Dr Juan Pablo

Dr Torres Papaqui

Fatima Robles

Driver, S M Alpaslan

Colberg, J. M G Altay

& Croft

Arag Ón-Calvo

Platen, E M A Van De Weygaert

The baryonic component of the Large Scale Structure (LSS) of the Universe is composed by concentrations of gas and galaxies forming groups, clusters, elongated filaments and widely spread sheets which probably underline the distribution of dark matter. Nevertheless, according to the current cosmological models, most of the baryonic material in the Universe has not yet been directly observed.

Numerical simulations suggest that from one-half to two-thirds of all baryons may be located out of clusters of galaxies, pervading the structures between them.

The most concentrated structures, which we call systems of galaxies (i.e., groups and clusters) usually contain high density hot gas (1 10 keV) that cools radiatively, emits at X-rays wavelengths and interacts with the cosmic microwave background at millimeter wavelengths (Sunyaev Zel'dovich effect, SZ). For the less dense structures, filaments and sheets, the baryons are probably in moderately hot gas phase (0.01 1 keV), commonly named as warm hot intergalactic medium (WHIM). In this PhD Thesis, we study the environmental effects associated to the different components of the LSS. For the galaxy systems, we aim to characterize the intra cluster medium (ICM) through the analysis of the S-Z effect. We employ the ACT and Planck data to analyze the gas pressure profiles of a sample of low mass galaxy clusters. For the least dense structures, we assembled a sample of filament candidates composed by chains of clusters that are located inside superclusters of galaxies. We aim to probe the filament structure skeletons and characterize their components (galaxies, groups/clusters and gas).

Resumen

La componente bari ónica de la estructura a gran escala del Universo est á compuesta por concentraciones de gas y galaxias formando grupos, c úmulos, filamentos elongados y amplias paredes. Dichas estructuras probablemente reflejan la distribuci ón de materia oscura en el Universo. Sin embargo, de acuerdo al modelo cosmol ógico actual, la mayor parte de la materia bari ónica en el Universo no ha sido observada a ún. No obstante, las simulaciones num éricas nos sugieren que entre la mitad y dos tercios de los bariones quiz á se encuentran entre c úmulos de galaxias, poblando las estructuras que los conectan. Las estructuras m ás concentradas, generalizadas por nosotros como sistemas (i.e. grupos y cúmulos), usualmente contienen gas a altas densidades y temperaturas (1 10 keV) que se enfría radiativamente emitiendo fotones observables en rayos X e interact úa con la radiaci ón c ósmica de fondo por efecto Sunyaev-Zel'dovich (SZ) observado a longitudes de onda milim étricas. En las estructuras menos densas, los filamentos y paredes, los bariones se encuentran probablemente en un estado menos denso y a una temperatura moderada (0.01 1 keV). Este gas es com únmente llamado medio intergal áctico templado. En esta Tesis de Doctorado estudiamos los efectos ambientales asociados a las diferentes componentes de la estructura a gran escala. En el caso de los sistemas nuestro objetivo es caracterizar el medio intracumular de c úmulos utilizando el efecto SZ. Para esto hacemos uso de observaciones de sat élite Planck y del ACT (Atacama Cosmological Telescope) para analizar el perfil de presi ón del gas contenido para una muestra de c úmulos de baja masa. Por otro lado, para el estudio de las estructuras de baja densidad, los filamentos, construímos una muestra de candidatos a filamentos que consiste en cadenas de cumulos dentro de supercumulos de galaxias. Nuestro objetivo es probar la naturaleza filamentosa de estas estructuras así como caracterizar sus componentes (galaxias, c úmulos y gas).

R ésum é

La composante baryonique de la structure à grande échelle de l'Univers est compos ée de concentration de gaz et de galaxies, donnant lieu à des groupes, à des amas, à des filaments allong és et à des murs étendus. Ces structures peuvent suivre la distribution de mati ère noire dans l'Univers. N éanmoins, selon le mod èle cosmologique actuel, l'ensemble des mati ères baryoniques dans l'Univers n'a pas encore ét é observ é. Cependant, les simulations num ériques nous sugg èrent qu'entre la moiti é et deux tiers des parties des baryons sont localis ées entre les amas de galaxies et peuplent les structures qui les relient. Les structures les plus concentr ées, que nous appelons ici ⌧ des syst èmes (i.e. groupes et amas), ont g én éralement des gaz à haute concentration et une temp érature élev ée (1 10 keV). Cette temp érature se refroidit en émettant des photons qui sont observables en rayons X. De plus les gaz interagissent avec les photons du fond diffuse cosmologique par l'effet Sunyaev-Zel'dovich (SZ) , observable à longueur d'onde millim étrique. Dans les filamentaires et murs qui sont des structures moins denses, les baryons sont probablement dans un état moins dense et à une temp érature mod ér ée (0.01 1 keV). Ces gaz ti èdes sont appel és WHIM (Warm Hot Intergalactic Medium). Pendant cette Th èse de doctorat nous étudions les effets environnementaux associ és aux diff érents composants de la structure à grande échelle de l'Univers. Pour les syst èmes, l'objectif est la caract érisation du milieu intra amas en utilisant l'effet SZ. Pour cela nous utilisons les observations du satellite Planck et de l'Atacama Cosmological T élescope (ACT) afin d'analyser les profils de pression pour un échantillon d'amas de faible masse. D'autre part, pour l' étude des structures à faible densit é (structures filamentaires). Nous avons construit un échantillon de candidats à filaments, cet échantillon se compose des chaînes d'amas reli ées en une structure de super amas de galaxies. Notre objectif est de prouver leur nature filamentaire et de caract ériser ses composants (galaxies, amas et gaz).

Introduction

With the availability of all sky extragalactic surveys, it has been observed that, at large scale, the galaxies (observable baryonic matter) in the Universe are organized in a web-like pattern. This pattern has been observed in several galaxy redshift surveys (e.g. [START_REF] Joeveer | Large Scale Structures in the Universe[END_REF]Davis et al., 1982;Shectman et al., 1996;Colless et al., 2001;Huchra et al., 2012). Such observations have shown that the large scale structure (LSS) was composed of elongated filaments, widely spread sheets and higher density knots. The latter are usually located at the intersection of filaments, where clusters and groups are hosted (e.g. [START_REF] Peebles | The large-scale structure of the universe[END_REF]. According to the current standard cosmological model (e.g. Riess et al., 1998) and observations of the cosmic microwave background (CMB) (e.g. Planck Collaboration et al., 2016b), the Universe is composed of 70% of dark energy and 30% of matter. Of the latter, about 85% is present in the form of cold dark matter (CDM) and only about 15% in the form of baryonic matter.

This model establishes that such structures of matter were formed through gravitational collapse, in a hierarchical scenario. In other words, the smaller halos (galaxies) formed first, then, they grew by fusion and accretion with other halos.

Since the baryonic matter follows, to first order, the distribution of the dark matter, the galaxies and gas populate these structures accordingly (e.g. Eisenstein et al., 2005). The groups and clusters of galaxies are the next step of this hierarchical process of forming the densest regions in the LSS. About 85% of the baryonic matter in these structures is present in the form of hot gas (T ⇠ 10 7 10 8 K, or kT ⇠ 1-10 keV). This gas can be directly observed by its X-ray emission or through N-body simulations have been used to unveil where these baryons might be located, e.g. the Millennium (Springel et al., 2005), the Magneticum (Dolag et al., 2016) and Illustris (Vogelsberger et al., 2014). Their results regarding this subject suggest that these baryons might be in a warm and low density gas phase ( T ⇠ 10 5 10 7 K or kT ⇠ 0.01-1 keV) filling filaments and sheets between galaxy clusters, constituting the so-called warm hot intergalactic medium (WHIM). The characterization of the WHIM thought observables such as X-rays or SZ effect is very challenging. However, deeper observations and the increase in detection sensitivity at millimetric, optical and X-rays wavelengths open the possibility to better study the dispersed component of the LSS while allowing the following subjects of study:

1. to detect and characterize the LSS components (e.g. topology, density, temperature, dynamical state, matter distribution and its evolution with time), 2. to better constrain the environment role in galaxy evolution, 3. to understand the mechanisms that shape the LSS matter distribution and 4. to evaluate and improve the current standard cosmological model.

In this framework, this Thesis is focused on studying the first and second subjects, characterizing the LSS components and investigating their effects on the galaxies evolution. By this, we aim to understand the mechanisms driving the LSS distribution, the third subject. Firstly, we present the characterization of LSS components (filaments, groups and clusters) along with the study of their environmental effects on the galaxy properties. Secondly, we present the characterization of galaxy clusters through the extraction of intra-cluster medium (ICM) pressure profiles from a high resolution SZ map.

In Chapter 1, we describe briefly the cosmological context that is used for our work and we introduce the current state of the art regarding the LSS components: galaxy clusters and filaments.

In Chapter 2, we introduce a general view of the current advances in detection of the disperse component of the LSS. Then, we describe in detail the methodology we implemented for the detection of clusters and filamentary structures.

Our method aims the detection of chain-like structures inside a sample of galaxy superclusters (from Chow-Martinez et al., 2014) in the Local Universe (z ⇠ 0.15).

As shown in Tanaka et al. (2007), the possibility to find elongated chain-like structures increases in superclusters.

In Chapter 3 we present the analyses we carried out to search for correlations between the galaxy properties (mass, morphology, activity, color and metallicity) and the environment in which these galaxies reside. For this analysis we used the Sloan Digital Sky Survey (SDSS) spectroscopic redshifts and sub-products (Albareti et al., 2017).

Chapter 4 is orientated towards the study of the gas component of galaxy clusters. We describe the methodology used for reconstructing the 3D radial profile of the thermal pressure for a sample of clusters, and the statistical analysis of the pressure distribution across the sample. These analyses were achieved using a composed SZ map from Planck and ACT (Atacama Cosmology Telescope) surveys, PACTmap (Aghanim et al., 2019a).

The final Chapter of this Thesis discusses the results of this work regarding the detection of LSS structures, their classification and characterization. We review the trends and correlations observed for galaxies inhabiting different components of the LSS detected by our algorithms, and discuss the possible environmental effects over their evolution. In addition, we discuss different approaches to carry out further analyses of the characterization of the gas component of clusters and filaments, in a similar way as the study carried out in this Thesis, using the SZ effect. We also discuss the achievements of, and our contribution to the LSS structure detection algorithms. Finally, the directions for further characterization of the LSS components using optical and gas components are presented. We also describe the future applications of the GSyF and GFiF algorithms. For this work we adopt (H 0 , ⌦ M , ⌦ ⇤ , ⌦ k , ⌦ r ) = (0.7, 0.3, 0.7, 0.0, 0.0).

Chapter 1 A Cosmology context

The different theories formulated in the history of cosmology aim to bring understanding on the mechanisms that govern the formation and distribution of matter and energy in the Universe. As the observational facilities provide deeper and more sensitive observations, in different wavelength regimes, the cosmological theories need to be improved in order to model the Universe as observed today.

The study and characterization of the LSS distribution and its content through observables can be used to evaluate the cosmological models and see if they reproduce what is observed.

In this Chapter we present the principal aspects of the cosmology formalism that are behind the most accepted cosmological model and introduce the current state of art regarding the study of the main components of the LSS.

The standard cosmological model 1.The establishment of the ⇤CDM model

The standard cosmological model, ⇤CDM (e.g. Bond & Szalay, 1983;Doroshkevich & Khlopov, 1984), sometimes referred to as the concordance model, was motivated by observational studies of the LSS and the observations of the CMB.

As summarized by Battaner & Florido (2000), Einasto (2009) and Einasto (2014), the cosmological model has changed to adapt to the observational facts along with the new theories about structure formation; here we introduce the most important contributions to this cosmological model. At the beginning the model suggested the hypothesis that the first galaxies were formed from primordial density fluctuations of the baryonic medium (Harrison, 1970). However, there were problems with physical and kinematic properties of galaxies and clusters such as the potential energy needed to keep these structures bounded (Oort, 1940;Roberts, 1966;Rubin & Ford, 1970). Then, to explain these discrepancies, a dark matter in the form of dark stellar population and gaseous halos was proposed (e.g Ostriker & Peebles, 1973;Bahcall & Casertano, 1985). With the first observations of the CMB the model was discarded since the observed density fluctuations were smaller than predicted. As an alternative, the Hot Dark Matter model was proposed. This model suggested a non-baryonic relativistic neutrino-like particle as candidate for the dark matter, which explained the small fluctuations observed in the CMB (Cowsik & McClelland, 1973;Szalay & Marx, 1976;Tremaine & Gunn, 1979;Doroshkevich et al., 1980;Chernin, 1981). However, in this scenario, the structures observed today would not have had enough time to build up and the model was also abandoned. This gave place to a new hypothetical dark matter particle which moves slowly leading place for structure formation. This model was called Cold Dark Matter (CDM) (Blumenthal et al., 1982;Bond et al., 1982;[START_REF] Peebles | [END_REF]Pagels & Primack, 1982;Doroshkevich & Khlopov, 1984). It was originally proposed as a theory opposed to the Hot Dark matter (HDM) neutrino model. Finally, supernovae observations showed that the Universe was in a state of accelerated expansion. This brought up the need for a return of the cosmological constant ⇤, see Section 1.1.3, to open space for a supposed vacuum energy, leading to the current ⇤CDM model.

The fundamental parameters

Considering the expansion of the Universe is uniform, the distance and velocity of an object can be expressed as:

r(t) = a(t) ⇥ D C (t), (1.1) ṙ = H(t)r(t) + a(t) ṙ, (1.2)
where D C (t) is the comoving distance, H(t) the Hubble parameter and a(t) the scale factor. The expansion rate is dictated by the term = H(t)r(t) which relates the separation and recession velocity of distant galaxies. Then, the Hubble-Lemaître law is approximated to:

v(t) = H(t)D C (t), (1.3)
for the Local Universe. By convention, the sub-index 0 denotes the current value for the Hubble parameter at z = 0, usually written as H 0 = 100 h km s 1 Mpc 1 , scaled in terms of h. For instance, Planck Collaboration et al. (2016b) measured h as 0.6772 ± 0.0046 using CMB measurements, while the Gaia mission measured a value of 0.7348 ± 0.0166 using a distance scale derived from Cepheid parallaxes (Riess et al., 2016). Another approach by Cuceu et al. (2019) measured h = 0.676 ± 0.011 using Baryon Acoustic Oscillations, while the H0LiCOW collaboration (e.g. Suyu et al., 2017) measured h = 0.733 ± 0.0175 using the time delay of lensed quasars. Another interesting result was the measurement by Hotokezaka et al. ( 2019) using the radio counterpart of GW170817, combined with gravitational wave and electromagnetic data, h = 0.703±0.0515. Considering that the Universe is isotropic at large scale and has a constant curvature, then, the space-time can be expressed by the Friedman-Robertson-Walker metric which, in spherical coordinates, is written as:

ds 2 = c 2 dt 2 + a 2 (t) ✓ dr 2 1 kr 2 + r 2 d⌦ 2 ◆ ,
(1.4) with a 2 > 0 and ⌦ 2 = d✓ 2 + sin 2 ✓d 2 . k determines the space curvature as:

k 8 > > > < > > > :
> 0 the space-time is closed (spherical-like topology), = 0 the space-time is flat, > 0 the space-time is open (hyperbolical-like topology).

Then, a useful observational measurement to estimate an object's distance is the redshift. The redshift is the result of the Doppler effect seen in the the galaxies optical spectra or magnitude, consequence of the expansion of space in all directions. Measuring the redshift of the spectral lines allow us to estimate when the light photons were emitted. The time between an object emitting photons and the observation can be defined as: Then, the redshift is deduced as:

v source v obs = a obs a source = 1 + z,
(1.6) with v source the velocity of the object and v obs observed velocity. For small redshifts, i.e. small distances, we can approximate z ⇠ vsource c .

Dynamics of a Universe in expansion

Considering that the Universe is homogeneous and isotropic, its evolution can be described, in General Relativity, by the Friedmann-Lemaître Equations:

( ȧ a ) 2 = 8⇡ G 3 ⇢ tot kc 2 a 2 + ⇤c 2 3 (1.7) ȧ a = 4⇡G 3 ⇢ tot + 3ptot c 2
with (1.8)

⇢ tot = ⇢ ⇤ + ⇢ m + ⇢ r , (1.9)
where ⇢ ⇤ = ⇤/8⇡G corresponds to the dark energy contribution. Here ⇤ is the cosmological constant 1 , ⇢ m = ⇢ c + ⇢ b corresponds to the matter density (where ⇢ b is the baryonic density and ⇢ c is the dark matter density); the density of radiation is ⇢ r while k is the Universe curvature. A detailed derivation of Equation 1.7 from Einstein's equation can be consulted in Padmanabhan (2003).

Then, the density and pressure can be expressed in terms of the cosmological constant as:

⇢ ! ⇢ + ⇤c 2 8⇡G and p ! p ⇤c 2 8⇡G
.

(1.10) and the Friedmann equations can be re-written in terms of energy density of pressure:

H 2 = ✓ ȧ a ◆ 2 = 8⇡ G 3 ⇢ tot kc 2 a 2 ,
(1.11) 1 Introduced by Einstein in 1917 to compensate the natural dynamics (expansion or contraction) of the Universe and make it static. Currently it is used to represent the dark or vacuum energy effect which causes an acceleration in the expansion of the Universe.

Considering Equation 1.11 with k = 0, i.e. a flat Universe, we can derive the critical density of the Universe as ⇢ c = 3H 2 0 8⇡G . The density parameter can be written in terms of the critical density as: ⌦ = ⇢(t)/⇢ c (t).

Then the ⇢ ⇤ , ⇢ m and ⇢ r can be re-written in terms of the density parameter [START_REF] Peebles | Principles of Physical Cosmology Penzias[END_REF]:

⌦ m = 8⇡G⇢ tot 3H 2 0 , ⌦ k = k a 2 H 2 0 , and ⌦ ⇤ = ⇤ 3H 2 0 (1.12)
The Friedmann equation can be re-written in terms of the density parameter as:

⌦ m + ⌦ r + ⌦ ⇤ + ⌦ k = 1 (1.13)
Then the curvature of the Universe can be defined as:

kc 2 = a 2 0 H 2 0 (⌦ tot 1) = a 2 0 H 2 0 (⌦ m + ⌦ r + ⌦ ⇤ ) (1.14)
Considering Equations 1.7, the fluid equation of state can be expressed as:

⇢ + 3H ⇣ ⇢ tot + p tot c 2 ⌘ = 0, (1.15)
In order to simplify, the pressure and energy can be related by p = p(⇢). The Equation 1.15 can be solved for a fluid with no torsion considering p = w⇢, where w = ( 1) is constant and ⇢ / a 3(1+w) , leading to the solution of the Friedman Equation of the form a / t 2/( 3(1+w)) . This solution can be used to estimate the evolution of energy density:

The Radiation dominated Universe: called Tolman Universe; it is defined by w = 1/3 and a radiation density ⌦ r ⇡ 1. Then the density and scale factor evolve as:

⇢ r (t) = ⇢ r0 ⇣ a 0 a ⌘ 4 with a(t) = a 0 ✓ t t 0 ◆ 1/2 (1.16)
Matter dominated Universe: if w = 0 then p = 0 then matter is pressureless, corresponding to the Einstein-de Sitter Universe with the values of energy density and scale factor:

⇢ m (t) = ⇢ m0 ⇣ a 0 a ⌘ 3 with a(t) = a 0 ✓ t t 0 ◆ 2/3
(1.17)

Curvature dominated Universe: In the case of an open Universe with k < 0, the Equation 1.7 does not have a solution, then:

⇣ a 0 a ⌘ 2 = k a 2 with a(t) / a 0 ✓ t t 0 ◆ . (1.18)
Energy dominated Universe: this is called de Sitter Universe. With w = 1 the scale factor has to be expanded by a Taylor series.

⇢ ⇤ (t) = ⇢ 0 with a(t) = a 0 e H(t t 0 ) .

(1.19)

Combining Equations 1.6, 1.14 and 1.13, the Friedmann equation now can be expressed in terms of redshift and densities as:

H 2 = H 2 0 (⌦ r (1 + z) 4 + ⌦ m (1 + z) 3 + ⌦ k (1 + z) 2 + ⌦ ⇤ ), (1.20)
Values of these densities have been recently measured using observations of the Planck satellite (Planck Collaboration et al., 2016b) results:

From the latter, we can highlight that, according to the ⇤CDM cosmological model, the Universe is predominately composed of dark energy while its matter content is mainly composed of cold dark matter, its curvature is flat and it is in a state of accelerating expansion.

Distance measurements in the Universe

Comoving distance in the line of sight Considering two objects moving with the Hubble flow, the measurement of the distance between them (proper distance) at different times needs to be scaled. The distance from us to an object in the line of sight, the comoving distance D C , is defined as:

D C = c H 0 Z z 0 dz 0 E(z 0 ) , (1.21) D C = D H Z z 0 dz 0 E(z 0 ) , (1.22)
with E(z), defined by [START_REF] Peebles | Principles of Physical Cosmology Penzias[END_REF], as:

E(z) = H(z) H 0 = p ⌦ r (1 + z) 4 + ⌦ m (1 + z) 3 + ⌦ k (1 + z) 2 + ⌦ ⇤ , (1.23)

Angular diameter distance and luminosity distances

The angular diameter distance D A is used to measure the actual size of objects observed with small angular sizes ( ✓), that is, separations perpendicular to the line of sight, defined as ✓ ⇥ D A . The angular diameter distance is used to convert from angular distances in physical separations and has the form:

D A = D m 1 + z . (1.24)
where D m is the comoving angular diameter distance which depends on the Universe curvature and is defined as:

D m 8 > > > > < > > > > : D H 1 p ⌦ k sinh ⇣ p ⌦ k D C D H ⌘ for ⌦ k > 0, D C for ⌦ k = 0, D H 1 p ⌦ k sin ⇣ p ⌦ k D C D H ⌘ for ⌦ k < 0,
Another useful distance measure is the luminosity distance which, in an expanding space, can be defined as:

D 2 L = L s 4⇡F , (1.25)
where F is the flux received from an emitting source with absolute luminosity L s .

The luminosity distance is related with the comoving angular diameter distance as:

D L = (1 + z)D m = (1 + z) 2 D A .
(1.26)

The Universe's thermal history

The combination of observations, the cosmological model and particles physics, allows us to study the early Universe by reconstructing the evolution of its components.

The Planck Era: T ⇠ > 10 32 K According to the current cosmological model, at the beginning the Universe was in an extremely hot, dense and in ionized state.

The study of the evolution of the Universe allows one to reconstruct its thermal history up to the so-called Planck's time, t p = 10 43 seconds after the Big Bang.

Before this time, quantum corrections become significant due to the extreme temperature, and density. At this moment the gravity ional force separated from the other forces. This corresponds to the moment at which the de Broglie wavelength of the Universe equals to its Schwarzschild radius:

mc = 2Gm c 2
(1.27)

The GUT Era: T ⇠ 10 32 10 29 K At z ⇠ 10 32 , t ⇠ 10 43 10 36 s the GUT theories propose a model in which the asymmetry between matter and antimatter produce a phase transition. This transition makes the Universe expand exponentially, giving rise to the inflation theory (Starobinsky, 1980;Guth & Pi, 1982;Linde, 1982).This model gives a solution to the so called homogeneity problem, allowing the formation of the structures observed today from primordial density inhomogeneities, at a Hubble radius.

The particle Era: T ⇠ 10 15 10 9 K When the Universe cools to a temperature about T ⇠ 10 16 K, (t ⇠ 10 12 s 2 min) the electromagnetic and nuclear weak forces separate. At this point the quarks, electrons, photons and gluons form a plasma in constant interaction. Afterwards, as the temperature decreases, at about T ⇠ 10 13 K, the strong nuclear force allow the transition between quarks and hadrons, forming the protons and neutrons.

The primordial nucleosynthesis: T ⇠ 10 16 K The neutrinos and anti-neutrinos stop their interactions with electrons. As the baryons cooled, at temperatures about T ⇠ 10 9 K, the first deuterium and helium nuclei were formed. This process is called primordial nucleosynthesis and depends on the expansion rate of the Universe. This processes also determines the amount of baryonic matter in the Universe, which is measured to be between 4% and 5% of the critical density of the Universe.

In the Big Bang Model, nucleosynthesis occurs in the radiation-dominated epoch.

The density of the Universe can be estimated as function of the temperature as

⇢(T ) = (⇡ 2 /30)N rel T 4
, where N rel is the effective number of bosonic degrees of freedom. Under this scenario: when a(t) ! 0, the density ⇢ ! 1 and T ! 1.

However, the primordial densities can be calculated assuming that the reaction:

p + e ! n + ⌫ e , (1.28)
occurs in thermal equilibrium, such that the interaction rate, (t) = nh ⌧ v rms i (where ⌧ is the Thomson cross section and v rms is the rms velocity), allows hydrogen to form.

Photon decoupling and recombination: T ⇠ 10 4 K At this temperature the Universe is dominated by relativistic particles and the matter and radiation densities are in equilibrium (t⇠ 47kyr,T⇠ 10 4 K, z⇡ 3600). Then, at temperatures of ⇠ 3 000 K the electrons combine with nuclei to form stable neutral atoms. At this moment, the photons decouple from the matter in all directions, as evidenced by the cosmic microwave background (CMB), See Section 1.3. One can define the temperature of the primordial photons at the moment of decoupling from the matter, dependent on the expansion as:

T (t) / 1 a(t)
.

(1.29)

The dark era and the formation of the first stars: T ⇠ 15 K The CMB temperature decreases as the Universe expands. During this time, under the effect of gravity the first dark matter halos formed the first galaxies which agglomerated giving plate to the first galaxy clusters following a hierarchical structure formation scenario. Moreover, clouds of gas formed under the effect of gravity inside these halos, giving place to the first stars giving place to the reionization Era 200Myr,20>z>6).

The cosmic microwave background

The cosmic microwave background (CMB) was first observed by accident by Penzias & Wilson (1965) while carrying out an observation for radio emission. Thanks to their discovery they were awarded with the Nobel prize in 1978. The CMB is observed as an isotropic emission in the microwave window, coming from all directions in the sky. Its power spectrum represents the Universe a little bit after the moment at which matter and radiation density were equal.

CMB electromagnetic spectrum

The CMB photons are uniformly distributed and have a temperature of 2.725 ± 0.00335 K (Fixsen, 2009) with a black body spectrum defined as:

B ⌫ (T CMB ) = 2h⌫ c 2 ✓ 1 exp ✓ h⌫ k B T CMB ◆◆ 1 [Wm 2 sr 1 Hz 1 ], (1.30)
where h and k B are the Planck and Boltzmann constants, respectively. The CMB observations suggest that the photons were indeed very close to equilibrium at some point in the early Universe. However, the CMB temperature presents small fluctuations (anisotropies) of the order T CMB = (T hT i)/hT i ⇠ 10 5 .

CMB angular power spectra

In general, the anisotropies of the CMB are quantified by their power spectrum.

These anisotropies are observed as a function of direction over the celestial sphere. Therefore, they are expressed in terms of spherical harmonics:

T (n) = 1 X `=0 X m= `T`m Y `m( n) (1.31)
where n is the direction of observation. The multipole index `quantifies the scale (long wavelength modes corresponding to low values of `). The CMB power spectrum as a function of `is defined as:

C `= h|T `m| 2 i (1.32)
The anisotropies of the CMB contain information of the primordial density fluctuations in the early epoch of the Universe. In addition, CMB photons, on their trajectory across the Universe, have been perturbed by gravitational potentials or scattered by inverse Compton effect with ionized media. Such interactions are called secondary perturbations. The Sachs-Wolfe effect is attributed to temporal variation of the gravitational potential along the photon trajectory (Sachs & Wolfe, 1967). Other anisotropies observed are attributed to gravitational lenses (Planck Collaboration et al., 2018). In this case, anisotropies are generated by the change on the trajectory of photons due to the gravitational potential of a very massive object, like galaxy clusters. Another gravitational effect, called the Rees-Sciama effect (Rees & Sciama, 1968), can induce anisotropies in the CMB due to evolving gravitational potentials of non linear or matter structures as a result of collapse or expansion. Moreover, along their journey through the Universe, the CMB photons also interact with the gas in galaxy clusters, via the Sunyaev-Zel'dovich effect (Zel'dovich, 1970;Sunyaev & Zeldovich, 1972). This interaction is of particular interest for the study of galaxy clusters and will be discussed with more detail in Section 1.4.4.

The peak in the CMB power spectrum observed at `⇡ 200 in the power spectrum (corresponding to an angular size of about 1 ) represents the largest scale that had time to collapse at recombination. At smaller values of `( 50), corresponding to very large scales, the spectrum is flat, which is just proportional to the nearly scale-invariant spectrum at the moment fluctuations cross the Hubble radius.

Figure 1.1 shows the angular power spectrum of the CMB as measured by the Planck satellite (Planck Collaboration et al., 2016b). The vertical axis of the CMB power spectrum correspond to `(`+ 1)C `, this is proportional to the square of the temperature fluctuations on the angular scale, ✓ ⇡ ⇡/`. In this representation, the CMB spectrum is about flat at large scales, `< 50.

The Large Scale Structure

Primordial overdensities and structure formation

In the ⇤CDM model, the initial state of perturbations is assumed to be adiabatic and scalar. Such perturbations grow under the effects of gravity, leading to the formation of structures. These overdensities are measured in terms of the density contrast:

= ⇢(r, t) ⇢bg (t) ⇢bg (t)

,

(1.33) with ⇢bg (t) representing the mean background density measured at a time t. Considering only the contribution of gravity [START_REF] Kaiser | [END_REF]) in a Universe with ⌦ tot = 1, the spectrum of density fluctuations may be written as:

P (k) = k n .
(1.34)

Considering k / 1/r and M / r 3 , the mass variance of fluctuations, 2 , can be expressed as:

2 (k) ⇠ k 3 P (k) / r (n+3) ⇠ M (n+3)/3 (1.35)
Under these assumptions, by definition the fluctuations are self similar. However, as mentioned by [START_REF] Kaiser | [END_REF], this property can only be applied at cluster scales, allowing to construct scaling relations, which are discussed in section 1.4.4.

Observations of the CMB power spectrum, as mentioned above, provide direct evidence of primordial perturbations. The initial density perturbations can be represented by Gaussian samples with mean zero, i.e. h i = 0, then the power spectrum is given by:

P (t, k) = h| k (t)| 2 i (1.36)
where k is the Fourier transform of (t, r). A complete characterization of the density perturbations at the time of decoupling is given by the CMB the power spectrum:

P (k) = Z (r) exp ikr d 3 x = 4⇡ Z (R) sin(kR) kR r 2 dR (1.37)
The spectrum is computed, when the density contrast is low, assuming a linear perturbation. However, when ⇠ 1 analytical solutions are needed, some examples of such solutions can be consulted in Padmanabhan (2002). This model is called spherical top-hat approximation. The linear density contrast can be derived from solving Equation 1.33 in the regime of nonlinear perturbations, in a matter dominated Universe and it is defined as:

L = 3 5 ✓ 3 4 ◆ 2/3 (✓ sin ✓) 2/3 . (1.38)
Figure 1.2 depicts the density as calculated from Equation 1.38. At the beginning, the perturbed region detaches from the cosmic expansion, starting to expand at lower rate. One can observe that at ✓ = 2⇡/3 the solution is no longer linear.

Afterwards, at ✓ = ⇡ the matter collapses after the so-called turnaround point.

Finally, bounded structures are formed at ✓ larger than 2⇡.

Now, if the density fluctuations are very small, << 1, then the solution to Equation 1.33 is non-linear and is then solved by an analytic model developed by Press & Schechter (1974), see Percival (2001) for details. Then the variance of the mass fluctuations is given by:

(R) 2 = Z k 2 (2⇡) 2 W 2 s (kR)P (k) dk, (1.39)
where W s is the top-hat filter in the Fourier space defining spheres of radius R. The amplitude of the power spectrum on the scale of 8 h 1 70 Mpc is called 8 , defined as the r.m.s. density variation when a top-hat filter of 8 h 1 70 Mpc is applied. It can be expressed as:

8 = 1 2⇡ 2 Z W k 2 P (k) dk, (1.40)
where W s is the top-hat filter in the Fourier space:

W s = 3j 1 (kR s ) kR s , (1.41)
with j 1 the first order of a spherical Bessel function.

Supercluster of galaxies

The Large Scale Structure (LSS) of the Universe, as observed today, shows a web-like pattern formed by groups and clusters of galaxies, elongated filaments, widely spread sheets, and voids (e.g. [START_REF] Peebles | The large-scale structure of the universe[END_REF]Davis et al., 1982;Bond et al., 1996). The superclusters of galaxies are individual fragments of this LSS, forming sheets or just a weblike structure connecting filaments. The nodes where these filaments cross are the focus of clusters and groups of galaxies. Thus, superclusters of galaxies can be defined as the largest and most massive structures ongoing gravitational effects, although they are not virialized. They probably just passed the quasi non-linear regime described by the Zel'dovich' approximation (1970, see also the "sticking model" by Shandarin & Zel'dovich 1989), and may be close in time to the turn around point. As a consequence, the inter-cluster medium embedded in them (dark halos, gas and galaxies) dynamically interacts and organizes by falling in to the gravitational potential of the massive halos, forming bridges between pairs of clusters and groups.

Superclusters can be identified from groups of clusters of galaxies (e.g. Abell, 1961;Zucca et al., 1993;Einasto et al., 2001;Chow-Martinez et al., 2014) but also from the galaxies distribution, their local density and luminosity (e.g. Luparello et al., 2011;Costa-Duarte et al., 2011;Liivam ägi et al., 2012). Recent numerical N-body simulations based on the ⇤CDM cosmological model (e.g. Millennium, Springel et al., 2005;Bolshoi, Klypin et al., 2011;Illustris, Vogelsberger et al., 2014) reinforce that these structures are assembled under the effect of gravity and the process of gravitational collapse is still ongoing.

Galaxy clusters

Since 85% of the ICM is present in the form of hot gas, observations of such gas may be subject of study in order to characterize the ICM of clusters. There exist multiple studies of the ICM carried out through X-ray and SZ observations (e.g. These studies present analyses of the gas density, temperature and pressure of the ICM which confirm the strong similarity, in shape, of the clusters. There exist several models to estimate the mass distribution of galaxy clusters using different observables. In the following paragraphs some examples used to model the clusters' density profiles are presented.

The isothermal sphere The distribution of galaxies in the central region of rich clusters can be approximated by the King distribution, (King, 1972):

n gal = n 0 gal ✓ 1 + r R c ◆ 3/2 , (1.42)
with R c the core radius and n 0 gal the central density. However, the mass estimated from this model diverges when r 0 and r 1. Moreover, observations of galaxy clusters suggest that the velocity dispersion of galaxies is proportional to their distance from the cluster center. This leads to the analytical model of an isothermal sphere with a density distribution of the shape:

⇢(r) = 2 v 2⇡Gr 2 .
(1.43)

This model, originally proposed to estimate the dark matter profile for a selfgravitating isothermal sphere (as detailed by [START_REF] Binney | Galactic dynamics Biviano[END_REF], is used to estimate the cluster properties in analytical analyses.

S érsic profile

The S érsic profile, (S érsic, 1968) is a surface brightness 2D profile for galaxies. It is defined by:

⇢(r) = ⇢ s exp( b n [ r r s ] 1/n 1). (1.44)
where ⇢ s is the surface brightness at radius r s , measured at the half bright surface. The parameter b n can be approximated as 2n 1/3, as shown by Ciotti & Bertin (1999), where n describes the shape of the light profile.

Beta profile Regarding the gas component of galaxy clusters, the density profile can be computed considering the beta profile (Cavaliere & Fusco-Femiano, 1976). This profile is a modified profile adapted for the distribution of gas. Here the gas distribution is given as: Nagai et al., 2007;Battaglia et al., 2010). The dark matter density profile of galaxy clusters is approximated by a Navarro-Frenk and White profile, (Navarro et al., 1997, hereafter, NFW):

⇢ gas (r) = ⇢ go " 1 + ✓ r r c ◆ 2 # 3 /2 , ( 1
⇢(r) = c ⇢ c (r/r s )(1 + r/r s ) 2 (1.47)
where ⇢ c is the critical density at the cluster redshift, r s is the scaled radius found by Navarro et al. (1997) and c is the characteristic density (for a concentration parameter c) defined as:

c = 200 3 c 3 ln(1 + c) c/(1 + c) (1.48)
Usually this profile is adjusted using an analytical solution of the NFW profile parametrized as:

⇢(r) = c ⇢ c0 x (1 + c ↵ 500x ) ( )/↵ , (1.49)
where ↵, and are the best fitted slopes for the density profile.

The generalisation of the Navarro et al. (1997) profile (gNFW) for the distribution of dark matter and gas derived from early numerical simulations, as given by Nagai et al. (2007) is:

P(x) = P 0 (c 500 x) [1 + (c 500 x) ↵ ] ( )/↵
(1.50) where x = r/r s , r s = r 500 /c 500 . r 500 and c 500 are the characteristic radius and the corresponding concentration encompassing 500 times the critical density of the Universe at the cluster redshift . ↵, and are the inner, external and transition slopes (at r s ) of the profile. The gNFW profile thus provides a simple parametric description easily tested against observational constraints (e.g., Arnaud et al., 2010b;Planck Collaboration et al., 2013a;Eckert et al., 2013;Sayers et al., 2016;Romero et al., 2017;Bourdin et al., 2017;Ruppin et al., 2018). The afore-cited works have found a very good agreement between the gNFW predictions and the actually observed pressure distribution in X-ray or SZ, at least within the central part of the galaxy clusters.

The X-ray observations

As mentioned before, the ICM gas is observed to have temperatures of about 10 8 K, corresponding to 1-30 keV. This gas cools by thermal Bremsstrahlung emission which depends quadratically of the gas density n e . Then, the X-ray surface brightness is used to estimate the gas density. The X-ray surface brightness by unit of solid angle is given by:

S x = 1 4⇡(1 + z) 4
Z n e ⇤(T e , Z)dl,

(1.51)

where dl refers to the line of sight, ⇤(T e , Z) is the cooling function which depends on the gas metallicity, Z and the temperature T e . ⇤(T e , Z) can be approximated as p T e Although the X-ray emission is suitable to characterize the ICM gas density and its metallicity, it depends on the cluster' density, then, at lower densities, photon detection requires larger observation times. Also, its redshift dependence makes it difficult to detect and characterize clusters at large redshift. Therefore, clusters can be studied using X-ray observations only in their densest region, i.e. close to the core. Analyses up to the cluster outskirts have as a consequence an increment in the observation time, also, the required instrumentation sensitivity increases, making such studies very challenging.

Scaling relations

In the hierarchical structure formation scenario, galaxy clusters are the largest gravitationally bounded structures. One can consider the hypothesis that clusters evolved purely by gravitational collapse, following a spherical collapse model, as proposed by Jeans (1902). Then, by assuming these systems are virialized, the matter contained in their gravitational potential will be in hydrostatic equilibrium. Also, one can assume the gas fraction in clusters, f gas = M gas /M vir is constant and representative of that of the Universe. Therefore, as a consequence of these approximations, galaxy clusters and groups halos have self-similar internal structure. This property allows to construct scaling relations between the cluster principal properties (Kaiser et al., 1995;Bertschinger, 1998). This behaviour is observed for their global thermodynamical properties (e.g., Giodini et al., 2013a) as for their internal distribution (e.g., Pratt et al., 2019). The gas thermal pressure is a remarkable example of this self-similar behaviour. The integrated pressure over the volume of the cluster, i.e., the SZ Comptonization parameter, has proven to be an excellent proxy of the total gas content, thus of the total mass of the halo, as the thermal pressure is mildly affected by nongravitational physics (AGN feedback, radiation cooling, etc) with respect to other proxies (e.g., X-ray total luminosity Pratt et al., 2019;Mroczkowski et al., 2019, for recent reviews).

Let us consider a spherical region of radius R c with a mean density of c⇢ c (z) at redshift z. The total mass is given by M c = (4⇡/3) c ⇢ c (z)R 3 c . The critical density is defined at any redshift as ⇢ c (z) = ⇢ c0 E(z), with E(z) as defined in Equation 1.23. Then the cluster radius as function of redshift can be approximated as:

R c / M 1/3 c F (2/3) z .
(1.52)

with F z the source flux. Now, considering the gas in clusters satisfies k B T / , M c /R c , then we have:

M c / T 3/2 F 1 z . (1.53)
This last equation can be used to derive scaling relations from X-ray observables.

These relations generally link by a power law the cluster mass with a measured proxy (e.g. the luminosity, gas temperature or the galaxies' velocity dispersion).

Some of the most used scaling relations are between X-ray luminosity and temperature, mass and temperature and luminosity-mass relations (e.g. Ettori et al., 2004;Arnaud et al., 2005;Kotov & Vikhlinin, 2005;Pratt et al., 2009;Giodini et al., 2013b, the latter provides a review regarding scaling relations for clusters):

F z M gas / T 3/2 , (1.54) F 1 z L x / T 2 , (1.55) F 1 z L x / (F z M gas ) 4/3 , (1.56) F 4/3 z S x / T, (1.57)
However, it is important to recall that scaling relations are a consequence of the assumption of hydrostatic equilibrium. In a more realistic scenario, the dynamical state of the clusters at radii larger than R 500 ( c = 500) is perturbed by accretion of the infalling material from the filaments and dynamical interactions. Then, in this region one can no longer consider the gas to be in a virialized state. Thus, the characterization of the gas in the cluster outskirts is a crucial step to understand the formation and evolution of these structures.

The SZ effect observations The Sunyaev-Zel'dovich (SZ) effect is a result due to the inverse Compton effect between the hot electrons in the ICM and the photons of the CMB. As a result of this interaction, the spectrum of the CMB shows a deformation toward the regions of clusters.

The intensity of the SZ effect is characterized by the dimensionless Comptonisation parameter y. As defined in Planck Collaboration Int. V (2013), the Comptonisation parameter corresponds to the product of the average fractional energy transferred per collision, by an electron to a photon, and the average number of collisions, such that:

y = T m e c 2 Z P (l)dl, (1.58)
Then the SZ flux expressed as the integrated Compton parameter, Y , within a given solid angle, ⌦, is proportional to the thermal pressure of the ICM gas integrated over the line of sight:

Y (⌦) = T m e c 2 Z ⌦ d⌦ Z los P (l) dl (1.59)
where T is the Thomson cross-section, m e is the mass of the electron, c is the speed of light and P is the pressure produced by the plasma of thermal electrons along the line of sight. Since the SZ effect is independent of the distance of the object to the observer, the SZ effect is related to the redshift only by the angular size at which the cluster is observed. The virial approximation for galaxy clusters is:

k B T e = µm p GM tot R , (1.60)
where M tot is the mas comprised in a sphere of radius R and is a mass distribution factor and µ the molecular mass of ICM particles. Then, assuming the ICM gas can be approximated as an ideal gas, the Y M relation is:

Y (R ) / ⌧ m e c 2 ⌫ ⌫ e ✓ G 2 H(z) 2 16 ◆ 1/3 f gas M tot, 5/4 , (1.61)
where e the electron mass, f gas is the ratio of the ICM gass mass to the total cluster mass, which is assumed to be constant.

As a complement to X-ray observations, SZ observations offer the possibility to study the integrated pressure over statistically significant samples of clusters (e.g. Planck Collaboration X, 2011; Planck Collaboration Int. III, 2013;Czakon et al., 2015;Bender et al., 2016;Dietrich et al., 2019) demonstrating a coherent view of their gas content between X-ray and millimetre measurements. The increasing coverage and improving resolution and sensitivity of SZ observations have also allowed to constrain the pressure distribution over the whole volume of clusters (Plagge et al., 2010;Planck Collaboration et al., 2013a;Sayers et al., 2013;Eckert et al., 2013).

The dispersed component of superclusters and the filaments

Filamentary structures in superclusters are observed between galaxy clusters forming bridges of galaxies or, at larger scales, composing chains of clusters.

The complex morphology of superclusters has been studied previously by several authors. Basilakos et al. (2001) studied the supercluster morphology using a differential geometry definition of shape. Their results suggest that filamentary morphology was the dominant feature for their supercluster sample. Moreover, Costa-Duarte et al. (2011) found, using Minkowsky functionals, that half of their sample have a pancake morphology while the other half exhibited filamentary morphology.

Due to its relatively low density and temperature, the WHIM is very difficult to observe with the current observational facilities (in X-rays and SZ effect). However, there exist some observational evidence of a WHIM in filaments. Among the best studied cases are the pairs of clusters: A222-A223 (Werner et al., 2008;Dietrich et al., 2012), A3391-A3395 [START_REF] Tittley | [END_REF]) and A399-A401 (Sakelliou & Ponman, 2004), which seem to be connected, in each case, by a gas bridge detected in X-rays. In another study, Planck Collaboration et al. (2013b) report an study of the SZ signal detected between pairs of clusters at separations up to 10

Mpc. More recently, Tanimura et al. (2017) found evidence of gas in filaments by stacking the SZ signal between pairs of luminous red galaxies (with a separation of between 6 and 10 Mpc). They estimated a gas temperature of T⇠ 8.2 ⇥ 10 7 K (kT = 7.1 ± 0.9 keV).

In this work, we define the material (galaxies, gas, dark matter) between two clusters or groups as a "bridge" if this material is, somehow, denser than the surroundings. Here we shall call a chain of three or more clusters/groups connected by bridges a "filament".

Moreover, it has been observed that the different components of the LSS are frequently aligned with each other. Indications of such alignments in the optical bands have a long history (e.g. Sastry, 1968;Carter & Metcalfe, 1980;Binggeli, 1982;Lambas et al., 1988;West, 1994;Plionis & Basilakos, 2002;Lee & Evrard, 2007;Hao et al., 2011). There are many important results connecting the cosmological alignments, the filaments and the evolution of galaxies and their systems.

In what follows we mention only some examples. Plionis & Basilakos (2002) analysed the dynamical evolution of clusters in a hierarchical scenario under the hypothesis of clusters merging within large scale filaments. They concluded that clusters with traces of dynamical activity are significantly more aligned with their nearest neighbours. Altay et al. (2006) found that the shapes of nearby clusters are aligned if the clusters are connected by a filament. They conclude that matter infalling along filaments is an important factor in galaxy cluster intrinsic alignments a hypothesis proposed originally by West (1994). Godłowski & Flin (2010) observed alignments of groups of galaxies within the Local Supercluster on scales up to 20 Mpc scales. Also, correlations between two clusters have been detected on scales up to 30 Mpc using X-ray observations (Chambers et al., 2002;Wang et al., 2009;Paz et al., 2011). On the other hand, Chen et al. (2017a) performed an analysis of the color, magnitude, morphological type and activity type of galaxies in the neighborhood of filament candidates. Their results show that the red galaxies are located nearer to the skeleton of the filament than the blue galaxies. Another study carried out by Zhang et al. (2015) presents the results from observations that suggest that the major axis of elliptical galaxies tends to appear orientated parallel to the filament.

In other words, there are many evidences that the evolution of galaxies and their systems is deeply connected to their environment, especially with the filamentary structure that patterns the LSS.

The galaxies that populate the LSS

Galaxies are currently classified by their shape, activity, metallicity, among other properties. For example, galaxies can be classified by their Hubble morphological type in elliptical (E), spiral (S) or irregular (I). Galaxies can also be classified by their color, defined as the difference in brightness between two bands.

Moreover, galaxies can also be classified based on their emission lines using the galaxy spectrum. In the following paragraphs we introduce the galaxy classifications used on this work.

Galaxy morphological and spectral classification

One way to classify the galaxies is according to their spectrum, e.g., Kennicutt (1992) found a relation between the spectra of galaxies with their morphological Hubble type establishing one of the most used spectral classifications.

The integrated spectrum of galaxies is the integrated spectrum of the stars, dust and gas (Jones & Lambourne 2014). For example, the optical spectrum of HII regions present the so called forbidden lines. These lines are produced only in regions of very low density (n e ⇠ < 10 3 cm 3 ). Strong forbidden lines like

[NII] 6548 Å and [OIII] 5007 Å are seen in HII regions. At higher densities collisional de-excitation begins to play a role (Osterbrock 1989). In spiral and irregular galaxies, the contribution of HII regions to the spectrum of the galaxy is significant while for the elliptical galaxies their contribution is not relevant since they do not have HII regions. Therefore, considering these emission lines, galaxies are classified in late (Sp,I) and early (E,S0) type.

The motion of the galaxy components, stars, dust and gas, within the galaxy, is observed as a Doppler shift of the spectral lines, and as a result absorption and emission lines become broader. Then, the systemic velocity of the galaxy can be measured from the wavelength shift of the spectral lines with respect to the rest frame wavelength.

Activity classification

Moreover, the spectrum of a galaxy can also provide information about the presence of an active galaxy nucleus (AGN) or star-formation (SF). AGNs come in a variety of types and using the optical spectra are classified as Seyfert 1/2, LIN-ERs, QSOs and blazars (Jones & Lambourne 2014). The unified model for AGNs (Barthel 1989;Antonucci 1993;Urry & Padovani 1995) proposes that the principal component, which powers the AGN, is a supermassive black hole (SMBH).

An active SMBH at the center of active galaxies is partially hidden by a torus of gas and dust. Under this model, the different types of AGNs can be explained by the orientation of the source with respect to our line of sight. Unlike normal galaxies, the integrated spectrum of a galaxy with an active nucleus, like the Seyfert 1/2 galaxies is identified by the presence of very-broad/broad H↵ emission lines. The BPT (Baldwin, Phillips & Terlevich, Baldwin et al. 1981) diagnostic diagram allows to classify the galaxies as Seyfert 2, LINER or star forming galaxies based on the presence and ratio of certain emission lines in the spectrum. Figure 1.3 depicts the diagnostic diagrams for SDSS galaxies (Kewley et al., 2006). The galaxies that lie below the dashed line are classified as HII-region-like galaxies and those that lie above the dashed line are classified as AGNs. Galaxies that lie in between these two classifications lines are a mix of AGN and H II and are classified as composites or TOs (transition objects). Composite galaxies are likely to contain a metal-rich stellar population plus an AGN (Kewley et al. 2006).

Galaxies in clusters

The galaxy population inside galaxy clusters is predominantly composed of early type galaxies and about 35% is observed to correspond to late type galaxies (e.g. Roncarelli et al., 2010). Dressler (1980) carried out an analysis over a sample of 55 galaxy clusters. His results shown that the fraction of spiral galaxies in clusters correlates strongly with the environment in which they reside (a fraction of 80% of galaxies in the field, 60% in the cluster outskirts and 0% in the cluster center). Generally, the brightest cluster galaxy (BCG) is located near the center of the clusters. For rich clusters, the BCG galaxy is typically classified as an elliptical galaxy (Lauer & Postman, 1992). A fraction of these clusters presents a very luminous elliptical galaxy with an extended low surface brightness envelope, called cD galaxy (Matthews et al., 1964). cD type galaxies are the result of several dynamical processes, Ostriker & Hausman (1977) suggest that the formation of these galaxies is the result of several mergers. Moreover, Dressler et al. (1997) found that the fraction of elliptical galaxies is higher in clusters at larger redshifts (z⇠0.5) compared to low redshift clusters. The observation and identification of the galaxy population of clusters have been used to detect clusters and determine the galaxy cluster membership (e.g Gladders & Yee, 2000, use the color-magnitude space to detect galaxy clusters).

The red sequence of galaxies in clusters

The color index of galaxies is observed to follow a straight relation with the galaxies' magnitude in clusters. When red galaxies are plotted in the color magnitude space, galaxies belonging to the cluster follow a linear distribution, called the red sequence. This configuration in the color magnitude diagram suggests that at a given moment galaxies were stick together, and evolved at the same time, z ⇠ 2 (e.g. Bower et al., 1992;Ellis et al., 1997;Gladders et al., 1998). The red sequence distribution can be adjusted by a line with a slope that suggest that the fainter galaxies are bluer than the brighter ones. Different analyses have shown that this sequence is related with the mass-metallicity relation, as shown by Kodama & Arimoto (1997) and Kauffmann & Charlot (1998) and not with the age of the cluster. As described by Kodama & Arimoto (1997), supernovae events in galaxy clusters would warm the interstellar medium and can evaporate the gas of low mass galaxies. This process results in an increment on the metallicity with the mass: the most massive and luminous galaxies have larger metallicities and are redder than low luminosity galaxies. Moreover, an analysis carried out by Trejo-Alonso et al. ( 2014), on a sample of 56 Abell cluster, found that Xray underluminous clusters show a flatter red sequence slope than X-ray normal luminosity clusters. They suggest that underluminous clusters may be younger systems than clusters of normal X-ray luminosity.

Chapter 2

Detection of large scale structures:

GSyF & GFiF algorithms

Recently, with the availability of large sky area databases, like the SDSS, the development of accurate structure detection algorithms has become a major concern in astronomy. Visually, the galaxy distribution shows filamentary chain-like structures which connect massive clusters and groups. However, the identification of these structures through a computational algorithm is not an easy task.

A good algorithm should provide an identification which resembles the human visual identification. It also should provide quantitative results and should be founded in a robust and well defined numerical theory and all of this in an acceptable amount of time with reasonable computational resources.

Currently, several structure finding algorithms are available. For example, Cau- Since different methodologies identify relatively distinct structures, and every one of them has different advantages and drawbacks, we developed our own methodology, trying to improve the results over the available ones.

Therefore, in this Chapter we present in detail the algorithms we developed for the detection of internal structures of superclusters using the galaxy positions (RA= ↵, Dec= and redshift= z). The Galaxy System Finding algorithm (GSyF)

objective is to detect clusters and groups of galaxies, hereinafter called systems of galaxies, using VT and hierarchical clustering (HC) analyses. The Galaxy Filaments Finding algorithm (GFiF) seeks to detect the more elongated structures (bridges, filaments, and tendrils) using classical pattern recognition and machine learning methods. Since these algorithms use only the position of galaxies, they can be applied to various galaxy surveys and catalogs. Hereafter, the N galaxies inside a volume box (containing the supercluster volume) are considered as a set of points x 1 , x 2 , ..., x N 2 X, all being part of a sample X.

Machine learning methods applied to astronomy

Density estimators

The local number density is a useful measurement to characterize the environment in which a galaxy resides. For this work we implemented two techniques for measuring this local density: VT and KDE. Both methods have different advantages and limitations. For instance, VT is suitable to measure with accuracy the local density at the galaxy position while the strength of KDE is to measure the density on larger scales.

VT density estimator Voronoi tessellation (Voronoi, 1908) can be applied both over spatial distributions of galaxies to estimate the local 3D volume number density and over surface distributions to estimate the local 2D surface number density. VT has been widely used for the detection of overdensity regions in sky slices (e.g. Scoville et al., 2013;Darvish et al., 2015). Another approach is presented by Cybulski et al. (2014) which uses VT for the identification of filamentary structures in the Coma cluster region.

The VT of a sample X, Vor(X), can be defined as the subdivision of a 2D plane or a 3D space into cells with the property that the seed point

x i 2 X is located in the cell v i if and only if the Euclidean distance D E (x i , v i ) < D E (x i , v j ) for each v j 2 X with j 6 = i, i.e.
VT partitions the space into optimal polygonal cells in a way that there is one cell for each galaxy position x i 2 X (e.g. Platen et al., 2011).

Then, the density at x i is determined as d i = 1/v i , with v i being the volume (or area) of the cell around the galaxy x i . One of the advantages of VT is that it provides a density estimation of high resolution, i.e. the density is estimated at the position of each galaxy.

Kernel density estimator

In some cases VT fails on the identification of large overdensity regions, as mentioned by Cybulski et al. (2014). An alternative for the estimation of the number density is to apply KDE. In general, KDE methods work by adjusting a kernel function over each observation in the sample. However, the choice of the correct kernel model and its intrinsic parameters are still under investigation within the community. Also, there are several attempts to apply adaptive Gaussian model kernels, in other words, to change the size of Gaussian model as a function of different parameters, e.g. the distance to the nearest neighbor (Chen et al., 2016) or a weighting function (Darvish et al., 2015).

For this work we set the kernels as Gaussian models inside VT cells. Therefore, VT method is first applied over the sample positions (see Section 2.1.1)

and Gaussian ellipsoids are fitted inside each VT cell. Afterwards the Gaussian kernels ⌃ are calculated from the eigenvalues and eigenvectors of the fitted ellipsoids. Then, each n-dimensional kernel ⌃ centered in µ with covariance matrix ⌃ is represented as:

⌃ (x µ) = (2⇡) d/2 |⌃| 1/2 e 1/2(x µ) T ⌃ 1 (x µ) . (2.1)
Then the KDE can be estimated as:

pKDE (x) = N X i=1 ↵ i ⌃ i (x x i ) , (2.2)
where ↵ i is a weight factor calculated from the VT cell volume as v i .

The identification of the overdensity regions is carried out through the projection of KDE kernels in 2D planes. This is done by superposing a regular rectangular grid to the data. Then, we estimate the density at each grid intersection by calculating the average density of all kernels that overlap at that point. Thus, observations closer to an evaluating point will contribute more to the density estimation than points that are far from it. Consequently, the density will be higher in areas with many observations than in areas with few observations. The identification of contiguous overdensity depends on the number of times the covariance of each kernel is being considered.

Hierarchical Cluster Analysis

Hierarchical clustering is a machine learning method whose objective is to group objects with similar properties. It has been used in different areas of science such as artificial intelligence, biology, medicine and business. In general, it can be used to carry out pattern recognition analysis, allowing to regroup, segment and classify any kind of data. This method is equivalent to a reduction of the dimensionality of the data and decreases considerable the computing time. In astronomy, the most popular application of HC has been for the detection of substructures inside galaxy clusters, following the algorithm developed by Serna & Gerbal (1996). This algorithm considers the positions, redshifts and potential binding energy between pairs of galaxies to detect substructures (see also Guennou et al., 2014).

In general, hierarchical clustering methods are suitable for this kind of application since they allow the detection of structures on different scales and can be applied over different coordinate reference frames.

For this work, we chose an agglomerative hierarchical clustering method with a Ward's minimum variance clusterization criteria, described in detail by Murtagh & Legendre (2014). A detailed description of the HC algorithm can be found in [START_REF] Theodoridis | Pattern Recognition (Fourth Edition)[END_REF]; [START_REF] Theodoridis | Introduction to Pattern Recognition: A Matlab Approach[END_REF] and Murtagh & Contreras (2011). In general, Ward's method works by merging the groups following the criterion:

D(c 1 , c 2 ) = |c 1 ||c 2 | |c 1 | + |c 2 | ||c 1 c 2 || 2 . (2.3)
where D is a term that measures the distance between two groups c 1 and c 2 , respectively.

In our case, initially each point is considered as a group, sub-cluster or singleton, then each group can be agglomerated with a neighbor that has the minimum D distance. The agglomeration continues until all points are grouped together into a single group.

The results of the HC clusterization can be represented by a dendrogram or hierarchical tree. A dendrogram represents, in a graphical form, the connections between elements and groups in different levels of agglomeration. The length of each connection line in the tree corresponds the distance between two elements or centroids connected. This representation also allows visualizing the principal branch structures where the singletons are the final leaves. The number of desired groups N cut is, therefore, obtained by cutting the hierarchical tree at a certain level. The exact value of this level depends on the characteristics of the sample or, more properly, on the underlying physics that is used to define the groups.

Each created group can be represented by a 2D/3D Gaussian model, P j (x). This allows us to classify the groups by their Gaussian properties, e.g. centroid (mean position, C j ), richness (number of members, N j ) and compactness (covariance, j ).

Graph definition

Graph theory-based algorithms have shown to be a suitable tool to analyze complex networks. Some of the most common subjects where these algorithms are applied successfully are social networks, computer vision, statistics, business and transportation networks.

A graph is a representation of the connections in a network. It is composed of "nodes" and "edges", where each node represents an object, and the edges represent the connections between each two nodes. Also, the edges can have weights that represent the strength of the connection. An undirected graph has edges that do not have direction. Generally, a graph is defined as G = (U, E, W ),

with n nodes (or vertices) u i 2 U , m edges e kl 2 E and a weight set W with a w kl for each edge e kl . The information of a graph can be represented by a square adjacency matrix. The values of the matrix elements indicate the weight of the connection between nodes. Hence, the adjacency matrix A of the graph G is defined as:

[A] kl = 8 < : 1 if (u k , u l ) 2 E 0 otherwise
where u k and u l are nodes in G.

Minimum Spanning Tree (MST)

A spanning tree connects nodes in a graph in a way that does not produce cycles.

A graph can contain several unconnected spanning trees. Since the edges in a graph can have weights, the minimum spanning tree algorithm (Graham & Hell, 1985) searches for a spanning tree that minimizes the total weight. This algorithm traces a tree-like continuous path for a group of edges and nodes in an optimal way. In particular, Kruskal's minimum spanning tree algorithm analyzes the edges in sequence, sorting them by weight. At the beginning, the shortest edge is analyzed and this is taken as the first tree branch. Then, the nodes are added to the tree under three conditions:

(i) only one node is added to the tree;

(ii) a node is added based on the number of connected edges;

(iii) their edges cannot be connected to another existing node in the tree.

The process continues with the following edges in the graph until all connected edges are analyzed. Finally, the tree is extracted from the graph and the process begins again with the remaining nodes until all are tested. As its name remarks, the result is a forest of minimized independent trees.

Dijkstra's shortest path

Dijkstra's algorithm (Dijkstra, 1959) is a classical method for searching the shortest path between two nodes in a graph. The path of length e kl is defined between two nodes u k and u l as a sequence of nodes connected u 1 , u 2 , ..., u m if k 6 = l 8 k, l 2 1, ..., m. In general Dijkstra's algorithm works as follows:

(i) The origin is selected by taking the node at the beginning of the path, u 0 .

(ii) A distance value is assigned to all nodes: set to zero for the origin, s(u 0 ), and to infinity for all the other nodes, s(u i ) = inf.

(iii) Then, all nodes are marked as unvisited and u 0 is marked as current node a.

(iv) Subsequently, the algorithm calculates the distance from the current node a to all the unvisited nodes connected by the edges e i as s new = s(e ai ) + w ai ; here s(e ai ) is the distance from a to the node u i and w ai is the weight of the edge e i .

(v) If s(e ai ) + w ai < s(e i ), then the distance is updated and the connected node label is updated as the current a.

(vi) After visiting all neighbors of the current node, they are marked as visited.

A visited node will not be checked again; then the recorded distance s(e ai )

is final and minimal.

(vii) Finally, if all nodes have been visited, the algorithm stops. Otherwise, the algorithm sets the unvisited nodes with the smallest distance (from the initial node u 0 , considering all nodes in the graph) as the next "current node" and continues from the second step.

A detailed description of the algorithm can be consulted in Santanu (2014).

Properties of systems

Coordinate transformation

In general, sky projected coordinates, ↵ and , and redshift z can be converted to rectangular coordinates by applying the following transformation:

X = D C cos ( ) cos (↵) , (2.4) Y = D C cos ( ) sin (↵) , (2.5) Z = D C sin ( ) , (2.6)
where D C is the co-moving distance obtained from Equations 1.23 and 1.22, by using the redshift and the cosmological parameters.

Velocity projection effects

In real astronomical observations one can observe that the use of radial velocity (redshift) is subject to projection effects in the line of sight called "Fingers of God (FoG)". This effect is a result of the galaxies peculiar velocities added to the system velocity. As a consequence, the distribution of galaxies that are members of gravitationally bounded systems is elongated along the line of sight.

Virial mass and radius estimation

The virial mass and radius were estimated in order to characterize the systems of galaxies and to correct the positions of their members for the FoG effects.

This was achieved by applying a simplified version of the algorithm proposed by Biviano et al. (2006). This algorithm calculates iteratively the system's virial mass and radius, under the assumption of dynamical equilibrium, relative isolation of the systems and roughly spherical shapes. For this implementation, the algorithm does not use the surface pressure term correction based on the concentration parameter. This can lead to an overestimation of the virial radius, but, for this geometric analysis, the virial approximation is enough.

In summary, this algorithm works as follows:

(i) The galaxies are selected, in the ↵ ⇥ projection, inside a cylinder of radius R a = 1 h 1 70 Mpc, hereafter, aperture. In the line-of-sight (LOS) direction, the galaxies are selected within a range in velocity up to S a = ±3000 km s 1 with respect to the mean cluster velocity.

(ii) The mean velocity, v LOS , and velocity dispersion, v , are calculated using as a robust estimation Tukey's biweight (See eq. 9 in Beers et al., 1990) for the galaxies inside the cylinder.

(iii) The projected harmonic radius R h of the galaxies inside the aperture within z is calculated as:

R h = N (N 1) P i>j R 1 i j , (2.7)
with R i j as the distance between the galaxies projected positions (Girardi et al., 1998).

(iv) The mass M a inside the cylinder of aperture R a is estimated as:

M a = 3⇡ 2G 2 v R h , (2.8)
where G is the gravitational constant and 3⇡/2 is the deprojection factor.

(v) The virial radius is estimated as:

R 3 vir = 2 v R h 6⇡ H 2 (z)

,

(2.9)

by assuming a spherical model for nonlinear collapse, that is, by taking the virialization density as

⇢ vir = 18⇡ 2 [3H 2 (z)]/[8⇡G]
, and approximating M vir as M a , (vi) Then, the aperture R a is updated to the calculated R vir value, the mean velocity to v LOS , and S a to v , defining a new cylinder.

The steps i-vi are repeated iteratively until the radius R vir converges. M vir is finally calculated at the end of the iteration process.

Then, the correction for the FoG effect is carried out by adjusting the position of the N mem galaxies inside the final cylinder. This is done by scaling their comoving distances along the cylinder to the calculated virial radius.

Galaxy System-Finding algorithm (GSyF)

The GSyF algorithm was developed to detect the denser components of the LSS, systems of galaxies, and to correct the position of the system's galaxy members for the FoG effect. These are necessary steps to carry out before the application of GFiF to detect elongated LSS structures.

In this context, we implemented two strategies for the detection of systems. The first detects groups of galaxies above certain density value. The second, refines galaxy membership through a approximation. We need to point out that we start with the projected distribution of the galaxies since we do not have a priori the space distribution of the galaxies due to FoG effects.

The implementation of a new technique for the detection of galaxy systems allows the identification of new systems possibly not known before (especially the galaxy groups). Also, this can lead to an improvement of the membership estimation of the superclusters themselves. In the following sections the GSyF algorithm is described in detail followed by a description of the optimization processes implemented1 .

Surface density baseline contrast

Since systems of galaxies are high to medium density galaxy concentrations, a measurement of the density contrast in terms of the density background is a convenient measure. However, since the distribution of galaxies in space is not isotropic, it is not possible to set directly a background density from the projected positions of the galaxies. Then, it is necessary to simulate a sample of equivalent isotropic distribution of the galaxies, in order to set the baseline value (see, e.g. Cybulski et al., 2014).

The methodology implemented by GSyF to measure the local surface density consists in:

(i) The baseline (background) density value, d bas is estimated by simulating 1,000 random isotropic galaxy distributions each with the same number of galaxies over the same area.

(ii) The local surface density is calculated for each galaxy by applying the VT method (section 2.1.1) to the galaxies projected distribution in the plane of the sky. The VT individual area of the galaxy can be directly converted to a surface density estimation (d i = 1/a i ), in this case in units of deg 2 .

d bas = 1 m m X j=1 1 n n X i=1 d 0 i,j , (2.10)
where d 0 i,j = 1/a 0 i,j corresponds to the area of the point x 0 i for the randomization j.

(iii) The density contrast, i , is calculated from the VT densities with respect to a baseline (background) as:

i = d i d bas d bas .
(2.11) (iv) Only the N gal galaxies with density contrasts above a certain value ( i g) or, equivalently, d i (1 + g) d bas are selected;

here, the g parameter needed to be set by an optimization step, described in section 2.5.2. The density contrast was used to find contiguous cells with similar contrast value. Since the distribution of galaxies is not homogeneous in the sky at different redshifts, we need to calculate independent baselines values for each volume box under study. The selection of galaxies above the background density baseline is equivalent to separate galaxies from under-dense regions, i.e. field and void galaxies.

Grouping the galaxies using HC

GSyF applies the HC clustering method (section 2.1.2) over the galaxy projected positions (RA, Dec, 1000z) (the 1000 factor corresponds to the weight needed for z values to be comparable to the sky coordinates values). The number of groups taken from the analysis is defined as a cut of the HC tree, fixed to N cut = N gal /f , with a segmentation parameter f , which is the expected mean number of elements per group. From the clusterization, only groups with N j 3 member galaxies were retained as system candidates. However, the selection of the optimal number of groups in the clusterization methods is still a topic under investigation in the pattern recognition community. Therefore, the value of f needed to be optimized for each volume under analysis (section 2.5.2).

Systems virial refinement

After identifying the galaxy system candidates, GSyF applies a refinement for galaxy membership and estimates the system's virial properties. This was achieved by applying the method described in section 2.2.3. In each iteration the virial estimation works as a filter for system membership. It also allows to re-group duplicated/ over-clustered groups and permits to discard false detections of HC systems. For the first iteration of the virial refinement, GSyF uses the position of the brightest galaxy of the HC group as the system center. When the virial radius R vir converges, the membership of the systems, N mem , is established and the virial mass M vir is calculated. Finally, the positions of the galaxies inside the final cylinder of radius R vir are corrected for FoG effects. This is done by scaling their co-moving distances along the cylinder to the calculated virial radius. The pseudo-code of the GSyF methodology is presented in Algorithm 1 (Appendix A.1).

Galaxy Filament Skeleton-Finding Algorithm

In order to achieve one of the objectives of this work, namely to detect elongated and low-density structures, we implemented the GFiF algorithm over the galaxy positions. The GFiF methodology defined by us uses clusterization and graph methods in order to search for links, bridges and filaments connecting groups of galaxies. To have an accurate detection of elongated structures (filaments) we applied GFiF over the 3D distributions of galaxies whose positions were previously corrected for the FoG effect, i.e. after applying the GSyF algorithm.

Detection of low density regions

The GFiF algorithm applies a combined VT+HC method to the galaxy positions in the rectangular 3D space. The galaxy position in rectangular coordinates (X, Y, Z) is calculated according to equations 2.4, 2.5 and 2.6. Then, the VT local number densities corresponds to volume densities in units of Mpc 3 . We define the density baseline as the mean box volume number density, d bas . However, for this analysis, the HC method is applied to all galaxies in the volume without density restrictions, that is, no baseline threshold is applied. Moreover, the application of HC is done in a way that allows to detect the more elongated and representative structures. This is achieved by using larger numbers on the segmentation parameter f , as compared with the GSyF f values. Afterwards, the GFiF algorithm performs as follows:

1. Once HC is applied, the Euclidean distance D E between groups is measured, this is, the distance from all group centroids (nodes) to all its group neighbors. These connections (edges) can be represented by an undirected graph as described in section 2.1.3. The weights W of the edges are set by the Bhattacharyya coefficient, BC, defined as:

BC(P 1 , P 2 ) = X x2X p P 1 (x)P 2 (x).
(2.12)

The Bhattacharyya coefficient quantifies the amount of similarity between two distributions P 1 (x) and P 2 (x). Thus, the orientation of the Gaussians of two groups weights the connection between them.

2. The mean lineal density of the edges is measured inside a cylinder of radius 1 h 1 70 Mpc defined along the edge. Then, the density is calculated as the number of galaxies inside the cylinder N edge divided by the cylinder volume.

3. An edge is considered as a real link of galaxies connecting the two nodes based on the following: The ensemble of these links is considered as an undirected graph G = (U, E), where U represents the nodes (the group's centroids), E the edges (connections between nodes) and W a matrix that gives weights to the connections. Each ensemble of connected links is a tree in the forest graph. 4. Then, Kruskal's minimum spanning tree algorithm (section 2.1.4) is used to identify independent trees and their dominant branches.

Chaining the filaments: GSyF + GFiF

In order to identify filaments connecting systems of galaxies, each GFiF tree is matched against the detected GSyF galaxy systems. However, richness of the detected systems depends on the redshift, because of the Malmquist effect. The number of galaxies in systems decreases with increasing redshift (see Figure 3.1). In other words, to have a comparable richness for two similar system, one at z = 0.03 and the other at z = 0.13, it is necessary to apply a correcting factor to the richness of the second one. Therefore, a lower limit for the richness of the systems at the supercluster redshift was set as:

log 10 N min = a log 10 z + b,
(2.13) with a = 1.0 and b = 0.2. This leads to a minimum richness of N mem = 30 to 5 galaxies, from the nearest and farthest supercluster in our sample respectively.

The GFiF detected structures are classified, based on the number of GSyF galaxy systems embedded in them, as:

(i) The nodes are defined as the HC group's centroids.

(ii) An edge is defined as any connection between two nodes.

(iii) The real links between the systems are defined as the most promising edges, filtered according to their proximity and density.

(iv) Spanning trees are acyclic optimal connections of links. Some nodes inside a spanning tree may be detected as galaxy systems by the GSyF algorithm.

(v) A bridge is defined as a sequence of links and nodes between two systems.

(vi) A filament is identified if a spanning tree links three or more systems connected by bridges.

(vii) A tendril is a spanning tree that contains none or only one system.

(viii) The skeleton is the medial line of a filament. The method for finding it, which intends to reduce the dimensionality of the objects (in our case, galaxy filaments), is known as skeletonization. The links forming filaments were refined using Dijkstra's algorithm (section 2.1.5).

This refinement allows the identification of the filament skeleton, i.e. the principal branch connection. According to the pattern recognition literature, a skeleton represents the principal features of an object such as topology, geometry, orientation and scale.

Algorithm optimization for the SDSS

Mock maps modeling

As mentioned before, the detection efficiency of the GSyF method depends on the value of the segmentation parameter f and the contrast level parameter g.

The strategy we implemented to find an optimized combination of these parameters was to simulate 30 mock galaxy maps for each supercluster of the sample. The properties of the synthetic galaxy systems were estimated by the relations described by Pearson et al. (2015). These galaxy-based relations were calculated for the SDSS database and follow a power law of the form log 10 (M 500 ) = ↵ log 10 ( x x 0 ) + , where x is the property under consideration.

Each mock map was constructed as follows: the simulated volume is filled with N synth synthetic systems, randomly distributed. Each of them is filled with synthetic galaxies in the range N elem = 10 200. The number of systems in the volume is set using the power function: Then, the systems are filled with galaxies following a normal distribution N elem (µ i , R vir )

log 10 [N synth (N elem )][h 3 70 Mpc 3 ] = m log 10 (N elem ) + b, ( 2
with µ i = {↵ i , i }.
The FoG effect is incorporated to the system galaxies by adding a velocity dispersion N elem (z i , v ). Finally, random galaxies are added to the box volume following the ratio: 60% of galaxies are distributed in the field, and 40% in the systems.

Optimization of GSyF parameters

The GSyF method was applied over the mock maps probing values for f in the range f = {3, 6, 9, ..., 36} and for g in the range { 0.25, 0.15, 0.0, 0.15, 0.25, 0.5}.

We observe that for larger values of f the HC grouping was not efficient in detecting individual systems. Moreover, the analysis on the g parameter suggests that the selection of this parameter does not impact the efficiency of GSyF detecting systems. Thus, we set the g parameter equal to 0.0 for all superclusters.

The comparative of detection at different values of g is depicted in Figure 2.3 (panels a-d). The analysis on the f parameter (see Figure 2.3) (panels a-d) suggests that GSyF has a higher detection rate for synthetic systems (completeness) (above 85%, arriving close to 100% for f < 5) for f values below 10. However, at these f values the contamination rate (false detection) is between 5 and 35%

decreasing for larger values of f . This analysis also reveals that the efficiency of the algorithm also depends on the final richness of the systems: success rates for richer systems (N mem 20) are much higher than success rates for poor ones (N mem 10), while failure rates do not change significantly, as shown in Figure 2.3 (panels e-f). The optimal value for f is chosen as the one that maximizes the completeness and minimizes the contamination, that is, the value that maximizes the function:

= N detec N synth + ✓ 1 N fail N synth ◆ .
(2.18)

Optimization of GFiF parameters

The results of the GFiF algorithm depend on several parameters, especially the number of HC groups, N cut (or, equivalently, f ), and the linking length D max2 .

This optimization was carried out on the real galaxy positions. The GFiF algorithm is evaluated by counting the number of filaments detected setting the linking length D max in the range of {D 1 ..., D end } and the segmentation parameter f in the range {f 1 , ..., f end } h 1 70 Mpc. The number of filaments for each evaluation is accounted for in a combination matrix of these parameters ⇧(f |D max ). Finally, the optimal f and D min parameters are set to:

N ske (f |D m ax) = max(⇧(f |D m ax)).
(2.19)

For the SDSS galaxy distribution, the linking length D max was evaluated in the range {8, ..., 40}, and the segmentation f was evaluated in the range {8, ..., 40}.

In practice, there is an optimal D max for each evaluated value of f . The results of the optimization process for the supercluster MSCC-454 are shown in Figure 2.4.

For this supercluster, the optimal parameter configuration is f = 10 and D min = 6, with 9 filaments detected, as can be seen in panel a.

Optimization results

The optimization for the GSyF algorithm f parameter was carried out for all supercluster in the present of study. Figure 2.6a shows the distribution of best f values for the superclusters in the sample with their mean redshift. Except for the first two points (the most nearby superclusters), one can see that there is no clear correlation between the two parameters, presenting a mean value around f = 10 with a considerable dispersion. In fact, for the two nearby superclusters the success rates are reduced because, as can be seen in Fig. 2.6b, for these superclusters the success rates are between 85%, while for all the others the success rates are around or above 90% (with a mean failure rate of about 10%). The low success rates for these two superclusters seem to be related to their higher number densities with respect to the others, as can be seen in Fig. 2.6c.

Discussion and conclusions of the Chapter

In this chapter we presented a new strategy for identifying clusters and groups of galaxies, the Galaxy Systems Finding algorithm (GSyF) and for identifying filaments, the Galaxy Filaments Finding algorithm (GFiF), inside superclusters of galaxies. We developed a methodology for GSyF that allows one to detect systems, their galaxy members, and to correct for FoG effects. This method uses the Voronoi Tessellation algorithm to measure local number densities and a Hierarchical Clusterization method to group the galaxies using their projected positions (RA,Dec,z) and surface density. Afterwards, the groups are refined by calculating their virial radius and mass iteratively. Through this refinement, groups are either classified as detected systems or rejected as group mis-detections. As a result, GSyF provides, for the detected systems, galaxy membership, the virial mass and virial radius. In order to evaluate the methodology implemented by GSyF we used a set of mock maps. The analysis of mock maps was used to set the GSyF free parameters: the minimum density contrast for detecting the systems and the cut in the number of groups for HC method (segmentation parameter).

The results of this evaluation shows that the GSyF algorithm has a completeness above 85% for 40 of our 46 superclusters, with a contamination (false positives) around 10%.

The GFiF algorithm uses the position of galaxies in 3D space to find links and bridges between concentrations of galaxies. For this algorithm, our methodology uses a combination of HC clustering, graphs and minimum spanning tree.

Grouping the galaxies using HC is equivalent to connect them according to their distance. This allows to reduce the dimensionality of the graphs, facilitating the application of MST. Otherwise, the size of the generalized graph would make it difficult to search for optimal trees. It is worth to note that the grouping of galaxies allows to reduce considerably the computational time (consider that a supercluster has tens of thousands of galaxies).

GSyF and GFiF are probabilistic algorithms in the sense that they define systems and filaments as a function of the position and orientation of the Gaussian groups, which are the result of a Hierarchical Clusterization method. For GSyF, these measurements are refined by using a virial approximation, allowing the detection of gravitationally bounded systems of galaxies and discern mis-detections.

For GFiF, the orientation and position of Gaussian groups are used to define a general tree from which independent structures are extracted.

However, we have shown that this methodology needs to be optimized for the number of HC groups and the linking length D max in order to detect the most promising filaments. The optimization of these parameters is proposed to be implemented on the real data in the analysis, by testing a range of parameters.

Then, the optimal combination of f and D min will correspond to the one that maximizes the number of identified filaments.

Chapter 3

Characterization of systems and filaments through optical galaxies

One of the objectives of this work aims for the detection and study of filaments of galaxies, which can be defined as chains of clusters connected by bridges of galaxies (and probably by gas and dark matter). To achieve this goal, the approach implemented consists of applying the GSyF algorithm for the detection of systems of galaxies and GFiF for the detection of bridges and filaments.

In this context, this Chapter describes the implementation of the algorithms described in the previous one. Both algorithms use only the position of the galaxies as measured from their projected positions and line of sight velocities to detect structures. This Chapter presents the results of our implementation of GSyF and GFiF to a sample of 46 boxes containing superclusters of galaxies. Then, we describe the samples of detected systems and filaments as well as the correlations between the principal features of galaxies and the structures they belong to.

The filament candidates sample

The supercluster sample used in this study consists of a selection of superclusters of galaxies from the Main SuperCluster Catalogue (MSCC) presented in Chow-Martinez et al. (2014). The full MSCC is an all-sky catalog that contains 601 superclusters, identified in a complete updated sample of rich Abell/ACO clusters, with redshifts from 0.02 to 0.15, by using a tunable FoF algorithm. Of these, only those superclusters with five or more clusters and those for which their box volume (see below) was completely inside of the SDSS-DR13 surveyed area were selected for the present study.

The selection of superclusters took into account a sample of filament candidates by Chow-Martínez et al. (2019, in preparation). Roughly speaking, these filament candidates were identified as chains of at least three clusters, members of the superclusters, separated by less than 20 h 1 70 Mpc from each other. Therefore, one of the objectives of this work is to validate these filament candidates by searching for bridges of galaxies connecting the galaxy clusters. However, there exists the possibility that some of the filament candidates do not present bridges of galaxies connecting clusters. Also, some bridges may exist, but not in the direction that straightly connects the clusters.

The final sample consists on 46 superclusters of galaxies, which are listed in Table 3.1. The ID of the supercluster in MSCC is shown in column 1, with its proper name in column 2, when available. Column 3 presents sky coordinates, RA (↵) and Dec ( ), of the supercluster mean position, while column 4 shows its mean redshift. Columns 5 and 6 list the richness (number of member clusters) and the number of filament candidates found previously in each supercluster (Chow-Martinez et. al. in prep). The IDs of the Abell/ACO member clusters are listed in column 7.

Both for the Abell/ACO clusters and for the galaxies in the superclusters box volumes (see section 3.1.1), the radial-angular coordinates were transformed to rectangular coordinates according to equations 2.4, 2.5 and 2.6.

The SDSS galaxies

The main galaxy sample of SDSS-DR13 is a suitable database to search for filamentary structures on the LSS since:

1. it covers a large sky area (14,555 square degrees), containing several MSCC superclusters; 2. it contains homogeneous photometric and spectroscopic data for galaxies with an astrometric precision of 0.1 arcsec rms and uncertainty in radial velocities of about 30 km s 1 (Bolton et al., 2012); Notes. The superclusters have five or more Abell cluster members, with z  0.15, and inside the SDSS-DR13 region. Superclusters with proper names are indicated in column 2.

3. it is roughly complete to the magnitude limit of the main galaxy sample (r P et = 17.77), which corresponds to an average z ⇠ 0.1, going (inhomogeneously) deeper for data releases after DR7 (Abazajian et al., 2009); 4. at the limit of our sample, z = 0.15, the SDSS spectra are complete for galaxies brighter than M r ⇠ 21.

The SDSS-DR7 joins the SDSS-I/II spectra for one million galaxies and quasars.

It has ⇠6% incompleteness due to fiber collisions (Strauss et al., 2002) and another ⇠7% incompleteness attributed to pipeline misclassification (Rines et al., 2007). These spectra are included in the final data release of the SDSS-III (Alam et al., 2015). The Barion Oscillation Spectroscopic Survey (BOSS) is part of the SDSS-III observations and has obtained spectra for another 1.4 million galaxies.

The BOSS observations are divided in two main samples, LOWZ (z< 0.4) and CMASS (0.4<z<0.7). The SDSS-DR13 (Albareti et al., 2017) includes spectra for more than 2.6 million galaxies and quasars.

For the present analysis, only objects listed on the SpecObj sample with spectroscopic redshifts available denoting an extragalactic object (that is, galaxies and low-z quasars) were selected (downloaded from the SkyServer web service). The SpecObj table contains the best spectra (unique within a circle of 2 arcsec) called "sciencePrimary" objects. The galaxies were extracted within a redshift range from 0.01 to 0.15. Only galaxies with spectra quality flag "good"

or "marginal" were used. A study of the 3D galaxy distribution is dependent on the galaxy distance measurement. Spectroscopic redshifts provide the accuracy needed for this kind of analysis. Nevertheless, several photometric redshift catalogs are available for the SDSS, which can be included to the sample in future analyses to test if their addition increases the signal of filament detection.

Moreover, there exist several sub-products that use the SDSS spectra to characterize the galaxy properties. In particular, the following catalogs were used to characterize the galaxy filaments: the MPA-JHU catalog (Brinchmann et al., 2004;Kauffmann et al., 2003;Tremonti et al., 2004) provides different galaxy properties (stellar mass, metallicity, activity type classification, star forming rate, among others). As explained by Tremonti et al. (2004), the galaxy properties in the MPA-JHU catalog are calculated by processing the galaxy spectrum in a way that even the weaker emission lines are detectable. The GRANADA group catalog is another SDSS-DR13 value added database that provides galaxy properties such as mass and metallicities calculated from the galaxy magnitudes (Conroy et al., 2009). The SDSS images and magnitudes have also been used to estimate the galaxy properties using neuronal networks. One example of this approach is the morphological classification provided by Huertas-Company et al.

(2011). These authors calculate a probabilistic morphological classification, for the SDSS-DR7 spectroscopic galaxies, by applying deep learning techniques that make use of their photometry. They also compare their automated classification with a sample of the Galaxy Zoo (Lintott et al., 2008(Lintott et al., , 2011) ) visual classification. They show that their classification into early and late types are in good agreement with the visual classification.

The superclusters' boxes

For this analysis the superclusters were confined to boxes defined in rectangular coordinates. The box walls were set at a minimum distance of 20 h 1 70 Mpc from the center of the farthest clusters in the supercluster. Then, all SDSS galaxies located inside its box volume were selected.

In Table 3.2 the box volumes (column 2) for each supercluster are listed as well as number of galaxies inside each volume (column 3), the mean volume and surface (sky projected) number densities (columns 4 and 5), the baseline density (column 6), the number of galaxies with surface density above the baseline density (column 7), the segmentation parameter f and the number of HC groups (see Section 2.3.2) (columns 8 and 9), FoG corrected groups of richness lower than 10 galaxies (column 10) and with richness higher than 10 galaxies (column 11), the ranges of radius and velocity dispersion for this last final list of groups (columns 12 and 13).

In particular, the superclusters MSCC 236, 314 and 317 lie close to the limits of the SDSS region: although all their member clusters are inside, their boxes were reduced to a margin of 10 h 1 70 Mpc in only one direction. For this reason, their analysis must be taken with caution due to this small data incompleteness. Notes. The value -99 is set when GSyF does not detect systems.

N d = 1/V dsup = N/A d bas N gal f N HC N F oG Rvir v (MSCC) [10 3 Mpc 3 ] (DR13) [Mpc 3 ] [deg 2 ] [deg 2 ] di > d bas Nj 3 Nmem < 10 Nmem [Mpc h 1 70 Mpc ] [km s 1 ] (1) (2) (3) (4) (5) (6) (7) (8) (

Implementation of GSyF and GFiF algorithms

In what follows the application of the detection algorithms presented in Chapter 2 to one of the superclusters in our sample, MSCC310, the Ursa-Majoris Supercluster (see Tables 3.1 and3

Application of GSyF to MSCC310

As mentioned before, the transformation from radial-angular coordinates to rectangular coordinates is more complicated for the galaxies. Their peculiar velocity may bias their redshift-space coordinate, especially when they are members of clusters and groups of galaxies, being subject to the "Finger of God" (FoG) effect.

Therefore, in order to detect systems of galaxies and correct this effect the GSyF algorithm was implemented over the galaxy distribution, as described in section 2.3.

First we applied the VT algorithm over the projected distribution of MSCC-310 galaxies to calculate the local surface density d i for each galaxy. The surface density baseline, d bas (15.7 deg 2 ) was calculated from 1 000 simulations of the galaxy distribution. Then the HC algorithm was applied to the N gal = 7 529 galaxies with i > 0. -140 -120 -100 100-80 FIGURE 3.2: 3D distribution of galaxies for the MSCC-310 supercluster volume. Top, galaxy positions before the application of the FoG correction. Bottom, Galaxy positions after correction for FoG effects. The color represents density as calculated from 3D VT. The higher density is represented in red color while greener to blue color represent lower density.

The best f parameter for the implementation of the HC algorithm was calculated from 30 mock simulations (f = 6, in this case), using the optimization methodology described in section 2.5.2. The HC implementation grouped the galaxies in N cut = 1 140 groups. As expected, these groups have, on average, ⇠ 6 members. Of these, 1 015 groups with N j 3 were selected.

For the first iteration of the virial refinement the center of each HC group was set at the position of the galaxy member brightest r-band and closest to the geometric HC centroid. For MSCC-310 groups, the mean difference between the geometrical center and their brightest galaxy position was found to be about 350 h 1 70 kpc. On average, the virial refinement needed six iterations to produce convergence of the virial radius. This refinement resulted in 139 systems with N j 10 for the MSCC-310 volume. The refinement also confirmed 116 smaller systems with 5  N j < 10.

In Table 3.3 the properties of the first 25 richest systems for the MSCC-310 supercluster are listed. Column 1 assigns a sequential number to the systems, while column 2 presents their richness. The coordinates of the brightest member of the system are indicated in columns 3, 4 and 5, while columns 6, 7 and 8 show the coordinates of the final position of the centroid. The other calculated properties of the systems -velocity dispersion, harmonic and virial radius -are presented in columns 9, 10 and 11 respectively. Column 12 denotes the cross-reference with Abell clusters. The range of virial radius of the GSyF systems with N mem 10 in MSCC-310 is from 0.7 to 2.5 h 1 70 Mpc. For groups with 5  N mem < 10 the range of virial radius lies is from 0.4 to 0.9 h 1 70 Mpc. After the refinement, the projected central position of the systems changed, on average, by 170 h 1 70 kpc, while the redshift was refined for some cases up to z ⇠ 0.001 or v ⇠ 300 km s 1 .

As an example, the richest system in MSCC-310 is the cluster A1291A. Lauer et al., 2014). This means that the position was mostly adjusted along the line of sight coordinate.

Finally, the comoving distance D C of the member galaxies in each system was corrected by re-scaling their dispersion range to the R vir of the system prior to conversion to rectangular coordinates. An example of the MSCC-310 volume, before and after the correction, is shown in Figure 3.2.

Application of GFiF to MSCC-310

The galaxy positions and redshifts were transformed from sky coordinates to rectangular ones following the equations 2.4, 2.5 and 2.6. This transformation was carried out after correcting the galaxies co-moving distances D C for the FoG effect. The N gal was now taken to be the total number of galaxies in the box of MSCC-310, 286, to which the GFiF method was applied. The VT algorithm was then applied to calculate the volumetric numerical densities. The optimization of the f and D E parameters was carried out as described in section 2.5.3.

With this, the HC method identified 768 low density groups using the optimal segmentation parameter f = 16. As expected, the application of the HC algorithm on all galaxies detected richer groups (⇠ 15 galaxies on average now) and more elongated, with a mean j of 1.8 h 1 70 Mpc compared with the mean j of 0.5 h 1 70 Mpc found with GSyF.

After, we calculated the Euclidean distance D E between the group centroids while the weight was set as the BC coefficient between groups. The linking length estimated by the optimization process (see section 2.5.3) was D max = 8 h 1 70 Mpc resulting on 334 edges. These edges were filtered by the minimum mean lineal density along the edge cylinders (in this case 0.008 gal.Mpc 3 ), resulting on 273 links. This resulted in 34 unconnected trees, obtained from the application of MST. As stated before, and following the definition by Chow-Martínez et al. (2019, in preparation), the objective of GFiF is to search for the filaments which have at least 3 galaxy systems connected by bridges. Only 9 trees were found linking 3 or more systems of galaxies with a richness N mem above 11 galaxies. The richness limit was calculated according to equation 2.13. The remaining trees correspond to isolated bridges (that is, connecting only one pair of system) and tendrils (connections between nodes with less than two systems embedded).

Although these structures are also a sub-product of the algorithm, the analysis presented in the following sections concern only the filaments. The filament are the largest structures in the volume, this result is shown in the dendrogram depicted in Figure 3.3 (top panel) which shows 9 dominant filaments for the MSCC-310 supercluster.

Concerning the systems embedded in the structures, from the 359 HC groups (nodes) in the spanning trees, 116 matched with the systems with N mem 11 identified with GSyF. From these, 61 were found to be in filaments (53%), 26 (22%) in bridges between pairs of systems, and 29 (25%) not connected by bridges, that is, relatively isolated.

The filaments detected by GFiF algorithm in the MSCC-310 supercluster and their main properties are listed in Table 3.4. Column 1 assigns a sequential number to the filament; column 2 lists the number of systems detected by GSyF linked by the filament; column 3 shows the number of galaxies attributed to the filament; columns 4 to 6 are the mean, minimum and maximum redshift of the filament; column 7 correspond to the mean number density inside the filament; column 8 is the mean transversal radius of the filament skeleton measured as

Validation of the methods

Checking the identified systems of galaxies

In order to validate the GSyF algorithm, the list of identified systems was compared with different cluster and group catalogs available for the SDSS region. For MSCC-310, GSyF detected 139 systems with ten or more galaxies and another 116 systems with 5  N mem < 10. A match was considered positive if the projected positions of the system in the two compared catalogs were not farther than 1 h 1 70 Mpc, while for redshift space the difference was set as z = 0.007 which corresponds to ±2100 km s 1 .

For the rich clusters, the GSyF results were compared with the original Abell/ACO catalog (Abell et al., 1989), based on the most recent parameter measurements for its clusters (e.g. Chow-Martinez et al., 2014). We also compared them with the galaxy positions provided by the brightest cluster galaxy catalog (BCG, Lauer et al., 2014). Regarding catalogs for the SDSS we compared with the C4 cluster catalog (Miller et al., 2005), which was computed for the SDSS-DR2. These comparisons were carried out using all systems detected by GSyF down to systems with a richness of 5 galaxies. By using a tolerance aperture of 1 h 1 70 Mpc, 19 of the 37 Abell/ACO clusters inside the MSCC-310 box were detected as systems of richness above 5 galaxies with our method (51% ), while the equivalent number was 26 (76%) for the 34 clusters in C4. There are 11 BCG clusters embedded in the volume and 8 (73%) of them have GSyF counterparts. However, incrementing the aperture to 2 h 1 70 Mpc results in an increase in the detection of Abell clusters to 29/37 (78%), C4 clusters to 33/34 (97%) and BCG clusters to 100%, see Table 3.6. The increase of ⇠ 21% 27% in all rich cluster matches when using a larger aperture size can be related to the fact that the mean separation of galaxy members increases for lower richness systems, and the determination of the cluster center then is subject to this separation, see Table 3.6. For example, A1452 and A1507B have a GSyF counterpart located at ⇠1.5 h 1 70 Mpc distance and v of ⇠ 630 km s 1 and 120 km s 1 respectively (See Table 3.3 systems No. 12 and 14), while their C4 counterparts are 0.7 and 0.4 h 1 70 Mpc , respectively. found via MSPM with richness larger or equal to 10 galaxies for the MSCC-310 volume. Our algorithm detected systems that correspond to 70% of the T11 clusters (167 detections) and 80% of the MSPM clusters (249 detections) within an aperture of 1 h 1 70 Mpc, see Table 3.6. On the other hand, one can observe that both catalogs, T11 and MSPM, have a larger number of systems matched with GSyF systems of richness between 10 and 5 galaxies, causing the match ratio to decrease. This is acceptable for our purposes since GSyF has been constructed to find the clusters that present a FoG effect, although our algorithm can clearly find poorer systems.

It is interesting to note that, for rich clusters (Abell, BCGL and C4), the mean separation (Table 3.6) between different catalogs is about 0.4-0.5 h 1 70 Mpc and 100-150 km s 1 , with 1 h 1 70 Mpc of tolerance, while for groups (T14 and MSPM) these numbers are 0. Similar analyses can be done for the other superclusters in our sample. For example, for the Coma supercluster (MSCC-295), the GSyF algorithm detected, in total, 160 systems. Among these, one can find A1656 cluster, which is composed of 579 galaxies. The estimated virial radius and mass for this system are respectively, 1.96 h 1 70 Mpc and 7.7 ⇥ 10 14 M . The second richest system is A1367, which has 243 galaxies and its radius and mass are, respectively, 1.73 h 1 70 Mpc and 5.3⇥10 14 M . These estimations are in good agreement with those measured by Rines et al. (2003).

Checking the filament skeletons

In order to check the efficiency of the GFiF algorithm, the filaments detected in MSCC-310 were compared against those presented by Tempel et al. (2014) (hereafter, T14) as extracted from their table 2. The T14 catalog is suitable to evaluate the GFiF filament detection since it lists filaments derivated from SDSS-DR7. The T14 filament position are given in survey coordinates (⌘ and ) with (⌘ and ) = (0.,0.), (RA, Dec) = (185., 32.5). The transformation to angular coordinates was carried out according to the following transformation:

Comparison with KDE density maps

For further validating the results from GSyF and GFiF algorithms a KDE method was applied to the galaxies in the MSCC-310 volume. As mentioned before, the KDE method makes use of the local density of the galaxies to estimate the density probability function that better describes de galaxy distribution. This validation was carried out over the 2D projections (density maps) of the 3D KDE (XY, XZ, YZ). For the KDE implementation, the kernel size was set as 1 ⌃ (see sec- volume. These density is expressed in units of the mean number density.

Filament Properties

Main properties of the filaments

The same methodology described for the MSCC-310 supercluster, was applied to the 46 superclusters of our sample, detecting about 1 500 systems of galaxies (see table 3.2) and 143 filaments in 40 superclusters which are summarized in table 3.7.

This table also lists the parameters used for GFiF for each supercluster: column 2 notes the segmentation parameter f , while column 3 presents the number of detected HC groups. Column 4 shows the linking length (D max ) used to connect HC groups. The process of filtering the connections can be followed through columns 5 to 10, which show, respectively, the number of detected edges, the number of filtered links, the number of trees detected after applying MST and the final number of filaments, N ske , number of isolated bridges, N brid , and tendrils, N tend . Column 11 lists the minimum richness considered for GSyF systems to be accepted as bridges. Column 12 to 14 present, respectively, the fraction of these systems included in the GFiF filaments, in isolated bridges and the ones not connected by bridges. Finally, columns 15 to 17 show the number of galaxies hosted by the GFiF filaments, N fil , and the filling factors calculated as V fil /V and

N fil /N .
The list of detected filaments for each supercluster volume can be consulted in Appendix B, in the same format as the one presented in Table 3.4. In particular, MSCC-55 and MSCC-579 superclusters did not have a complete coverage by the SDSS. Thus, GFiF algorithm was not able to detect filaments for these volumes.

The filaments detected by GFiF have lengths from 9 to 130 h 1 70 Mpc. Figure 3.9 depicts the length distribution for all the detected filaments. The distribution shows that the majority of the structures' lengths range from 15 up to 80 h 1 70 Mpc. There are two structures longer than 100 h 1 70 Mpc. A 130 h 1 70 Mpc long filament is located in MSCC-323, containing the Abell clusters A1449B and A1532A, the second of 105 h 1 70 Mpc in MSCC-335. Excluding these two particular cases, the mean length of the filaments is about 37 h 1 70 Mpc while the median corresponds to 29 h 1 70 Mpc.

Distribution of galaxies along the filaments

It is expected that the environment inside filaments is denser than in the dispersed component of the supercluster or in the general field. Therefore, longitudinal density number profiles were extracted, to evaluate the environment along the filaments. Figure 3.10 depicts the longitudinal distribution of galaxies for all bridges forming filaments in the supercluster MSCC-310, along the path from one system to another. These distributions show that the density of galaxies is higher in the extremes of the bridges, as expected, and decreases through the midpoint between systems. Then, density profiles for bridges were extracted from the systems to the midpoint, by counting the galaxies that lie within a cylinder of radius 1 h 1 70 Mpc with medial axis set by the bridge skeleton. The galaxies are counted in bins of size d = 0.5 h 1 70 Mpc. We also extracted longitudinal profiles after stripping the systems (considered at 1.5 R vir ) from their bridges, in order to evaluate the environment of pure filaments. These profiles allow to compare the mean density of the filaments with the background density. Figure 3.11 shows the longitudinal number density profile for all filaments detected in our sample. The stacked longitudinal profile including galaxies in systems is depicted by a blue line. The dispersion about the stacked profile is represented by a blue shaded area. The pure profiles (excluding the systems' galaxies) is represented by the red line, and its corresponding dispersion by a red shaded area. As can be seen, the mean density contrast along the filament is ⇠ 10, that is, the filament is about FIGURE 3.11: Longitudinal VT density distribution for galaxies for all bridges on filaments detected by GFiF. Profiles are considered from the system center to the middle of the bridge. The blue line depicts the mean longitudinal profile for bridges including galaxies in systems. The thide red line corresponds to the mean longitudinal profile for all filaments excluding galaxies belonging to systems within 1.5R vir . Blue and red shaded areas are the dispersion about the stacked profile.

Transversal profiles

The extraction of transversal profiles allows to further characterize the filament environment and their effect on the galaxies. These profiles are calculated by setting up a series of concentric cylinders with axes orientated along the filament skeletons. Then, a bin is considered to be the volume within two concentric cylinders of radius R cy and R cy + R cy . The occurrence of a galaxy proxy in each bin is determined according to the galaxy distance to the filament edges D fil .

The total count of galaxies per bin is weighted by the bin volume, in a similar way as making a normalized histogram. In order to compare samples of different sizes, a normalization is done by dividing the number of events in a bin by the total number of galaxies in the sample.

Density in transversal profiles

While the longitudinal profiles allow to characterize the mean number density along filaments, the transversal profiles allow to characterize the filaments up to and beyond their influence region.

The extraction of transversal density profiles was carried out excluding the galaxies located in systems, within a radius set as 1.5 R vir . This allow to characterize pure filaments. The density profile is calculated as described in section 3.5. The cylinder radii R cy were chosen from 0 up to 10 h 1 70 Mpc in steps of R cy = 0.5 h 1 70 Mpc.

The transversal galaxy number density profile for filaments is calculated in two ways:

• The local number density profile is calculated by counting the number of galaxies within concentric cylinders and dividing them by the volume within the cylinders.

• The VT number density profile is calculated as the mean VT number density within concentric cylinders, d i , as described in Sec. 2.1.1.

The local number density and VT number density profiles are expressed as a density contrast (w.r.t. d bas ) and stacked together.

Figure 3.12 shows the stacked profile for all filaments detected by GFiF. One can observe, in both local and VT density profiles, that the overdensity extends up to 2 -3 h 1 70 Mpc. Beyond 5 h 1 70 Mpc, the density profiles tend to reach values below the mean density, as expected since the mean density accounts for both, the filaments and background field. However, this effect is less obvious in the VT density profile, beyond 5 h 1 70 Mpc the density profile is noisier but lies within to 2 -3 ⇥ d. distribution shows that radii range from 0.6 to 4.5 h 1 70 Mpc with a mean value of about 2.4 h 1 70 Mpc . The bottom panel of the figure depicts the filament radius as a function of the filament length. From these results one can conclude that the filament length does not correlate with the filament radius, as expected for a "universal" pattern for the filaments. However, it is important to note that the mean radius does not represent the radius along the whole filament path.

Afterwards, the filling factor was calculated in two ways: the first takes the ratio between the number of galaxies inside the filament radius N gf il and the total number of galaxies N . The second is calculated as the rate between the filaments volume, estimated from the filaments length and radius, and the total volume of the supercluster box.

Properties of galaxies in filaments

Stellar mass profile

The stellar mass profile for all filaments was extracted as described in section 3.5.

Before the extraction the mass was weighted by the average mass of the volume under analysis to remove the redshift dependence of the stellar mass (Chen et al., 2017b). This weighting is equivalent to a normalization of the stellar mass and allows to carry out a stacking procedure in order to increase the signal of the profiles. Without this weighting, the stacked mass profiles do not present any particular trend and the error increases, as shown in figure 3.14. them (beyond 3 h 1 70 Mpc), indicating that the stellar mass correlates with the distance to the filament axes. These results are in good agreement with the results presented by Chen et al. (2017b) for the MGS sample from DR7 Abazajian et al. (2009). Also they are compatible with the results presented by Kraljic et al. (2018), which present a similar trend for the filaments found for the GAMA spectroscopic survey, for a redshift range 0.03  z  0.25.

Morphological type

Morphology profiles were calculated in order to analyze if there is some morphological trend in the population of filament galaxies (as may be expected from the morphology-density relation). For this analysis we used the Huertas-Company et al. ( 2011) morphological classification. They classify the galaxies in four morphological types. For this analysis we used the probability p(Early) = p(E) + p(S0) which classifies galaxies in early type p(Early)> 0.5 and late type p(Early)< 0.5.

Therefore, the distribution of both galaxy types was calculated as a function of the distance to the filament. These distributions were normalized so they can be compared and stacked for all filaments in the sample in a similar way as a profile extraction, excluding galaxies in systems, see Figure 3.16. The results of this analysis show that the density of early type galaxies is higher than the population of late types near the filament axis. This effect is more notorious when computed as an early to late type ratio. We can see that at distances lower than 2 h 1 70 Mpc, the fraction of early types reaches almost twice the fraction of late types. At larger distances (that is, towards the dispersed supercluster population) the fractions tend to be similar. Moreover, these results are consistent with those presented by Kuutma et al. (2017) for the Huertas-Company et al.

(2011) sample. They also observe that early type galaxies are more abundant near the filament axes.

Activity type

For the analysis of the activity type, we employed the activity classification from the MPA-JHU group, (Brinchmann et al., 2004;Kauffmann et al., 2003;Tremonti et al., 2004) described in Section 3.1.1. The distribution of the different galaxy activity populations as function of the filament axis distance is presented in Figure 3.17. The distributions are normalized for all filaments and then stacked together.

Although the statistical signal is poor, it seems that the three activity types (SF, AGN and LINER) have a suppression when the galaxies "approach" the filament axes; while the passive galaxies increase their number towards the filaments skeleton. This decrease in activity has its maximum at about 2 h 1 70 Mpc for AGNs and LINERS and about 0.5 h 1 70 Mpc for star forming galaxies.

Red sequence analysis

In order to study the color-magnitude and color-mass distributions in filaments, galaxies were separated into three environments: systems, filaments and the disperse component. Color-mass and color-magnitude diagrams are often used in galaxy clusters to separate the early type galaxy population from the late type one. Moreover, the early type galaxies in clusters form a sequence on the color magnitude diagram which is called the "red sequence". The best fit of the red sequence forms the so called color magnitude relation (CMR). The dispersion, color and slope of the red sequence in clusters have been used to study the evolution of their galaxies with redshifts up to z⇠ 1 (e.g. Bower et al., 1992;Aragon-Salamanca et al., 1993;Gladders et al., 1998;De Lucia et al., 2006;Trejo-Alonso et al., 2014, see Section 1.5.3). We used the SDSS photometry to produce color magnitude diagrams as shown in Figure 3.18. We carried out FIGURE 3.18: Color magnitude diagrams for the MSCC-310 supercluster galaxies as measured for galaxies in the clusters, filaments and field, from left to right.

this analysis using the apparent r-band magnitude m r . Afterwards, galaxies were assigned to the red and blue clouds using a k-means classification, see Figure 3.19.

In Figure 3.18 we can observe the red sequence for system galaxies identified in our sample. Moreover, we also observe that galaxies associated to filaments, present also a red sequence while galaxies in the field and disperse component do not show the same trend. Moreover, one can observe, in Figure 3.19 clearly the red and blue clouds for clusters. One can observe a low number of galaxies in the transition region, also called green valley, located in between the red and blue

clouds. An accurate classification for the blue, red and green valley requires an iterative processes. This will be calculated for future analyses in order to increase the precision in the red sequence fit. A similar trend is observed for filaments although we observe a larger number of galaxies in the transition region. As counterpart, in the field we observe a large number of galaxies in the green valley.

Conclusions

In this Chapter we presented the analyses we carried out for the study of clusters, groups, bridges, filaments and tendrils of galaxies in the environment of superclusters of galaxies as well as the dispersed component and field galaxies.

These analyses were obtained by using the implementation of the Galaxy Systems Finding algorithm GSyF and the Galaxy Filament Finding algorithm GFiF. These algorithms were applied to a sample of SDSS galaxies with spectroscopic redshifts in boxes containing 46 superclusters of galaxies selected from MSCC catalog in a redshift range from 0.02 to 0.15.

The comparison of systems detected by GSyF with previously reported system catalogs confirms the reliability of the GSyF system detection. Specifically, for rich clusters, the match rate ranges from 78% for the Abell catalog to about 100% for the BCG and C4 catalogs, while for group catalogs (T14 and MPSM) the match rate is of about 80%, as estimated for groups with richness above 5 galaxy members at redshifts Z¡0.11 and with a tolerance of 2 h1 70 Mpc . However, we observed that for richness below N gal < 10 the match rate increases to 90% but the difference between measured richness increases. This difference in galaxy richness is a consequence of the algorithm design, limits and search range. Moreover, the velocity dispersions and virial radii measured by GSyF algorithm are in good agreement with those measured by other system catalogs. The GSyF algorithm detected a total of 2705 systems in 45 supercluster volumes. Of these, 159 systems with richness above 10 galaxies were not previously reported in the literature 1 . Moreover, the KDE analysis confirms that the overdensity regions correspond to clusters and rich groups of galaxies.

The GFiF algorithm detected a total of 143 filaments and 63 isolated bridges for 40 supercluster volumes. The detected filaments have skeleton lengths from 8.5 up to 130 h 1 70 Mpc while the isolated bridges have lengths between 5 and 15 h 1 70 Mpc . For most of the cases, the number density inside the filaments is measured between 5-15 times the background density. The measured radii for the filament skeleton ranges from 0.4 up to 4-5 h 1 70 Mpc .

Then, the filaments were characterized based on the properties of the galaxies that populate them. For the local number density, the conclusion is the following:

i) The distribution of galaxies along the filament, within a 1 h 1 70 Mpc cylinder radius, shows that the typical density contrast of the filaments is about 10 times the background density. ii) The transversal local and VT number density profiles for pure filaments show that at distances up to 2 -3 h 1 70 Mpc from the skeleton, the filaments are considered to have an overdensity above three times the mean box density. iii) That overdensity was used to measure the filament skeleton radius which goes from 2-3 h 1 70 Mpc. A comparison of our detected filaments with the Tempel et al. ( 2014) filaments has been carried out and one can observe that the filaments we define are on average four times larger, resulting in a significantly lower number of filaments. However, a comparison with isolated bridges and tendrils (a sub-product of our algorithm) shows a match of 80% with T14 filaments and a comparable filament length. A comparison of the GFiF detected filaments with those of Tempel et al. (2014) lead to the conclusion that GFiF detects as filaments the structures that present the highest probabilities to be real galaxy filaments.

The analyses regarding the galaxies stellar mass, morphology and activity type suggest a correlation with the distance of the galaxies from the filaments. These analyses lead to the following conclusions:

1. Near the filament skeleton and up to 3 h 1 70 Mpc the galaxy stellar masses are higher than the ones at larger distances from the filament. This result drives to two hypotheses: (a) that the mass of the galaxy is sensitive to the environment, or (b) the dynamical evolution brings massive galaxies into the potential well of the filaments. This result confirms several analyses that suggest that stellar masses are sensitive to the environment (Alpaslan et al., 2015;Poudel et al., 2016;Chen et al., 2017b;Malavasi et al., 2017;Kraljic et al., 2018).

2. For the morphological types, one can observe a correlation with the filament distance. The fraction of early type galaxies has its maximum at the center of the filament and the ratio of early to late type galaxies remains above unity up to a distance of 1.5 h 1 70 Mpc . This result is compatible with a similar work carried out by Kuutma et al. (2017) for the SDSS.

3. Concerning the activity type, our analysis suggest that the number of active galaxies (AGN, SF and LINER) decreases when the galaxies are nearer than the filament skeleton and up to 2 h 1 70 Mpc , while passive galaxies appear to be more common near the filament skeleton. These analyses suggest that the filaments environment might impact the galaxies activity.

The GSyF and GFiF algorithms can be used to search for these LSS structures in different surveys, using spectroscopic or photometric redshifts. One of the future directions of this work is to incorporate to this analysis SDSS photometric redshifts in order test the improvements on the detections.

Chapter 4

Characterization of galaxy clusters using SZ

As mentioned in Chapter 1, galaxy clusters are the most massive gravity collapsed systems of the LSS. Moreover, X-ray observations had shown that the majority of their baryonic content is present in the form hot gas called intracluster medium (ICM). The inner part of these semi-spherical structures is considered to be virialized and in hydrostatic equilibrium. However, in the outskirts, the ICM is subject to shocks and turbulent motions as a consequence of LSS filament matter in-falling on the cluster potential well.

Thus, the study and characterization of the ICM in the cluster outskirts is of particular interest for the study of the evolution and dynamical state of the ICM. Recent analyses have shown that SZ observations are suitable for the characterization of the clusters ICM up to the outskirts. Following this approach we reconstructed pressure profiles for a sample of clusters using SZ observations. In this Chapter we present and discuss the results from the recovery of pressure profiles for a sample of 31 clusters using only SZ data. Our analysis was carried out using a high resolution map, constructed from the Planck and ACT data. We describe the methods applied in order to reconstruct the gas pressure profiles from the SZ signal extraction as well as the profiles stacking method. We also present the validation procedure of the resulting pressure profiles.

The Planck and ACT sample and SZ data

The combined SZ map

In order to reconstruct the pressure profiles up to the outskirts for a sample of clusters, we employed the SZ maps (PACT y-map and its associated noise map) reconstructed from the linear combination of Planck (Planck Collaboration VIII, 2016) and ACT (D ünner et al., 2013) frequency maps. The resulting map integrates the best of the Planck frequency coverage and ACT spatial resolution which can be approximated by a 1.4 arcmin FWHM Gaussian (corresponding to the ACT spatial resolution). The PACT reconstruction was performed with an independent internal linear combination (ILC) method: MILCA (Modified Internal Linear Combination Algorithm; Hurier et al., 2013). This method allows to optimally combine frequency maps in a scale dependent way accounting for the intrinsic noise (instrumental and astrophysics) for the reconstruction of a targeted frequency dependent signal, the SZ effect in our case. A detailed description of the PACT map reconstruction and characterization can be found the main PACT paper (Sec. 3.2 of Aghanim et al., 2019b).

For validation purposes, we also made use of the Planck all-sky MILCA y-map (2015 data release Planck Collaboration et al., 2016c), which has an angular resolution of 10 arcmin FWHM (corresponding to the 100 GHz channel of the HFI instrument). We also used another (non-public) version of the MILCA y-map reconstructed at 7 arcmin FWHM. This map has been previously used for the extraction of the Planck SZ signal by the X-COP collaboration (Tchernin et al., 2016;Eckert et al., 2017;Ghirardini et al., 2017). Through out this Chapter, the integrated measured SZ fluxes will be expressed in arcmin 2 and the SZ luminosities in h 2 70 Mpc 2 .

The cluster sample

The cluster samples used for this work were selected from galaxy cluster catalogs obtained from the SZ Planck (Planck Collaboration VIII, 2011; Planck Collaboration XXIX, 2014; Planck Collaboration XXVII, 2016, ESZ, PSZ1, PSZ2, respectively) and ACT (Hasselfield et al., 2013a;Hilton et al., 2018) surveys. For instance, the PSZ2 catalog contains 1 203 confirmed clusters while a total of 119 clusters are detected within the ACT footprint. For this work we selected a sample of 34 clusters detected by both Plank and ACT. From these, 2 clusters were excluded, due to the partial coverage at the edges of ACT footprint and because its location was next to mask of the Planck point sources used to construct the PACT y-map. Thus, the final sample, listed in Table 4.1, comprehends 31 clusters of galaxies (hereafter referred to as PACT31) with 18 sources distributed in the equatorial strip and 13 in the southern one. By construction our sample is neither representative nor complete. The clusters range between 0.16 and 0.7 in redshift and 3.7 ⇥ 10 14 to 1.3 ⇥ 10 15 M in mass. The mean signal-to-noise ratio (SNR) of the sample is 6.0 in the Planck catalogues and 6.26 in ACT's. The range of angular size is 2.5 < ✓ 500 < 7.9 arcmin, with a mean value of 4.2 ± 1.1 arcmin.

Table 4.1 is organized as follows: column 1 lists the name of the cluster as we define it. Column 2, 3 and 4 list the ACT, PSZ1 and PSZ2 cluster name respectively; columns 5, 6, and 7 correspond to the cluster coordinates, right ascension, declination and redshift, respectively. Column 8 lists the cluster radius in arcmin units.

Column 9 lists the cluster PSZ2 M 500 and column 10 corresponds to the radius R 500 in h 1 70 kpc. Columns 11,12 and 13 list the signal to noise, SNR, measured for the cluster in the different catalogs, ACT, PSZ1 and PSZ2, respectively. Moreover, in order to assess, in Sec. 4.3, the robustness of our PACT pressure profiles (see Section 3.3.2) we derive pressure profiles of the hot intra-cluster gas for the sample of 62 massive local clusters (hereafter PLCK62) used by Planck

Reconstruction of the gas pressure profile

In order to recover the pressure profiles from the SZ y-map, we strictly followed the method described and used by Planck Collaboration Int. V (2013). The general aspects of this method are described in the following paragraphs:

Let us consider a spherically symmetric galaxy cluster, in this case, the radial dependence of the pressure is assumed to follow a generalized Navarro-Frenk-White (GNFW) (Nagai et al., 2007) profile:

P(x) = P (r) P 500 = P 0 (c 500 x) [1 + (c 500 x) ↵ ] ( )/↵ , (4.1)
with x = r/R 500 ; P 500 is the expected self-similar pressure at R 500 , c 500 is the concentration parameter defined at R 500 ; the slopes of the profile are defined by ↵, and for the inner, intermediate and outer regions: (x < 1/c 500 ), (x ⇠ 1/c 500 ) and (x > 1/c 500 ) respectively. Under this assumption, the Comptonization parameter y is a cylindric projection of the cluster' spherical pressure profile. Then, equation 1.59 can be expressed as:

y(r) = T m e c 2 Z R b r 2P (r 0 )r 0 dr 0 p r 02 r 2 , (4.2)
with r is the sphere/cylinder radius. Since y is dimensionless, it can be expressed as y(✓) or y(r). The integration over a frequency band accounts here for the effect of the weakly relativistic velocities of the electrons as a function of the gas temperature (e.g., Pointecouteau et al., 1998). This is however neglected in the y-map reconstruction as accounting for these effect would require a priori knowledge on the gas temperature distribution across the cluster). However, in real SZ observations, the observed Comptonization parameter profile is a geometric projection along the axis of the line of sight convolved with the instrument response (PSF), f PSF as:

ỹ(✓) = f PSF ⌦ y(✓). (4.3)
In order to reconstruct the pressure profile of the cluster, its y-profile needs to be deconvolved from the effect of the PSF and deprojected. Therefore, we employ a deconvolution + deprojection method (Croston et al., 2006) but adapted to poorer statistics (lower number of bins per radial profile), as described in Section 4.2.3.

Reconstruction of the SZ profile

For the extraction of the SZ profiles we used the SZ y-maps and their associated error maps. We extracted patches of side length 20 ⇥ ✓ 500 centered on the ACT cluster position from the y-map and error maps. Since the angular pixel size is different for all cluster patches, a standard pixel size was defined in constant units of ✓ 500 . Then, all cluster patches have the same dimension, defined under the same scale units. However, scaling the pixel size implies a sampling of the PSF that could lead to an oversampling of the y-map pixel. We keep track and propagate this redundancy using an associated pixel index map.

The azimuthal y-profile extraction for each cluster was performed as follows:

1. Point sources (positive and negative) were masked manually from the ymap with a 2.5 criterion clipping method.

2. The background offset was estimated for radii greater than 5 ⇥ R 500 and subtracted from the y-map. The use of the cluster surrounding area allows to take into account the astrophysical contamination in the cluster neighborhood as well as the instrumental and systematic noises.

3. Then, the y-profile is extracted on a radial grid. The y value of each radial bin is calculated as the mean y of the pixels falling on each annulus.

4. The power spectrum of the noise (background emitting sources, instrumental and systematic) was calculated in the region surrounding the cluster

(✓ > 5 ⇥ R 500 ).
5. The covariance matrix associated to the y-profile is calculated as:

(a) 1 000 realizations of the noise patch are simulated, after which the same profile extraction is performed as for the y-patches.

(b) the covariance matrix is constructed from the profiles of the noise simulations as C = P n T P n where P n is an n points ⇥ m matrix of simulated noise profiles.

Stacking the y profiles

Due to the expected-similarity property of the galaxy clusters, the profiles, once scaled, can be stacked together. This allows to increase the SNR by averaging out the background contaminants and noise. Stacking is a well-known method to obtain a more generalized representation of the clusters profiles. For this work we followed the stacking procedure described in Planck Collaboration Int. V (2013, Sec. 4.3.2, Eq. 14) to stack the y profiles.

Since all profiles are computed on the same grid (i.e. they are scaled in radius) the stacking consists in the calculation of the average value of all profiles at each grid radial point. Each y i -profile and its respective covariance matrix C i , are stacked as following:

ỹ = 1 n n X i y i i and e C = 1 n 2 n X i C i 2 i , (4.4) with = Y 500 /R 2 500
, n the number of clusters in the sample, y i the individual y profile and C i the associated covariance matrix.

PSF correction and deprojection

In order to maximize the SNR, the profiles were rebinned to the largest possible radii. As mentioned before, we assumed our clusters to have a spherical symmetry. Then we applied a regularized PSF deconvolution and geometrical deprojection algorithm. Since this method was originally designed for X-ray surface brightness profiles, which have higher resolution than the SZ profiles, the methodology needed to be adapted to a lower number of bins per radial profile. The errors encoded in the y-profile covariance matrix are propagated via its randomization over 10 000 realizations after its Choleski decomposition (assuming correlated Gaussian noise). Each y-profile is deconvolved from the PSF and deprojected.

As noted in (Croston et al., 2006), this can be formalised as a projection matrix, P, and a redistribution matrix, B. The projected and PSF convolved Comptonization profile reads as:

y(✓) = A p2y B P P(x) (4.5)
where the conversion from a universal pressure profile to an observed Comptonization parameter is expressed making use of Equation 4.1 and Equations 13 to 16 in Arnaud et al. (2010b):

A p2y = 1.65 ⇥ 10 3 ✓ M 500 3 ⇥ 10 14 M ◆ 2/3+↵p T m e c 2 1 D A E(z) 8/3 (4.6)
where T is the Thomson cross-section, m e the mass of the electron, c the speed of light, ↵ P = 0.12. This conversion assumes a scaling relation between the pressure and the total mass, assuming self similarity.

In this process each point of the y-profile is weighted by the value of the flux dispersion in the corresponding radial bin. The covariance matrix of the pressure profile is derived from the combination of all realizations. Then the profile and covariance matrix are scaled in physical units.

Stacking pressure profiles

The pressure dependence with mass near a density contrasts = 500 is almost constant with radius. Here we adopted the formulation derived by Arnaud et al.

(2010b, see Equation 13) when calibrated on the REXCESS representative sample of X-ray local clusters (B öhringer et al., 2007). Then, the relation between mass and pressure can be approximated as in Arnaud et al. (2010a, Equation 9):

P (r) P 500 = P(x)  M 500 3 ⇥ 10 14 h 1 70 M 0.12 . (4.7)
From the above and Equation 4.4, the observed stacked profile can be formalised as:

ỹ(✓) = 1 n " n X i A p2y,i B i P i i # P(x). (4.8)
Here we recall that r is the radius to the cluster center and x = r/R 500 . Since y is dimensionless, it can be expressed as y(✓) or y(r). 4.2) for the definitions of the various configurations. For the profile plots the dispersion across the sample is shown as shaded area, and the error bars picture the square root of the diagonal of the covariance matrix and therefore bear a certain degree of correlation between points.

Validation of the PACT profiles

In what follows we describe the comparisons between the individual SZ y profiles and the integrated SZ flux Y 500 over the PACT31 and PLCK62 samples for various setups. The radial profiles, y(✓), are derived from the y-map together with their correlation matrix as described in the previous section.

In the case of PACT clusters, the profile was centered at the ACT coordinates with R 500 fixed, and was projected and convolved by the Planck PSF, while for the PACT31 clusters, the center was set at the XMM-Newton flux peak position. Then, the individual integrated SZ fluxes were computed for each y profile

Y 500 = 2 Y 500 M T C 1 P, (4.9) 2 = (M T C 1 M ) 1 . (4.10)
For both the PACT31 and PLCK62 samples, we computed y(✓) and Y 500 over the public and non-public Planck MILCA y-maps, with 10 and 7 arcmin FWHM, respectively.

We chose as reference fluxes the estimation of Y 500 as derived from the multimatch filter (MMF) procedure described and used in the main PACT paper (Aghanim et al., 2019b). These fluxes were extracted with the MMF positioned at the

ACTcluster coordinates and with a filter size fixed to ✓ 500 for each source. For the profile comparison, we have cross-checked the stacked profile over the whole two samples, adopting as reference the y stacked profiles (and its dispersion envelope) derived for the PLCK62 sample by Planck Collaboration Int. V (2013). 1.09 ± 0.13, 1.10 ± 0.07 and 1.07 ± 0.07 for PIPV, D10 and D7, respectively. The profiles for the three cases (see Figure 4.4, bottom left) are also fully consistent in shape (the more peaked central D7 profiles only reflects the smaller PSF which was used to convolve the actual y profile). This agreement demonstrates that, for profiles computed with a radial sampling of r/R 500 = 0.25, there is no systematic difference between the first full sky survey and the full DR2015 Planck survey, and neither between the flux estimations from the 10 arcmin to 7 arcmin FWHM reconstructed MILCA y-map. We thereby adopted the latest D7 setup for further comparisons.

Extraction of profiles from

Extraction of profiles from Planck DR2015 7 0 : improving the sampling

We recomputed the profiles over the 7 arcmin FWHM y-map, with a sampling of r/R 500 = 0.08 and calculated the resulting associated fluxes (i.e., D7 120 setup). The comparison of the D7 setup from the previous section with the D7 120 setup is depicted in Figure 4.4, middle column.

The value r = 0.08 was chosen in order to properly sample the PACT PSF accounting for the angular extension of our clusters (see Table 4.1). As we extracted our profiles over a regular grid in units of R 500 out to a value of 10, the number of radial bin is fixed by the cluster in our sample with the largest angular extension, i.e., C32 with ✓ 500 = 8.30 arcmin. This led to a minimum of 112 bins with 10 ⇥ ✓ 500 , that was rounded up to 120 points. The PSF sampling is thus compliant with the Nyquist-Shannon criteria for all our objects, with the PSF oversampling rate increasing towards the cluster with smaller angular extension, and ranging from 2.1 to 6.6 with an average value of 4.2.

The profiles derived with this setup as well as their integrated fluxes are fully consistent with the MMF fluxes having an average ratio of 1.06 ± 0.07 D7 120 . This leads to the conclusion that no bias is introduced by further oversampling the PSF, as long as the increased bin-to-bin correlation is being properly encoded in the correlation matrix.

Samples and y-maps: from PLCK to PACT

Finally, we studied the PACT31 sample and computed the profiles and fluxes from the Planck 7 arcmin FWHM DR2015 map with a sampling factor of r/R 500 = 0.08, i.e., P7 120 setup, and over the PACT maps using the same sampling factor, i.e., the P7 setup (see Table 4.2). The latter is the nominal setup for the results on the PACT map and sample presented hereafter in this paper. The comparison of fluxes and profiles (see Fig 4.4, allows us to assess that no bias is introduced due to the change from the PLCK62to the PACT31sample.

The differences between the D7 120 and P7 120 stacked profiles exhibits the intrinsic difference between the PACT31 and PLCK62 samples. As shown in Fig. 4.5, they are sampling different regions of the mass and redshift plane. While the range of mass is similar, though the PLCK62 sample covers a broader range in mass, the main difference lie in the redshift coverage of the two samples. As a consequence, the angular sizes of the PACT31 clusters are smaller, hence the increased dilution in the Planck beam explains the flatter y profile for the P7 120 setup. As a further consequence, the profile convolution by the beam redistributes the power towards larger scales and explains the slightly shallower shape at larger radii.

Unsurprisingly the stacked y-profiles for the PACT sample as measured from the PACT map are more peaked at r < R 500 than the one obtained from the Planck data only, which in turn are shallower at radii larger than R 500 . This is due to the difference in smoothing by the PSF, i.e., 1.4 arcmin versus 10 arcmin for PACT and Planck respectively. However the match in fluxes demonstrates that no bias is introduced in the total integrated SZ flux when switching to the PACT maps. The average ratios to the reference MMF values are 1.24 ± 0.27 and 0.95 ± 0.12 for P7 120 and P7 respectively. The PACT results are further discussed in the next section. Table 4.2 gathers the definition of the various setups used in the validation procedure.

PACT profiles

Following the validation procedure presented in the previous section, in what follows only PACT maps with the adopted configuration P7 as defined in Table 4.2 for the PACT31 sample are considered. For the following analyses, we employed the cluster mass value M 500 as provided by the PSZ2 and PSZ1 (for clusters not detected by PSZ2) catalogs (Planck Collaboration XXVII, 2016; Planck Collaboration XXIX, 2014). i.e. 18 and 13 clusters, respectively. Within the limit of our statistics, we did not find any significant difference between the two subsamples, and hereafter the PACT31 sample is considered as a whole.

PACT31 y-profiles

To further consolidate our result, we followed the procedure of Planck Collaboration Int. V (2013) and stacked the individual y-maps across the sample. Each individual map, m i , was rescaled by the factor i (see Equation. 4.4) and randomly rotated by 0, 90 , 180 or 270 before averaging. The stacked map was finally back normalized in units of the Comptonisation parameter by h i i. A null test map is built from P ( 1) i m i . The RMS values of this null test map and of the stacked SZ map, outside 5 ⇥ R 500 , are 8.9 ⇥ 10 6 and 4.7 ⇥ 10 6 , respectively, and are consistent. They are also compatible with the average value of the stacked error y map, 8.8 ⇥ 10 6 . The the stacked map is shown on Fig. 4.6.

Stacked pressure profiles

After verifying the reliability of the PACT31 y-profiles obtained from the PACT maps, we reconstructed the pressure profiles following the methodology presented in Planck Collaboration Int. V (2013) and recalled in Sec. 4.2.4). Then, in a similar way to the SZ profiles, we stacked the individual PACT31 sample pressure profiles. The profiles were scaled in units of R 500 and P 500 according to In order to further quantify the compatibility with previous works we adopted a Monte Carlo Markov Chain to fit our pressure profile, see Table 4.3. Accounting for the difficulties to efficiently apply our algorithm of PSF deconvolution and deprojection (Croston et al., 2006) to our sample, Monte Carlo Markov Chain is used to directly adjust a gNFW pressure profile (see Equation 4.1) to our stacked y profile. Sayers et al. (2013Sayers et al. ( , 2016)), respectively, and tested against our average stacked profile. P7 corresponds to the best fit parametrization for this work. Values of best fit parameters are printed in boldface.

Conclusions and perspectives

We extracted y-profiles for 31 low SNR galaxy clusters using the new PACT SZ map. This map, product of the combination of the Planck and ACT data, takes the best of the ACT higher spatial resolution and the Planck large scale coverage.

From our stacked average y-profile, we detect SZ signal out to a radius of ⇠ 2.5R 500 and reach r = 0.04 ⇥ R 500 towards the cluster center, i.e. the PACTmap allows us to have more detail near the cluster center. This can be compared to the SZ standalone and joint X-ray plus SZ derived pressure profiles for the PLCK62 sample by Planck Collaboration Int. V (2013), which reach 0.125 and 0.02 ⇥ R 500 , respectively (see Figure 4.7).

Our stacked average y-profile is slightly less extended than the Planck profiles (Planck Collaboration Int. V, 2013), and we attribute this difference to the difference in sample and to their coverage of the M z plane.

Even though the PACT data does not reach the resolution of X-ray observations (i.e. does not arrive as close to the cluster center, we had demonstrated that the PACT data is suitable to investigate the ICM gas pressure from standalone SZ observation, allowing a better sampling towards the cluster centers. Therefore SZ observations are a good alternative for the characterization of clusters when X-ray observations are not available.

We carried out a validation using different sampling setups for the ACT 1.4 arcmin FWHM and Planck 10 and 7 arcmin FWHM DR2015 map, using the PLCK62 and PACT31 cluster samples. We demonstrated that the integrated SZ flux and derived y-profiles for the D10 and D7 setups are compatible and consistent with the reference fluxes Y 500 , as derived from the multi-match filter (MMF). Then, we showed that the oversampling of the PSF does not have effects in the extracted SZ signal. Finally, using the improved sampling of the PSF, we extracted y-profiles from the PACT map for the PACT31 sample. The comparisons of the integrated SZ flux Y 500 measured from the derived y-profiles, are consistent with the reference fluxes Y 500 , as derived from the MMF. Moreover, the stacked yprofile as well as the derived pressure profile, as obtained from the PACT map, are compatible (within the dispersion) with the previously published profiles by Planck Collaboration Int. V (2013).

As shown in Figure 4.3, the PLCK62 and PACT31 samples describe two different areas of the mass-redshift plane. As a consequence, both samples cannot be directly compared. Therefore, considering only clusters in the common redshift and mass interval of 0.15 < z < 0.45 and 5 ⇥ 10 14 < M 500 < 10 ⇥ 10 14 M , we obtained averaged values for the SZ flux (i.e., the integrated Comptonisation parameter Y 500 ) of 2.4 ⇥ 10 3 and 1.3 ⇥ 10 3 arcmin 2 , from 25 and 20 clusters for the PLCK62 and PACT31 samples, respectively. We observe that the PACT31 clusters are, on average, fainter in their SZ signal than the PLCK62 clusters by a factor of two. As a consequence, the detection of the SZ signal for the PACT31 clusters is more difficult, especially out to larger radii.

Recalling that the PACT31 sample was built from detected clusters in both ACT and Planck catalogs, it still has a reasonable statistical size. However it is not representative of the cluster population. A proper assessment of the pressure distribution from SZ-only observation in clusters of galaxies would need to be built from a representative sample spanning the mass range sufficiently large to characterize possible variation with the halo mass. As done for X-ray studies with, e.g., the REXCESS sample (B öhringer et al., 2007), it would provide a solid reference in the local Universe, a mandatory step to provide the necessary data for evolution studies (that requires also, to sample the redshift range in a representative way). consists in a new catalog of filaments inside superclusters and the identification of galaxies as filament members. GFiF identified a total of 143 filaments which were characterized by their membership, radius and galaxy density.

This catalog provides the properties of bridges of galaxies linking three or more galaxy clusters. Also, as a sub-product, smaller bridged structures were also catalogued as isolated bridges and tendrils. The nature of these smaller structures can be of interest for future analyses of less dense LSS structures. Once identified, we characterized the detected structures by their length, radius and member galaxies. We also searched for correlations with the properties of the galaxies embedded in them. Our results show that the galaxy morphology and mass correlates with the distance to the nearest filament. This result confirms previous results by Chen et al. (2017b) and Kraljic et al. (2018).

Regarding the gas component of galaxy clusters, our analyses were focused on the gas component, studied through the Sundayev Zeldovich effect. We carried out an extraction of the gas pressure profiles for a sample of 31 galaxy clusters using a high resolution y-map. The PACT maps combine the large frequency range from the Planck satellite observation with the high resolution of the ACT map. The analysis of these pressure profiles using the PACT map allowed us to extract y-profiles for the inner part of the clusters, from 0.03 R 500 up to 2 R 500 .

We have shown that the resulted stacked profile is in good agreement with the previously reported pressure profiles from Planck Collaboration Int. V (2013).

The differences we observed in the pressure profiles can be related with the fact that these clusters occupy a different range in redshift and have different angular sizes as compared to the PIP-V clusters. We have shown that the use of the PACT map allows the characterization of clusters with angular sizes up to 4 arcmin. Since the SZ signal does not depend on the redshift, only on the angular size, the use of high angular resolution maps open the possibility to carry out further analyses of clusters at higher redshifts using the SZ effect.

Further analyses of galaxy properties can be carried out in order to better constrain the possible environmental effects on galaxies. For instance, an analysis of galaxy metallicity and color index can help to further investigate the effect of environment in filament galaxies.

Other analyses are orientated towards the SDSS spectra using different diagnostic diagrams, in order to further investigate the effects of environment on the galaxy activity. Moreover, another follow up to be done is to measure the position angle of galaxies belonging to filaments, with respect to the filament axis, e.g. Zhang et al. (2015) only studied the spin of spiral galaxies but not the ellipticals.

This analysis can bring also information regarding the environment in which a galaxy resides. Following this approach, statistical analyses regarding the preferential orientation of radio galaxies with respect to the environment they reside can also be carried out.

Moreover, our new filament catalog aims to identify the best sky regions to carry out X-ray and millimeter observations. Therefore, future analyses orientated to the gas component of filaments can shed light on the evolution and dynamical state of this structures. One direction of this work is to better constrain the most concentrated regions in superclusters, i.e. their filament core. In this region galaxy systems are connected by bridges of high galaxy density, therefore, they are subject to interaction effects with the IGM in the filaments. This makes the study of filament cores of particular interest in order to understand the dynamical processes involved in such interactions. Then, a possible follow up is the characterization of the gas component for the systems belonging to the superclusters'

cores. An analysis of this nature can allow to better understand some mechanisms in galaxy clusters such as their gas metallicity enrichment. Another direction of this work is to compare with the current analyses of gravitational lensing in the direction of superclusters' cores. Since gravitational lensing is an indirect tracer of the matter distribution, it can allow to better constrain the filaments path in order to carry out further observations of the gas component.

Conclusiones y perspectivas

El objetivo de esta tesis de Doctorado fue estudiar las diferentes estructuras que conforman la estructura a gran escala del Universo. Bajo este contexto, hemos utilizado las posiciones de las galaxias para estudiar filamentos, c úmulos y grupos así como la componente gaseosa de una muestra de c úmulos para extraer sus perfiles de presi ón. Los c úmulos y superc úmulos son estructuras de gran inter és para el estudio de la evoluci ón de las galaxias y gas que habitan en ellos dado que fueron formados en conjunto bajo el efecto de la gravedad.

Para el estudio de las galaxias, seleccionamos galaxias con redshift espectrosc ópico a partir de la base de datos del SDSS. Esta selecci ón fue basada en la necesidad de una medida precisa de la velocidad de las galaxias en la línea de visi ón dado que nuestro m étodo es sensible a esta coordenada, como hemos descrito en el Capítulo 2. La metodología implementada propone la identificaci ón de estructuras dentro de superc úmulos utilizando la posici ón de las galaxias. Para la deteccion y caracterizacion de c úmulos y grupos desarrollamos el algoritmo "Galaxy System Finding (GSyF)". Como hemos descrito en los Capítulos 2 y 3, uno de los objetivos principales de este algoritmo es la correcci ón del efecto de dedos de Dios. Sin embargo, para lograr dicha correcci ón, los c úmulos y grupos deben ser detectados con precisi ón. Como subproducto de dicha detecci ón obtuvimos un nuevo cat álogo de sistemas.

A partir de la aplicaci ón de GSyF detectamos un total de 2 705 grupos y c úmulos de galaxias, de los cuales 159 no han sido reportados previamente. Hicimos una comparaci ón con otros catalogos de c úmulos a partir de la cual podemos concluir que GSyF es compatible con cat álogos de c úmulos (Abell, C4 and BCG) y de grupos (MSPM and T11) disponibles en la literatura.

Para la identificaci ón de puentes de galaxias y filamentos, desarrollamos una nueva metodología que implementa t écnicas de machine learning en nuestro algoritmo Galaxy Filament Finding (GFiF). Como resultado de la aplicaci ón de GFiF en nuestra muestra de galaxias obtuvimos un nuevo cat álogo de filamentos dentro de superculos, así como la identificaci ón de sus galaxias miembro.

GFiF identific ó un total de 143 filamentos caracterizados por sus miembros, radio y densidad de galaxias. Este cat álogo provee las propiedades de puentes de galaxias conectando tres o m ás c úmulos de galaxias. Como subproducto de la aplicaci ón de GFiF catalogamos puentes cortos y aislados llamados por nosotros tendrils. La naturaleza de estas estructuras aisladas puede ser de inter és en futuros an álisis de la componente menos densa de la estructura a gran escala del Universo.

Una vez identificadas, las estructuras fueron carcterizadas por su radio, longitud y galaxias miembro. Adem ás, analizamos las propiedades de las galaxias miembro de estructuras para buscar correlaciones. A partir de este an álisis observamos un relaci ón entre la morfología de las galaxias y la distancia a la estructura m ás cercana. Nuestros resultados confirman el an álisis previo de Chen et al.

(2017b) y Kraljic et al. (2018).

Respecto a la componente gaseosa de los c úmulos de galaxias, nuestro estudio se enfoc ó en caracterizar el gas utilizando observaciones del efecto Sunyaev Zeldovich Para esto llevamos a cabo un estraccion del perfil de presi ón de gas para una muestra de 31 c úmulos utilizando un mapa de Comptonizacion de alta resoluci ón, PACT. El mapa PACT combina el amplio rango de frecuencia del sat élite Planck con la alta resoluci ón del para ACT. Nuestro an álisis de los perfiles de presi ón utilizando el mapa PACT nos permitio extraer perfiles y desde la parte interna de los c úmulos, 0.03 R 500 , hasta radios de 2 R 500 .

Como parte de nuestros resultados mostramos que el perfil promedio de presi ón es compatible con los resultados previamente obtenidos para perfiles de presi ón por Planck Collaboration Int. V (2013). Las peque ñas diferencias que observamos en los perfiles de presi ón pueden estar relacionadas con el hecho de que estos c úmulos cubren un rango diferente en tama ño angular y masa comparado con los c úmulos de la muestra de c úmulos PIP-V, utilizada por Planck Collaboration Int. V (2013). Hemos mostrado que el uso del mapa PACT permite la caracterizaci ón de los c úmulos con tama ños angulares de hasta 4 arcmin. Dado que la se ñal SZ no depende del redshift pero el tama ño angular si, la utilizaci ón de mapas de alta resoluci ón nos da la posibilidad de caracterizar c úmulos a redshifts mayores a trav és del efecto SZ.

A partir de los resultados presentados en esta Tesis se pueden llevar a cabo an álisis dedicados a la caracterizaci ón de los efectos ambientales sobre las galaxias. Por ejemplo, un an álisis de la metalicidad e índice de color puede ser utilizado par estudiar el efecto del ambiente de los filamentos sobre la evoluci ón de las galaxias.

Adicionalmente, se pueden llevar a cabo otros an álisis utilizando diagramas de diagn óstico sobre espectros del SDSS con la finalidad de investigar m ás profundamente dichos efectos ambientales sobre la actividad de las galaxias. Otra propuesta es medir las orientaciones del ángulo de posici ón de las galaxias con respecto al eje del filamento al cual corresponden, por ejemplo, Zhang et al. (2015) estudi ó el spin de galaxias espirales pero no la orientaci ón de galaxias elípticas. An álisis de esta naturaleza pueden dar informaci ón respecto al ambiente en el cual las galaxias se encuentran. Bajo este contexto, se puede llevar a cabo un an álisis estadístico de la orientaci ón del eje preferencial de radio galaxias con respecto al ambiente en el cual ellas residen.

Dado que nuestro nuevo cat álogo de filamentos tiene como objetivo ayudar a identificar regiones del Universo con alta densidad de materia, puede ser utilizado como referencia para llevar a cabo observaciones en rayos X y en longitudes de onda milim étricas, favoreciendo de este modo estudios de la componente gaseosa en filamentos. Esto permitir á caracterizar la evoluci ón y estado din ámico de estas estructuras. Otra propuesta a futuro es delimitar las regiones m ás concentradas en superc úmulos, es decir su n úcleo. Es esta regi ón las galaxias est án conectadas por puentes de alta densidad de gas. Esto puede provocar efectos de interacci ón entre el medio en filamentos y las galaxias que residen en el. Por esta raz ón, estudiar estas regiones es de un inter és particular para comprender los procesos din ámicos de estas interacciones. Otra propuesta es estudiar la componente gaseosa de los cumulos y sistemas que forma los puentes del centro del superc úmulo para comprender diversos mecanismos como por ejemplo el enriquecimiento del gas.

Finalmente, como propuesta de trabajo a futuro, proponemos comparar nuestro resultados con los resultados obtenidos por lentes gravitacionales en la direcci ón de los n úcleos de superc úmulos. Dado que las lentes gravitacionales ponen en evidencia la distribuci ón de materia oscura, mapas de lentes gravitacionales pueden ayudar a delimitar la distribuci ón de los filamentos para llevar a cabo futuras observaciones de la componente gaseosa.

Conclusions et perspectives

L'objectif de cette th èse de Doctorat a ét é d' étudier les diff érentes structures qui composent la structure à grande échelle de l'Univers. Dans ce contexte, nous avons utilis é la position des galaxies d'une part pour l' étude des structures filamentaires et d'autre part pour l' étude de la composante gazeuse, afin de faire l'extraction des profils de pression pour les groupes et amas de galaxies. Les amas et superamas sont des structures de grande importance pour l' étude de l' évolution des galaxies et des gaz qui s'y trouvent, en raison de leur formation li ée à des effets gravitationnelles.

Pour l' étude des galaxies, nous avons s électionn é un échantillon de galaxies avec redshift spectroscopique provenant de la base de donn ées SDSS. Cette s élection a permis d'avoir une mesure pr écise de la troisi ème coordonn ée de la vitesse des galaxies dans la ligne de vision. Pour l'identification des ponts des galaxies et des structures filamentaires, on a d évelopp é une nouvelle m éthodologie en impl émentant des techniques de machine learning dans notre algorithme, Galaxy Filament Finding (GFiF).

Le r ésultat de l'impl émentation de l'algorithme GFiF à notre échantillon de galaxies, a permis d'obtenir un nouveau catalogue des structures filamentaires à l'int érieur des superamas, permettant ainsi l'identification des galaxies li ées à ces filaments.

GFiF a identifi é un total de 143 structures filamentaires qui ont ét é caract éris ées par leur radius, leurs galaxies membres et leur densit é de galaxies.

Ce catalogue nous donne les propri ét és des ponts de galaxies qui font la jonction d'au moins trois amas de galaxies. En plus, nous avons produit un catalogue des ponts de moins de trois amas isol és que nous appelons ici tendrils. La nature de ces structures isol ées peut avoir un int ér êt pour les analyses futures de la composante moins dense de la structure à grande échelle de l'Univers.

Nous avons analys é les propri ét és des galaxies membres des structures avec pour objectif de trouver des relations entre elles. A partir de cet analyse nous avons observ é qu'il existe une relation entre la morphologie de la galaxie et sa distance à la structure à laquelle elle appartient. Nos r ésultats ont confirm é les analyses du Chen et al. (2017b) et Kraljic et al. (2018). Les r ésultats obtenus pendant cette th èse peuvent être poursuivies par des étude d édi és à la caract érisation des effets environnementaux du milieu intergalactique chaud sur les galaxies. Par exemple, une analyse de la m étallicit é et l'indice de couleur des galaxies qui habitent dans structures filamentaires peut donner des informations sur l'environnement et son influence sur l' évolution des galaxies.

De plus, une analyse de l'effet environnemental sur l'activit é des galaxies peut être appliqu ée en utilisant le spectre SDSS des galaxies. Aussi, une analyse de l'orientation de l'angle de position des galaxies par rapport à l'axe du filament à laquelle elles appartiennent. Par exemple Zhang et al. (2015) ont étudi é l'orientation de la rotation des galaxies spirales. Un étude statistique de l'orientation des galaxies peut donner des informations sur l'environnement dans lequel la

FIGURE 1

 1 FIGURE 1.1: Power spectrum of the CMB as measured form Planck DR15 results. Figure extracted from Planck Collaboration et al. (2016b).

FIGURE 1

 1 FIGURE 1.2: Evolution of an overdense region in a spherical top-hat approximation. Here a nl refers to non-lineal and a coll to collapse.Figure extracted from Padmanabhan (2002).

  Arnaud et al. (2001); Pointecouteau et al. (2005); Croston et al. (2008); Arnaud et al. (2010a); Planck Collaboration et al. (2011, 2013a); Bourdin et al. (2017)).

  and White cluster profile Numerical simulations of structure formation have provided a solid description of the gas behaviour under the influence of the key physical processes governing the intra-cluster medium (ICM

  Plagge et al. (2010) extracted the pressure profiles of 15 clusters up to 2 ⇥ R 500 using the South Pole Telescope. Their analysis shows a consistency with the Xray cluster parameters. Planck Collaboration et al. (2013a) presented an analysis of the extracted SZ signal from the Planck satellite for 62 clusters. Their results combine X-rays for r < R 500 and SZ signal for r > R 500 to extract the pressure profiles up to 3 ⇥ R 500 . Another study carried out byBourdin et al. (2017) used the Planck full mission data to extract the pressure profiles for two samples of galaxy clusters, 61 clusters at z⇠ 0.15 and 23 clusters at z⇠ 0.56. They combined X-ray for the inner part of the clusters and SZ for the outskirts.

FIGURE 1

 1 FIGURE 1.3: (a) The [NII]/H↵ versus [O III]/H diagnostic diagram for SDSS galaxies. The extreme starburst galaxies are located near the solid line and the AGN and HII-region-like galaxies are divided by the dashed line. (b) The [SII]/H↵ versus [OIII]/H diagnostic diagram. c) the [O I]/H↵ versus [O III]/H diagnostic diagram. Figure extracted from Kewley et al. (2006) .

FIGURE 1

 1 FIGURE 1.4: Color-magnitude diagrams for normal luminosity clusters at different redshift. The dotted lines are the first selection in colour and the black solid rectangles are the final red-sequence selections. The red solid and red dashed lines are the regression fit and errors, respectively. Figure extracted from Trejo-Alonso et al. (2014).

  tun et al. (2013) proposed an automated algorithm which takes into account the density, tidal field, velocity divergence and velocity shear of the galaxies. Their results show a reliable identification of structures over a N-body simulation. Another approach, presented by Arag ón-Calvo et al. (2010), makes use of segmentation techniques to trace the spines of the filaments. They applied their algorithm over a selected N-body simulation and compared their results against a heuristic Voronoi tessellation (VT). Moreover, there have been several attempts to trace the distribution of the cosmic web using the SDSS database. For example, Platen et al. (2011) applied a Delaunay triangulation and VT over the galaxy positions to estimate the local density. Then, they interpolated the density between neighbors to recover contiguous high density regions. Tempel et al. (2014) applied a Bissous model which adjusts cylinders to trace the filament spine. A different approach is presented by Chen et al. (2016): they apply kernel density estimators (KDE) in order to smooth the galaxy distribution with a Gaussian kernel. Along the same path, Bond et al. (2010) applied a smoother Hessian major axis filament finder for the SDSS. They extracted the filaments by computing the Hessian of the density distribution of the galaxies.Also, combinations of different techniques have proven to be suitable for the identification of LSS structures.Smith et al. (2012) applied a multi-scale density estimator in combination with a Friends of Friends (FoF) algorithm over the SDSS galaxies. Their method allows them to recover structures from clusters up to filaments of ⇠10h 1 Mpc length. Moreover, Alpaslan et al. (2014) found, using the Galaxy and Mass Assembly survey (GAMA), that there are fine filaments embedded inside the SDSS voids. These structures, called 'tendrils', have a lower density than the SDSS filaments and appear to be morphologically distinct, they are more isolated and span over shorter distances.

  (a) The edge length D E is smaller than a threshold, D max (hereafter, linking length). (b) The mean lineal density of the edge is above d = N/V .

Figure 2 .

 2 Figure 2.1 provides a schematic of the definitions and Figure 2.2 shows schematically the steps of the GFiF algorithm.

  FIGURE 2.1: Representation of a filament. Graph nodes are represented by white circles and edges by dark lines. The three systems connected are represented by a dotted circle of radius R vir . A bridge connecting two systems is represented as a bold black line. The distance from galaxies to the filament, dashed line, is measured in the perpendicular line to the edges.

  FIGURE 2.2: Illustration of the steps of the GFiF algorithm. In the first box (topleft) one can see the distribution of galaxies. In the second one (top-right) the HC groups are marked, with denser red colors representing the richer HC groups. The filtered edges (links) among the groups of the spanning tree are displayed in the third box (bottom-left). The last box (bottom-right) presents the systems (green circles), bridges (brown lines) and other links (blue lines) found among the groups of the preceding step.

  FIGURE 2.3: Optimization of the segmentation, f (x axis), and minimum contrast density, g (lines of different colors in panels a-d), for the supercluster volumes of MSCC-310 (z=0.06) and MSCC-454 (z=0.04), from the mock simulations. (a, b) Success rates; (c, d) failure rates; (e, f) detection rates for systems with N mem 10 (green) and N mem 20 (blue), with N mem been the final number of members after the virial refinement. The failure rates are shown in brown.

  Figure 2.5a depicts the projected distribution of the found filaments for the optimal parameter configuration, while Figure 2.5b depicts the results for the second-best configuration, f = 20 and D min = 8.

  FIGURE 2.4: Optimization of the segmentation, f , and linking length, D min , parameters for the supercluster MSCC-454. This optimization is based in the number of relatively dense and long filaments detected.

  FIGURE 2.6: a) Distribution of best f values with redshift (z). b) Distribution of mean success rates with z. c) Distribution of mean success rates with volume number densities in each supercluster volume. Mean numbers are from the 30 mock simulations for each of the 42 superclusters.

Figure 3 .

 3 Figure 3.1 shows the diminution of mean volume density of the boxes with redshift, due to Malmquist bias. The fitted function will be used as the selection function for the SDSS galaxies used in this work.

  Its HC initial centroid position (set as the position of the brightest galaxy in the HC group: ↵ = 172.73, = 56.49 and z = 0.0611) changed by 13 h 1 70 Mpc after 17 iterations of the virial refinement (the final centroid position corresponds to ↵ = 173.01, = 56.09, z = 0.0535). This position is 240 h 1 70 kpc from the brightest galaxy detected of A1291A which has coordinates (↵ = 173.05, = 56.048, z = 0.0585,

  FIGURE 3.3: Results of GFiF algorithm for the supercluster volume MSCC-310. Top: The 9 detected filaments are shown in color over the SDSS galaxies distribution, gray points. The most prominent segments are depicted in dark-gray color. Bottom: Dendrogram color is set according to structures. The y axis on the dendrogram plot indicates the distance at each level of the tree.

FIGURE 3 . 4 :

 34 FIGURE 3.4: Projected distribution in the sky of systems detected by GSyF. Top: Systems detected for the MSCC-310. Bottom: Systems detected for the MSCC-295 supercluster. The system radii is shown as a circle of r = R vir . For comparisons, the position of systems reported by Abell, C4, MSPM and T11 catalogs are depicted by color points: red, pink, blue and green, respectively.

For

  FIGURE 3.5: Comparison of MSCC-310 supercluster GSyF system richness against the richness measured by other catalogs for the matching systems. Symbol colors are the same as the ones in the top figure. The dashed line represents the identity.

  35 h 1 70 Mpc and about 200 km s 1 . The systems detected in the main portion of the MSCC-310 supercluster are depicted, on a sky projected distribution, in Figure 3.4, by black circles with radius equal to the measured virial radius. The system positions from Abell, C4, BCG, MSPM and T11 catalogs are depicted as red, pink, cyan, blue and green symbols.

Dec

  = sin 1 {cos( ) ⇤ sin(⌘ + 32.5)} , 630 T14 filaments that lie in the sampled volume of MSCC-310 supercluster. These filaments have a mean length of 9 h 1 70 Mpc while the largest one has a length of 48 h 1 70 Mpc. As a comparison, the filament skeletons detected by GFiF have a mean length of 42 h 1 70 Mpc and the largest one has a length of 62 h 1 70 Mpc. The T14 filaments are a sequence of contiguous points forming a line. Then, the match rate was evaluated as the mean distance from the points to the skeleton of the GFiF filaments. The GFiF filaments show a match of 40% with the T14 filaments. Moreover, this number increases to 80% when comparing with GFiF isolated bridges and tendrils. The mean distance between the medial axis of the T14 filaments matching the nearest filament/tendril detected by GFiF is ⇠ 1.5 h 1 70 Mpc. The detected GFiF filaments are depicted over T14 filaments in Figure 3.6. As can be seen in this Figure, GFiF detects the most prominent (dense) filaments of these listed by T14.

  FIGURE 3.6: Comparison of GFiF filaments for the MSCC-310 supercluster against the T14 filaments for the SDSS DR8. Gray lines are T14 filaments.Colored lines depict filaments from the present work.

  FIGURE 3.7: RA.Dec. projected density map as measured from 3D-KDE with 1⌃ in terms of the density contrast. The GSyF systems are represented by white circles with radius equal to the estimated R vir . Density is indicated through a color scale displayed on the right, where denser regions are redder and less dense zones are bluer.

  FIGURE 3.8: KDE projected results. The denser regions are represented by light red color while the less dense regions are colored as blue. The filaments are overlaid in white color. Density is indicated through a color scale displayed on the right, where denser regions are redder and less dense zones are bluer.

  FIGURE 3.10: Galaxy density along bridges connecting pairs of systems for the nine MSCC-310 filaments. All bridges are scaled to length 1.0.

  FIGURE 3.12: Stacked density profiles for the 143 filaments identified by GFiF. Individual profiles are represented by thin gray lines. Top: The red line corresponds to the mean local density (stacked) profile. Bottom: Mean VT density stacked profile. The solid line indicates the mean profile while the shaded area represents the dispersion of the profile. The solid black line depicts the density contrast 10 ⇥ ¯ .

  FIGURE 3.14: Stacked mass profile not weighted for 143 filaments detected by GFiF. Errors correspond to the variance of the stacked profiles.

Figure 3 .

 3 Figure3.15 shows the stacked weighted mass profile for all filaments. The dispersion of the profile is depicted by the dashed red lines. Statistically, the fraction of massive galaxies is larger within 2 h 1 70 Mpc from the filaments than outside

  FIGURE 3.16: Top: Stacked morphological type profiles for 143 filaments detected by GFiF. Weighted error are depicted as error bars. Bottom: early to late type ratio as function of the distance to the filament axis.

  FIGURE 3.17: Stacked activity type profiles for 144 filaments detected by GFiF. The black bar on the left represents the typical errors on the stacked profiles, not overlaid for clarity.

FIGURE 3 .

 3 FIGURE 3.19: Color mass diagrams for the MSCC-310 supercluster for galaxies in clusters, filaments and field, from left to right. Solid and dashed lines represent the best fit for the red sequence and its dispersion respectively. Black crosses represent the centroid of the k-mean group.

FIGURE 4

 4 FIGURE 4.1: All-sky Comptonization y-map in Galactic coordinates (with the Galactic center in the middle, 10 arcmin resolution). The ACT equatorial and southern stripes are illustrated in red color.

FIGURE 4 . 2 :

 42 FIGURE 4.2: Maps of the Comptonization y parameter for the Southern ACT area. Top panel: 148GHz-ACT map at 1.5 arcmin resolution with scales larger than 7 arcmin filtered out. Middle panel: Planck y-map reconstructed with MILCA at 7 arcmin resolution. Lower panel: PACT y-map reconstructed with MILCA at 3 arcmin resolution. Circles indicate some known clusters in the selected area. The ACT point sources are masked in all three panels (grey areas). Figure extracted from Aghanim et al. (2019a).

Figure 4 .

 4 Figure 4.3 provides the distribution of the two samples in the M 500 z, M 500 ✓ 500 and ✓ 500 z planes. For PACT31 the quantities are obtained from the PSZ1 and PSZ2 catalogs, while for PLCK62 we used those provided by Planck Collaboration Int. V (2013). For the last case, the masses, M 500 are hydrostatic masses obtained from the XMM-Newton observations. Masses included in PSZ2 are derived from an Y 500 M 500 relation calibrated with Planck SZ integrated fluxes and XMM-Newton hydrostatic masses (Planck Collaboration XX, 2014; Planck

FIGURE 4 . 3 :

 43 FIGURE 4.3: Distribution of the PACT31 (red dots) and PLCK62 (blue dots) in the M 500 z (left), M 500 ✓ 500 (middle) and T 500 z (right) planes. Crosses picture the median value and associated maximum absolute deviation of each sample. Masses, radii and temperature values are taken from the PSZ2 catalogue (Planck Collaboration et al., 2016a)

FIGURE 4

 4 FIGURE 4.4: (Top One-to-one comparison of the integrated SZ flux, Y 500 , using x-axis values computed from the PACT maps as presented in Aghanim et al. (2019b) as references. (bottom) Average stacked y profiles in units of Y 500 /R 2 500 as function of radius in units of R 500 . Columns present the various steps of validation: (top left) Planck data 2013 and 2015 and y-map resolution. (bottom left) Investigate of Planck dataset version and y map resolution. (middle) Check of the impact of the radial sampling factor r . (right) Comparison of profiles derived from Planck and PACT maps and samples. We refer to the text (Sec. 4.3 and Table4.2) for the definitions of the various configurations. For the profile plots the dispersion across the sample is shown as shaded area, and the error bars picture the square root of the diagonal of the covariance matrix and therefore bear a certain degree of correlation between points.

  We first compared the integrated SZ fluxes and profiles derived from the first single full sky Planck survey (Planck Collaboration Int. V, 2013) on PLCK62 with those derived for the second Planck public release, which account for more than five co-added all sky surveys (hereafter DR2015) for both the all sky y-map reconstructed with a 10 arcmin (D10) and 7 arcmin (D7) resolution FWHM. We used exactly the same setup adopted by Planck Collaboration Int. V (2013) for the radial sampling, with a bin width r = ✓/✓ 500 = r/R 500 = 0.25. The correlation between successive radial bins for each profile is encoded in the correlation matrix.The comparison of fluxes and profiles is shown onFig. 4.4,. We can observe that all three flux estimations are consistent with each other and with the PACT MMF one. The average ratio to the PACT MMF fluxes over the sample is

Figure 4

 4 Figure 4.5, left, presents the individual y-profiles for the whole PACT31 sample, along with their corresponding stacked average and median profiles. The two stacked profiles do not present any significant differences, since, we chose to use their average for further analyses. The right panel shows the individual and associated stacked profiles for both equatorial and southern strip subsamples,

  FIGURE 4.5: y profiles for the PACT31 sample. (left) Stacked average (red) and median(blue) profiles. (right) Average stacked profiles for the clusters in the Equatorial (green) and Southern (yellow) strips. The reported errors are correlated and correspond to the square root of the diagonal value of the covariance matrix for the y profile. Individual profiles are shown as solid lines.

FIGURE 4 . 6 :

 46 FIGURE 4.6: Stacked scaled y map over the PACT31 sample (side size corresponds to 8 ⇥ R 500 ). Individual maps were rescaled by i (see Sec. 4.2.2) before averaging, and then multiplied by h i i.

FIGURE 4 . 7 :

 47 FIGURE 4.7: Stacked average pressure profiles over the PACT31 sample. The red solid line, labelled P7, shows the best gNFW pressure profile fitted over the data. The profiles by Arnaud et al. (2010a); Planck Collaboration Int. V (2013); Sayers et al. (2013, 2016) are over-plotted as green, purple, yellow and blue lines and labelled as A10, P13, S13 and S16, respectively. The red shaded area pictures the dispersion of the stacked profiles in each radial bin for the PACT31 (red) and the PLCK62 (purple) samples (as published by Planck Collaboration Int. V, 2013), respectively. The reported errors on the data points are correlated and correspond to the square root of the diagonal valued of the covariance matrix for the pressure profile.

  Cette s élection est n écessaire, car notre m éthode est d épendante de cette troisi ème coordonn ée, comme nous l'avons d écrit dans le Chapitre 2 de cette th èse. La m éthodologie impl ément ée propose l'identification des structures à l'int érieur des superamas en utilisant la position des galaxies. Pour la d étection et la caract érisation des amas et des groupe, nous avons d évelopp é l'algorithme Galaxy System Finding (GSyF). Comme d écrit dans les Chapitre 2 et 3, l'un des objectifs de cet algorithme est la correction de l'effet fingers of God. Cependant, pour avoir cette correction, les amas et les groupes doivent être identifi és avec pr écision. A partir de cette d étection, nous avons obtenu un nouveau catalogue de syst èmes. Apr ès l'application de l'algorithme GSyF nous avons d étect é au total 2 705 groupes et amas de galaxies dont 159 n'ont pas ét é réf érenc és dans la litt érature. Ensuite, nous avons fait une comparaison avec d'autres catalogues à partir desquels nous pouvons conclure que notre catalogue GSyF est en accord avec les catalogues d'amas (Abell, C4 and BCG) et des groupes (MSPM and T11) existant dans la litt érature.

D

  'autre part, nous avons analys é la composante gazeuse des amas de galaxies en utilisant des observations de l'effet Sunyaev Zeldovich. Cet étude a ét é faite par l'extraction des profils de pression de gaz et de densit é pour un échantillon de 31 amas à partir d'une carte de Comptonization de haute r ésolution (PACT). Les r ésultats que nous avons obtenus de cet extraction nous ont permis d'analyser les profils des amas de la partie centrale 0.03 R 500 jusqu' à 2 R 500 . En plus, nous avons montr é que le profil moyen de pression est en accord avec ceux obtenus par Planck Collaboration Int. V (2013). Les diff érences observ ées peuvent être li ées à la diff érence entre la taille angulaire et la masse moyenne de notre échantillon (PACT) par rapport à l' échantillon d'amas utilis é par (Planck Collaboration Int. V, 2013, PIP-V). D'autre part, nos r ésultats ont montr é que l'utilisation de la carte de haute r ésolution PACT permettait de faire la caract érisation des amas qui ont un taille angulaire jusqu' à 4 arcmin. Vue que l'effet SZ ne garde pas la relation avec redshift mais la taille angulaire elle oui, l'utilisation des cartes de haute r ésolution SZ peuvent donner la possibilit é de caract ériser les amas à haute redshifts.

  galaxie se trouve. Vue que notre nouveau catalogue de structure filamentaires a pour objectif d'identifier des zones à haute densit é de mati ère dans l'Univers, il peut être utilis é comme r éf érence pour effectuer des observations futures au rayons X et micro ondes. Ce type d' étude donne la possibilit é d' étudier en profondeur la composant gazeuse des structures filamentaires et mieux comprendre leur dynamique.Une autre possibilit é d' étude est d'identifier les filaments les plus denses au centre du noyau des superamas. Dans cette r égion les galaxies sont li ées par des pont de haute densit é gazeuse. Cela peut entraîner des effets d'interaction avec les galaxies qui y sont localis ées. Dans le m ême contexte, l' étude de l'interaction entre les groupes et amas avec les filaments qui les lient peut donner des informations sur divers effets comme l'enrichissement du gaz dans ce milieu. Finalement, une comparaison entre les superamas que nous avons étudi é et les r ésultats de lentilles gravitationnelles peut nous informer sur la distribution de mati ère dans le milieu.

TABLE 1

 1

	.1: Cosmological parameters.
	h	0.6772,
	100 ⌦ ⇤ 100 ⌦ m 100 ⌦ c h 2 11.88 ± 0.10, 69.11 ± 0.62, 30.89 ± 0.62, 100 ⌦ b h 2 2.23 ± 0.014, 100 ⌦ r 5 ⇥ 10 3 , 100 ⌦ k 0.00 ± 0.50.

TABLE 3 .

 3 1: Sample of MSCC superclusters.

	SCl ID Name	RA, Dec	z N Cl N fil Abell/ACO
	(MSCC)		[deg, deg]		clusters
	(1)	(2)	(3)	(4)	(5) (6)	(7)
	55		17.75, 15.44 0.0614	5 1 A0150 A0152A A0154B A0158B A0160B
	72		25.17, 0.64 0.0802	5 1 A0181A A0208A A0237A A0267B A0279A
	75		28.09, -5.15 0.0937	7 1 A0256A A0256B A0266 A0269 A0274A A0274B A0277
	76		28.35, -2.61 0.1299 16 3 A0211 A0233e A0255 A0256C A0261B A0265 A0267C A0268B A0271 A0274C A0279B
					A0281 A0285 A0295D A0303C A0308e
	175		125.29, 17.07 0.0942	6 1 A0635A A0650B A0651A A0657A A0658A A0659
	184		130.10, 30.24 0.1056	6 1 A0671B A0690C A0694 A0695B A0699B A0705A
	211		147.87, 64.88 0.1191	8 1 A0764 A0802 A0804B A0845 A0871e A0906e A0975 A1014A
	219		153.99, 19.14 0.1155	5 1 A0938B A0942A A0952A A0991B A0994A
	222		155.14, 49.21 0.1382 10 2 A0915B A0927A A0950A A0965A A0990 A1002A A1003C A1003D A1004 A1040C
	223		155.24, 62.94 0.1399	5 1 A0917 A0947A A0962A A1025A A1025B
	229		156.14, 33.03 0.1423	7 2 A0924 A0951 A0982 A1007B A1036 A1045 A1053B
	236		156.76, 10.38 0.0328	6 1 A0938A A0957A A0999A A1016A A1020A A1142A
	238		156.98, 39.55 0.1068 21 2 A0967A A0971A A0971B A0972A A0995A A0997A A0997B A0997C A1010B A1021B
					A1021C A1021D A1026B A1028A A1031A A1031B A1033 A1040A A1050A A1054A A1055
	248		159.49, 44.26 0.1246	5 1 A1040B A1050B A1054B A1056 A1074A
	264		165.29, 12.20 0.1161	8 1 A1105C A1116A A1129A A1141A A1147A A1157 A1201B A1209A
	266		165.91, 11.85 0.1273	8 1 A1131 A1137B A1141B A1147B A1152 A1159 A1183A A1209B
	272		167.83, 41.33 0.0760	6 1 A1173 A1174A A1187 A1190 A1193A A1203
	277		169.41, 49.67 0.1103	7 1 A1154 A1202B A1218B A1222 A1225 A1227A A1231A
	278 Leo 169.37, 28.46 0.0333	6 1 A1177B A1179B A1185A A1228A A1257A A1267A
	283		170.79, 20.34 0.1379 12 3 A1177C A1188 A1230B A1232B A1242A A1243B A1247e A1251 A1268 A1272 A1274 A1278
	295 Com 173.63, 23.11 0.0223	5 1 A1100A A1177A A1179A A1367 A1656
	310 UMa 175.91, 55.23 0.0639 21 1 A1212 A1270 A1291A A1291B A1291C A1318A A1318B A1324A A1324B A1349A A1349B
					A1377 A1383 A1396A A1396B A1400A A1400B A1400C A1436 A1452 A1457A
	311		176.12, 9.93 0.0833	8 1 A1337A A1342A A1358A A1362B A1372A A1379 A1385A A1390
	314		177.07, -2.01 0.0788	6 1 A1364A A1376A A1386A A1389A A1399A A1404A
	317		177.42, -1.59 0.1278 13 1 A1373A A1373B A1376C A1386D A1386E A1386F A1389C A1389D A1392 A1399C A1407
					A1411 A1419B
	323		179.66, 27.26 0.1396 12 1 A1384A A1403A A1403B A1413B A1420C A1425B A1431B A1433C A1444C A1449B
					A1455C A1495
	333		181.43, 29.34 0.0813	9 1 A1423A A1427 A1431A A1433A A1444B A1449A A1455B A1515A A1549A
	335		182.42, 29.50 0.0732	6 1 A1444A A1455A A1478A A1480B A1486A A1519A
	343		183.88, 14.31 0.0809	5 1 A1474 A1481A A1499A A1526C A1527A
	360 Dra 190.94, 64.41 0.1055 11 1 A1518A A1539A A1544A A1559 A1566 A1579A A1621 A1640A A1646 A1674A A1718A
	386		199.50, 38.33 0.0715	5 1 A1680A A1691 A1715A A1723B A1749B
	407		208.55, 26.70 0.1364	6 2 A1797B A1817C A1817e A1818C A1819 A1824
	414 Boo 211.31, 27.32 0.0709 24 1 A1775A A1775B A1781B A1795 A1797A A1800 A1817A A1818A A1831A A1831B
					A1832A A1863A A1869A A1869B A1873B A1873C A1874A A1886A A1898A
					A1903A A1908A A1909A A1912B A1921A
	419		212.33, 7.17 0.1122	5 1 A1850 A1862 A1866A A1870 A1881
	422		213.21, 28.95 0.1430	9 1 A1832B A1840B A1854 A1867A A1874B A1891B A1903C A1908B A1912E
	430		216.72, 25.64 0.0982	6 1 A1909B A1910A A1912A A1912C A1926A A1927
	440 BooA 223.17, 22.28 0.1170	9 1 A1939B A1972 A1976 A1980 A1986 A1988B A2001A A2006 A2021C
	441		223.22, 28.40 0.1249	5 1 A1973A A1982D A1984 A1990A A2005B
	454		228.28, 7.33 0.0456	6 1 A2020A A2028A A2033B A2040B A2055A A2063B
	457		228.59, 6.98 0.0789	6 1 A2028B A2029 A2033C A2040C A2055B A2063C
	460		229.70, 31.17 0.1142	9 1 A2025D A2034A A2049A A2056C A2059B A2062 A2067B A2069 A2083B
	463 CrB 232.18, 30.42 0.0736 14 1 A2056A A2056B A2059A A2061A A2065 A2067A A2073A A2079A A2079B
					A2089 A2092A A2106A A2122A A2124
	474 Her 241.56, 16.22 0.0363	5 1 A2147 A2151 A2152A A2153A A2159A
	484		245.57, 42.39 0.1364	7 1 A2158B A2172 A2179 A2183 A2196 A2198D A2211A
	579		351.82, 14.79 0.0427	5 1 A2572 A2589 A2593A A2593B A2657
	586		354.20, 23.67 0.1274	5 1 A2611e A2619B A2627 A2647e A2650e

TABLE 3 .

 3 2: Properties of the galaxies in the sampled superclusters.

	SCl ID box volume

  Distribution of mean volume densities, for the 46 superclusters in our sample, with redshift, blue points. The red line corresponds to the best fit of a power law function. Residuals of the fitting are showed in the bottom panel.MSCC579 and MSCC55 were excluded from the fitting.

		0.03
		295
			a*10 b*z
	density	0.02
		0.01	310
			175
		579	55
		0
	.2) is described in detail. This supercluster contains 21 Abell clusters, with redshifts in the range from 0.05 to 0.08 and its volume is the fourth largest in the sample: it occupies an area in the sky of about 1 700 deg 2 , equivalent to a volume of (116 h 1 70 Mpc) 3 (including the 20 h 1 70 Mpc added to the box limits from the farthest clusters). The volume is filled by N = 12 286 SDSS galaxies with spectroscopic redshift. 0.04 0.06 0.08 0.1 0.12 0.14 0.04 0.06 0.08 0.1 0.12 0.14 redshift (z) -10 -5 0 5 residuals 10 -3 This corresponds to a mean surface density of 24 gal.deg 2 or 0.008 gal.h 3 0.02 FIGURE 3.1:

see Table

3

.2.

TABLE 3 .

 3 3: Main properties for the 25 richest systems identified in the volume of the supercluster MSCC-310.

	System N mem		C BGM		C F oG centroid	v	R h	R vir	cross-ref
	No.	#	RA Dec	z	RA Dec	z LOS [km s 1 ] [h 1 70 Mpc] [h 1 70 Mpc] ACO Nr.
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
	1		173.10 55.97 0.0515 173.01 56.09 0.0535 1182.20	1.09	2.54	A1291A
	2		174.01 55.08 0.0571 174.18 55.20 0.0587 1103.00	1.28	2.56	A1318A
	3		180.27 56.37 0.0648 180.07 56.20 0.0649 761.62	1.04	1.87	A1436
	4		167.10 44.15 0.0587 167.11 44.07 0.0590 643.51	0.81	1.53	A1169
	5		176.84 55.73 0.0515 176.81 55.69 0.0518 712.05	0.80	1.64	A1377
	6		177.19 54.52 0.0601 177.06 54.64 0.0604 845.19	0.95	1.94	A1383
	7		168.85 54.44 0.0695 168.91 54.51 0.0700 659.12	0.91	1.63
	8		175.28 55.19 0.0593 175.26 55.30 0.0609 1103.10	1.30	2.58	A1349A
	9		163.40 54.87 0.0716 163.54 54.84 0.0722 639.99	0.89	1.58
	10		172.33 54.13 0.0689 172.45 54.08 0.0690 582.26	0.75	1.40	A1270
	11		158.25 56.75 0.0448 158.33 56.82 0.0454 459.21	0.69	1.16
	12		180.23 51.42 0.0666 180.47 51.65 0.0649 1069.30	1.08	2.37	A1452
	13		152.32 54.21 0.0465 152.41 54.42 0.0460 414.65	0.68	1.08
	14		183.70 59.91 0.0600 183.60 59.90 0.0599 443.38	0.75	1.17	A1507B
	15		168.07 57.08 0.0471 168.13 57.05 0.0467 490.66	0.77	1.26
	16		178.38 52.69 0.0716 178.60 52.77 0.0695 760.89	0.84	1.74
	17		151.22 54.57 0.0470 151.00 54.66 0.0472 459.58	0.64	1.13
	18		163.28 56.33 0.0772 163.36 56.34 0.0745 1003.20	0.89	2.13
	19		172.43 55.38 0.0685 172.45 55.42 0.0684 534.44	0.54	1.19
	20		162.95 55.39 0.0739 162.90 55.35 0.0737 367.35	0.68	1.00	A1112A
	21		182.19 53.33 0.0813 182.19 53.32 0.0821 572.89	0.66	1.33
	22		181.31 43.17 0.0529 181.41 43.20 0.0526 503.74	0.67	1.23
	23		177.05 52.85 0.0503 177.05 52.60 0.0505 555.54	0.67	1.31
	24		178.57 55.47 0.0508 178.68 55.20 0.0512 583.72	0.82	1.45
	25		151.31 53.15 0.0463 151.32 52.99 0.0451 430.60	0.68	1.11

Notes. The complete version of this table and the tables of systems of the other superclusters can be found electronically at: www.astro.ugto.mx/catalog

TABLE 3 .

 3 4: Main properties of the filaments extracted with GFiF for the supercluster MSCC-310.

	Fil.	N sys N gf il		redshift		mean density	R fil	N nod		L fil
	Nr.	systems gals. [mean, min,	max]	[h 3 70 Mpc 3 ] [h 1 70 Mpc] filament skeleton [h 1 70 Mpc]
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
	MSCC-310-F1	10 714 0.0609 0.0518 0.0689	0.4180	2.81	18	11	61.6
	MSCC-310-F2	8 696 0.0502 0.0443 0.0588	0.5210	2.84	22	11	51.8
	MSCC-310-F3	7 506 0.0481 0.0427 0.0528	0.3486	2.50	19	10	49.0
	MSCC-310-F4	8 490 0.0656 0.0585 0.0710	0.4263	2.46	14	10	59.0
	MSCC-310-F5	7 461 0.0700 0.0642 0.0774	0.5303	2.60	13	7	47.6
	MSCC-310-F6	6 409 0.0725 0.0651 0.0791	0.2986	1.97	12	9	39.3
	MSCC-310-F7	4 385 0.0551 0.0479 0.0619	0.4062	2.76	7	5	20.7
	MSCC-310-F8	4 254 0.0546 0.0485 0.0617	0.2118	2.22	9	7	33.7
	MSCC-310-F9	4 155 0.0464 0.0437 0.0528	0.1464	1.13	9	6	17.9

TABLE 3 .

 3 5: Glossary of parameters used by GSyS and GFiF algorithms

	Param.	Description

v , v LOS , R vir , M vir Properties of FoG

TABLE 3 .

 3 6: GSyF systems listed in other catalogs for the MSCC-310 supercluster.

			Aperture=1 h 1 70 Mpc
	Other catalog Number Fraction Number Fraction	separation
		N gal > 5		N gal > 10		h 1 70 Mpc	v
	C4	26/34	76%	24/34	71%	0.43	100
	Abell	19/37	41%	17/37	46%	0.45	295
	BCG	8/11	73%	8/11	73%	0.5	340
	MSPM	142/213	67%	63/79	80%	0.34	145
	T11	192/315	61%	73/105	70%	0.33	230
			Aperture=2 h 1 70 Mpc
		N gal > 5		N gal > 10
	C4	33/34	97%	32/34	94%	0.77	166
	Abell	29/37	78%	24/37	65%	0.82	300
	BCG	11/11	100%	11/11	100%	0.80	430
	MSPM	167/213	78%	68/79	86%	0.55	193
	T11	249/315	79%	85/105	81%	0.64	320

TABLE 3 .

 3 7: Summary of filaments detected by GFiF for the superclusters in table 1. MSCC f N HC D max N edges N links N trees N ske N brid N tend N min

	N sys	N fil	V fil V	N fil N gal

TABLE 4 .

 4 1: Properties of the PACT31 sample. It is composed of clusters which are present in the ACT(Hasselfield et al., 2013b) catalog and the Planck Catalog(Planck Collaboration et al., 2016a). The signal to noise in both detections is noted. The mass, redshift and radius values were taken from the Planck catalog.

	Name		name		Ra	Dec	z	✓ 500	M 500	R 500	SNR
		ACT-CL	PSZ1	PSZ2 [Deg] [Deg]		arcmin M 14 M	[kpc] ACT PSZ1 PSZ2
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10) (11)	(12)	(13)

TABLE 4

 4

		.2: Definition of setups for the validation procedure
	Name Sample	y-map	FWHM	r/R 500
	PIPV PLCK62 PC-internal 10 arcmin	0.25
	D10	PLCK62 DR2015	10 arcmin	0.25
	D7	PLCK62 DR2015	7 arcmin	0.25
	D7 120 PLCK62 DR2015	7 arcmin	0.08
	P7 120 PACT31 DR2015	1.4 arcmin	0.08
	P7	PACT31 PACT	1.4 arcmin	0.08
	assuming a universal pressure profile (Arnaud et al., 2010b), P (r). The Y 500 opti-
	mal solution minimizing the chi-square and folding in the profile covariance matrix
	C reads as:

TABLE 4 .

 4 3: Best fit parameter for the gNFW pressure profile.

		P 0	c 500	↵	¯ 2 stat	N dof
	A10 6.32 1.02 0.31 1.05 5.49 3.8	15
	P13 6.41 1.81 0.31 1.33 4.13 0.9	13
	S13 6.41 1.81 0.31 1.33 4.13 0.9	13
	S16 6.41 1.81 0.31 1.33 4.13 0.9	13
	P7	6.41 1.81 0.31 1.33 4.13 0.9	13
	Note: A10, P13, S13 and S16 are the parameterizations provided by Arnaud et al. (2010b),
	Planck Collaboration et al. (2013a),

TABLE B .

 B 1: Main properties of the filaments extracted through GFiF.

	Fil.	Nsys N gf il		redshift		mean density	R fil	N nod		L fil
	Nr.	systems gals. [mean, min,	max] [h 3 70 Mpc 3 ] [h 1 70 Mpc] filament skeleton [h 1 70 Mpc]
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
	MSCC-55-F1	4	297 0.0619 0.0529 0.0706	0.1570	4.31	3		10.5
	MSCC-55-F2	3	211 0.0585 0.0527 0.0680	0.1911	0.60	2		9.7
	MSCC-72-F1	5	370 0.0790 0.0722 0.0868	0.5636	3.57	6		28.4
	MSCC-72-F2	4	354 0.0801 0.0718 0.0866	0.3688	3.46	5		24.6
	MSCC-72-F3	5	299 0.0777 0.0717 0.0839	0.3043	3.89	6		19.5
	MSCC-72-F4	3	238 0.0850 0.0787 0.0917	0.2012	3.49	4		26.5
	MSCC-175-F1	6	429 0.0912 0.0841 0.0996	0.1541	3.08	8		41.8
	MSCC-175-F2	3	298 0.0978 0.0885 0.1032	0.2260	3.19	3		35.0
	MSCC-175-F3	3	221 0.0937 0.0883 0.1001	0.1714	1.79	5		47.4
	MSCC-175-F4	3	195 0.0923 0.0867 0.0995	0.2184	2.86	3		37.5
	MSCC-184-F1	5	768 0.1071 0.0994 0.1171	0.0488	2.88	8		49.3
	MSCC-184-F2	3	332 0.0980 0.0911 0.1029	0.0838	3.09	3		39.5
	MSCC-211-F1	3	555 0.1205 0.1100 0.1297	0.0465	4.46	13		27.9
	MSCC-219-F1	10	608 0.1125 0.1063 0.1207	0.1169	2.96	17		81.8
	MSCC-219-F2	3	170 0.1235 0.1183 0.1287	0.0347	0.79	3		40.2
	MSCC-222-F1	3	408 0.1422 0.1311 0.1522	0.0418	1.87	14		70.0
	MSCC-222-F2	5	377 0.1349 0.1238 0.1460	0.0461	0.70	11		78.8
	MSCC-223-F1	3	342 0.1367 0.1286 0.1472	0.0245	0.86	12		48.7
	MSCC-229-F1	3	204 0.1445 0.1361 0.1514	0.0389	1.96	9		63.1
	MSCC-236-F1	5	545 0.0324 0.0228 0.0415	0.3382	1.49	16		39.3
	MSCC-236-F2	4	492 0.0411 0.0361 0.0461	0.2409	2.65	7		38.5
	MSCC-236-F3	5	452 0.0331 0.0274 0.0399	0.4889	2.62	8		20.0
	MSCC-236-F4	3	358 0.0296 0.0255 0.0364	0.3971	2.24	5		19.6
	MSCC-236-F5	3	337 0.0354 0.0286 0.0422	0.4448	2.47	5		20.8
	MSCC-236-F6	3	247 0.0330 0.0276 0.0373	2.3032	2.66	2		16.8
	MSCC-236-F7	3	177 0.0333 0.0297 0.0391	0.4359	1.53 1	4		16.4
	MSCC-238-F1	5	673 0.1190 0.1075 0.1309	0.0558	2.95	11		85.3
	MSCC-238-F2	6	645 0.0915 0.0802 0.1010	0.0928	2.98	14		76.1
	MSCC-238-F3	3	553 0.1054 0.0979 0.1115	0.0782	2.64	11		99.0
	MSCC-238-F4	3	176 0.0957 0.0896 0.1024	0.1467	0.71	3		28.6
	MSCC-238-F5	3	162 0.1016 0.0934 0.1099	0.0285	0.67	3		32.5
	MSCC-238-F6	3	128 0.1096 0.1040 0.1156	0.0398	0.88	4		30.4
	MSCC-248-F1	3	476 0.1256 0.1161 0.1355	0.0895	3.35	10		82.1
	MSCC-266-F1	5	452 0.1282 0.1188 0.1344	0.0366	2.94	9		75.8
	MSCC-272-F1	6	432 0.0752 0.0694 0.0808	0.8405	2.93	6		17.5
	MSCC-272-F2	3	200 0.0757 0.0714 0.0814	0.1245	2.66	4		10.3
	MSCC-277-F1	10	798 0.1124 0.1031 0.1208	0.1268	2.99	21		89.3
	MSCC-277-F2	5	650 0.1053 0.0956 0.1135	0.0805	2.93	16		69.0
	MSCC-278-F1	7 1262 0.0328 0.0251 0.0398	0.9871	2.41	36		56.3
	MSCC-278-F2	3	443 0.0322 0.0273 0.0361	0.4963	1.70	24		20.8
	MSCC-278-F3	4	352 0.0319 0.0266 0.0386	0.3810	1.18	14		24.4
	MSCC-278-F4	8	301 0.0254 0.0221 0.0298	1.0335	1.86	27		36.9
	MSCC-278-F5	3	185 0.0348 0.0297 0.0387	0.4401	1.76	7		11.1
	MSCC-283-F1	4	532 0.1339 0.1245 0.1470	0.0701	3.96	7		47.7
	MSCC-283-F2	5	347 0.1364 0.1284 0.1465	0.0655	3.26	6		49.1
	MSCC-283-F3	3	304 0.1357 0.1296 0.1496	0.0397	0.96	2		24.2
	MSCC-295-F1	7 1233 0.0230 0.0160 0.0284	2.1243	1.89	37		44.6
	MSCC-295-F2	7 1060 0.0228 0.0158 0.0299	2.2694	2.37	34		18.2
									Continued on next page

Table B .1 -continued from previous page

 B

	Fil.	Nsys N gf il		redshift		mean density	R fil	N nod		L fil
	Nr.	systems gals. [mean, min,	max] [h 3 70 Mpc 3 ] [h 1 70 Mpc] filament skeleton [h 1 70 Mpc]
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
	MSCC-295-F3	4	626 0.0232 0.0189 0.0283	0.5824	1.36	44		26.5
	MSCC-295-F4	4	209 0.0218 0.0188 0.0255	0.6254	1.83 1	10		30.8
	MSCC-310-F1	10	714 0.0609 0.0518 0.0689	0.4180	2.81	18		61.6
	MSCC-310-F2	8	696 0.0502 0.0443 0.0588	0.5210	2.84	22		51.8
	MSCC-310-F3	7	506 0.0481 0.0427 0.0528	0.3486	2.50	19		49.0
	MSCC-310-F4	8	490 0.0656 0.0585 0.0710	0.4263	2.46	14		59.0
	MSCC-310-F5	7	461 0.0700 0.0642 0.0774	0.5303	2.60	13		47.6
	MSCC-310-F6	6	409 0.0725 0.0651 0.0791	0.2986	1.97	12		39.3
	MSCC-310-F7	4	385 0.0551 0.0479 0.0619	0.4062	2.76	7		20.7
	MSCC-310-F8	4	254 0.0546 0.0485 0.0617	0.2118	2.22	9		33.7
	MSCC-310-F9	4	155 0.0464 0.0437 0.0528	0.1464	1.13	9		17.9
	MSCC-311-F1	13 1140 0.0813 0.0753 0.0892	0.2812	3.54	14		74.5
	MSCC-311-F2	5	372 0.0847 0.0769 0.0937	0.3235	3.69	4		23.5
	MSCC-311-F3	3	322 0.0888 0.0821 0.0937	0.1900	4.32	2		15.3
	MSCC-311-F4	3	302 0.0826 0.0746 0.0901	0.2447	3.58	2		19.5
	MSCC-314-F1	4	100 0.0819 0.0769 0.0893	0.1201	1.88	4		29.6
	MSCC-314-F2	3	83 0.0777 0.0715 0.0844	0.1610	2.78	2		12.3
	MSCC-317-F1	4	187 0.1331 0.1224 0.1417	0.0282	1.73 1	15		71.7
	MSCC-317-F2	4	176 0.1187 0.1102 0.1264	0.0528	0.69	10		75.5
	MSCC-323-F1	7	802 0.1380 0.1262 0.1540	0.0436	3.73	14		129.3
	MSCC-323-F2	3	441 0.1383 0.1309 0.1535	0.0261	1.66	5		29.4
	MSCC-333-F1	3	219 0.0760 0.0723 0.0833	0.1205	2.36	5		29.8
	MSCC-333-F2	4	173 0.0803 0.0752 0.0880	0.1519	2.83	5		24.5
	MSCC-333-F3	4	126 0.0794 0.0729 0.0835	0.2052	2.46	5		34.6
	MSCC-335-F1	10	745 0.0779 0.0705 0.0843	0.1260	2.60	21		105.0
	MSCC-335-F2	4	219 0.0665 0.0613 0.0731	0.0650	0.75	9		83.8
	MSCC-335-F3	4	195 0.0762 0.0712 0.0814	0.1113	2.45	6		45.9
	MSCC-343-F1	4	291 0.0822 0.0786 0.0874	0.1394	2.51	7		28.7
	MSCC-343-F2	3	202 0.0798 0.0733 0.0876	0.2638	2.50	3		19.3
	MSCC-343-F3	3	194 0.0824 0.0738 0.0876	0.1991	2.65	6		15.6
	MSCC-360-F1	4	633 0.1050 0.0967 0.1159	0.1367	2.95	9		60.8
	MSCC-360-F2	3	348 0.1074 0.1004 0.1152	0.0870	1.52	6		49.3
	MSCC-360-F3	3	203 0.1033 0.0973 0.1093	0.0416	1.46	3		29.9
	MSCC-386-F1	7	422 0.0734 0.0657 0.0805	0.4163	2.91	18		34.0
	MSCC-386-F2	4	157 0.0708 0.0636 0.0765	0.1969	1.92	10		39.6
	MSCC-386-F3	5	115 0.0627 0.0591 0.0705	0.1760	1.56	13		43.2
	MSCC-386-F4	4	44 0.0617 0.0594 0.0664	0.1703	0.92 1	7		21.3
	MSCC-407-F1	5	327 0.1388 0.1254 0.1468	0.0177	3.61	10		59.2
	MSCC-414-F1	4	556 0.0626 0.0537 0.0691	0.6269	2.51	19		38.1
	MSCC-414-F2	6	294 0.0628 0.0548 0.0667	0.3793	2.54	12		34.0
	MSCC-414-F3	6	262 0.0750 0.0688 0.0809	0.5198	2.53	12		27.1
	MSCC-414-F4	5	227 0.0641 0.0585 0.0675	0.3705	2.52	10		13.5
	MSCC-414-F5	4	216 0.0748 0.0684 0.0810	0.4251	2.53	10		22.1
	MSCC-414-F6	3	173 0.0657 0.0613 0.0701	0.3368	2.01	7		22.9
	MSCC-414-F7	3	159 0.0616 0.0576 0.0647	0.2329	1.97	10		14.1
	MSCC-414-F8	3	157 0.0657 0.0603 0.0722	0.1197	1.82	7		29.9
	MSCC-414-F9	4	143 0.0663 0.0594 0.0726	0.3001	2.50	5		22.9
	MSCC-414-F10	4	133 0.0546 0.0518 0.0590	0.4163	1.99	6		29.9
	MSCC-414-F11	5	127 0.0616 0.0589 0.0657	0.1262	1.64	14		35.1
	MSCC-414-F12	3	101 0.0762 0.0696 0.0801	0.1126	0.66	4		9.8
									Continued on next page

Table B .1 -continued from previous page

 B

	Fil.	Nsys N gf il		redshift		mean density	R fil	N nod		L fil
	Nr.	systems gals. [mean, min,	max] [h 3 70 Mpc 3 ] [h 1 70 Mpc] filament skeleton [h 1 70 Mpc]
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
	MSCC-414-F13	4	89 0.0640 0.0614 0.0674	0.1692	1.94	4		19.2
	MSCC-414-F14	4	82 0.0727 0.0686 0.0758	0.4275	1.78	7		23.6
	MSCC-414-F15	3	50 0.0607 0.0563 0.0640	0.1070	1.80	3		9.0
	MSCC-419-F1	3	226 0.1139 0.1084 0.1210	0.1849	4.03	2		12.8
	MSCC-419-F2	3	137 0.1099 0.1044 0.1182	0.1816	3.20	2		18.1
	MSCC-419-F3	4	86 0.1127 0.1080 0.1191	0.0693	1.79	5		25.2
	MSCC-422-F1	3	398 0.1424 0.1321 0.1528	0.0291	0.95	8		45.0
	MSCC-430-F1	4	361 0.0975 0.0880 0.1066	0.1391	2.78	7		39.2
	MSCC-430-F2	4	215 0.0937 0.0867 0.0999	0.1684	1.50	5		41.1
	MSCC-430-F3	3	126 0.0942 0.0891 0.1015	0.0691	1.89	2		21.2
	MSCC-430-F4	3	13 0.1024 0.0973 0.1041	0.0225	0.00 2	2		18.3
	MSCC-440-F1	6	697 0.1173 0.1074 0.1284	0.1550	2.93	8		50.2
	MSCC-454-F1	13	689 0.0389 0.0334 0.0466	2.7338	2.39	23		63.5
	MSCC-454-F2	6	587 0.0446 0.0377 0.0500	2.3032	2.57	20		29.1
	MSCC-454-F3	3	148 0.0520 0.0464 0.0557	4.0214	2.48	3		9.3
	MSCC-454-F4	3	140 0.0490 0.0425 0.0551	1.5093	2.42	3		12.8
	MSCC-454-F5	3	41 0.0438 0.0424 0.0460	1.1194	0.83 1	3		8.6
	MSCC-457-F1	19 1287 0.0786 0.0709 0.0877	0.4021	3.37	23		78.4
	MSCC-457-F2	8	508 0.0758 0.0673 0.0830	0.1594	2.69	12		52.5
	MSCC-457-F3	6	209 0.0846 0.0768 0.0896	0.2454	2.48	7		30.6
	MSCC-457-F4	3	197 0.0829 0.0757 0.0881	0.1691	2.80	3		22.2
	MSCC-457-F5	3	101 0.0756 0.0676 0.0785	0.0982	1.97 1	3		16.8
	MSCC-457-F6	3	39 0.0816 0.0779 0.0872	0.0649	0.74	3		23.3
	MSCC-460-F1	12	885 0.1142 0.1067 0.1242	0.1862	3.61	17		69.3
	MSCC-460-F2	6	485 0.1139 0.1043 0.1237	0.1195	3.62	9		57.9
	MSCC-460-F3	6	310 0.1080 0.1003 0.1159	0.0695	2.55	6		59.7
	MSCC-460-F4	5	253 0.1218 0.1155 0.1304	0.0522	2.51	7		27.6
	MSCC-463-F1	9	575 0.0722 0.0652 0.0788	0.3732	2.77	16		57.4
	MSCC-463-F2	6	530 0.0765 0.0699 0.0839	0.3129	2.67	15		39.0
	MSCC-463-F3	11	388 0.0768 0.0696 0.0842	0.2787	2.27	13		73.6
	MSCC-463-F4	3	361 0.0657 0.0585 0.0743	0.4589	2.77	5		20.8
	MSCC-463-F5	5	358 0.0655 0.0600 0.0730	0.4039	2.08	10		41.9
	MSCC-463-F6	7	328 0.0837 0.0775 0.0894	0.2868	2.56	7		36.9
	MSCC-463-F7	4	191 0.0688 0.0654 0.0739	0.0878	0.68 1	8		26.8
	MSCC-463-F8	4	159 0.0663 0.0628 0.0698	0.4765	2.59	6		12.5
	MSCC-463-F9	4	147 0.0706 0.0660 0.0764	0.2416	1.87	6		31.9
	MSCC-463-F10	3	133 0.0701 0.0651 0.0754	0.3595	2.05	4		12.7
	MSCC-463-F11	3	130 0.0802 0.0748 0.0861	0.1864	2.64	4		14.8
	MSCC-474-F1	3	765 0.0369 0.0300 0.0444	2.7548	2.63	13		10.5
	MSCC-474-F2	5	404 0.0340 0.0296 0.0387	1.3043	2.06	13		23.4
	MSCC-474-F3	3	277 0.0368 0.0318 0.0412	0.2423	1.98	9		16.5
	MSCC-474-F4	3	260 0.0321 0.0284 0.0388	0.7372	1.75	7		16.5
	MSCC-474-F5	3	229 0.0337 0.0292 0.0372	0.3332	1.51	10		17.2
	MSCC-474-F6	4	205 0.0365 0.0324 0.0423	0.5697	1.90	6		15.3
	MSCC-474-F7	3	23 0.0379 0.0328 0.0406	0.1777	0.00 1	10		28.3
	MSCC-484-F1	4	681 0.1361 0.1243 0.1501	0.0130	3.89	7		54.6

The description of GSyF algorithm as well as the strategy to optimize its parameters using simulated mock volumes is presented inSantiago-Bautista et al. (2019b)

The optimization for these parameters is described in detail inSantiago-Bautista et al. (2019b).

These systems are available in an electronic table.

Acknowledgements

Also, I would like to give thanks to Genevieve Soulcail, director of the SDU2E Doctoral school, for all her help, effort and support provided during my enrollment to the University Paul Sabatier in a joint program with the University of Guanajuato. My thanks to Mrs. Cathala and Mrs. Laura Salas for all the help given during all the administrative processes for both universities. I'm grateful to DAIP and CONACYT,

Conclusions and perspectives

The objective of this thesis was to study the different structures that conform the cosmic web. In this context, we used the galaxy positions to study filaments, clusters and groups, and the gas component to extract pressure profiles of galaxy clusters. Since clusters and superclusters are structures that have formed under the effects of gravity, they are of particular interest to study the evolution of their galaxies and gas components.

Concerning the analysis using the optical galaxies, we selected SDSS galaxies with spectroscopic redshifts. This selection was based on the need of an accurate measurement on the line of sight velocity for the galaxy position, because our methodology is sensitive to this coordinate, as described in Chapter 2. We implemented a methodology that identifies various structures embedded in superclusters by using the optical galaxy positions.

For the detection and characterization of clusters and groups, we developed the Galaxy System Finding algorithm (GSyF). As described in Chapters 2 and 3, one of the main objectives of this algorithm is the correction of the Finger of God effects. However, in order to achieve this correction, an accurate detection of clusters and groups was necessary. Then, we created a new catalog of systems as a sub-product of this work. From the application of GSyF methods, we were able to detect a total of 2 705 groups and galaxy clusters, of which 159 were not previously reported. We also performed a comparison with other cluster catalogs, which leads us to conclude that GSyF is in good agreement with both, cluster (Abell, C4 and BCG) and group catalogs (MSPM and T11) available in the literature.

For the identification of the galaxy bridges and filaments we developed a new methodology implementing machine learning techniques, the Galaxy Filament Finding Algorithm (GFiF). Regarding this subject, the main result of our work

Appendix A

Algorithms

Algorithm 1: Mock maps generator Input: Supercluster volume and number of galaxies. Output: Simulated distribution of galaxies in clusters, groups and field of the supercluster.

1. The simulated volume is filled with N synth synthetic systems of galaxies with N elem = 10 200. 4. Fill the systems with galaxies (elements) following a normal distribution N elem (µ i , R vir ) with µ i = {↵ i , i }.

5. Add FoG effects to galaxy systems by adding velocity dispersion N elem (z i , v ).

6. Add random galaxies to the box volume following the ratio: 60% galaxies are located in field, and 40% in systems.

Algorithm 2: Galaxy systems finding algorithm (GSyF)

Input: Supercluster's galaxy positions ↵, and z. Output: Galaxy systems, membership and member galaxy positions corrected for FoG effect.

(i) Compute local surface density of galaxies using VT.

(ii) Construct 1,000 randomizations of galaxy positions to calculate the baseline surface density, d bas .

(iii) Calculate the density contrast of galaxies, i , with respect to d bas .

(iv) Select galaxies with density contrast above the reference value (1 + g) d bas .

(v) Group galaxies by their position (↵, and 1, 000 ⇥ z), using the HC algorithm.

(vi) Filter resulting groups by number of members N i 3.

Virial refinement and FoG correction

(a) Select galaxies in a cylinder of radius R a = 1 h 1 70 Mpc projected in the sky, centered on the brightest galaxy close to the group's centroid, and within cz ± 3000 km s 1 along the line-of-sight, centered on the group mean z.

(b) Calculate virial radius using Eq. 2.9 using the bi-weighted velocity dispersion, harmonic radius and redshift. (f) Correct co-moving distance of the member galaxies for FoG effect by rescaling the cylinder length to the R vir size.

(g) Calculate galaxy corrected rectangular coordinates.

Appendix B

Filament properties 118

Author : Iris Santiago-Bautista Title: The environmental effects of the LSS: Characterization of the baryonic components

Abstract:

The baryonic component of the Large Scale Structure (LSS) of the Universe is composed by concentrations of gas and galaxies forming groups, clusters, elongated filaments and widely spread sheets which probably underline the distribution of dark matter. Nevertheless, according to the current cosmological models, most of the baryonic material in the Universe has not yet been directly observed. Numerical simulations suggest that from one-half to two-thirds of all baryons may be located out of clusters of galaxies, pervading the structures between them. The most concentrated structures, which we call systems of galaxies (i.e., groups and clusters) usually contain high density hot gas (1 -10 keV) that cools radiatively, emits at X-rays wavelengths and interacts with the cosmic microwave background at millimeter wavelengths (Sunyaev Zel'dovich effect, SZ). For the less dense structures, filaments and sheets, the baryons are probably in moderately hot gas phase (0.01 -1 keV), commonly named as warm hot intergalactic medium (WHIM).

In this PhD Thesis, we study the environmental effects associated to the different components of the LSS. For the galaxy systems, we aim to characterize the intra cluster medium (ICM) through the analysis of the S-Z effect. We employ the ACT and Planck data to analyze the gas pressure profiles of a sample of low mass galaxy clusters. For the least dense structures, we assembled a sample of filament candidates composed by chains of clusters that are located inside superclusters of galaxies. We aim to probe the filament structure skeletons and characterize their components (galaxies, groups/clusters and gas).

Key words: galaxies, galaxy groups, clusters, large scale structure of the Universe, cosmology, galaxies evolution, data analisis