crossed by the same sightlines. As we will see, it implies two geometries that are used in parallel, the geometry of the cells used for the inversion, unique (we we call it the inversion geometry), and the geometries computed at each step for the error estimates only and that vary all along the computation (we will call them the intermediate geometry).

Cells shape An important choice in the building of metadata (or metastars) is the choice of the cell shapes for the inversion geometry. The main goal is to obtain metadata cells as regularly spaced as possible, and with similar volumes (for a given step), however the structure must be also compatible with the computation scheme. A simple choice could be cubic cells, since most computations within the inversion use cartesian coordinates, and it would to be easy to define cells of identical volumes and to compute the mean distance between our meta-stars. However it becomes impractical when we come to the point of calculating the errors as discussed above. Another choice could be to simply divide the space in cells defined by constant intervals in distance, longitude, and latitude. This choice is perfect to calculate errors, because all lines of sight to the stars in a given cell cross the same foreground cell, but evidently having constant distance, longitude and latitude intervals implies increasing distances along the ortho-radial direction and increasing volumes of the cells with increasing distance, which is opposite to our main goal. Keeping constant intervals in longitude and latitude and decreasing the radial dimension to keep a constant volume is also a unappropriated solution since the cells will become increasingly flattened.

At the end, I chose a solution that is based on constant radial distance intervals and variable longitude and latitude intervals in such a way the volume is roughly conserved in all cells. The geometry is shown in Fig 11 .2 and in the left part of Fig. 11.3 for the first, second, and third ranks around the Sun. As discussed in the previous section, such a geometry does not allow to estimate the variance in the cell, and and additional decomposition in cells with a different and adapted geometry must be recomputed and used at each step.

For the inversion geometry I start by selecting the mean distance U that I want between the meta-stars, and divides the 3D space in series of spherical shells, with widths U. If the maximum accepted distance is DMAX I divide DMAX by U and retain the integer Ns the closest to the ratio. Ns is the number of spherical shells. Then, each shell is divided in angular bins in longitude and latitude in order to obtain cells with volumes as close as possible to U 3 . This is obtained by dividing the perimeter of the shell in sections of equal length l as close as possible to U (again, since the number of cells is an integer, one can Metadata calculation in the cell After having chosen the cell shape [l, b, d], for each cell C the selection code extracts from the initial database the stars contained within the cell and simultaneously it extracts the foreground cell FC, using the same constraints for angular position but using a distance smaller by the quantity U. Note that, doing so, we do not use any uncertainty on target longitudes, latitudes, and distances. The nest step is to calculate for the subsample the mean distance and its associated error, the mean excess of colour and the variance on excess of colour. The following additional constraints are imposed:

• Every cell retained for the inversion must contain a minimum number of objects, sufficient to get obtain a statistically significant average.

• To be part of the inversion at a given step, a cell in a specific direction must have cells filled with targets in the same direction and closer to the Sun, i.e. ensuring a foreground without any observational hole

These constraints reduce significantly the useful volume in case of inhomogeneous databases. The reason for the second requirement is not only the need for homogeneous constraints, but the need to calculate errors associated to the metastar excess of colour, as explained above. The way these constraints are implemented is as follows (for an imposed minimum number of targets N in one cell): if the foreground cell FC does not contain N stars, then the cell C is removed from the inversion. This is not an optimal implementation of the second constraint because I could test at this step that each foreground cell contains the minimum stars number before accepting the background cell, but since most selection biases are functions of distance, I assume that if there are enough targets at a given distance, this is also true at smaller distances.

Final selection A final selection takes in account all the calculated metadata and verifies that each metadata has at least one other metadata closer than U. This selection is important because it suppresses possible far isolated cells. In Fig 11 .4 is illustrated why it is possible to have isolated cells; if there is a large concentration of stars located after a hole, it can provide some calculated metadata, because the foreground cell is not empty. As measured are limited in distances in the observational survey, these cases are quite rare: the stellar catalogs usually contains number of objects that decrease with the distances.

Example of metadata preparation and hierarchical inversion

In what follows is presented one of the several tests I did to guide and test the metadata calculations and the choices of the inversion parameters. I used the large dataset of extinction-distance pairs estimated based on spectroscopic observations with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) in China. The data I used are from the data release DR4 (Cui et al., 2012) Chapter 12

EXAMPLE OF METADATA PREPARATION AND HIERARCHICAL INVERSION 149

Hierarchical method and data quality

As in other inversion techniques it is difficult to estimate the influence of uncertainties associated with the data on the resulting distribution, globally and at each point in space. As a matter of fact, there are complex interdependencies between the error bars, the volume density of targets and the cloud clumpiness along the sightlines. This is true also for the hierarchical technique and, since the metadata are calculated differently at each step, it is important to understand how errors on input distances and reddening values influence the inversion at each different step. On the other hand, the step-by-step evolution brings additional information and sheds additional light on these influences. I used two distinct subsamples of the LAMOST DR4 data, the first one being the one presented in the last section (called ODD) and another set of data, completely independent and with the same number of data points (called EVEN). As their names indicate, the ODD-EVEN selection was very simply made from the initial catalog based on the line number in the file (ODD or EVEN number). Since the ordering was based on the location in the sky, the two datasets cover the same regions and correspond to random selections everywhere.

The goal here is to compare the results obtained with the two different datasets, from both direct and hierarchical inversions, and to study how the data uncertainties influence the quality of the results at the various steps of the hierarchical inversion.

Direct Inversion

I inverted the two ODD and EVEN datasets using the direct code, and made some tests. Inversions here were performed locally on our Mac server and took ∼ 20 days. Data with l = (152 • , 183 • ) were retained, with no limitations in latitude other than those of the survey. The inversion parameters were σ 0 0.9, ξ 0 50.0, σ 1 1.0, ξ 1 25.0. The EVEN inversion used 29359 stellar targets and the ODD one 29448.

In the input catalog, there are not threshold for the errors, but mostly associated relative errors on distances and on excess of colour have values lower than 50%. In Fig 12 .1 the histograms illustrate the relative errors distribution each step and understand the actual minimum size of the structures that can be inverted with this dataset at each distance.

HIERARCHICAL INVERSION FOR EVEN AND ODD SUB SETS155

To do so, I inverted the two EVEN and ODD datasets in parallel, using the same hierarchical technique for both. The parameters for the different steps are listed in Tab 11. 1. In Fig 12.4 and 12.5 we can observe the evolution of the two distributions and infer until which step the two results remain compatible (note again that the comparison has to be done only for the region well covered by data, i.e. between latitude -35 • and 0 • ). In particular we can see that the two separate inversions start to diverge at step 5, i.e for 60 and 50 pc kernels. The full computation of the 5 steps takes less then half an hour, i.e. it is considerably faster than the direct inversion.

As a conclusion, the tests with the hierarchical inversion show that it will be impossible to reach a resolution much better than 50 pc with this LAMOST dataset, even if one can expect a better performance for the ODD+EVEN combined catalog. However, one advantage of the hierarchical method is that the step 5 inversion should be reliable at ALL distances, thanks to the basic principles, something impossible to guarantee with the direct method (for this latter method, there may be artefacts at large distance). The difficulty of Local Cavity (or Local Bubble) mapping with the LAMOST data only The maps derived from direct or hierarchical inversions with the LAMOST DR4 dataset show Taurus clouds very close to the Sun, in contradiction with previous maps that all well reveal the cavity around the Sun, the Local Bubble. We have investigated this problem and believe it is due to the absence of target stars closer than 30 pc and also to large uncertainties on the distances (estimated from photometry). In the absence of constraints at small distances the inversion is distributing the absorbing matter measured towards the distant stars all along the lines of sight, including at very small distances. To test this hypothesis we made an additional inversion, this time including target stars from our own catalog located within 150 pc in the Taurus direction. Chapter 13

HIERARCHICAL INVERSION FOR EVEN AND ODD SUB SETS159

Hierarchical method and data characteristics

In this chapter I present a hierarchical inversion based on a combination of extinctions from LAMOST DR3 (190 858 targets) and APOGEE DR14 (7 146 targets). Everything was done before the Gaia Data Release 2 (DR2), so we used either Gaia DR1 (TGAS) distances or photometric distances estimated with the Gaia DR1 calibration. We also used in addition our old catalog, the one used in [START_REF] Capitanio | Three-dimensional mapping of the local interstellar medium with composite data[END_REF], which contains a combination of data with photometric or Gaia DR1 parallax distances. The inclusion of this catalog is important because of the numerous stellar targets at short distance and within the Local Bubble: other catalogs have only a few targets at short distance. Moreover, extinctions deduced from Bayesian statistics tend to have increased biases for small extinctions, while the Stromgren or Geneva photometric calibrations that form the majority of the old catalog provide accurate data for small extinctions and individual targets. I analysed again the Taurus region, well covered by the LAMOST survey, and in order to be able to compare with the other inversions.

Metadata generation

Every metadata generation must be adapted to the set of stellar data. Target distances vary from one dataset to the other, therefore limits in distances for the cells must change accordingly to adapt to each dataset distribution. Here we study a small region, because our goal is to identify a convenient strategy for the following inversions with more data and future Gaia accurate parallaxes. Another important aspect is the choice of the quality criteria requested to enter the database to be inverted. In the context of our hierarchical method, we do not use errors on the distance in the calculation of metadata, i.e. only mean distances are used to locate a star in a given cell. Therefore, if we want a minimum accuracy on the distances we must impose a criterion at the beginning during the choice of the targets to consider for the inversion, and reject data in catalogs that do not possess the requested quality. For the tests shown in this section, we did not add additional constraints on distance or extinction and considered that the catalogs were of sufficient quality. A test on LAMOST data shows that except for a few percent of the targets the relative error on the estimated distance is smaller than 30% (note that for the 162 CHAPTER 13. HIERARCHICAL METHOD AND DATA CHARACTERISTICS posterior inversions with new LAMOST DR4 we will impose additional quality criteria). For APOGEE data, we rely on the distance estimate made by Carine Babusiaux, who made series of tests for their quality. For the old catalog, we also rely on the quality of the catalogs. I select stars from the APOGEE and LAMOST catalog in the Taurus direction, using the following geometrical criteria: The strong increase of longitude and latitude interval widths at short distance ensures a minimum number of stars around the Sun to be part of the closest cells. As a matter of fact, using pure limitations in angles reduces too strongly the allowed volumes (see, e.g. Fig. 11.8). The total number of stellar targets was 201 079 objects, and I made metadata with mean excess of colour values in cells having mean distances of 200,100,80,70,60,50,40,30,20,15 pc. These metadata were maintained in the inversion process only if they contained at least 12 targets, excepted for metadata with cells of 15 pc, for which the limit was decreased to 5 stellar targets. In Fig 13.1 and 13.2 are shown the histograms of the distances of the metadata at the various steps. The double peaks are due the existence of changes in the stellar selection criteria as a function of distance. The second bump, at larger distances, is due to intrinsic limitations in the stellar catalog. In Fig 13 .3 we can observe the metadata projected on the sky, in the Taurus region. The colour scale indicates the reddening. There are some irregular patterns in the sky projection, they are consequences of our cell shapes and of the survey's observational fields. For the large cells of the first steps, the projections extend to all the Taurus clouds, but for the small cells of last steps only those close to the Sun contain enough targets to remain selected. As a consequence only the closest clouds are represented in the metadata.

•

Inversion and results

I made the hierarchical inversion in 10 steps, corresponding to structures of sizes decreasing from 400 pc to 30 pc, and using the exponentially decreasing analytical prior at the beginning (the length scale is still 200 pc, that corresponds to a value above the dust scale height). The steps for the inversion are listed in Tab 13.1. Some examples of the evolution of the 3D distribution are shown in Fig 13 .4, for steps 5, 6, 8 and 10. In these figures it is possible to observe how structures are increasingly detailed during the progression of the inversion steps. The results are encouraging, since there is apparently a coherent evolution at each step, and the inversions have good χ 2 , which confirms a general agreement between our statistical data and the modelled distribution after convergence. The Local Bubble is apparently very strongly shrunk in these Taurus maps: indeed, at step 10, the inversion predicts some matter closer then 50 pc. This is closer than for all previous maps from direct inversions. One explanation is 2017) with superposed isocontours from hierarchical inversion step 10 bis. Clouds beyond 500 pc could not be present in the old map due to lack of targets at large distance.

the dominant role here of extinctions deduced from Bayesian techniques and we know that they may over -estimate excess of colour for the smallest values close to the Sun, or have large error bars compared to other methods like Stromgren or Geneva photometry. To test this hypothesis and reinforce the weight of individual measurements with good accuracy for nearby stars, I added to the metadata of the last step all individual data from the old catalog corresponding to distances lower than 50 pc, well adapted for weaker extinctions. This new inversion is in 13.1 and referenced as STEP 10 bis. It can be seen in Fig 13.6 (left top, and left bottom) that the step 10bis distribution has effectively a wider cavity close to the Sun, as if matter had been pushed away at larger distance. This shows that our hypothesis is correct. However, it is also probable that using metadata is not a well adapted technique at short distance, unless one decreases even more number of objects per cell (one target per cell), which ultimately is equivalent to the direct inversion.

In the same figure is a comparison with the Capitanio et al. ( 2017) map in the same plane (right panel): also show at top are the targets used to generate this previous map. As can be seen, there are considerable differences (however, comparisons are valid only for negative latitudes between -5 • and -30 • ): first, all in the old map, in this direction there are two concentred clouds 200 pc and 300 pc. Any clouds could be present in the [START_REF] Capitanio | Three-dimensional mapping of the local interstellar medium with composite data[END_REF] map because there are not targets behind 1000 pc.

Chapter 14

Influence of dynamics parameters

The hierarchical method requires to build efficiently metadata from the stellar dataset, but also to choose adequate inversion parameters. This latter aspect is quite challenging, because the optimal choice depends on a complex way on the dataset characteristics and what we want to extract from the data in each region. As explained in the introduction on the inversion, the way the absorbing matter is distributed in 3D space is mainly governed by the four parameters ξ 0 , ξ 1 , σ 0 , σ 1 . ξ 0 , ξ 1 act on the minimum sizes of the structures, as illustrated for a very simple case in Fig 8 .1, and σ 0 , σ 1 control the relative influences of the prior and the data, as illustrated in Fig 8 .2. The previous inversion for example is not optimised, because apart from concentration of matter in the clouds there are completely empty spaces in the regions where we have no metadata. This is not realistic, because without data, the inversion should keep the prior values, i.e. a dust density decreasing with the distance from the Plane.

In Fig 14 .1 is represented the reason of this anomaly: for this inversion we have used relatively high σs, as we had previously done for the direct inversions. However, during the first steps of the hierarchical inversion with very wide cells and accordingly very large ξ values, the large size of the modeled clouds and their influences at very large distance from their cores, combined with the allowance for very strong departures from the prior (high σ) has permitted solutions with empty regions along the Plane where there are no data. Since these regions become the new prior and there are no data to influence them at the next steps, they are kept empty until the last steps, whatever the final ξ value. Clearly, there must be some better adaptation of the σ parameter to the fist steps.

Following this idea, I tested exactly the same inversion as previously except for a change of the values of the σ parameters. The results are compared to the previous results in Fig 14 .1. The result of the inversion is also shown towards the directions opposite to Taurus, where there are no data, in order to show clearly the shape of the prior. The comparison indicates that a low value for the dynamic parameters is more appropriate for the first step in a hierarchical inversion.

CHAPTER 14. INFLUENCE OF DYNAMICS PARAMETERS

LAMOST after GAIA DR2

In April, the Data Release 2 of Gaia was available, and we crossmatched the most recent LAMOST dataset available, i.e. LAMOST DR4, with the Gaia DR2 catalog, to substitute the photometric distances with distances derived from the Gaia parallaxes. In this section I show the changes due to the new distances and the new dynamical parameters, using the new LAMOST DR4 dataset.

This inversion was done in ten steps similar to those in previous chapter. In Tab 14.1 are listed the used parameters. The inversion was now done both with the former σs and σs lower than in the previous tests. In 4 there are some differences, these are mainly due to more accurate distances. For step 10 at l=160 • , the structure previously located at 600 pc is now clearly separated in two parts, a dominant one at 400 pc and a less dense, more distant one. As we will see in Chapter 22, the elongated cloud at 400 pc is the well-known California complex. The cavity between ∼100 and ∼200 pc is confirmed, although smaller. More generally, all nearby structures are now smaller or more fragmented. This is a very positive sign, demonstrating that the data are more coherent. This is clearly due to the more accurate parallaxes.

LAMOST AFTER GAIA DR2

Part V

Full-sky hierarchical method applied to Gaia DR2 extinctions Chapter 15

Application of the hierarchical inversion to full-sky data

The main interests of the hierarchical method are its adaptability to massive, full-sky datasets and to inhomogeneous target distributions (in practical, mostly distance-dependent target densities). These are the characteristics of Gaia-based data, namely present and future extinction estimates and future DIB measurements. The series of tests presented in previous sections and limited to a specific region has been done in this perspective of extending the inversion to full-sky data.

The final exploitation of the future Gaia DIB catalog, in the context of ISM studies, is a DIB carrier 3D map based on full-sky measurements of the DIB equivalent width. As Gaia RVS spectra are not yet available, here I tested a full-sky hierarchical inversion of dust colour excess excess of colour derived from Gaia DR2 data. We did not use extinctions made publicly available from the Gaia website since they were determined from the broad-band photometric measurements of Gaia only; that caused a strong degeneracy between stellar temperature and extinction determinations [START_REF] Arenou | Gaia Data Release 2: Catalogue validation[END_REF]. Instead, we used a new catalog of extinction estimates computed by C. Babusiaux (paper in preparation). The extinction A 0 is converted into colour excess excess of colour using a simple proportionality A 0 =3.1 excess of colour. The extinction is deduced from the combination of Gaia and 2MASS photometry. The inclusion of 2MASS eliminates the degeneracy.

The main characteristics of the catalog we have used are listed in Tab 15.1. Most important for our purpose, it is limited to targets with relative uncertainties on the parallax lower than 20%, a point that is essential for mapping. This limitation, in turn, implies relatively bright targets, and explains why 94% of stars are closer to the Sun then 3000 pc, even if the maximal distance reaches 17 kpc. A small fraction of the sky is not covered -see Fig 15 .1 -but in theory with the hierarchical inversion this problem is less important, especially because the resolution will remain limited in those directions and no spurious features can be created where there is no information. Moreover, these small holes are at high galactic latitudes, while the Galactic plane is extremely well covered, and, because the Plane is the richest region in dust, these holes should not impact the results.

• 160 pc, with metadata calculated in distances slices of 80 pc, max distance 2500 pc

• 100 pc, with metadata calculated in distances slices of 50 pc, max distance 1750 pc

• 60 pc, with metadata calculated in distances slices of 30 pc, max distance 1400 pc

Further steps are in progress, however will not be entirely computed before the end of preparation of this document. As we have a huge quantity of input data, the production of metadata was slow, so I imposed some specific limitations. The first limitation is on the altitude above/below the galactic plane, because during the inversion I do not use data that are too far from the disk, is it not useful to produce them. The second limitation was on the extinction uncertainty. Input targets were selected in the DR2 catalog with a threshold of 10% on the relative parallax error, so I have very precise data in distances. I impose then for excess of colour lower then 0.3, I accept only data with absolute error lower then 0.1; for excess of colour higher then 0.3, the relative error must be lower then 20%. To get only the best metadata I selected only cells with at least 50 objects par cells.

Inversion

To make this inversion I started with an analytical prior distribution, with an opacity decreasing exponentially at increasing distance from the Plane. Our motivation was to obtain results with only Gaia data. I used only the Gaussian correlation function:

C(x) = σ ξ1 2 exp -x 2 ξ 1 (15.1)
and not the two-term function C 1 8.13 used in all the previous inversions that contains a hyperbolic cosine. The tails in the C 1 cosh term are very important for the mapping of small structures, i.e. when we use small correlation distances (∼10pc), because it allows to represent two phases of the clouds, a compact phase for the dense central part and a more diffuse external part. Here however, for all the first steps of the hierarchical inversion with large correlation distances, the cosh term introduces very extended tails and imposes a correlation between very distant points that has any physical meaning.

As our errors on excess of colour are really small, I kept the additional error of 0.01 mag, as in others inversions.

First step -800 pc For the first step 879 cells were selected.

• σ 1 = 0.3 and χ 1 = 400 pc

• Beginning χ 2 = 41.18 • End χ 2 = 2.14 • CPU time = 210505 • Threads number = 6 15.2. INVERSION • Real time = 8h57m
Second step -400 pc For the second step 5223 cells were selected.

• σ 1 = 0.4 and χ 1 = 400 pc

• Beginning χ 2 = 35.05 • End χ 2 = 2.20 • CPU time = 198959 • Threads number = 6 • Real time = 11h 48m
Third step -200 pc For the third step 23488 cells were selected.

• σ 1 = 0.4 and χ 1 = 200 pc

• Beginning χ 2 = 17.59 • End χ 2 = 1.50 • CPU time = 1741599 • Threads number = 6 • Real time = 4d 14h 35m
Fourth step -160 pc For the first step 35610 cells were selected.

• σ 1 = 0.5 and χ 1 = 160 pc • Beginning χ 2 = 24.70

• End χ 2 = 1.28 • CPU time = 5911498 • Threads number = 6 • Real time = 15d 15h
Fifth step -100 pc To diminish the computational time, I separated the metadata in two parts, centre and anti-centre, and I merged the results as explained in Section 10.9. Centre inversion was done with data from l = (-95 ; 95) and 35492 targets were selected; anticentre was inverted with data in the longitude interval l = (85; 275), and 26140 targets were used.

• σ 1 = 0.6 and χ 1 = 100 pc • Beginning χ 2 centre = 9.75, anticentre = 13.52

• End χ 2 centre = 1.08, anticentre = 1.09

• CPU time centre = 4026913 ; CPU time anticentre = 1880766

• Threads number = 6

• Real time centre = 11j 4h, real time anticentre = 6j 10h TO FULL-SKY DATA Sixth step -60 pc Also in this case I spitted the inversion in four parts, for the four quadrants on the galactic plane. First, second, third and fourth quadrants contains respectively data in longitude intervals [-5

• : +95 • ], [85 • : 185 • ], [175 • , 275 • ] and [-95 • : 5 • ].
The targets belonging at these intervals and used for the inversion are respectively 27416,17787,19320,29789.For these inversions the calculation time is higher than expected, and also too high by comparison with the computational time in the previous step at 100 pc. We believe that the way the work-space in our computer was configured was not adapted. In the future, the same inversions with other computers and the same algorithm will be performed to discern the origin of this problem.

• σ 1 = 0.

Results

The results are really encouraging, because the strong point in this technique is the suppression of non-realistic features (given the resolution achived at each step), and it seems that the objective is reached. Looking at the Galactic plane, at first steps the matter is located as as a semi-ring around the Sun, with a bloc in the Galactic centre direction - While the first steps show extended blobs centred below the Plane, in further steps there are important fragmentations into smaller structures, e.g. between step 3 (200 pc) and step 4 (160 pc); starting with steps 5 and 6, the locations of the cloud cores are stabilised, but they become thinner: the cavity between 200 and 400 pc near the plane is emptier, the structure at 100 pc is separated in two smaller cores. Note that for this figure the final resolution is 60 pc, still above the one achieved for the same area after the previous inversions that were spatially limited to Taurus (25 pc).

RESULTS

181

In Fig 15 .6, there are some examples of distributions in vertical planes for the step 6. The original analytical prior is not discernible, and this at all longitudes. This reflects the fact that the initial dataset is really homogeneously distributed and the metadata fill entirely the space where we are computing the extinction. This is the strenght of Gaia data over ground-based surveys.

Errors estimation

For the hierarchical method it is simple to estimate errors on distances to the structures, because it is intrinsically related to the metadata size and sampling. Based on the histograms' bumps in Fig 15 .2, I can assume that after step 6 all structures closer to 1000 pc have distance errors on the order of 50 pc, those between 1000 pc and 1500 pc an error of 80 pc, and between 1500 and 2000 pc an error of ∼ 100 pc.

At variance with the case of distances, any estimate of errors on the reddening excess of colour is challenging because in this case we have different input data set. A possibility could be to calculated the mean difference from excess of colour of metadata and the results. Another possibility is to implement a test as in Chapter 12, selecting subsample and inverting step by step to understand if the dataset contains some bias. Moreover, I could change the geometry of our metadata, for example shifting the angles, and observe potential changes. All this possibility are interesting, but this investigation it is too slow for my 3 years thesis.

Comparison with other maps

The same dataset with exactly the same targets and extinction values has been used by our collaborator Jean-Luc Vergely to enter a different type of inversion. This newly developed mapping technique (here after called technique-2) is not a full 3D like the one I handled: the inversion is hierarchical but with two different computations at each step of resolution: the first part considers each line of sight individually and builds series of reddening profile, then during the second part an azimuthal average is performed to smooth the structures. His map is computed directly in extinction A 0 and not in excess of colour but as we said the difference is simply a scaling factor. This technique is completely independent, and it is interesting to compare a different map build with the same dataset. In Fig 15 .7 are shown the Galactic planes distributions for the Vergely map with final resolution 25 pc and for step 6 of our inversion.

The figure shows that globally the maps are in very good agreement, taking into account that our 60 pc resolution is poorer than the 25 pc resolution of the second inversion. Most importantly, some of the features looking like fingers of God in the technique-2 map are not present in our map. This is very important, since it demonstrates that our full-3D hierarchical method may provide a safetycheck for other non full-3D inversions where radial artefacts remain.

While, as said above, our step 6 hierarchical map and the technique-2 map are similar, the main difference is close to the Sun in the so-called Local Bubble area. This region does not appear empty in our step 6 map, while it is a visible cavity in the other map. There are several potential reasons for this difference and their investigation is still in progress. Maybe metadata boxes are too wide, or it is due to my strict condition for the excess of colour relative error. Another (likely) possibility is that it is due to the four separate inversions for four complementary regions I did, since I made the separation based on the coordinates only. Boxes close to the Sun do not contain enough targets to really constrain the small opacity and the prior distribution forces the filling near the Sun. For each inversion I should have included all targets close to the Sun until a given distance whatever the coordinates, as done for the Taurus region.

Rezaei [START_REF] Kh | Detection of the Milky Way spiral arms in dust from 3D mapping[END_REF] have published a large scale map based on APOGEE DR14 measurements; they use a non-parametric method to infer the dust distribution in 3D space (Rezaei Kh. et al., 2016); as it is based only on APOGEE DR14 they map a small part of the Galactic plane. Fig 15 .8 displays their map with our last step map superimposed. Our map is dedicated at the local interstellar medium, on the contrary their objective is to study the spiral arm structure in the galaxy, but in the zoom (bottom of the figure) it is possible to compare our results: the filaments elongated near the Sun are coherent in two maps, and in third quadrant our map find a cavity and a new group of clouds at 1000 pc which have a counterpart in their map. For the filament in the direction of the Galactic centre, we find it located at 1000 pc, but their map suggest a more distant wall of matter. This discrepancy could be caused by the fact that this direction is at the boundary of the APOGEE target distribution over the sky, or there is a bias in this direction for the Gaia parallaxes. Others maps with different datasets or using the new Gaia calibration shall clarify this point.

Conclusion and perspective

The hierarchical approach for full 3D mapping seems to be a satisfying solution adapted to massive datasets and works well, as shown by comparison with maps made with other techniques. It is also particularly well adapted to catalogs of targets uniformly distributed over the sky: the comparison with the direct inversion from [START_REF] Lallement | Threedimensional maps of interstellar dust in the Local Arm: using Gaia, 2MASS, and APOGEE-DR14[END_REF] that was largely based on APOGEE DR14 photometric data with very limited and inhomogeneous sky coverage demonstrates well that the spatial uniformity provides better reliability of the structures.

On the other hand, the metadata calculation is still too slow and not optimised. Using smarter algorithms with faster metadata calculation, it should be possible to create different metadata set and inverse them, to better understand the sources of biases in the maps due to the metadata and to better constrain the structures locations. Another important study to be done is varying the choices for the steps and resolutions, and check whether the iterations converge toward the same structures, to better assess the hierarchical method reliability. This will be possible with faster computers.

As we have seen, it can be used to detect artefacts in maps based on other techniques, especially radial features that are otherwise very difficult to dismiss.

Chapter 16

First 3D map completely based on the inversion of DIB measurements

In the perspective of a large Gaia DIB dataset at Data Release 3, it is important to understand how such data can be used for 3D mapping and what can be learned from these maps. Evidently, an inversion based on a given DIB only will give us the 3D distribution of the interstellar species responsible for the absorption. On the other hand, since all DIBs are at least partially correlated with the amount of IS matter, DIB distributions should be very similar to dust or gas distributions. This is why DIBs may also potentially be used a an additional tracer to be used e.g. in conjunction with extinction (this has been already presented in Chapter 9.

We did a first test with data from the SDSS/APOGEE data release 14 (DR14), because this data release has been accompanied by large excess of colour catalogs, based on different statistical techniques and because the DIB located at 15 273 Å has been studied extensively by my colleague M. ElYajouri. She has fitted the spectra and extracted the DIB with high precision, and these absorptions, after conversion into extinctions, have been used to improve extinction maps, as I have shown in Chapter 9. The idea of the present chapter is different: we have performed an inversion for the same stellar targets, using the excess of colour provided by photometric calibrations on the one hand, and the DIB absorption (converted into extinction with a simple scaling factor) on the other hand.

Our goal is to compare the maps to understand the difference between the location of the dust (through the reddening) and the location of the macromolecules causing the DIB absorptions. At the same time such comparisons are additional tests of our inversions and we infer whether our inversion technique needs particular adaptations in case of DIB-absorption inversions.

Description of the dataset

Source of extinction values There are several extinction catalogs associated with the APOGEE DR14 dataset; the APOGEE team istelf proposes different extinction estimates. I used the so-called BPG estimate based on the

INVERSION OF DIB MEASUREMENTS

Starhorse technique [START_REF] Santiago | Spectrophotometric distances to stars: A general purpose Bayesian approach[END_REF][START_REF] Queiroz | StarHorse: a Bayesian tool for determining stellar masses, ages, distances, and extinctions for field stars[END_REF].1

Target distances The BPG catalog was crossmatched with Gaia DR1 to extract stellar targets with Gaia parallaxes; I compared the relative error on distance based on parallaxes with those based on photometry and in used in each case the one with the smallest relative error.

Conversion of DIB data I used the full catalog of 120 362 stars with a DIB measurement and fitted the relationship between the DIB equivalent width and the extinction with a simple linear relation -Fig 16 .1:

E (B-V ) = EW 0.063 * 3.1 (16.1)
This conversion factor was used for all DIBs.

Inversion Because the total number of targets is large, in order to reduce the computation time I made the inversion in two parts as in Chapter 10.9: the centre-inversion was done with all targets in the galactic longitude interval (0 • : 145 • ) and the anticentre-inversion used targets in the galactic longitude interval (135

• : 360 • ).
Sky coverage of DIB-extinction targets Fig. 16.2 shows the location of the APOGEE target stars used for the inversion. It can be seen that the sky coverage is very limited and very far from uniform. This is extremely important here: it implies that the derived 3D maps will be very limited and very far from complete, and they will not be appropriate to any astrophysical use: on the other hand, since the DIB and extinction inversions are made exactly for the same targets and suffer from the same limitations, we can use the two maps for our own comparisons.

Comparison between the map based on DIBs and the map based on extinctions

We warn again here that the inverted maps are not reliable interstellar medium distributions. A 3D inversion needs a dataset as uniform as possible and here the target distribution is far from reaching this requirement: the data are grouped into regions of several degrees width with large empty regions between and almost no data far from the galactic plane. The real interesting result here is the comparison between the reddening per parsec distribution derived from DIB absorption and the one derived from extinction. Both maps reveal structures in the Plane that are very roughly distributed in the same way, however there are marked differences. E.g. there are some similar structures such like the filament at 1000 pc toward the Galactic centre, or the horseshoe structure in third quadrant between x=[-800, -400] pc and y INVERSION OF DIB MEASUREMENTS [200,800] pc, but there are very different cloud distributions in the longitude interval of [60 • , 90 • ]. Clearly the data sampling and the uncertainties on the two quantities are such that the cloud locations are not very accurate.

To help the comparisons isocontours were derived from the DIB-based distribution and they are superimposed on the extinction-based distribution in Fig 16 .4. The figure shows that in general isocontours based on DIBs absorptions correspond to wider structures, however with smaller dense cores. This suggests that DIB carriers do not follow exactly the dust grains but more numerous in cloud envelopes and less numerous in cloud cores. This , in fact, corresponds to the results of studies of specific regions (e.g. DIBs in the Barnard 68 cloud, see Elyajouri et al. (2017a)). Fig. 16.5 shows the dust and DIB matter distributions in vertical planes containing the Sun. For some of these planes the two distributions are very different (e.g. the l=90-270 • Plane) , for others the main structures look similar (e.g. the l=135-315 • Plane). This suggests that the combination of data distribution and data quality is not sufficient to perform maps with good significance. On the other hand, a striking result is the presence of DIB carriers in the Local Bubble at high altitude above or below the Plane, while the map based on the extinction reveals a completely empty area. This is probably not related to the target distribution very surprising and needs further investigations with other DIBs.

Comparison of input extinction and DIB data for series of lines of sight

On order to understand the source of the marked discrepancies between the two maps and especially to determine whether the results for the Local Bubble are really constrained by the input data or are due to the inversion process, we have directly compared the input data in several regions. In Fig 16 .6 is shown how excess of colour varies with distance at various different latitudes and for the longitude l=90 • . The general trend is that that on the plane DIB carriers and dust follow each other, but at higher latitude there are a number of high values for the DIB carriers. This would be compatible with the hypothesis that absorbing macromolecules are more closely linked with the gas distributions than with the dust grains. My colleague M. ElYajouri is currently reaching similar conclusions about the DIB APOGEE carriers with others analyses.

Conclusion

This is only a first test, but it returns some important information. First, to convert a DIB EW into an extinction we shall be very careful about possible variations of the ratio between the two quantities that may vary from one direction to another, in longitude and latitude. The future map based on Gaia DIBs will be very interesting because the target distribution will be more regular and the map itself will be more reliable.

We have used in Chapter 9 APOGEE DIB absorptions converted into extinction and, for the inversion, we have allowed for a very large associated uncertainty. This uncertainty can account for the DIB to extinction ratio variability. The addition of this dataset has added information about the matter distribution, but in this case it was a small fraction of the full dataset. If we want a pure DIB carriers distribution we need both good DIB measurements -as it is the case for the ElYajouri catalog -and better targets distribution. In the case of the Gaia DIB and the DR3 catalog, both requirements will be reached.

To improve the APOGEE DIB map in the context of the current catalog, it could be interesting to study the EW/ Av ratio for different ISM environments. Moreover, for the DIB-based map a new analytical prior could be introduced, with a different scale height and/or a different opacity on the galactic plane. Similar tests shall be done in preparation of the pure Gaia DIB.

Chapter 17

To the 3D kinematic

The position of clouds on the sky and their distances are not sufficient to have a detailed knowledge of the mutual relations between clouds. In fact, in order to understand the origin and evolution of a system of clouds, it is important to know also the velocities of the structures. The kinematics of the cloud, that is the set of the global velocities of the particles, is an information that we can obtain from the deviation from the central position of the interstellar absorptions, due to the Doppler effect. I have not done a study of the visibility of Gaia's DIB as a function of its relative velocity with the star in the background, because with GOG simulations it has not been possible to modify the relative velocity between star and interstellar absorption; however we can predict that knowing the theoretical profile of the DIB it will be possible to encode a fit profile with "multi-clouds" analysis as we did for gas lines. DIBs in general are not optimal for studying kinematics because they are very large absorptions, so it is difficult to distinguish the difference between various velocities (Puspitarini et al., 2015): however, they can be used effectively for very different velocities, such as for the different arms of the spiral. I coded a fit profile for the sodium and potassium gas lines with a Python code, adapted for hot and cold stars, so as to have star parameters for all Gaia DR3 spectra; I studied the Taurus nebulae, using stellar spectra recorded with NARVAL and ESPaDOnS in the frame of dedicated observing programs, already performed before the beginning of my thesis and/or continued during the last years. Then, we compared the results of the resulting radial speeds with the radial speeds corresponding to the CO emission lines in the same directions; I also used the series of observations in a synthetic way and assigned to different clouds at different distances their own speeds.

The Taurus clouds complex is located in direction of the Taurus constellation, below the Galactic anticentre, between galactic longitudes 150 • and 180 • and galactic latitudes -5 • and -50 • ; it is very well known as a conspicuous emissive structure in CO radio bands, as it is shown in

NARVAL and ESPaDOnS spectra

Stellar spectra used for the atomic lines profile fitting come from two twin instruments: ESPaDOnS (Echelle SpectroPolarimetric Devicefor the Observation of Stars) and NARVAL, respectively available at the Canada-France-Hawaii Telescope (CFHT, Mouna Kea Observatory) and the Telescope Bernard Lyot (TBL, Pic du Midi Observatory). They are two high resolution (∼ 76000) spectro-polarimeters, whose first scientific motivation is the measure of stellar magnetic fields. Here, we used them in their spectrometric mode.

Spectra were measured partially on purpose for this research and others were available on the database Polarbase; PolarBase spectra are downloadable1 in ASCII format. I selected only hot stars to avoid complex stellar spectra and faciliate the extration of IS lines. All spectra are in the heliocentric frame.

Profile-fitting and measurements of radial velocities

The implemented profile-fitting code is based on the scipy optimisation packages from the Python software. The absorption lines are modelled as Voigt functions, with for each cloud three free parameters: temperature [K], line center position (or cloud radial velocity) [km/s] and optical thickness of the absorber. Each 202 CHAPTER 17. TO THE 3D KINEMATIC Particular cases among the various fits For V * AA Tau and TYC 2397-44-1 spectra, which show clearly additional stellar absorptions, I did not calculate a stellar synthetic profile, but only added "by hand" a Gaussian component to the fit. The results of these fits are uncertain. For TYC 2864-514-1, HD 279953 and HD 27923 I allowed for 5 absorbing clouds, but only in the TYC 2864-514-1 spectra the fitting code converges with five components. For 2MASS J04282605+4129297, I constrained the fit within -10 and +50 km/s to avoid the stellar components in the bluer part of the spectra.

I show some examples of fit results in Fig 17 .3. The whole set of figures showing the fits are in Appendix B with the Table of the fit results. The spectra are in the heliocentric reference frame (more precisely the BSR, see below), and fits are done in this reference. Note that, after the fit, all velocities are transformed to be in the same system as CO observations, i.e. the LSR frame in its kinematic definition (see also below).

Velocity reference frames Ground-based optical observations use the socalled barycentric standard-of-rest (BSR) that considers the barycentre of the Solar System as the reference point. Since the difference between barycentric and heliocentric velocities is extremely small and negligible in most cases, the BSR frame is also often referred to as the heliocentric standard-of-rest (HSR) frame.

For objects very far from the Sun, the peculiar solar motion with respect to the general quasi-circular motion of Milky Way stars and gas in our Galaxy corner is taken into account and removed to obtain the radial velocity in the Local Standard Rest (LSR) frame. This is the commonly used frame for radio velocities, in particular the CO velocities used in our investigation. The difference between the LSR and BSR velocities depends on the position on the sky defined by Galactic coordinates glon, glat, and it is obtained from the following calculation: w1 = cos(glon) cos(glat) w2 = sin(glon) cos(glat) w3 = sin(glat) glon sun = 56.1602 π/180 glat sun = 22.762 π/180 sun1 = cos(glon sun ) cos(glat sun ) sun2 = sin(glon sun ) cos(glat sun ) sun3 = sin(glat sun ) δ v = (w1 sun1 + w2 sun2 + w3 sun3)•20

i.e., it assumes that Sun moves at 20 km/s towards (glon, glat)= (56.1602,22.762). I converted all interstellar medium absorption velocities into LSR velocities instead of converting CO velocities into BSR ones, because it was simpler to change several individual values than a full spectral cube.

3D map in the Taurus region

In this section, I show some vertical cuts in the opacity map produced by Jean Luc Vergely, that I presented in Chapter 15. Superimposed are the lines-ofsight to the analysed stars, and the observed velocities. The colour scale, mag per pc, is the same for all figures and green, yellow, pale orange, and reds 204 CHAPTER 17. TO THE 3D KINEMATIC isocontours lines are respectively (0.005, 0.002, 0.001, 0.00043, 0.0002) mag pc-1. We draw the attention to the fact that, here, the colour scale does not refer to excess of colour/pc, but A V /pc -different from the other maps in the thesis that I produced by inversion. Since we consider that extinction and reddening are simply proportional, the maps are not different.

Following there are a series of figures with annotated velocities: these are the velocities assigned to the structures as suggested by the whole set of stellar velocities and the geometry of the lines-of-sight. They were derived from logical deductions, and not from automatic computation. We do not have a uniform distribution of stellar targets for the fit profile and more numerous and accurate assignations will be given in future thanks to new absorption data.

CO velocities maps

We used 12 CO J= 1:0 observations at 115 GHz from the CfA survey of the Galactic plane [START_REF] Dame | The Milky Way in Molecular Clouds: A New Complete CO Survey[END_REF][START_REF] Dame | A Large Extension of the CfA Galactic CO Survey[END_REF]. For Taurus the survey is based on a 0.125 • x 0.125 • Cartesian grid and the LSR velocity step is 0.65 km/s.

In this section I thoroughly analyse the region between 155 • and 180 • using our 3D extinction maps, the CO emission spectral maps and the spectral information on interstellar potassium absorption to assign position and kinematics to the interstellar clouds. My decomposition of velocities for CO is based on a work contained in the thesis of Quentin Remy, in particular his Fig 12 (private communication), pag 18.

Comparing our 3D map, the atomic absorptions and the CO emissions it is possible to identify molecular clouds positions and surrounding atomic gas velocities.

Main Taurus

Main Taurus is a complex cloud from 178 • to 160 • in longitude and from -3 • to -20 • in latitude. It is characterised by velocities from 4 km/s to 10 km/s. It is closer than California, and I tried to identify both the beginning and the end of the complex thanks to the spectra of stars at different distances and the 3D map. In particular Fig 17.15,17.14,17.12,17.11,17.10,17.9,17.8 are the vertical slices in the map, and I can use them to understand the evolution in distances. It is evident that in 3D there are various structures in these directions.

In Main Taurus direction we have a lot of targets but all closer than 500 pc. In Fig 17 .24 and 17.24 are shown velocities and distances for stellar targets in this region, globally and separated for the different velocities. In the central core of the cloud (between 175 • and 165 • longitude) I found several absorption components; for stars at distance lower than 176 pc only a component is present, but for more distant stars than this value I found two components, coherent with the range. In direction from 167 • and 162 • , there are four stellar targets and they have wide range of distances (from 176 to 500 pc), but only one component.

From Fig 17.18 and 17.19, there is a coherence with the higher velocities around 10 km/s for these longitude as in

South Taurus

Properly called South Taurus Clouds have CO velocities from 5 to 15 km/s, and are located between l = (175

Perseus

Perseus Cloud is characterised by a velocity interval in CO from 0 to 8 km/s, in l = (162, 157) and b = (-25, -20) and we have four stellar targets in that region.

In Fig 17 .21 there are slices to understand: the so-called Perseus cloud in CO is actually two clouds, first one between 150 and 200 pc ("Near Perseus") and the second one from 260 and 310 pc ("Far Perseus"). The more distant cloud show its core in Fig 17.9,, but (-25, -15). From -20 and -15, for the CO classification the emission from 0 to 8 km/s belongs to the Main Taurus, but is is more coherent to associate it with "Far Perseus".

Auriga

Auriga Cloud is characterised by a velocity interval from 0 to 6 km/s, near the Galactic Plane. Its position on the sky is longitude (170 • , 163 • ) and latitude from -5 • to -7.5 • . We have not stars well centred on Auriga but in the direction with the border Auriga/California. Far star HD 279974 at 1370 pc has not a good spectra, so I did not use it.

HD 27086 has a absorption in the Auriga range but not in the California (see later) velocity range, so Auriga clouds should begin closer then 210 pc and only beyond there is California.

Using HD 280006 and HD 279943, it seems that the three components are yet present closer than 531 pc, and beyond we have not important dense clouds. and 17.21, the only structure with compatible in longitude and latitude is located at 200 pc; it is a small elongated overdensity in 5 • direction from the core to 130 pc, and it could cause the weak absorption for stars HD 31648, V* V402 Au and HD 3164. This structure has not a CO corresponding part, but those stars has absorptions at gas velocities corresponding with Auriga's ones.

From the 3D map and the interstellar absorptions available, it seems that Auriga is a part of a close cloud which correspond largely with Main Taurus, simply closer to the Galactic Plane.

Per is far, but it doesn't show any absorption in this range, probably because it is on the border of the structure.

Using the 17.12, 17.11, 17.10, 17.9, 17.8, 17.7, 17.6 it is possible to name as California at structure from 400 to 600 pc, which starts at longitude 175 • and ends at 155 . Since V* V 579 Per has two components comparable in absorption, I suppose they are the same clouds with poli -component, as for example the beginning of North Taurus (from -1 to 5 km/s).

• ∼ 5 km/s, near the plane, closer then 150 pc,pale light blue • ∼ 2 km/s, from

Conclusion

Using CO emission, potassium absorption and the 3D map, it is possible to draw a coherent kinematic picture for the Taurus complex. Molecular and atomic gas and dust are not in the same ISM positions, but using various ISM components, the global puzzle of Taurus nebulae is assembled. Each component adds some information about the nebula. The velocity analyses derived from potassium absorption are already ready also for the Cepheus Nebula region, and a similar reconstruction work will surely be carried out. Chapter 18

Conclusion and perspectives

Conclusion

This thesis was developed as a test work, to be prepared to Gaia data analyses. My main goal was to develop and test essential tools for the analysis and the exploitation of the Gaia DIB in the RVS spectra.

For the DIB analysis, I coded a profile fitting program in Python and I applied it to a series of synthetic spectra to estimate how many good DIB profiles we may expect to have from the RVS spectra. I used two simulations: the Gaia Universe Model Snapshot [START_REF] Robin | Gaia Universe model snapshot. A statistical analysis of the expected contents of the Gaia catalogue[END_REF] and the Gaia Object Generator [START_REF] Luri | Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator[END_REF]. To obtain the results I tested several profile fitting functions, and I retained the function which returns the best results in reasonably short time. Finally, I found that a reliable DIB measurement-with uncertainty on the fitted DIB strength (or equivalently extinction) lower than 50%-should be obtained for ∼3 million objects.

To improve the full 3D inversions, I tested new techniques to be ready to big data and the Gaia catalog. I tested the inversion with combined data, in particular with reddening derived from photometry of individual stars, spectrometry (APOGEE DIB) again for individual stars, and from statistical processes (Pan-STARRS) applied to groups of stars. We are able now to estimate uncertainties on cloud distances and on integrated extinctions in our maps, despite the fact that full error calculations require too long computation times to be applied to our maps. I developed also a new technique, following the intuition of J. L. Vergely, called "hierarchical technique", which has the two advantages of a shorter calculation time and a more realistic representation of structures, with a new adaptation to the spatial density of stellar targets. I made several tests, partially discussed in this thesis, to understand how to control the inversion code in this context and I applied this technique to a very large sample of extinctions estimated from Gaia photometry. Hierarchical maps suppress artefacts, i.e. they allow structures to emerge from the prior's values only when they are strictly constrained by data, and for this reason this kind of maps can be used as validation tools for other techniques. The map is build using the lines of sight, but for it-own inversion we have not radial effect. Some improvements for this technique are suggested: testing different geometrical configurations, i.e. translating the angles for the determination of the cells, it will be possible to recognise eventual artefacts or uncertain fea-236 CHAPTER 18. CONCLUSION AND PERSPECTIVES tures. I was very conservative in the cells' selection, but the results can reach fine resolution for larger volume using lighter constraints.

I also show, benefit from the my colleague M. ElYajouri competence on the profile fitting of the APOGEE DIB, how it is possible, with large DIB absorption datasets, to map the DIB carriers distribution, and I illustrated the results; this kind of studies is still embryonic, but it gives us important indication about the future maps that will be based on Gaia DIBs. We should inverse the DIB taking in account in the prior a different height scale respect to the extinction inversion, perhaps doing several test to understand for each DIB the most appropriate parameter; we must remember also the importance in this frame of the not-detection measurements or upper-limit detections, because they impose the Local Bubble bounds.

In the small Taurus region, a kinematical map was produced, based on profile fitting of interstellar potassium absorptions, on CO radio emission and on 3D maps. These totally new types of maps will be useful because they will help constraining the dynamical evolution of clouds and their interactions. These maps will be designed for various regions, we have yet the data for the Cepheus region.

Perspectives

Using future Gaia DIB measurements From my estimations, RVS will provide millions of interesting 862.0 nm DIB measurements, well distributed over the sky. After the publication of the spectra, it is trivial to say that the priority will be the extraction of the maximum number of DIBs, for all stars with a RVS magnitude brighter than 15 mag. Additionally, it will be also possible to extract DIBs from lower SNR data using stacked spectra, (Elyajouri et al., 2017a).

Respect to previous catalog, Gaia data will have various and strong advantages: numerous, clean of telluric lines, full sky coverage. They should provide very valable constraints.

In general, massive DIB data may provide several types of information. First, some information on the DIB carrier properties (location of formation, destruction) thanks to their distribution on the space and the proportion with dust and other gas component. Since the DIBs carriers are essentially matter, we can use the DIBs information to make a ISM tomography.

At the end, the DIBs can be add information on ISM kinematic because it will be possible to extract the DIB radial velocities for the strong DIBs and the most distant objects, even if the large DIB width hinders a very simple extraction (Puspitarini et al., 2015). As a matter of fact, since the DIB is broad, only clouds with velocities differing by at least 5-10 km.s -1 can be extracted and it will mainly concern clouds belonging to different arms.

Tomographic techniques and future 3D maps (dust or DIB carriers)

The hierarchical technique that I developed guarantees the possibility to inverse a large database; new DIB maps will be charted and a more precise scale height will be provided, allowing accurate comparisons between excess of 18.2. PERSPECTIVES 237 colour-and DIB absorption-based maps. These maps will bring constraints on the environments that are favourable for the formation and survival of the GAIA DIB carriers. At the moment there is no specific study of the sites of formation of the Gaia DIB, but according to Kos et al. (2014) the DIB is linked with the gas, and it means that we will be able to make a 3D map of the gas distribution, to compare with the 3D dust maps provided by extinctions. Our hierarchical methods are unique and adapted to future datasets. One can foresee applications to most ground based surveys for both extinctions or DIB measurements. Others large surveys can provide new large DIB catalogs in optical or infrared bands, that we will be able to use and compare with the Gaia DIB. WEAVE is a new multi-object spectrograph for the 4.2-m William Herschel Telescope (WHT) at the Observatorio del Roque de los Muchachos. The first light is scheduled for May 2019. The instrument is designed to make large stellar surveys in the spectral interval from 370 to 960 nm, and in this range there are a lot of observable optical DIBs. MOONS (Multi Object Optical and Near-infrared Spectrograph) is another interesting instrument in the infrared (range 0.65 -1.8 micron), mounted on the VLT; it will start scientific observations at the end of 2020. Measurements with this instrument will allow to explore the infrared DIBs (Cirasuolo et al., 2014). In addition to these data, other spectra at high resolution will be potentially available using the new SPIRou (SPectropolarimètre InfraROUge) facility, [START_REF] Moutou | SPIRou: a spectropolarimeter for the CFHT[END_REF]. The spectrograph is mounted on the 3.6m Canada-France-Hawaii telescope located on top of Mauna Kea, and it provides YJHK spectra from 0.95 to 2.35 microns in a single shot, at a spectral resolution of 75,000. With this very precise instrument it is possible to measure the Gaia DIB at high resolution, allowing to extract a new and more detailed shape of the DIB.

Our methods have their own advantages (they take benefit from omni directional links, from full hierarchy of sizes), and also their own shortcomings (difficulties for error estimates, limited angular resolution): ideally they should be combined with other Bayesian techniques to take benefit of all positive aspects.

In the frame of Gaia, derivations of stellar populations properties for stars too faint to be observed by the RVS will benefit from dust maps and reciprocally additional extinction estimates for individual objects will serve to improve the maps, this can be done iteratively. Still in the Gaia frame, comparisons between the locations of stellar populations of different ages and the dust clouds will give clues to the history of star formation.

A completely different contest, detailed dust maps and associated properties linked to dust (reddening law, beta parameter) are crucial for foreground removal in CMB measurements. The galactic dust emits in microwave, and it pollutes the cosmological measurements, but more and more precise maps will permit to remove this spurious component. The Planck measures opened in the last years one important question at large scale about the extinction laws, in particular the the Planck Collaboration et al. (2014) β coefficient map shows a variability in β which is not linkable with any known dust, gas or stellar structure. To understand this variability, [START_REF] Schlafly | Mapping the Extinction Curve in 3D: Structure on Kiloparsec Scales[END_REF] tried a comparison with their extinction profiles based on Pan-STARRS photometry, looking at the variability over the sky of the Rv value and they found some links with Planck β: the explanation may be that since Rv varies in response to the grain size distribution, this distribution is not spatially uniform, and it is reflected in β variations. Such informations on the grain sizes and their favoured locations on the large scale will help constraining the Galactic evolution.

Future astrophysical studies of the galactic mechanism will pass through detailed interstellar medium maps for the different components -gas species, dust species and macro molecules species. In this sense techniques as the 3D inversions, that is replicable for various sources, will permit us direct comparisons.

Kinetic tomography

Our study of the Taurus clouds is a precursor of what could be done on the large scale by means of the combination of emission data (HI, CO), absorption measurements (gaseous lines, DIBs) and dust maps, i.e. the construction of a dynamical picture of the ISM on the large scale. Such a tool would be particularly useful in the frame of Gaia, allowing to build and test dynamical models of the Milky Way including stars and gas, and predict star formation. In particular comparing the dust distribution, the populations distribution, the clouds and the stellar velocities, a complete analysis of the motions and history of our galaxy. These maps can also be used at much smaller scalesas the Taurus one -in star-forming regions to better understand cloud collapse and feedback from newly born stars. We have yet compared our maps with X-ray observations, but we can better understand the bubble generated by supernovae using a kinetic tomography.

And for me, that's all.

  Conclusion and perspectives 18.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Inversion parameter example B Fit NARVAL and ESPaDOnS spectra for Taurus C Others NARVAL and ESPaDOnS fits Bibliography Part I

  Fig 1.5 representes the maser positions for the Local Arm maser from Lépine et al. (2017), based by the Bar and Spiral Structure Legacy Survey2 key science project, the European VLBI Network3, and the Japanese VLBI Exploration of Radio Astrometry project.

Figure 1

 1 Figure1.5 -Maser source emission position on the galactic plane for Local Arm[START_REF] Lépine | The Dynamical Origin of the Local Arm and the Sun's Trapped Orbit[END_REF]. The Sun is is (0,0), the x axis is the Galactic Center direction, distance units are in parsec.

  Fig 2.4 there is the Local Bubble as charted in 2014 from individual excess of colours for some tens thousand of stellar targets. Another local structure is the Gould belt, a ring of young stars

Figure 2

 2 Figure 2.3 -Artistic Milky Way representation, based on observational consideration. Credits: NASA/JPL-Caltech/R. Hurt (SSC/Caltech).

Figure 2

 2 Figure 2.4 -Top ) Excess of colour per pc map of the Local Bubble, slice on the Galactic plane of the map Lallement et al. (2014). The Sun is at (0,0) and the Galactic centre to the right. Longitudes increase counter-clockwise. Bottom) Local Bubble in a vertical plane long the direction of galactic longitude 0/180 • . Colour scale is the same, colour units are mag/pc -1 and distance scale are parsec. Blue contours are for excess of colours per pc (1 e-05, 6 -05, 11 E-05, 16 E-05, 21 E-15).

Figure 3

 3 Figure 3.2 -Only yet published Gaia DIB from RVS spectra. Credits: ESA/ Gaia/ DPAC/ CU6/ Observatoire de Paris-Meudon/Olivier Marchal, Carine Babusiaux and David Katz

Figure 3

 3 Figure 3.5 -APOGEE DR12 distribution on the sky of the stellar targets.

Figure 5 . 1 -

 51 Figure 5.1 -Examples of RVS spectra for stars with increasing temperature.The stellar lines must be very precisely modelled and adapted to all types if we wants to extract the diffuse interstellar band from the data.

  Fig 5.11 and 5.

Figure 8 Figure 8

 88 Figure 8.1 -Three exemple of one-dimensional inversion with same data and different kernel parameters.

Figure 9

 9 Figure 9.1 -Top) Target distributions for the Lallement14 catalog (green crosses) and the added DIBs absorptions (violet crosses) on the sky. Bottom) Target distributions for the Lallement14 catalog (green crosses) and the added DIBs absorptions (violet crosses) on the galactic plane, only targets with distances to the plane in the range (-50,+50) pc are represented.

Figure 9

 9 Figure 9.2 -Illustration of the various categories of DIB extraction: a) Detected; b) Recovered; c) Narrow; d) Recovered and Narrow; e) Upper limit. APOGEE spectra are shown with solid black curves. The initial stellar model provided by APOGEE and the model obtained after application of the scaling factor are shown in solid blue and green respectively. The DIB absorption alone is represented in orange. The solid magenta curves represent the final stellar+DIB modelled spectrum.

Figure 9

 9 Figure 9.3 -Left) Galactic plane for the 3D map based on the Lallement et al. (2014) catalog, with Gaia DR1 distances. Right) Galactic plane for the 3D map based on the Lallement et al. (2014) catalog with new Gaia DR1 distances and the addition of the selection of APOGEE DIB-based extinctions..

  Fig 10.1 are shown some examples for different lines of sight, the extinction curve from Green et al. (2015) and the selected points. In Fig 10.2 is shown the sky distribution of the virtual stars. A fraction of the sky is not covered by the Pan-STARRS survey (norther hemisphere data), unlike the initial catalog.

  -4.0_.txt (b) Linesight l = 87 b = -4.

  -4.0_.txt (c) Linesight l = 160.59 b = -4.

  -4.0_.txt (e) Linesight l = 237 b = -4.

  .0_.txt (f) Linesight l = 261 b = 17.

Figure 10

 10 Figure10.1 -Example of lines of sight and targets. For each line of sight the reliable excess of colour values as inGreen et al. (2015) and red points are the selected virtual stellar targets.

Figure 10

 10 Figure 10.2 -Distribution on the sky of Pan-STARRS selected targets. a) x axis: galactic longitude, y axis: distance [pc]. b) x axis: galactic latitude, y axis: distance [pc]. c) Comparison on the sky between the total Green et al. (2015) distribution (violet points) and the selected points (green points).

Figure 10

 10 Figure 10.3 -General comparison of spatial distribution between Lallement14 catalog (orange points) and new selected points (green points). a) x axis: galactic longitude, y axis: distance [pc]. b) x axis: galactic latitude, y axis: distance [pc]. c) Comparison on the sky.

  10.4. BUILDING THE PRIOR 111 (a) Galactic plane for the inversion Lallement14 + our selection. (b) Galactic plane for the inversion Lallement14.

Figure 10

 10 Figure 10.4 -a) Galactic plane for my inversion based on the Lallement14 catalog and my selection from Green15 map, Sun in (0,0) point, x axis [-1000,1500] pc, y axis [-1200,1200] b) Galactic plane for inversion based on the Lallement14 catalog, Sun in (0,0) point, x axis [-1000,1500] pc, y axis [-1200,1200] b). Color scale in magnitude per parsec.

Figure 10

 10 Figure 10.5 -Vertical cut of different planes in the 3D map. Comparison between old and new map, based on only Lallement14 catalog and the combined catalog. Colour scale as in Fig 10.4.

Figure 10

 10 Figure 10.6 -Galactic plane cut for the built prior based on Pan-STARRS map. The Sun is at (0,0) and the Galactic centre to the right. Longitudes increase counter-clockwise. Color scale in magnitude per parsec.

  (a) Cut l= 0 • . (b) Cut l= 45 • . (c) Cut l= 90 • . (d) Cut l= 135 • .

Figure 10

 10 Figure 10.7 -Vertical cut of different longitude planes in the 3D map; c) and d) vertical cuts have the negative parts in the part of the prior which remains as the analytical one, because in that directions there are not Pan-STARRS data. Colour scale as in 10.6.

Figure 10

 10 Figure 10.9 -Same plane for the same map but with three different colorscale, to compare the difference. a) Logaritmic color scale with the real value mag/pc in the map. b) Linear color scale with the real value mag/pc in the map. c) Colourblind friendly linear color scale, with color in range [0:0.001]. d) Coloured linear color scale, with color in range [0:0.001]

  Figure 10.11 -Galactic planes for the inversions used to reach at the global map Lallement et al. (2018) a) the Galactic plane for the anti-centre inversion, b) the Galactic plane for the centre inversion, c) the Galactic plane for the merging matrix, d) the final Galactic plane. Colour scale for panel a), b), d), it is like 10.9 -panel d). The colour scale of panel c) is the interval (0,1).

Fig. 1 :

 1 Fig. 1: Location of the targets from the LVV catalog compilation (green crosses) and of the APOGEE target stars retained for the DIB extraction and the inversion (violet signs). Coordinates are Galactic. Also shown are the directions of the molecular clouds of the Schlafly et al. (2014) catalog mentioned in section 5.2 (red signs).

Fig. 2 :

 2 Fig. 2: Illustration of the various categories of DIB extraction: a) Detected; b) Recovered; c) Narrow; d) Recovered and Narrow; e) Upper limit. APOGEE spectra are shown with solid black curves. The initial stellar model provided by APOGEE and the model obtained after application of the scaling factor are shown in solid blue and green respectively (note that in many cases they are very similar). The DIB absorption alone is represented in orange. The solid magenta curves represent the final stellar+DIB modeled spectrum.

Fig. 3 :

 3 Fig. 3: Galactic plane cut in the very low-resolution 3D opacity distribution to be used as a prior in the inversion. It is based on Pan-STARRS reddening measurements of Green et al. (2015). The Sun is at (0,0) and the Galactic center to the right. Longitudes increase counter-clockwise. Units are mag pc -1 .

Fig. 4 :

 4 Fig. 4: Galactic plane cut in the 3D opacity distribution resulting from the four successive inversions: a) A distribution: color excess data alone and Hipparcos or photometric distances. b) B distribution: same as A except for the replacement of 80% of the initial distances with Gaia-DR1 (TGAS) values. For the 20% of stars without Gaia distance we kept the previous value. c) C distribution: same as B except for the addition of DIB-based color excess estimates for stars with a Gaia-DR1 parallax. d) D distribution: same as C except for the use of a Pan-STARRS based prior distribution instead of a homogeneous distribution. Color scale, direction of Galactic center, and Sun position are the same as in Fig 3 . DISTRIBUTION DATA INITIAL χ 2 FINAL χ 2 A LVV catalog, Hipparcos+phot 5.361 1.100 B LVV catalog, Gaia-DR1+phot 5.810 1.085 C LVV catalog + APOGEE, Gaia-DR1+phot 5.080 1.023 D LVV catalog + APOGEE, Gaia-DR1+phot , Pan-STARRS prior 3.521 1.006

Fig. 5 :

 5 Fig. 5: Planar cut along the Galactic plane in the inverted 3D distribution D shown in Fig 4, panel d. The color scale is same as in Fig 3. Top: the entire 4000pc × 4000pc computed area. Bottom: Zoom in a 1000 pc × 1000 pc area around the Sun.

  Fig 9 (Orion), Fig 10 (anticenter), Fig 11 (Cepheus), and Fig 12 (Perseus)

  Fig. 8 is a zoom in on these 2D maps of A and D integrated color excesses, this time in a limited region of the sky close to the anticenter direction. Compared to our previous inversion, D leads to better agreement with the Schlegel et al. (1998) contours at low reddening, demonstrating that the inclusion of DIB-based data has improved the detection and location of the structures.

Fig. 7 :

 7 Fig. 7: Full-sky 2D map of opacity distribution integrated from the Sun to the boundaries of our computational domain (abs(Z)=300pc, abs(X)=2kpc, abs(Y)=2kpc). Top: LVV results are shown (distribution A). Bottom: the final inversion with APOGEE data and the Pan-STARRS based prior distribution are shown (distribution D). Isocontours from Schlegel et al. (1998) for E(B-V) = 0.025 and E(B-V)=0.32 are superimposed as dotted and continuous black lines. The map is in Aitoff Galactic coordinates. Longitudes decrease from +180 • to -180 • from left to right. The color scale refers to E(B-V), linear, in units of mag.

Fig. 8 :

 8 Fig. 8: Same as Fig. 7 for limited regions in the anticenter area. Left: LVV data are shown. Right: final inversion is shown. Isocontours from Schlegel et al. (1998) for E(B-V) = 0.025 are superimposed as dashed black lines.

  Fig. 9: Comparison between the three B-C-D distributions (see Sect. 4 and Fig. 4) for a vertical plane along l= 212 • . The Xaxis is within the Galactic plane, the Y-axis is toward the North Galactic pole direction. The color scale is the same as in Fig. 3. Iso-contours are superimposed for ρ 0 = = 0.0002, 0.00035, 0.00076, 0.001, and 0.002 mag.pc -1 . The green crosses in top panel are the positions of the targets from the LVV catalog in a slice of 10 degrees around the considered vertical plane, violet crosses in middle panel are the targets from the APOGEE catalog, and the black circles in bottom panel are the molecular clouds positions and associated uncertainties based on the catalog of Schlafly et al. (2014).

Fig. 10 :

 10 Fig. 10: Same as fig 9 for the vertical plane along l= 180 • (anticenter region).

Fig. 11 :

 11 Fig. 11: Same as fig 9 for the vertical plane along l= 110 • (Cepheus region).

Fig. 12 :

 12 Fig. 12: Same as fig 9 for the vertical plane along l= 158 • (Perseus region).

  Fig. 13: Error in the distance due to the limited target space density, in the Galactic plane, as estimated from the radii of the smallest spheres that contain at least 10 targets (left figure) or from the target density in a cube of side 200 pc (right). The pale pink color corresponds to errors larger than 200 pc.

Fig. 14 :

 14 Fig. 14: Estimated error on the integrated color excess for the Galactic plane computed as the mean difference between data and model in a restricted volume (see Sect. 5.1). The pale pink color corresponds to errors larger than 0.4 mag.

Fig. 15 :

 15 Fig. 15: Four vertical planar cuts in the 3D opacity maps in planes containing the ROSAT 3/4 keV X-ray bright spots labeled 1 to 4 in Puspitarini et al. (2014) and here as a) to d); the black dashed ellipses show the likely locations of the corresponding SNRs; the latitudinal grid is every 10 deg.

Fig. 16 :

 16 Fig. 16: Vertical cut in the 3D opacity distribution for D inversion along the meridian plane l=0-180 • . Color scale and iso-contours as in Fig 9.

Fig. 17 :

 17 Fig. 17: Same as Fig. 16 for the vertical plane along l=30-210 •

Fig. 18 :

 18 Fig. 18: Same as Fig. 16 for the vertical plane l=60-240 •

Fig. 19 :

 19 Fig. 19: Same as Fig. 16 for the vertical plane l=90-270 • (the rotation plane)

143Figure 11

 11 Figure 11.1 -Galactic plane resulting from inversion D of Capitanio et al. (2017): input targets within 20 pc from the Plane are superimposed (black plus signs). Targets like those circled at top left will be eliminated along the hierarchical process, since the target density at their location is too small to contribute to the definition of small structures. They will be taken into account at the first steps only. Colour scale is like 10.9 -panel d)

  . The distance-extinction pairs are based on the work of Wang et al, 2016. I selected targets stars located in the interesting region of the nearby Taurus clouds. From the initial LAMOST published dataset I extracted 29 448 objects within the interval l = (155 • , 180 • ) and b = (-30 • , Table 11.1 -Parameters used for the LAMOST-Taurus hierarchical inversion. D is the distance between cells. N is the minimum numbers of targets required to keep the cell in the inversion process. Ns is the number of cells. ξ i and σ i are the correlation length and variance for the two kernels (Gaussian and 1/cosh)

Figure 11 . 5 -

 115 Figure 11.5 -Hierarchical step 1: a) Vertical cut at longitude 165 • in the inverted distribution after the first step, with input metadata overlapped (green crosses). The colour scale represents the differential reddening excess of colour/pc in mag.pc -1 , as in 10.6. b) Metadata (green crosses) and initial stellar targets (red dots) along the Galactic plane and in the vertical plane of a).

Figure

  Figure 11.6 -Same as Fig. 11.5 for the hierarchical step 2

Figure

  Figure 11.7 -Same as Fig. 11.5 for the hierarchical step 3.

Figure 11 . 8 -

 118 Figure 11.8 -Same as Fig. 11.5 for the hierarchical step 4.

Figure 11 . 9 -

 119 Figure 11.9 -Same as Fig. 11.5 for the hierarchical step 5.

  (a) l = 155 • . (b) l =160 • . (c) l =165 • .

Figure 12

 12 Figure 12.2 -Direct inversion: comparison between the EVEN (left) and ODD (right) databases in three different vertical planes. Colour scale as 10.9 -panel d).

  (a) l = 170 • . (b) l = 175 • . (c) l = 180 • .

Figure 12

 12 Figure 12.3 -Same as figure 12.3 for three more vertical planes.

  Fig 12.6 shows three vertical cuts in the 3D inverted distribution for -a) the direct inversion with LAMOST data only and for the 25 pc resolution, b) the hierarchical inversion for LAMOST data (ODD) only and for the step 5 (structures of 50 pc) and c) the direct inversion with the distribution b) as prior and both LAMOST DR4 ODD data and stars from the previous catalogue closer than 150 pc. I.e., the last inversion c) is combining the hierarchical and direct techniques. It takes 3 hours, using 9724 stellar targets. It can be seen that there is some decrease of the density close to the Sun -the Local Bubblefor the last inversion (although, due to the coarse resolution, the improvement12.2. HIERARCHICAL INVERSION FOR EVEN AND ODD SUB SETS157

Figure 12

 12 Figure 12.4 -Hierarchical inversion steps 1-2-3, for EVEN (left) and ODD (right) datasets, vertical plane at longitude 165 • . Colour scale as 10.9 -panel d).

Figure 12

 12 Figure 12.5 -Hierarchical inversion steps 4-5, for EVEN (left) and ODD (right) datasets, vertical plane at longitude 165 • . Colour scale as 10.9 -panel d).

  (a) Direct inversion, 25 pc structures ODD dataset (b) Hierarchical inversion step 5 -ODD dataset. (c) Direct inversion with prior from hierarchical step 5 and adding data within 150 pc to the LAMOST ODD dataset.

Figure 12

 12 Figure 12.6 -Tests of direct-hierarchical combination, adding nearby stars (see text). Colour scale as 10.9 -panel d).

  for stars farer then 200 pc, longitudes from 150 • to 180 • and latitudes for -30 • and -5 • • for stars between 100 and 200 pc, longitudes from 110 • and 225 • and latitudes for -60 • and +25 • • for stars closer then 100 pc, longitudes from 65 • to 270 • and latitudes for -90 • and +55 •

Figure 13

 13 Figure 13.4 -Hierarchical inversion: some steps for the vertical plane at longitude 160 • . Black crosses are the metadata used in the inversion, with sizes increasing with the mean excess of colour.

  Figure 13.5 -Vertical cuts for the final step of the hierarchical inversion. Longitude: 150 • , 160 • , 170 • , 180 • . The green lines delineate the volume allowed for stars closer than 100 pc, the red lines delineate the volume allowed for stars between 100 and 200 pc, the light blue lines the volume containing all stars farther than 200 pc.

  Figure 13.6 -Last inversion steps and comparisons: left) Inversion step 10 (top) and step 10 bis (bottom). Note the difference at short distance (see text). Right top: last direct inversion of Capitanio et al. (2017) (called the old map) with superposed isocontours from hierarchical inversion step 10. Also shown are the targets used in the old map inversion. Note that comparisons are valid only for negative latitudes between -5 • and -30 • . Right bottom: last direct inversion of Capitanio et al. (2017) with superposed isocontours from hierarchical inversion step 10 bis. Clouds beyond 500 pc could not be present in the old map due to lack of targets at large distance.

  Figure 14.1 -Vertical cut at l = 160 • , comparison between different dynamical parameters.

  Fig 14.2 is shown a comparison of the results based on the new LAMOST catalog for the same parameters as in Tab 13.1 and the new ones. The difference is very significant in regions where there are no data, showing the influence of the dynamical parameters. It is clearly not realistic to empty regions along the Plane in regions without data. In areas well covered by data, the inversions reproduce about the same structures, since the influence of data is dominant. Looking at differences between Fig 14.2 and panel a) in Fig 13.

  Figure 14.2 -Vertical cut at longitude 160 • , for the steps 10 in hierarchical inversion after Gais DR2, using the same set of metadata based on LAMOST catalog, with two different dynamic: the smaller dynamic parameters drive to more realistic results.

Figure 14

 14 Figure 14.3 -Distribution in several vertical planes, after the last step of the hierarchical inversion LAMOST DR4-Gaia DR2. Coloured lines have the same meaning than in Fig 13.5.

••

  7 and χ 1 = 60 pc • Beginning χ 2 first quadrant = 4.43, second quadrant = 4.88, third quadrant = 1.97 , fourth quadrant = 2.78 • End χ 2 first quadrant = 1.08, second quadrant = 0.90, third quadrant = 0.60 , fourth quadrant = 0.82 • CPU time first quadrant = 18 310 103; CPU time second quadrant = 6 177 830; CPU time third quadrant = 6094402 ; CPU time fourth quadrant = 19 595 894 Threads number = 6 Real time first quadrant = ∼37j, real time second quadrant = 18j; real time second quadrant = 17j; real time fourth quadrant = 40j

  Fig 15.3. In the third quadrant appears a large cavity without matter. Step by step, the structures are effectively located, and prior values are kept at distances without meta-stars. No fingers of God are present on the Galactic plane, even at smaller scales, see Fig 15.4. Such features are generally present in other inversion techniques that are not full-3D inversions. At 60 pc resolution, the Galactic plane map shows two non-radial thick chains of clouds in the second and third quadrants, and a more distant and parallel filament in the Galactic centre direction. Fig 15.5 illustrates the evolution away from the Galactic plane, showing the Taurus clouds.

Figure 15

 15 Figure 15.3 -Galactic plane differential extinction distribution after step 1, step 2 and step 3. Targets with distances to the Plane smaller than 200 pc are represented with a cross whose dimension represents the reddening excess of colour. Colour scale as in Fig 10.9 -panel d).

Figure 15 Figure 15

 1515 Figure 15.4 -Galactic plane for inversion for step 4, step 5 and step 6. Colour scale as in Fig 10.9 -panel d).

Figure 15

 15 Figure 15.6 -Distribution in vertical planes for the step 6 inversion, at different longitudes.

  Fig 16.3 shows the galactic Plane distribution from the inversion based on DIB absorption (top panel) and on photometric extinction (medium panel).

Figure 16

 16 Figure 16.3 -Top) Galactic plane for the inversion based on excess of colour derived from the photometric extinction. Medium) Galactic plane for the inversion based on excess of colour derived from the APOGEE DIB absorption.

  Figure 17.1 -CO map of the Taurus nebula with superposed all targets in our sample -black/yellow cross symbols. Colour scale depends on the CO column measured in radio units.

Figure 17 Figure 17 Figure 17 Figure 17

 17171717 Figure 17.4 -Slice at longitudes 150 • from the 3D map, with stellar targets closer then 2 • at the plane.

Figure 17

 17 Figure17.12 -Slice at longitudes 170 • from the 3D map.

Figure 17

 17 Figure 17.14 -Slice at longitudes 175 • from the 3D map.

Figure 17 Figure 17

 1717 Figure 17.16 -Slice at longitudes 180 • from the 3D map.

  Figure 17.24 -Structure in CO maps at for the velocity range of Main Taurus, total on the top and separated by velocities. Colour scale of the stellar targets represents the distance.

  Figure 17.25 -Structure in CO maps at for the velocity range of Main Taurus, separated by velocities. Colour scale of the stellar targets represents the distance.

  Figure 17.26 -Structure in CO maps at for the velocities range of South Taurus, total on the top and separated by velocities. Colour scale of the stellar targets represents the distance.

  Figure 17.27 -Structure in CO maps at for the velocity range of Perseus region, total on the top and separated by velocities. Colour scale of the stellar targets represents the distance.

  Figure 17.28 -Structure in CO maps at for the velocity range of Auriga region, total on the top and separated by velocities. Colour scale of the stellar targets represents the distance.

  20

  Figure 17.30 -Structure in CO maps at different velocities and stellar targets for California region. Colour scale of the stellar targets represents the distance.

Figure 17

 17 Figure 17.31 -Slice in the 3D map, with stars with galactic longitude between 148.75 • and 151.25 • for a) and b) and between 151.25 • and 153.75 • .

  15 Application of the hierarchical inversion to full-sky data 15.1 Metadata selection . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.4 Conclusion and perspective . . . . . . . . . . . . . . . . . . . . Description of the dataset . . . . . . . . . . . . . . . . . . . . . 16.2 Comparison between the map based on DIBs and the map based on extinctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	VIAstrophysical information in maps	189
	16 First 3D map completely based on the inversion of DIB mea-
	surements
	16.1

17 To the 3D kinematic 17.1 NARVAL and ESPaDOnS spectra . . . . . . . . . . . . . . . . 17.2 Profile-fitting and measurements of radial velocities . . . . . . . 17.3 3D map in the Taurus region . . . . . . . . . . . . . . . . . . . 17.4 CO velocities maps . . . . . . . . . . . . . . . . . . . . . . . . . 17.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  THE INTERSTELLAR MEDIUM

	Component Scale height
	CO and H 2 Atomic gas	∼ 80 pc 115 pc
	Ionised gas	>200 pc
	Dust	117 pc
	862 nm DIB	209 pc
	Table 2.1 -Different scale heights for interstellar medium component, Ferrière
	(2001); Kos et al. (2014).

TiO molecular band HIP 114114 (M6-8.5e)

	50	CHAPTER 5. SIMULATED ANALYSES OF GAIA RVS SPECTRA
		1.0						1.0
	Normalized counts [e-]	0.6 0.8					Normalized counts [e-]	0.6 0.8
		0.4						0.4
		8450	8500	8550	8600	8650	8700	8450	8500	8550	8600	8650	8700
					Wavelengths [A]						Wavelengths [A]
			.2. The spectrum is the one of the cool targets from

Ca Ca Ca Fe Fe Ti Fe Fe Fe Fe Fe,Ti Fe Si Si HIP 23311 (K3)

		1.0
	Normalized counts [e-]	0.6 0.8
		0.4
		8450	8500	8550	8600	8650	8700
					Wavelengths [A]

Ca Ca Ca Fe Fe Fe Fe Fe Fe Fe Si Si HIP 42291 (G0)

								1.0	H	H	H	H
							Normalized counts [e-]	0.6 0.8	Ca	Si
								0.4		Ca	HIP 9452 (F0)	Ca
								8450	8500	8550	8600	8650	8700
										Wavelengths [A]
		1.0	H	H	H			1.0
	Normalized counts [e-]	0.6 0.8	Ca	Ca		Ca H	Normalized counts [e-]	0.6 0.8	H	H	H	H
		0.4			HIP 50933 (A0)			0.4
		8450	8500	8550	8600	8650	8700	8450	8500	8550	8600	8650	8700
					Wavelengths [A]					Wavelengths [A]

C He He HIP 12387 (B2)

Table 7 .

 7 2 -Statistics on extinctions for targets stars with DIB detections at conditions COND1 and COND2.

	A V [mag]	COND1	COND2
	0.0	1 168 245	553 220
	0.6	813 278	211 713
	1.2	535 581	54 523
	1.8	392 596	148 227
	2.4	246 939	116 238
	3.0	366 214	90 297
	3.6	175 257	69 534
	4.2	112 861	42 464
	4.8	65 344	38 208
	5.4	62 157	12 501
	Table 7.3 -Statistics on distances of targets stars with DIB detections at
	condition COND1 and COND2
			COND1	COND2
	0 < dist < 1000 [pc]	1 439 928	631 250
	1000 < dist < 2000 [pc]	602 581	159 744
	2000 < dist < 3000 [pc]	561528	139 838
	3000 < dist < 4000 [pc]	397 939	142 233
	4000 < dist < 5000 [pc]	283 772	100 618
	5000 < dist [pc]		652 724	163 242

Table 1 :

 1 Article number, page 4 of 18 L. Capitanio et al.: Three-dimensional mapping of the local interstellar medium with composite data Fitting constraints of λ15273 NIR DIB for the selected APOGEE spectra. RA, RB, RC are the standard deviation in three spectral ranges A = [λ c -10Å, λ c + 10Å], B= [15890-15960] Å and C= [15200-15250] Å, respectively.

	Flags	λ c	Width	Depth
		Å	Å	Å
	Detected (4861) Narrow DIBs (364) Recovered DIBs (2515) Narrow recovered DIBs (420) [15 268 -15 280] [1 -1.4[ [15 268 -15 280] [1.4 -5.5] [1.5× max(RA,RB,RC) -0.1] [15 260 -15 280] [1 -1.4] [1.5× max(RA,RB,RC) -0.1] [15 268 -15 280] [1.4 -5.5] [2× RA -1.5× max(RA,RB,RC)] ]2× RA -1.5× max(RA,RB,RC)] Upper limit (1753) [15 268 -15 280] ≤1.4 ≤ 2×RA

Table 14 .

 14 1 -Inversion parameters for hierarchical inversion.

  • , 170 • ) and b = (-20 • , -25 • ). In that direction, we have only 8 stellar targets, and the velocity puzzle seems to be quite simple to understand. The part with velocities higher than 10 km/s are in the lower latitudes, as clear in Fig 17.26. In particular HD 26572 arranges the higher velocity part behind 144 pc, while HD 27742 positions the slower part behind 177 pc. It is very interesting because in Fig 17.14 b) there is a core in 175 • with latitude lower then 20 • , that I can identify as the source of this absorptions. Using the vertical cut, Fig 17.13 and 17.12, I can identify the cloud South Taurus between 150 and 220 pc. I include in this paragraph also a small cloud with same velocities but longitude (167 • , 165 • ). Here we have 5 stars near each others in position and distance and only the furthest stars HD 23489 at 139 pc has a very small absorption: I cannot propose it as the border of the cloud and only suggest that this fragment is behind 140 pc, Fig 17.11 and 17.10.

  Between 149 • and 152 • In Fig 17.31 the vertical cuts in JLcube1 Gaia for 149 • , 150 • and 152 • . I can identify the velocity of cloud part in figure as a pale pink like a cloud with velocity around ∼-7 km/s behind 537 pc. Using *c Per, it is evident that the component at ∼5 km/s is near the plane: this component is also absent for V* V 579 Per, whose latitude is 11

• .

Table B .

 B 1 -Fit NARVAL and ESPaDOnS spectra for Taurus, * symbols are for velocities from stellar lines, T symbols are for velocities from telluric lines. Table B.2 -Fit NARVAL and ESPaDOnS spectra for Taurus, * symbols are for velocities from stellar lines, T symbols are for velocities from telluric lines. Table B.3 -Fit NARVAL and ESPaDOnS spectra for Taurus, * symbols are for velocities from stellar lines, T symbols are for velocities from telluric lines. Table C.2 -Fit NARVAL and ESPaDOnS spectra. Table C.3 -Fit NARVAL and ESPaDOnS spectra. Table C.4 -Fit NARVAL and ESPaDOnS spectra. APPENDIX C. OTHERS NARVAL AND ESPADONS FITS Table C.5 -Fit NARVAL and ESPaDOnS spectra. Table C.6 -Fit NARVAL and ESPaDOnS spectra. Table C.7 -Fit NARVAL and ESPaDOnS spectra. Table C.10 -Fit NARVAL and ESPaDOnS spectra.

	APPENDIX C. OTHERS NARVAL AND ESPADONS FITS APPENDIX C. OTHERS NARVAL AND ESPADONS FITS APPENDIX C. OTHERS NARVAL AND ESPADONS FITS	identifier HD BD+49 915 HD TYC 2342-639-1 BD+45 783 HD HD 281160 HD 275941 TYC 2864-514-1 158.771 glon 143.115 146.201 149.002 159.44 149.968 149.295 160.446 157.586 LS V +43 157.031 HD 157.021 HD 276436 161.045 HD 276446 161.241 HD 276453 161.552 HD 279943 164.309 HD 276449 161.474 HD 276454 161.729 HD 279953 164.771 HD 279974 165.88 HD 280006 165.113 HD 285016 179.632 HD 179.534 HD 179.57 HD 284938 178.843 HD 180.904 identifier HD HD HD HD 279890 HD 281305 HD HD BD+30 540 HD HD 278942 HD BD+30 564 HD HD NGC HD HD HD HD HD HD * 62 Tau HD HD 284421 HD HD HD HD 283677 HD 2MASS J05164313+2307495 2MASS J05164313+2307495 TYC 1850-644-1 TYC 1861-830-1 identifier 2MASS J05411140+2816123 2MASS J05411140+2816123 TYC 2397-44-1 2MASS J04282605+4129297 2MASS J04282605+4129297 2MASS J03232843+0944216 2MASS J03232843+0944216 * 17 Tau * c Per HD 23489 V* V1229 Tau HD 23763 V* HZ Aur * 17 Aur HD 34790 HD 23753 V* RZ Tau V* V402 Aur V* V579 Per V* AA Tau V* DG Tau * eps Per * eps Per HD 24640 HD 27742 HD 31648 V* IQ Aur * omi Per * ksi Per V* XY Per name 19cep 19cep 19cep 19cep 19cep 19cep 19cep 2massj00052394+6347207 2massj00103725+5844536 2massj00104636+5846102 2massj00215670+6330397 2massj00330087+5856180 2massj00362292+6313162 2massj00380988+6251111 2massj00401172+5854561 2massj00535454+5945115 2massj01022616+5822498 2massj02102704+4846405 2massj02205086+5519394 2massj02255659+5500312 2massj11073631-1036344 2massj11260029+0357048 2massj11522069-1107291 name 2massj11572921-1701023 284.884 glat -5.264 -5.333 -7.6 -21.247 1.75 pi 3.04 4.06 1.86 -8.134 1.55 -5.116 1.58 -17.892 3.13 -10.669 2.19 -11.62 1.39 -5.384 0.47 -5.247 1.07 -5.259 1.02 -5.25 0.93 -5.411 2.16 -7.93 1.88 -5.172 0.5 -5.367 0.88 -7.99 2.57 -8.886 0.73 -7.198 0.54 -13.001 1.28 -12.022 1.96 -11.935 1.28 -11.227 0.96 -11.794 3.39 glon glat 147.903 -5.744 147.903 -5.744 147.903 -5.744 164.537 -8.903 162.941 -17.32 157.685 -24.114 157.984 -23.975 157.971 -21.238 164.675 -24.272 159.85 -18.61 156.373 -14.038 160.769 -18.877 158.42 -10.751 166.685 -17.54 165.534 -15.288 174.687 -22.504 158.575 -6.452 167.14 -14.778 161.998 -9.136 171.024 -16.953 159.717 -5.979 172.763 -17.393 173.375 -17.507 173.435 -17.518 167.263 -11.861 170.735 -14.353 174.327 -16.765 170.369 -12.895 184.347 -3.645 181.337 -8.603 181.337 -8.603 179.625 -7.772 183.363 -4.494 glon glat 180.056 -1.177 180.056 -1.177 171.634 -3.585 160.539 -5.014 160.539 -5.014 173.188 -37.879 173.188 -37.879 166.18 -23.849 153.654 -3.045 166.369 -23.502 166.535 -23.319 166.678 -23.121 171.157 -4.19 172.767 -2.233 176.572 -4.124 167.332 -23.826 179.214 -18.724 172.788 -6.445 153.746 -11.339 174.321 -15.395 171.842 -15.672 157.354 -10.088 157.354 -10.088 160.469 -13.974 175.317 -19.665 173.466 -7.902 172.865 -2.128 160.364 -17.74 160.372 -13.107 156.796 -11.902 glon glat 104.871 5.391 104.871 5.391 104.871 5.391 104.871 5.391 104.871 5.391 104.871 5.391 104.871 5.391 117.874 1.37 117.647 -3.704 117.67 -3.686 119.65 0.827 120.552 -3.848 121.237 0.399 121.419 0.02 121.478 -3.924 123.244 -3.117 124.377 -4.46 136.096 -12.064 135.482 -5.35 136.279 -5.395 265.733 44.633 257.853 59.128 280.442 49.149 glon glat 43.956 2.67 v0 HBR 1.294 5.366 6.425 11.603 3.252 -4.443 14.341 0.703 5.538 3.236 1.44 7.986 5.586 6.89 12.165 7.7 0.026 7.8 -30.0 8.669 9.591 19.359 21.025 17.542 19.052 pi 7.41 7.41 7.41 2.0 3.04 4.02 4.94 3.19 7.66 1.92 4.64 4.26 5.16 2.0 2.14 6.91 8.81 5.66 4.74 3.11 1.51 4.46 4.32 3.94 3.42 5.8 3.53 2.97 4.69 1.28 1.28 1.43 0.83 pi 0.91 0.91 0.29 0.67 0.67 0.89 0.89 8.7 5.93 7.22 7.57 7.84 4.69 6.72 10.05 7.72 4.52 5.29 2.34 7.29 8.25 12.16 12.16 2.32 5.64 6.18 6.88 2.91 1.38 2.14 Table C.1 -Fit NARVAL and ESPaDOnS spectra. v1 HBR v2 HBR v3 HBR v0 LSR v1 LSR -3.094 9999.0 9999.0 1.56 -2.828 -0.031 9999.0 9999.0 4.634 -0.764 0.626 9999.0 9999.0 4.495 -1.303 6.816 17.254 -6.605 4.851 0.064 7.516 -6.045 9999.0 0.945 5.209 -0.058 4.964 9999.0 -6.138 -1.753 10.301 9999.0 9999.0 7.633 3.593 6.362 -3.25 10.381 -4.32 1.339 0.493 13.361 9.465 0.035 -5.009 -6.682 -18.698 -2.091 -0.953 -10.871 7.344 -12.157 -2.899 -2.728 3.176 2.938 9999.0 9999.0 2.559 -2.489 9999.0 9999.0 9999.0 0.1 9993.514 9993.514 v2 LSR 9999.266 9998.268 9997.07 10.501 -8.352 3.27 9992.292 -8.273 7.858 -22.887 -16.325 9993.573 10.47 9999.0 9999.0 1.288 4.867 9993.397 4.103 8.47 9999.0 5.408 -2.655 1.713 2.311 -3.854 9999.0 2.151 -3.238 -9.403 10.111 6.54 28.523 -5.626 4.459 0.888 12.065 16.473 9999.0 0.896 5.161 9.569 9999.0 9999.0 9999.0 -37.343 9991.657 9991.657 3.959 11.989 -50.0(T) 1.757 -2.953 5.077 18.522 14.714 2.794 -2.061 6.87 3.063 12.345 9999.0 9999.0 7.825 0.811 9987.466 14.961 9999.0 9999.0 9.49 3.426 9987.464 10.53 9999.0 9999.0 6.267 -0.745 9987.725 9999.0 9999.0 9999.0 7.182 9987.13 9987.13 v0 HBR v1 HBR v2 HBR v3 HBR v0 LSR v1 LSR -50.0 -50.0 4.22 9999.0 -51.332 -51.332 1.278 9999.0 9999.0 9999.0 -0.054 9997.668 -56.912(T) v3 LSR 9999.266 9998.268 9997.07 -13.358 9996.693 9997.306 9992.292 5.358 3.962 -6.279 -7.067 9993.573 9993.514 9993.397 9992.243 9993.451 22.871 9992.096 9991.657 -8.858 9987.466 9987.464 9987.725 9987.13 v2 LSR 2.887 9997.668 1.812 9999.0 9999.0 9999.0 0.479 9997.668 9997.668 6.558 12.452 3.176 9999.0 -0.384 5.51 -3.766 13.578 -17.683(*) 9999.0 9999.0 6.191 -25.07(*) 9991.613 12.015 9999.0 9999.0 9999.0 5.491 9992.476 9992.476 10.43 -50.0(*) 9999.0 9999.0 3.833 -56.597(*) 9992.403 11.577 7.858 9999.0 9999.0 5.256 1.537 9992.678 -50.0(T) 9999.0 9999.0 9999.0 -58.52(T) 9990.48 9990.48 14.4 11.029 18.286 9999.0 7.794 4.423 11.68 7.053 9999.0 9999.0 9999.0 2.004 9993.951 9993.951 12.11 -10.937 -16.651(*) -4.358(*) 5.205(*) -17.842(*) -23.555(*) 5.586 9999.0 9999.0 9999.0 0.295 9993.709 9993.709 14.527 9999.0 9999.0 9999.0 6.03 9990.503 9990.503 13.924 9999.0 9999.0 9999.0 5.982 9991.058 9991.058 22.08 14.769 9999.0 9999.0 10.982 3.671 9987.901 13.634(*) 7.936(*) 19.392(*) 1.219(*) 8.825(*) 3.126(*) 14.582(*) -50.0(*) 14.037 -44.025(*) 9999.0 -58.358(*) 5.678 -52.384(*) 10.008 -32.252(*) -40.731(*) 9999.0 3.809 -38.451(*) -46.929(*) 16.948 12.889 9999.0 9999.0 7.274 3.216 9989.326 1.929 7.032 -3.612 9999.0 -3.176 1.927 -8.717 14.622 17.922 9999.0 9999.0 4.428 7.728 9988.806 14.377 19.856 9999.0 9999.0 4.006 9.485 9988.629 13.996 18.084 9999.0 9999.0 3.607 7.696 9988.611 14.987 5.858 11.471 9999.0 6.898 -2.23 3.383 14.699 9999.0 9999.0 9999.0 5.35 9989.651 9989.651 15.507 19.373 9999.0 9999.0 4.94 8.805 9988.432 11.256 14.628 9999.0 9999.0 2.157 5.53 9989.901 21.024 9999.0 9999.0 9999.0 9.153 9987.129 9987.129 -20.409 14.778 -15.453 19.06 -32.072 3.115 -27.116 -16.644 15.182 -21.91 19.318 -28.307 3.52 -33.572 18.068 13.284 22.404 26.792 6.945 2.161 11.282 16.107 19.716 11.636 24.259 4.384 7.993 -0.087 v0 HBR v1 HBR v2 HBR v3 HBR v0 LSR v1 LSR v2 LSR v3 LSR τ 0 0.541 0.613 0.372 1.05 0.267 0.15 0.571 0.932 0.218 0.643 0.639 0.215 0.24 0.182 0.257 0.317 0.412 0.518 1.0 1.03 0.458 0.221 0.54 0.439 0.927 9999.0 τ 1 0.243 0.161 0.164 0.153 0.121 0.185 0.556 0.698 0.102 0.386 0.234 0.072 9999.0 0.093 0.298 0.176 0.143 0.253 9999.0 0.251 0.211 0.207 0.2 0.354 v3 LSR 9997.668 9997.668 9997.668 9992.058 9991.613 9992.476 9992.403 9992.678 9990.48 9992.394 9993.951 -11.263(*) 9993.709 9990.503 9991.058 9987.901 -3.591(*) 9990.642 9992.802 9989.326 9993.895 9988.806 9988.629 9988.611 9990.911 9989.651 9988.432 9989.901 9987.129 7.397 7.655 15.669 12.536 τ 0 -50.0(*) 15.673 9.839 -44.639 -60.442(*) 5.231 -0.603 -55.081 1.67 -50.0(*) 15.722 10.484 -44.08 -60.442(*) 5.28 0.042 -54.522 1.674 4.0 10.248 -3.381 -16.561 -4.4 1.848 -11.781 -24.961 1.306 5.153 -7.965 -2.622 9.705 -0.086 -13.204 -7.861 4.467 0.289 -7.548 5.395 -2.802 10.601 -12.786 0.156 -8.041 5.363 0.33 14.121 4.203 19.32 9999.0 2.755 -7.163 7.954 9987.634 0.354 19.743 14.193 4.003 9999.0 8.377 2.827 -7.363 9987.634 0.375 -29.761 9999.0 9999.0 9999.0 -38.664 9990.097 9990.097 9990.097 0.007 9999.0 τ 2 9999.0 9999.0 9999.0 9999.0 τ 3 9999.0 9999.0 0.081 0.075 0.043 9999.0 0.109 9999.0 9999.0 9999.0 0.206 0.161 0.264 1.429 0.15 0.34 0.177 0.264 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 0.944 9999.0 0.109 9999.0 0.133 0.042 0.122 9999.0 9999.0 9999.0 0.403 0.088 0.232 0.047 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 τ 0 τ 1 0.031 0.0 0.014 τ 2 0.013 9999.0 9999.0 0.016 9999.0 9999.0 0.423 0.273 0.256 1.239 0.19 9999.0 0.034 9999.0 9999.0 0.056 0.096 9999.0 1.448 0.174 9999.0 0.096 9999.0 9999.0 1.462 0.184 0.109 0.048 9999.0 9999.0 0.88 0.146 0.104 0.354 9999.0 9999.0 0.408 9999.0 9999.0 0.838 9999.0 9999.0 0.888 0.052 9999.0 0.268 0.26 0.175 0.841 0.218 0.111 0.293 0.05 0.049 0.684 0.302 9999.0 0.351 0.186 0.077 0.447 0.339 9999.0 0.463 0.288 9999.0 0.379 0.396 9999.0 0.107 0.046 1.442 0.759 9999.0 9999.0 0.568 0.169 9999.0 1.288 0.898 9999.0 0.196 9999.0 9999.0 0.672 0.465 0.573 0.694 0.383 0.624 0.8 0.286 1.307 1.19 0.78 0.245 τ 1 τ 2 τ 3 0.561 0.262 0.14 0.525 0.262 0.101 0.895 0.836 0.341 0.29 0.133 0.098 0.305 0.187 0.078 0.226 0.328 9999.0 0.381 0.175 9999.0 9999.0 9999.0 7.733 9999.0 9999.0 9999.0 4.92 9996.187 9996.187 9996.187 0.132 9999.0 9999.0 9999.0 17.281 9999.0 9999.0 9999.0 8.353 9990.072 9990.072 9990.072 0.012 9999.0 9999.0 9999.0 -4.138 9999.0 9999.0 9999.0 -13.097 9990.04 9990.04 9990.04 0.011 9999.0 9999.0 9999.0 -49.899 9999.0 9999.0 9999.0 -58.883 9990.017 9990.017 9990.017 0.011 9999.0 9999.0 9999.0 10.865 9999.0 9999.0 9999.0 2.527 9990.662 9990.662 9990.662 0.091 9999.0 9999.0 9999.0 -9.276 9999.0 9999.0 9999.0 -17.831 9990.445 9990.445 9990.445 0.002 9999.0 9999.0 9999.0 -50.0 9999.0 9999.0 9999.0 -59.868 9989.132 9989.132 9989.132 0.132 9999.0 9999.0 9999.0 -41.615 9999.0 9999.0 9999.0 -50.834 9989.781 9989.781 9989.781 0.004 9999.0 9999.0 9999.0 20.582 16.715 9999.0 9999.0 8.571 4.704 9986.99 9986.99 0.372 0.149 9999.0 9999.0 15.641 9999.0 9999.0 9999.0 6.559 9989.918 9989.918 9989.918 0.098 9999.0 9999.0 9999.0 6.53 2.367 9999.0 9999.0 2.622 -1.542 9995.091 9995.091 0.221 0.187 9999.0 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bd+66104 125.717 4.732 1.15 name glon glat pi v1 v2 v3 v4 T1 T2 T3 T4 tau1 tau2 tau3 tau4 hd218323 111.799 3.728 1.07 -23.406 9999.0 9999.0 9999.0 20000.0 9999.0 9999.0 9999.0 1.233 9999.0 9999.0 9999.0 hd218323 111.799 3.728 1.07 -23.431 9999.0 9999.0 9999.0 20000.0 9999.0 9999.0 9999.0 1.261 9999.0 9999.0 9999.0 hd224424 116.21 -2.45 0.27 -9.912 -16.811 -23.797 -6.6 20000.0 20000.0 20000.0 20000.0 0.418 0.053 0.082 0.131 hd224424 116.21 -2.45 0.27 -16.608 -24.178 -6.522 -9.949 20000.0 20000.0 20000.0 20000.0 0.068 0.083 0.128 0.42 hd229049 76.995 1.351 0.43 -9.502 -25.614 -4.529 -14.664 20000.0 12430.872 20000.0 20000.0 0.053 0.075 0.053 0.315 hd2619 120.74 2.49 0.96 -14.899 -19.829 -11.039 -7.218 20000.0 20000.0 20000.0 20000.0 1.02 0.117 1.869 0.338 hd2619 120.74 2.49 0.96 -19.0 -14.685 -11.149 -7.854 20000.0 20000.0 20000.0 20000.0 0.143 0.936 1.75 0.41 hd344784 59.402 -0.153 1.74 -10.608 9999.0 9999.0 9999.0 20000.0 9999.0 9999.0 9999.0 0.946 9999.0 9999.0 9999.0 hd344880 60.287 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94.964 10.729 2.25 -24.327 -19.664 -15.477 -11.455 20000.0 20000.0 20000.0 20000.0 0.253 1.056 1.415 0.677 hip101903 92.779 8.906 2.82 11.625 9999.0 9999.0 9999.0 20000.0 9999.0 9999.0 9999.0 0.147 9999.0 9999.0 9999.0 hip102187 94.323 9.487 3.29 -24.247 -27.604 -31.74 -20.224 20000.0 20000.0 20000.0 20000.0 0.932 0.758 0.212 0.245 hip102449 85.574 2.09 0.02 -10.861 -20.201 -5.495 -16.697 20000.0 20000.0 20000.0 20000.0 0.519 0.261 0.1 0.47 hip102518 102.434 14.779 2.32 -11.386 -15.386 9999.0 9999.0 20000.0 20000.0 9999.0 9999.0 0.159 0.098 9999.0 9999.0 hip102699 108.664 18.844 3.28 -22.735 -31.997 -15.656 -27.089 20000.0 20000.0 20000.0 20000.0 0.69 0.49 0.883 1.614 hip102926 93.274 7.131 1.15 -7.223 -12.659 -16.723 -20.079 20000.0 20000.0 20000.0 20000.0 0.12 0.724 1.427 0.241 hip102926 93.274 7.131 1.15 -19.275 -12.736 -16.493 -7.201 20000.0 20000.0 20000.0 20000.0 0.367 0.696 1.276 0.101 hip102969 107.589 17.846 5.72 -0.872 -1.873 9999.0 9999.0 1000.035 2327.414 9999.0 9999.0 0.031 0.022 9999.0 9999.0 hip103188 92.23 5.681 1.94 -0.094 5.016 -5.015 -11.119 20000.0 20000.0 20000.0 20000.0 1.521 0.459 1.087 1.097 hip103245 92.267 5.584 1.54 -11.691 -17.212 -8.804 -20.347 20000.0 20000.0 20000.0 20000.0 0.73 0.714 0.289 0.722 hip103292 97.201 9.538 1.78 -22.037 -17.062 -11.369 -27.337 20000.0 20000.0 20000.0 20000.0 1.255 1.527 0.589 0.399 hip103474 103.511 14.217 3.03 -19.473 -11.397 -15.117 -6.95 20000.0 20000.0 20000.0 20000.0 0.279 1.21 1.072 0.288 hip103530 90.111 3.061 3.02 4.503 9999.0 9999.0 9999.0 500.0 9999.0 9999.0 9999.0 0.0 9999.0 9999.0 9999.0 hip103530 90.111 3.061 3.02 21.029 33.154 9999.0 9999.0 3077.347 1070.662 9999.0 9999.0 0.058 0.0 9999.0 9999.0 hip103530 90.111 3.061 3.02 48.161 9999.0 9999.0 9999.0 14616.406 9999.0 9999.0 9999.0 0.024 9999.0 9999.0 hip103543 107.286 16.982 5.33 -2.629 -0.67 9999.0 9999.0 1712.85 6227.412 9999.0 9999.0 0.008 0.024 9999.0 hip103549 97.827 9.541 3.27 8.028 -9.235 2.352 -2.979 20000.0 20000.0 20000.0 20000.0 0.206 0.136 0.311 hip103606 94.378 6.519 3.25 -9.062 -17.042 -13.361 -21.549 20000.0 20000.0 20000.0 20000.0 0.308 1.041 1.116 hip103619 108.956 18.12 3.9 -10.177 -2.751 -6.11 1.097 20000.0 20000.0 20000.0 20000.0 0.164 1.012 0.773 hip103763 104.062 14.193 2.77 -26.927 9999.0 9999.0 9999.0 20000.0 9999.0 9999.0 9999.0 0.032 9999.0 9999.0 hip103763 104.062 14.193 2.77 -2.097 3.736 9999.0 9999.0 1000.0 1014.506 9999.0 9999.0 0.002 0.006 9999.0 hip103772 99.319 10.315 2.3 -11.883 -7.875 9999.0 9999.0 20000.0 7085.26 9999.0 9999.0 0.626 0.061 9999.0 hip103772 99.319 10.315 2.3 -15.757 -13.089 -11.039 -11.127 8422.305 6743.493 20000.0 1525.435 0.069 0.183 0.478 hip103875 106.829 16.22 3.07 -17.63 -22.295 -14.102 -9.892 20000.0 20000.0 20000.0 20000.0 1.271 0.211 1.126 0.256 0.14 9999.0 9999.0 9999.0 0.229 0.282 0.26 9999.0 9999.0 name glon glat pi v1 v2 v3 v4 T1 T2 T3 T4 tau1 tau2 tau3 tau4 hip104211 92.133 3.106 2.04 -11.236 -7.362 -4.443 9999.0 20000.0 20000.0 20000.0 9999.0 0.32 0.957 0.287 9999.0 hip104366 99.855 9.71 1.76 -22.021 -12.582 -5.894 -16.797 20000.0 20000.0 20000.0 20000.0 0.021 0.455 0.028 0.352 hip104573 95.012 4.899 1.85 -16.495 9999.0 9999.0 9999.0 20000.0 9999.0 9999.0 9999.0 0.298 9999.0 9999.0 9999.0 hip104573 95.012 4.899 1.85 -16.008 9999.0 9999.0 9999.0 20000.0 9999.0 9999.0 9999.0 0.311 9999.0 9999.0 9999.0 hip104849 108.94 16.789 6.73 16.784 49.871 9999.0 9999.0 1000.0 19999.909 9999.0 9999.0 0.0 0.0 9999.0 9999.0 hip105137 105.389 13.323 3.13 -16.874 -21.287 -8.977 -13.244 20000.0 20000.0 20000.0 20000.0 0.712 0.168 0.293 1.139 hip105490 108.272 15.451 3.66 -1.455 -0.69 -1.523 9999.0 1000.027 1000.0 1000.0 9999.0 0.0 0.019 0.005 9999.0 hip105490 108.272 15.451 3.66 22.702 9999.0 9999.0 9999.0 2265.483 9999.0 9999.0 9999.0 0.005 9999.0 9999.0 9999.0 hip105635 106.482 13.609 1.85 -10.766 -15.858 -18.198 -17.587 8854.747 10753.758 15452.996 1000.0 0.018 0.161 0.369 0.097 hip105635 106.482 13.609 1.85 -17.546 -15.32 -17.666 -9.652 1000.0 2760.785 17545.803 20000.0 0.075 0.04 0.412 0.027 hip105690 97.063 4.272 1.01 -11.731 -22.98 -17.183 -7.54 20000.0 20000.0 20000.0 20000.0 0.309 0.046 1.371 0.103 hip105891 94.891 1.551 6.06 -0.134 9999.0 9999.0 9999.0 6492.165 9999.0 9999.0 9999.0 0.021 9999.0 9999.0 9999.0 hip106585 104.449 10.029 2.72 1.904 9999.0 9999.0 9999.0 1491.28 9999.0 9999.0 9999.0 0.013 9999.0 9999.0 9999.0 hip106733 104.936 10.243 1.54 -10.835 -15.086 -6.107 -20.9 20000.0 20000.0 20000.0 20000.0 0.871 1.0 0.339 0.217 hip106830 100.339 5.054 1.28 -20.772 -11.512 -8.321 -16.454 20000.0 20000.0 20000.0 20000.0 0.207 1.161 0.212 1.977 hip106948 108.82 14.027 5.07 3.727 9999.0 9999.0 9999.0 13489.869 9999.0 9999.0 9999.0 0.015 9999.0 9999.0 9999.0 hip107025 108.429 13.507 3.01 -30.605 -25.928 -11.238 -20.818 20000.0 20000.0 20000.0 20000.0 0.559 1.452 0.153 0.45 hip107025 108.429 13.507 3.01 -30.555 -25.929 -20.877 -11.115 20000.0 20000.0 20000.0 20000.0 0.558 1.443 0.47 0.141 hip107123 100.26 4.234 0.93 name glon glat pi v1 v2 v3 v4 T1 T2 T3 T4 tau1 tau2 tau3 tau4 TYC 132-864-1 208.985 -7.195 0.82 -22.071 9999.0 9999.0 9999.0 500.0 9999.0 9999.0 9999.0 0.0 9999.0 9999.0 9999.0 TYC 3152-864-1 77.274 -0.188 0.61 -19.065 -5.968 -1.357 -13.634 19903.442 20000.0 20000.0 20000.0 0.93 0.26 0.073 0.39 TYC 3152-864-1 77.274 -0.188 0.61 -13.817 -19.175 -6.034 -1.653 20000.0 20000.0 20000.0 20000.0 0.418 0.924 0.267 0.076 TYC 3185-1390-1 88.856 -12.655 0.92 -18.928 -11.697 9999.0 9999.0 20000.0 20000.0 9999.0 9999.0 0.672 0.076 9999.0 9999.0 TYC 3590-2213-1 90.339 -3.212 1.36 -18.608 -22.768 -14.982 -10.941 20000.0 20000.0 20000.0 20000.0 0.972 0.228 1.005 0.344 TYC 3682-1132-1 128.28 -3.959 0.81 -15.815 -3.213 -20.658 -9.147 20000.0 20000.0 20000.0 20000.0 0.168 0.368 0.167 0.124 TYC 3698-2525-1 134.622 -1.405 0.68 -15.782 -8.74 -4.124 0.508 20000.0 20000.0 20000.0 20000.0 0.763 0.811 1.459 0.919 TYC 3698-2525-1 134.622 -1.405 0.68 -9.134 -15.968 0.576 -4.323 20000.0 20000.0 20000.0 20000.0 0.785 0.706 0.874 1.566 TYC 3990-1799-1 103.694 -0.511 0.61 -14.867 -10.628 -22.173 -8.159 20000.0 11077.741 20000.0 1510.133 0.133 0.357 0.222 0.041 TYC 3990-1799-1 103.694 -0.511 0.61 -21.702 -11.647 9999.0 9999.0 20000.0 20000.0 9999.0 9999.0 0.179 0.311 9999.0 9999.0 TYC 4014-3145-1 117.478 -1.798 0.36 -27.578 -18.77 9999.0 9999.0 20000.0 20000.0 9999.0 9999.0 0.154 0.338 9999.0 9999.0 TYC 4014-3145-1 117.478 -1.798 0.36 -18.728 -27.006 9999.0 9999.0 20000.0 20000.0 9999.0 9999.0 0.33 0.16 9999.0 9999.0 TYC 4018-914-1 117.379 0.559 0.13 -11.352 9999.0 9999.0 9999.0 20000.0 9999.0 9999.0 9999.0 0.821 9999.0 9999.0 9999.0 TYC 4018-914-1 117.379 0.559 0.13 -11.235 9999.0 9999.0 9999.0 20000.0 9999.0 9999.0 9999.0 0.841 9999.0 9999.0 9999.0 TYC 4287-238-1 113.503 2.914 1.09 -0.055 9999.0 9999.0 9999.0 20000.0 9999.0 9999.0 9999.0 1.745 9999.0 9999.0 9999.0 TYC 3045-332-1 62.412 59.364 3.73 -39.405 -34.749 -25.194 -30.913 20000.0 20000.0 16037.143 20000.0 0.176 0.634 0.091 0.44 TYC 430-1922-1 28.957 10.605 1.42 -14.311 -12.206 9999.0 9999.0 19999.994 16635.024 9999.0 9999.0 0.275 0.145 9999.0 9999.0 TYC 431-1605-1 28.121 9.491 2.84 -9.653 -17.795 -11.665 -14.162 13517.203 20000.0 3381.555 13481.353 0.131 0.316 0.083 0.545 TYC 431-394-1 29.805 9.917 1.63 -26.066 -18.667 -14.658 -10.516 4667.427 19999.999 20000.0 20000.0 0.027 0.1 1.056 0.385 TYC 431-812-1 28.749 9.323 2.22 -19.691 -14.317 9999.0 9999.0 20000.0 20000.0 9999.0 9999.0 0.421 1.341 9999.0 9999.0 TYC 431-835-1 28.933 9.481 0.84 -20.762 -17.351 -13.797 9999.0 20000.0 20000.0 20000.0 9999.0 0.331 1.89 0.267 9999.0 TYC 432-1126-1 29.282 7.232 2.05 -8.419 -25.575 -17.901 -13.226 20000.0 20000.0 20000.0 20000.0 0.267 0.059 0.577 1.362 TYC 434-4617-1 29.621 10.893 2.08 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0	τ 3 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 0.082 9999.0 9999.0 9999.0 9999.0 0.114 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 9999.0 0.296 0.298 0.361 0.117

CHAPTER 1. INTERSTELLAR MEDIUM GENERAL PROPERTIES

http://argonaut.skymaps.info

https://www.cosmos.esa.int/web/gaia/news-2018#DataReleaseUpdate2018]

(a) (b) C

stilism.obspm.fr

http://www.sdss.org/dr12/ Article number, page

of 18 L. Capitanio et al.: Three-dimensional mapping of the local interstellar medium with composite data

http://www.wavemetrics.com

Article number, page 6 of 18 L. Capitanio et al.: Three-dimensional mapping of the local interstellar medium with composite data

Article number, page 8 of 18 L. Capitanio et al.: Three-dimensional mapping of the local interstellar medium with composite data

AppendixArticle number, page 16 of 18 L. Capitanio et al.: Three-dimensional mapping of the local interstellar medium with composite data

[http://www.sdss.org/dr14/data_access/value-added-catalogs/?vac_id= apogee-dr14based-distance-estimations/]

http://polarbase-dev.irap.omp.eu/Espadons_Narval/index.php

Acknowledgements. We deeply thank our referee Katia Ferriére for careful reading of the manuscript and numerous constructive comments. Her corrections and suggestions resulted in significant improvement of the article. L.C. acknowledges doctoral grant funding from the Centre National d'Etudes Spatiales (CNES). R.L. and A.M.-I. acknowledge support from "Agence Nationale de la Recherche" through the STILISM project (ANR-12-BS05-0016-02) and the CNRS PCMI national program. M.E. acknowledges funding from the "Region Ile-de-France" through the DIM-ACAV project. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.

<l>25000</l> ! maximum lines of sight number <isec>0</isec> ! if 1, code uses a sec norm, otherwise a gaussian norm <ml>10</ml> <switchbloc>1</switchbloc> ! if 1, it divided in blocks the dataset <groupb>500</groupb> ! physical dimension of blocks, here 500x500 pc <switchcarteprior>0</switchcarteprior> ! if 0, analytical prior; if 1 external prior <switchautocorr>1</switchautocorr> ! choice of autocorrelation function <ro0>0.00025</ro0> ! density on the prior in the Galactic plane <h0>200</h0> ! scale height <sr0>0.8</sr0> ! σ0 for the autocorrelation function <sr1>1.0</sr1> ! ξ0 for the autocorrelation function <xi0>30.0</xi0> ! σ1 for the autocorrelation function <xi1>15.0</xi1>! ξ1 for the autocorrelation function <errmin>0.01</errmin> ! minimum error on the excess of colour <lmax>2500.0</lmax> ! selected target closer to the Sun then lmax [pc] <hmax>500.0</hmax> ! selected target closer to the Galactic plane then hmax [pc] <resolution>10</resolution> ! resulution for the integration on the line of sight <longmin>0.</longmin> ! selected target with longitude highr then longmin <longmax>2.</longmax> ! selected target with longitude lower then longmax <hsig>10000.0</hsig> <spri>1.</spri> ! typical error on the prior <ndlimi>20.0</ndlimi> ! reciprocal influence distance ndlimi*max(xi0,xi1)) for the density extimation <ndd0>12.0</ndd0> ! maximal distance between two target to be taken in account during the integration ndd0*max(xi0,xi1) <dmax>2000.0</dmax> ! half-base cube dimension [pc] <dmaxz>300.0</dmaxz> ! half -altitude cube dimension [pc] <pas>5.0</pas> ! sampling in cube <nsigdata>3.0</nsigdata> ! how many sigma difference between datapoint and model to be considered outlier <repres>resultscramer</repres> ! directory for the results Table C.8 -Fit NARVAL and ESPaDOnS spectra. name glon glat pi v1 v2 v3 v4 T1 T2 T3 T4 tau1 tau2 tau3 tau4 hip13003

Part II

Gaia DIB: previsions and tools

Part IV

Mapping improvements: building and testing a full 3D hierarchical method

California

California is a molecular cloud in the Taurus complex, in the interval l = (155 • , 170 • ) and b = (-12.5 • , -7.5 • ). Its velocities are between -10 and 0 km/s and it could be decomposed in four parts, which respectively velocities from -8 to 6.5 km/s, from -6.5 to -4.0 km/s, and from -4.0 to 0 km/s and a bloom of little structures with variable velocities. Fig 17.30 shows at the top the structure at velocity from -4 km/s to 0 km/s in CO emission and our stellar targets. It is indicated for the stars in the direction of the CO structure the stellar identifier, the distance and the velocity corresponding to the structure, where it is measured. Our spectra allows us to chart two structures; first one in the longitude from 160 • and 170 • , positioned the beginning between 390 pc and 500 pc, and it is properly the California cloud. Second one, it is closer and from longitude 162 • to 150 • .

In the bottom) Fig 17 .30, it is shown the structure with velocities from -6 km/s to -4 km/s. It is evident the same cloud from longitude 162 • to 150 • . Thanks to the stellar target positions, I can chart its beginning definitely between 210 and 456 pc.

At centre, it is possible to constrain also the structure at velocity from -10 km/s to -6 km/s, as the previous one. It is interesting that the star V * XY Appendix A

Inversion parameter example

Exemple of configuration file for the inversion.

Appendix C

Others NARVAL and ESPaDOnS fits

As I cannot use all the NARVAL and ESPaDOnS spectra available and fitted in potassium to make a kinematic analysis like for Taurus, I present here the results for future employments. APPENDIX C. OTHERS NARVAL AND ESPADONS FITS