#  Star formation quenching in the infall region around galaxy clusters

Juan Manuel Salerno1, Hernán Muriel1,2, Valeria Coenda1,2, Sofía A. Cora3,4,
Luis Pereyra1, Andrés N. Ruiz1,2, Cristian A. Vega-Martínez5,6

1Instituto de Astronomía Teórica y Experimental (CCT Córdoba, CONICET, UNC),
Laprida 854, X5000BGR, Córdoba, Argentina
2Observatorio Astronómico, Universidad Nacional de Córdoba, Laprida 854,
X5000BGR, Córdoba, Argentina
3Instituto de Astrofísica de La Plata (CCT La Plata, CONICET, UNLP),
Observatorio Astronómico, Paseo del Bosque S/N, B1900FWA,
La Plata, Argentina
4Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La
Plata, Observatorio Astronómico,
Paseo del Bosque S/N, B1900FWA, La Plata, Argentina,
5Instituto de Investigación Multidisciplinar en Ciencia y Tecnología,
Universidad de La Serena, Raúl Bitrán 1305, La Serena, Chile
6Departamento de Astronomía, Universidad de La Serena, Av. Juan Cisternas 1200
Norte, La Serena, Chile

(Accepted 2022 October 13. Received 2022 October 13; in original form 2022 May
13)

###### Abstract

We analyse the connection between the star formation quenching of galaxies and
their location in the outskirts of clusters in the redshift range $z=[0,2]$ by
estimating the fraction of red galaxies. More specifically, we focus on
galaxies that infall isotropically from those that are infalling alongside
filaments. We use a sample of galaxies obtained from the semi-analytic model
of galaxy formation sag applied to the MultiDark simulation. mdpl2. In
agreement with observational results, we find that the infall regions show
levels of star formation that are intermediate between those of galaxies in
clusters and in the field. Moreover, we show that, in the redshift range
[0-0.85], the quenching of the star formation is stronger in the filamentary
region than in the isotropic infall region. We also study the fraction of red
galaxies as a function of the normalised distance to the cluster centre and
find that, for radii $R/R_{\textup{200}}>3$, the fraction of red galaxies in
the filamentary region is considerably larger than in the isotropic infall
region. From the analysis of properties of the main progenitors of galaxies
identified at $z=0$, we find that they have different evolutionary behaviours
depending on the stellar mass and environment. Our results confirm the
observational findings that suggest that the infall regions of clusters play
an important role in the pre-processing of galaxies along most of the
evolutionary history of galaxies.

###### keywords:

galaxies: evolution – galaxies: clusters: general – galaxies: star formation –
galaxies: statistics.

††pubyear: 2022††pagerange: Star formation quenching in the infall region
around galaxy clusters–Star formation quenching in the infall region around
galaxy clusters

##  1 Introduction

The distribution of galaxies on scales of tens of Mpc presents large
anisotropies. The pattern of these anisotropies is known as the cosmic web,
and presents structures such as clusters, walls, filaments, and voids (Bond et
al., 1996; Aragón-Calvo et al., 2010; Cautun et al., 2013). Galaxy clusters
are the most massive systems in the Universe, with stellar masses of $\sim
10^{14-15}\,h^{-1}{\rm M_{\odot}}$ and velocity dispersions of $\sim
700-800\,\rm{km~{}s^{-1}}$. These systems, which are connected between them by
filaments, can be in virial equilibrium and are characterised by a deep
gravitational potential well and an intracluster medium (ICM) filled with hot
ionized gas (Binney & Tremaine, 2008; Kaiser, 1986; Dressler & Gunn, 1983).

Dense environments, like galaxy clusters, are the place of several quenching
processes that shut down the star formation (SF) activity, and galaxies in
these environments tend to be red, early-type, with little or no ongoing SF.
These quenching processes can depend either on the stellar mass or on the
density of the environment in which galaxies reside, and are referred to as
mass and environmental quenching, respectively (Dressler 1980; Gómez et al.
2003; Martínez et al. 2008; Peng et al. 2010). The latter involve processes
such as ram pressure stripping (RPS, Gunn & Gott, 1972; Abadi et al., 1999),
tidal stripping (TS, Merritt, 1983) and galaxy harassment (Moore et al.,
1999). These phenomena can remove an important fraction of the hot and cold
gas of the cluster galaxies, with the consequent decrease of the star
formation rate (SFR). The removal of the warm gas from the galactic halo by
the ICM is known as starvation (e.g., Larson et al. 1980; Balogh et al. 2000;
McCarthy et al. 2008; Bekki 2009; Bahé et al. 2013; Vijayaraghavan & Ricker
2015). This process cuts off the supply of gas, thus inhibiting any subsequent
SF, a process that can happen even with a gradual removal of the hot gas (Cora
et al., 2019). Even though this mechanism is more effective at the central
regions of clusters, it also has been reported in less massive systems (e.g.
Rasmussen et al. 2006; Jaffé et al. 2012). On the other hand, mass quenching
involves internal, self-regulated physical processes, being the most important
ones the stellar feedback (e.g., Stringer et al. 2012; Bower et al. 2012;
Hopkins et al. 2014; Chan et al. 2018) and the feedback from active galactic
nuclei (AGN, Bower et al. 2012; Hasinger 2008; Silverman et al. 2008). Stellar
feedback is efficient in galaxies with low and intermediate stellar masses
(Trujillo-Gomez et al., 2015), while at the massive end, the AGN phenomenon is
expected to be the dominant effect (Beckmann et al., 2017).

Galaxy quenching has been studied in the state-of-art hydrodynamical
cosmological simulations like EAGLE 111https://eagle.strw.leidenuniv.nl/
(Schaye et al., 2015; Crain et al., 2015) by Pallero et al. (2019) or
IllustrisTNG222https://www.tng-project.org/ (Pillepich et al., 2018) by
Donnari et al. (2021) and Walters et al. (2022), and in cluster resimulations
such as The Hundred Project333https://www.nottingham.ac.uk/
ppzfrp/The300/index.php (Cui et al., 2018) by Wang et al. (2018). This topic
has also been addressed by several semi-analytic models of galaxy formation
(Henriques et al., 2017; Stevens & Brown, 2017; Cora et al., 2018, 2019; Xie
et al., 2020). All of these works stand out the importance of environment in
galaxy quenching and the role of the pre-processing, mostly for satellites or
galaxies residing in low mass hosts. On the other hand, SF of central galaxies
tend to be quenched in-situ via mass quenching mechanisms like AGN feedback.

Galaxy clusters grow by the accretion of galaxies and groups of galaxies from
their outskirts, a phenomenon that occurs preferentially alongside filaments
(e.g. Colberg et al. 1999; Ebeling et al. 2004; Knebe et al. 2004; Rost et al.
2019; Kuchner et al. 2022) and, to a lesser extent, from other directions
(isotropic infall region). Martínez et al. (2016) (hereafter, M16) studied the
properties of galaxies in filaments between groups of galaxies in the Sloan
Digital Sky Survey Data Release 7 (SDSS DR7, Abazajian et al., 2009) up to
$z=0.15$. They found systematic lower values of the specific star formation
rate (sSFR, defined as the ratio between SFR and stellar mass) in filaments
than in the isotropic infall region, thus providing evidence that galaxies
infalling alongside filaments have experienced stronger environmental effects
than galaxies infalling from other directions. Similar analysis have been done
using the VIMOS Public Extragalactic Redshift Survey (VIPERS, Guzzo et al.,
2014; Scodeggio et al., 2018) for the early Universe in Salerno et al. (2019,
hereafter Paper 1), and using OmegaWINGS spectroscopic survey (Gullieuszik et
al., 2015; Moretti et al., 2017) in the redshift range $0.04\leq z\leq 0.08$
in Salerno et al. (2020, hereafter Paper 2), confirming the important role
played by filaments in quenching galaxies up to $z\sim 0.9$.

Post-starburst (PS) galaxies are a peculiar class of objects that are
experiencing a rapid transition from being star forming to quiescent.
Approximately $\sim 1{\rm Gyr}$ before the observing time, they are supposed
to have had a large burst of SF but the observed spectra show very little or
no ongoing SF. The evidence of a recent burst of SF comes from the presence of
strong Balmer absorption lines typical of young stars (Couch & Sharples,
1987). Paccagnella et al. (2019) found that the frequency of PS galaxies is
strongly dependent on the environment; they observe an increasing fraction
from individual objects, binary systems, groups and clusters, suggesting a
progressive increase with the halo mass. Similar results are found in Paper 2;
in particular, they found that the filamentary region shows a fraction of PS
galaxies greater than the isotropic infall region.

In this paper, we study the properties of a population of simulated galaxies
that are falling to clusters/groups with the aim of characterising the
connection between the quenching of SF in these galaxies and the different
infalling regions in which they are found. Thus, we distinguish between
galaxies that are infalling into clusters/groups along filaments and those
that are infalling isotropically. To identify filaments, we use a sample of
massive dark matter (DM) haloes (filament nodes) from the MultiDark Planck 2
cosmological simulation (mdpl2, Klypin et al., 2016). Galaxy properties are
derived from these haloes by populating them with galaxies generated from the
semi-analytic model of galaxy formation sag (Cora et al., 2018), giving place
to a sample of galaxy clusters. In order to evaluate the evolution of the
properties of infalling galaxies, we analyse the galaxy population at three
different redshifts: $z=0\,,z=0.65\,,z=0.85$. We focus the analysis on the
comparison between the model predictions and the observational results found
in M16, Paper 1 and Paper 2. We complement the analysis by comparing the
evolutionary history of galaxies residing in the different environments, i.e.
filaments and isotropic infall regions, that end up with the same stellar mass
at $z=0$.

This article is organised as follows: In Section 2, we present our data sets
and our method to detect filaments; Section 3 deals with our galaxy samples in
different environments. In Section 4, we compare the fraction of red galaxies
in clusters, field, filaments and the isotropic infalling region, and its
redshift evolution. We discuss the implications of our results in Section 5.
Finally, we summarise our main results in this section as well.

Figure 1:  Left panel: scheme of the different regions found in the outskirts
of a cluster (represented by a red sphere) in units of $R_{200}$: filamentary
infall regions (orange structures; arrows indicate the direction towards the
corresponding filaments) and isotropic infall regions (remaining green regions
of the larger sphere). Right panel: an example extracted from simulated
results, where cluster members are shown as filled red circles, isotropically
infalling galaxies are shown as green diamonds and orange triangles represent
galaxies in the filamentary infall region.

##  2 Simulated galaxy clusters and their outskirts

We simulate the formation and evolution of galaxies within clusters and in
their surroundings by applying the semi-analytic model of galaxy formation sag
to the haloes and subhaloes (and their corresponding merger-trees) extracted
from the mdpl2 cosmological simulation. In the following, we briefly describe
the main aspects of both the mdpl2 simulation and the sag model. Then, we
present the sample of DM haloes selected to construct the set of galaxy
clusters and explain the procedure followed to identify filaments, which allow
us to define two infall regions for further analysis.

###  2.1 The mdpl2 simulation

The mdpl2 is part of the suite of DM cosmological simulations with Planck
cosmologies of the MultiDark project (Riebe et al., 2013; Klypin et al.,
2016), publicly available at the CosmoSim
database444https://www.cosmosim.org/. The simulation follows the evolution of
$3840^{3}$ DM particles in a comoving box of $1\,h^{-1}$ Gpc on a side, from
an initial redshift $z=120$ to $z=0$. The cosmological parameters are
consistent with Planck measurements of a flat $\Lambda$CDM model (Planck
Collaboration et al., 2014): $\Omega_{\rm m}=0.307$, $\Omega_{\Lambda}=0.693$,
$\Omega_{\rm b}=0.048$, $\sigma_{8}=0.823$, $n=0.964$, and $h=0.678$. The
simulation counts with several halo catalogues derived from different post-
processing techniques. In particular, we use the haloes catalogue and merger-
trees constructed with Rockstar (Behroozi et al., 2013a) and ConsistentTrees
(Behroozi et al., 2013b) codes, respectively. This catalogue can be found as
mdpl2.Rockstar555doi:10.17876/cosmosim/mdpl2/006 in the database. The outputs
of the simulation are stored in $126$ snapshots between $z=17$ and $z=0$.

###  2.2 The SAG model

The semi-analytic model of galaxy formation and evolution sag has its roots in
the Munich model (Springel et al., 2001), and has been highly developed and
improved as described in Cora (2006), Lagos et al. (2008), Tecce et al.
(2010), Orsi et al. (2014), Muñoz Arancibia et al. (2015), Gargiulo et al.
(2015), and Cora et al. (2018). The model includes the main physical processes
relevant to galaxy formation and evolution such as radiative cooling of hot
gas (both in main haloes and subhaloes), quiescent SF, starbursts generated by
disc instabilities and galaxy mergers that contribute to form both a stellar
bulge and a super massive black hole, feedback from both supernovae explosions
and AGN, and a detailed treatment of chemical enrichment. These processes
regulate the circulation of baryons between different galactic components: hot
gas halo, cold gas disc, stellar disc and bulge, reservoir of ejected mass.
The gas phases are identified by the way in which they are generated, i.e. no
temperature threshold is assumed to separate the hot gas from the cold gas.
Thus, when a DM halo is identified for the first time, we assume that baryons
are shocked and heated during their cosmic accretion onto the DM halo, and the
mass of hot gas is computed from the baryon fraction of its virial mass. Once
a hot gas halo is formed, a pressure-supported disc of cold gas is generated
as a result of gas cooling. Quiescent SF takes place in this cold gas disc. As
the galaxy evolves, the corresponding hot gas halo is redefined at each
snapshot of the DM simulation by substracting from the baryon fraction of the
virial mass the mass of cold gas, stars and super massive black hole of the
galaxy itself and of surrounding satellite galaxies contained in the main host
DM halo; since the hot gas of galaxies is gradually removed by environmental
effects when they become satellites, the hot gas mass of satellite galaxies is
also discounted from the estimation of the hot gas of the main host halo at
each snapshot (see eq. 2 of Cora et al., 2018). The modelling of environmental
effects, namely RPS and TS, are relevant for the purpose of the current study.
The implementation of RPS is based on a new analytic fitting profile that
model the ram pressure exerted over satellite galaxies in different
environments and epochs (Vega-Martínez et al., 2022). sag considers orphan
galaxies to track the remnant satellites of haloes that are not longer
resolved by the underlying simulation, whose positions and velocities are
consistently calculated using an analytical model that considers dynamical
friction and mass-loss by TS (Delfino et al., 2022)666 In the current work, we
use a previous version of the orbital evolution code that assumes an
isothermal sphere to describe the mass profile of both the host halo and
unresolved subhaloes instead of the NFW profile adopted by Delfino et al.
(2022)..

The work of Cora et al. (2018) presents the results of the dependence of the
fraction of quenched MultiDark-sag galaxies as a function of stellar mass,
halo mass and halo-centric distance for two versions of the model. They only
differ in the dependence of the efficiency of supernova feedback on redshift.
The amount of reheated and ejected mass produced by supernova explosions is
proportional to the number of supernovae arising in each star-forming event
and the energy released by a single supernova, and inversely proportional to
the square of the virial velocity of the host (sub)halo of the corresponding
galaxy, which is a measure of its potential well. Both the estimations of the
reheated and ejected mass (which are respectively transferred from the cold
gas reservoir to the hot gas halo and to a reservoir of ejected mass for a
later gradual reincorporation) involve efficiencies that are free parameters
of the model. They also include a dependence on redshift through the factor
$(1+z)^{\beta}$, being $\beta$ another free parameter of the model (see their
Eqs. (10) and (12)). In this work, we apply the version of sag characterised
by $\beta=1.3$, which allows to recover the observed fraction of $z=0$
quenched galaxies (see their fig. 11).

###  2.3 Sample of cluster-size haloes

The set of galaxy clusters is constructed by selecting cluster-size DM haloes
from the mdpl2 simulated volume. We select all the haloes at $z=0$ with mass
$M_{200}\geq 10^{15}h^{-1}{\rm M_{\odot}}$, computed within the spherical
region that encloses $200$ times the critical density, characterised by a
radius $R_{200}$. We exclude from our analysis those haloes undergoing a major
merger. This is done by restricting the analysis to objects that have no
companion haloes more massive than $0.1\times M_{200}$, within $5\times
R_{200}$. Our selection results in a set of $34$ of the $85$ haloes more
massive than $10^{15}h^{-1}{\rm M_{\odot}}$ in the mdpl2 volume.

Selecting the most massive haloes at $z=0$ guarantees that their progenitors
at $z\sim 0.9$ have already been formed. This criterion allows us to work with
the same structures through the cosmic time within the redshift range of
interest.

###  2.4 Filament identification

To identify the filamentary structures, we use the code developed by Pereyra
et al. (2020). They assume that filaments are bridges of matter connecting
high-density peaks. The identification is based on the standard tools Minimal
Spanning Tree (MST) and the Friends-of-Friends algorithm (FoF). The code is
applied to the outputs of the mdpl2 simulation. All the DM haloes with mass
greater than $5\times 10^{11}h^{-1}{\rm M_{\odot}}$ are considered as nodes in
the identification of the filaments. Nevertheless, in the following analysis,
we only consider the filaments that connect with any of the $34$ more massive
haloes identified as described previously (first node). Therefore, the
secondary node has at least a mass of $M_{200}>5\times 10^{11}h^{-1}{\rm
M_{\odot}}$. For more details about the filaments identification, see Pereyra
et al. (2020) and Rost et al. (2020).

As a result of applying this code to mdpl2 at $z=0$, we obtain $49$ filaments
that connect with any of the $34$ DM haloes of our sample. If the algorithm is
applied to the main progenitor of the $34$ DM haloes at $z=0.64$ and $z=0.85$,
we identify a total $89$ and $99$ filaments, respectively. It is clear that
clusters are typically associated with more than one filament, being the
number of filaments per node between two and five.

###  2.5 Infall regions

We are mainly interested in the properties of galaxies in the outskirts of
clusters. There, we distinguish two different kinds of infall regions that are
defined according to the properties of the identified filaments. We consider
the direction that connects each filament, determined by the code of Pereyra
et al. (2020), with their corresponding node to define a cone of revolution
with an angle of $45^{\circ}$. This allows us to define two infall regions
that extend beyond the limit of the cluster-size haloes, i.e. $1<R/R_{200}\leq
5$, where $R$ is the distance to the cluster centre at the corresponding
redshift:

  1. 1.

The filamentary infall regions, which are volumes of space detected inside the
cones defined by the filaments.

  2. 2.

The isotropic infall regions, which are the remaining volumes located outside
the cones.

It is important to highlight that the general results presented in the
following sections are robust to changes in the aperture angle of the cones.
It is also important to note that, as we move away from a node, the cone
becomes increasingly wide. Consequently, the filamentary region can reach an
excessively large size. Thereby, in order to avoid this problem, we impose a
limit on the width of the defined filamentary infall regions. According to the
typical sizes considered in previous works, we choose $3.4\,h^{-1}\,\rm Mpc$
as the maximum width (Martínez et al., 2016; Salerno et al., 2019; Salerno et
al., 2020). When the base of the cone reaches this diameter, the filamentary
infall region is restricted by a cylinder with the same axis as the cone. In
the left panel of Fig. 1, we show a scheme of the different regions described
above in units of $R_{200}$. The red sphere represents the cluster region. The
orange areas depict the cones of revolution that continue as cylinders and
represent the filamentary infall regions. Finally, the remaining parts of the
sphere, painted in green, correspond to the isotropic infall region.

Figure 2: The ${}^{0.1}(g-r)$ colour distributions for the whole sample of sag
galaxies at $z=0$ (top panel) and at intermediate-high redshifts (bottom
panel). Dashed lines indicate the adopted separations for red and blue
galaxies following eq. (1). PS galaxies at $z=0$ (upper panel) are shown as
turquoise points.

##  3 Galaxy samples

To compare the predictions of the sag model with the observational results on
the quenching of galaxies in clusters and in the infall regions, as well as
the evolution with redshift of this phenomenon, we choose the snapshots
corresponding to $z=0$, $z=0.65$ and $z=0.85$, which we will refer to as low,
intermediate and high redshift bin, respectively. These choices are motivated
by the mean redshifts considered in the observational studies previously
described. The model predictions in the low redshift Universe will be compared
with the results found in M16 and Paper 2 using the SDSS DR7 and OmegaWINGS,
respectively. At intermediate and high redshift bins, model predictions will
be compared with the results of Paper 1 based on VIPERS.

For each of the $34$ DM haloes, we select all the sag galaxies that are at a
distance $R/R_{200}\leq 5$ from the cluster centre at each redshift analysed.
Thus, we construct three different galaxy catalogues for further analysis:
cluster galaxies (CG), galaxies in filamentary infall regions (FRG) and
galaxies in isotropic infall regions (IRG).

To be consistent with Paper 2, in this work we consider as CG all those
objects that lie within the $R_{200}$ of the cluster (or of its main
progenitor at higher $z$) , i.e. $R/R_{200}\leq 1$. On the other hand,
infalling galaxies reside either in any of the two infall regions. The right
panel of Fig. 1 shows an example of sag galaxies identified in the different
regions in the space of comoving coordinates $(X,Y,Z)$ with respect to the
centre of the cluster. Cluster members are shown in red, FRG in orange, and
green symbols correspond to IRG.

Besides, we define a representative population of field galaxies to be used as
a control sample. This was constructed by selecting a sub-volume of the mdpl2
simulation at $z=0$, so that the main host haloes enclosed in the region
satisfy that $M_{200}\leq 2\times 10^{14}\,h^{-1}\,\mathrm{M}_{\odot}$, and
the resulting halo mass function below $10^{13}\,h^{-1}\,\mathrm{M}_{\odot}$
is consistent with that obtained from the complete simulation. Following these
criteria, our selected region consists in a cubic volume of $\sim
43\,h^{-1}{\rm{Mpc}}$ of side–length, and its most massive halo has
$M_{200}=1.63\times 10^{14}\,h^{-1}\,\mathrm{M}_{\odot}$. With this selection,
we ensure that all the galaxies within the cube are not gravitationally
associated with large potential wells.

In all cases, we use the halo merger trees to extract the complete set of
progenitors of the selected haloes to define the corresponding samples at
higher redshifts.

###  3.1 Red, blue and post-starburst galaxies

To study how the environment and the stellar mass affect the SF in galaxies,
we use the ${}^{0.1}(g-r)$ colour to classify galaxies which characterises
their stellar population. The use of colour allows us to make a direct
comparison with observational results like those presented in Paper 1. We use
a band shift to a redshift $z=0.1$ to approximate the mean redshift of the
main galaxy sample of SDSS (York et al., 2000). Dividing the sample in five
bins of stellar mass, we use the ${}^{0.1}(g-r)$ colour distributions to
separate the population of galaxies in red and blue. Red galaxies at $z=0$ are
those with

$^{0.1}(g-r)>-\,a+b\log\left(\frac{M_{\star}}{M_{\odot}}\right),$ (1)

where $a=(0.23\pm 0.03)$ and $b=(0.11\pm 0.03)$. The adopted threshold is
shown in the upper panel of Fig. 2 where we plot the ${}^{0.1}(g-r)$ color-
mass diagram for our sample of galaxies. For the less evolved Universe
($z=\left[0.65,0.85\right]$), we use slightly different parameters: $a=(1.2\pm
0.03)$ and $b=(0.28\pm 0.03)$, as we show in the bottom panel of Fig. 2. The
parameters of the thresholds are obtained by assuming the colour bimodality
and using a method of density estimation based on gaussian mixture models
(Taylor et al., 2015; Hahn et al., 2019). The procedure is applied to eight
bins of stellar mass. The selection by colour does not necessarily mean that
red galaxies are passive, however, there is a very good correlation between
the ${}^{0.1}(g-r)$ colour and the sSFR: using a threshold of ${\rm
log}($sSFR$/{\rm yr})=-10.7$ to separate passive from star-forming galaxies
(Cora et al., 2018; Wetzel et al., 2012), we find that, $\sim 99$ per cent of
the galaxies classified as red, are passive, while $\sim 13$ per cent of the
blue galaxies are in fact passive. From now on, we will use the terms red,
passive or quenched galaxies indistinctly.

Consistent with the observational studies previously described, PS galaxies
are only analysed in the low redshift Universe. To select PS galaxies we
assume that they stopped their SF around $\sim 10^{7}$ years before (Fritz et
al., 2014b; Paccagnella et al., 2017). Accordingly, we classify as PS all
galaxies that at $z=0$ are classified as red, but at $z=0.09$ (this redshift
corresponds to a backward time of $\sim 10^{9}$ years) are blue. It is
important to note that according to our selection based on colour, PS galaxies
at $z=0$ are also red galaxies, however, they have been excluded from the
general sample of red galaxies. In the top panel of Fig. 2 we show in
turquoise points the galaxies classified as PS. In Fig. 3, we present the
${}^{0.1}(g-r)$ colour distribution for the same galaxies as in Fig. 2,
distinguishing if they are red, blue or PS. The latter ones are associated
with a population in transition (e.g. Patel et al. 2009; Vulcani et al. 2010;
Paccagnella et al. 2016) and, therefore, it is expected that their colour
distribution is between the red and the blue population. On the other hand, we
see the classical colour-bimodality observed in many spectroscopic studies
(e.g., Strateva et al. 2001; Hogg et al. 2002; Bell et al. 2004; Fritz et al.
2014a).

In Table 1, we show the total number of galaxies located in the different
regions (CG, FRG, IRG, field galaxies), and the corresponding numbers of
passive (in three redshift bins) and PS (at $z=0$) galaxies.

Figure 3: The normalised ${}^{0.1}(g-r)$ colour distribution for the total sample of galaxies at $z=0$. Red and blue galaxies are selected following eq. (1) and PS galaxies are identified with the method described in Section 3.1; although PS galaxies are red, they have been excluded from the general sample of red galaxies. | Total |  | RED |  | PS
---|---|---|---|---|---
| $z=0$ | $z=0.65$ | $z=0.85$ |  | $z=0$ | $z=0.65$ | $z=0.85$ |  | $z=0$ |
Field Galaxies | 1728 | 4559 | 12699 |  | 392 (22%) | 801 (17%) | 2461 (19%) |  | 22 (1.3%) |
IRG | 13469 | 8249 | 5034 |  | 4984 (37%) | 1728 (20%) | 1479 (29%) |  | 221 (1.6%) |
FRG | 2087 | 1578 | 2500 |  | 801 (39%) | 433 (27%) | 816 (32%) |  | 42 (2.0%) |
CG | 8006 | 1320 | 1823 |  | 4903 (61%) | 599 (45%) | 909 (49%) |  | 202 (2.5%) |
Table 1: Number of total, red and PS galaxies as a function of the environment
and redshift (PS are only analysed at $z=0$). The corresponding percentages of
red galaxies and PS galaxies with respect to the total number of galaxies in
each case are shown between brackets.  Figure 4: Top panels show in solid
lines the fraction of red galaxies, excluding PS galaxies, as a function of
stellar mass and environment. The fractions of red galaxies in clusters are
shown as red solid circles, while the red fraction of FRG, IFG and field
galaxies are represented by orange triangles, green diamonds, and blue
squares, respectively. Left panels correspond to $z=0$, central panels to
$z=0.5$, and right panels to $z=0.85$. At $z=0$, the fraction of red galaxies,
including PS galaxies, are shown in dashed lines. Shaded areas represent the
errors computed by using the bootstrap re-sampling technique. Bottom panels
show the differences between the fractions of red galaxies relative to the
fractions of field galaxies.  Figure 5: Fraction of red FRG and IRG as a
function of the normalised cluster-centric distance. Each panel corresponds to
a different stellar mass bin. Error bars are calculated using the bootstrap
resampling technique. Colours and symbols are as in Fig. 4. Red and blue
dashed lines indicate the mean fractions of red galaxies in clusters and in
the field, respectively.

##  4 Results

###  4.1 Fractions of red galaxies at different redshifts

In the top panels of Fig. 4, we show the fractions of red galaxies ($F_{\rm
red}$) as a function of the stellar mass in the four environments considered.
The left panels correspond to the local Universe ($z=0$), the central panels
show the fractions at redshift $z=0.65$, and the right panels correspond to
redshift $z=0.85$. Errors are computed by the bootstrap re-sampling technique.
In the bottom panels, we show the residuals between each distribution relative
to the field. The solid lines at $z=0$ correspond to the general sample of the
red galaxies selected in Section 3.1, while the dashed lines show the
fractions when PS galaxies are included.

The fraction of red galaxies grows with the stellar mass, and the same
behaviour is observed in all the environments considered, and for all redshift
bins. These results are in agreement with previous works (M16, Paper 1, Sarron
et al. 2019). Moreover, the fraction of red galaxies in each environment
differs from each other, with the exception of the one corresponding to the
highest stellar mass bin ($\log{(M_{\star}/h^{-1}{\rm M_{\odot}})}\sim 11.5$),
for which all the environments show similar fractions of red galaxies,
independently of the redshift bin. As an overall trend, at fixed stellar mass,
galaxies in clusters are more quenched than those in filamentary regions. In
addition, the fractions of red galaxies in filamentary regions are larger than
the fractions of red galaxies located in the isotropic infall regions. This
difference between red galaxies in filaments and in the isotropic infall
region is better appreciated in the bottom panels of Fig. 4, being the largest
difference at $z=0.85$. Finally, galaxies in the field have the lowest
fraction of red galaxies, in all redshift ranges considered. For the lowest
stellar mass bin, we observe that the difference between galaxies in clusters
and in the field is greater at $z=0$, being the largest difference about $\sim
0.4$, as we can see in the bottom panels of Fig. 4. Our results suggest that
the isotropic infall region is able to affect the SF in galaxies even at
$z=0.85$. More interesting, galaxies that are falling into clusters along
filaments undergo an extra SF quenching in comparison to those infalling
isotropically.

Figure 6: The differences between the fractions of red FRG and red IRG
predicted by sag (solid lines) and derived from observational data (dashed
lines). The upper left and upper right panels show the comparison with SDSS
(fig. 7 of M16) and with OmegaWINGS (fig. 3 of Paper 2), respectively. The
bottom panels present the comparison with VIPERS at two different redshifts
(fig. 2 of Paper 1). Figure 7:  Meadian values of the stellar mass as a
function of redshift for galaxies in the four selected environments. Each
panel corresponds to different mass bins at $z=0$. Each point represents the
median of the stellar mass for the corresponding output of the sag model.
Bottom panels show the differences between the stellar masses of CG, FRG and
IRG relative to that of galaxies in the field. Colours and symbols are as in
Fig. 4.

Fig. 5 shows the fractions of red galaxies as a function of the cluster-
centric distance normalised to $R_{200}$ at $z=0$. We split our sample in
three bins of stellar mass: $\log(M_{\star}/h^{-1}{\rm
M_{\odot}})=[9.30,9.65]$, $[9.65,10.30]$ and $[10.30,11.65]$. The size of bins
were chosen to have equal number of objects. The red and blue dashed lines
correspond to the mean fractions of red galaxies in clusters and in the field,
respectively. For the low and intermediate stellar mass bins, we observe that
red galaxies in filaments and in the isotropic infall regions have fractions
between the mean values of the red galaxies in clusters and in the field. For
the same bins of stellar mass, the fractions of red FRG and IRG are similar
for $R/R_{\textup{200}}\lesssim 3$, while for $R/R_{\textup{200}}\gtrsim 3$
the fraction of red FRG increases considerably. In the high stellar mass bin,
we observe that, for $R/R_{\textup{200}}\gtrsim 2$, FRG are systematically
more quenched than their counterparts in the infall regions, giving place to a
higher fraction of red FRG, closer to the value achieved within clusters.

###  4.2 Post-starburst galaxies

PS galaxies can be a valuable tool to analyse the impact of the infall region.
Studying a sample of galaxies in the OmegaWINGS777A wide area spectroscopic
survey of more than $40$ clusters of galaxies in the nearby Universe
($0.04<z<0.07$) that provides estimates of star formation rates, stellar
masses, and measures of observed equivalent widths for the most prominent
spectral lines, both in absorption and in emission (Gullieuszik et al.,
2015)., Paccagnella et al. (2017) find that it is composed by galaxies with
different infall times, including both backsplash and virialized galaxies. As
galaxies approach $R_{200}$, processes like ram pressure could induce a burst
of SF and a subsequent fast quenching, producing the characteristic PS
spectrum of these galaxies. However, these mechanisms could begin at several
virial radii (Paccagnella et al., 2017). In Paper 2, the authors analyse the
abundance of PS galaxies in clusters and in their outskirts. These authors
find that the lower fraction of PS galaxies corresponds to the field and the
higher one to clusters, while infall regions show intermediate values, being
in the filamentary region slightly higher than in the isotropic infall region.

Here, we analyse the behaviour of PS galaxies in the sag model. We observe in
Fig. 2 and Fig. 3 that the ${}^{0.1}(g-r)$ colours of PS galaxies are located
between the distributions of the red and blue populations. PS galaxies are, by
definition, red at $z=0$, however, the fact that they are not as red as the
general population of red galaxies is a consequence of the recent SF quenching
that these galaxies have experienced. As can be seen in Table 1, the fraction
of PS galaxies also depends on the environment, where the filamentary regions
tend to have a larger fraction of PS galaxies than the isotropic infall
region. From Table 1, we can extract the PS fractions at $z=0$ by environment:
2.5 per cent in clusters, 2.0 per cent in filamentary regions, 1.6 per cent in
the isotropic infall regions and 1.3 per cent in the field. These trends are
in agreement with the observational results reported in Paper 2, however, our
percentages are systematically lower. This systematic shift in the PS
fractions could be due to the different methods applied to select the star-
forming galaxies (see the discussion in the next section). Again, both the
observational results and the predictions of the sag model show that the
infall regions, both filamentary and isotropic ones, play an important role in
the pre-processing of galaxies.

###  4.3 Comparison of the predictions of the SAG model with observations

The observational results presented in M16, Paper 1 and Paper 2 were derived
using different methods to define passive galaxies and the infall regions,
making a direct comparison with model predictions particularly difficult. In
relation to the definition of passive galaxies, in Paper 2 the sample of
passive galaxies was obtained through the analysis of emission lines using the
method originally proposed by Dressler et al. (1999) and Poggianti et al.
(1999), and more recently described by Fritz et al. (2014a). This
classification uses the equivalent width of the lines $\rm[OII]$, $\rm[OIII]$,
$\rm H_{\delta}$ and $\rm H_{\alpha}$. On the other hand, in M16 and Paper 1,
passive galaxies are selected using the sSFR and the diagram colour-colour,
respectively. In M16 the SFR is obtained by combining the stellar mass and the
SFR likelihood distributions as outlined in Appendix A of Brinchmann et al.
(2004); passive galaxies are selected by applying a threshold in the sSFR. In
Paper 1, VIPERS galaxies are classified as passive using the $NUV-r$ vs. $r-K$
diagram of Fritz et al. (2014a) and the code Hyperzmass to estimate absolute
magnitudes and stellar masses.

The observational works also present differences in the way of defining the
infall regions. M16 and Paper I select pairs of groups of galaxies with a
difference in the radial velocities of their baricentres, $\Delta V_{12}$,
lesser than $1000\,\rm{km~{}s^{-1}}$, and a projected distance between the
baricentres, $\Delta_{12}$, smaller than $10\,h^{-1}\,\rm Mpc$. They consider
the filamentary region as a rectangular cuboid in redshift space connecting
the baricentres with a width $\Delta_{12}/2$, a length $1.5\,h^{-1}\,\rm Mpc$
and $\Delta V<1000\,\rm{km~{}s^{-1}}$. In Paper II, the authors select all
pairs of systems that are separated by less than $14\,h^{-1}\,\rm Mpc$ in
redshift space. They consider the outskirts of clusters as the projected
volume defined by $1\leq R/R_{200}\leq 2$, and $|\Delta V|\leq 4\sigma$, being
$\sigma$ the radial velocity dispersion of the cluster. Galaxies in filaments
are those that are located within $45^{\circ}$ from the projected direction to
the other node of the filament. Finally, it should be noted that in M16, Paper
I and Paper II, the environments are defined in redshifts space, while model
results are analysed in 3D.

The diverse methods to select passive galaxies and to define the infall
regions could explain the differences between the fractions found in the
observational works. For example, M16 found that, for high-mass galaxies at
$z=0$, all environments show passive fractions above 0.8, while in Paper 2 the
fraction of passive galaxies is clearly below this value in clusters and does
not exceed 0.4 in the field. Our analysis, which is based on a selection by
colour, allows a more direct comparison with the results presented in Paper 1.
However, in order to include all the observational results in our analysis,
the comparison is focused on the relative differences between the fractions of
red galaxies in different environments rather than on absolute fractions.
Furthermore, we have limited the comparison to differences between the
fractions of red FRG and red IRG.

In Fig. 6, we show the differences between the fractions of red FRG and red
IRG as a function of stellar mass predicted by sag (solid lines) and the
different observational results (dashed lines): SDSS (M16; left top panel),
OmegaWINGS (Paper2; right top panel) and VIPERS (Paper 1; bottom panels). The
solid lines show the differences between the trends shown in Fig. 4 for FRG
and IRG, depicted by orange and green colours, respectively. The dashed lines
were calculated from the observational data published in the corresponding
articles. At $z=0$, we observe two different behaviours. As shown in the left
upper panel of Fig. 6, the differences between the results from SDSS and sag
are small ($\leq 0.05$), except for the highest stellar mass bin. On the other
hand, we observe larger differences and opposite trends between OmegaWINGS and
sag (right upper panel). As already mentioned, the fractions of passive
galaxies derived from OmegaWINGS data were obtained by using methods that
differ substantially from those used by M16 and those applied in the analysis
of sag outputs, thus providing a possible explanation for the lack of
agreement between observational and simulated results. Beyond these
differences, it is important to note that, for both observations and sag , the
samples of FRG have a higher fraction of red/passive galaxies than the samples
of IRG. At redshift $0.64$ and $0.85$, we found a good agreement between sag
and VIPERS. Interestingly, for the high-mass bin at redshift $0.64$, both the
model and VIPERS show fractions of passive galaxies that are larger in the IRG
than in the FRG, a result that should be investigated in more detail.

###  4.4 Evolution of galaxy properties

The properties of galaxies we observe at the present epoch are the result of a
variety of internal and external physical mechanisms acting throughout the
entire galaxy life. Through the study of the properties of galaxies in sag
over an extended redshift range ($0<z<2$), we also have the opportunity to
understand the relative influence of the environments in different epochs of
the Universe.

In this section, we study the evolution of the properties of galaxies
depending on the environment in which they are identified at $z=0$. For each
subsample, we analyse different properties of galaxy progenitors as a function
of redshift. It is important to note that we do not consider that a galaxy
inhabited the same environment throughout its history. With this methodology,
we want to investigate how the properties of galaxies that at $z=0$ inhabit a
given environment evolve. We divide the galaxy samples into four stellar mass
bins: $\log({\rm M_{\star}}/h^{-1}{\rm M_{\odot}})=[9.30,9.55]$,
$[9.55,9.85]$, $[9.85,10.30]$ and $[10.30,11.65]$. The size of the bins are
chosen to have equal number of objects at $z=0$. For each bin, we track the
properties of main progenitors of the selected $z=0$ galaxies across different
snapshots of the simulation. Finally, for each environment and bin of stellar
mass, we calculate the median of each property in all simulation outputs and
analyse them as a function of redshift. We focus our analysis on the median
values of stellar mass, hot gas, cold gas and SFR.

####  4.4.1 Evolution of the stellar mass

Fig. 7 shows the evolution of the stellar mass as a function of redshift. Each
point represents the median of the stellar mass for the corresponding
environment and snapshot. By construction, all curves end at the same value.
That is, we analyse how galaxies in each environment assembled the same amount
of stellar mass. For a better visualisation, bottom panels show the residuals
between the stellar mass of galaxies in clusters, in filamentary regions and
in isotropic infall regions, relative to field galaxies.

We observe a similar trend in all panels of Fig. 7, where main progenitors of
CG show the highest stellar mass values throughout the whole redshift range
probed, while field galaxies are characterised by the fastest stellar mass
growth. In other words, galaxies that at $z=0$ are in clusters assembled most
of their stellar mass much earlier than galaxies in the other environments. In
particular, IRG and FRG show intermediate values between those for galaxies in
the field and within clusters. For the first three stellar mass bins, the
progenitors of FRG are slightly, but systematically, more massive than IRG.
Only in the highest stellar mass bin, the trends remain indistinguishable
throughout the entire redshift range.

Figure 8: Median values of the mass of the halo hot gas as a function of
redshift for galaxies in the four selected environments in bins of stellar
mass as in Fig. 7. At the bottom of each panel, the differences between the
mass of hot gas of galaxies in denser environments relative to the mass of hot
gas of field galaxies are shown.  Figure 9: raction of the main progenitors of
CG, FRG, IRG and field galaxies identified at $z=0$ that are classified as
satellites at different epochs ($F_{\rm sat}$).

####  4.4.2 Evolution of the hot and cold gas mass

The rate of stellar mass growth is a direct consequence of the evolution of
the SFR, which results from the complex circulation of mass between hot and
cold gas reservoirs regulated by internal and external processes. Then, we
focus first on the evolution of the hot gas mass. Top panels of Figs. 8
present the evolution with redshift of the median values of the mass of hot
gas in the halo, $M_{\textup{hot}}$, of galaxies residing in different
environments for the same stellar mass bins as in Fig. 7; bottom panels show
the difference between the hot gas mass of galaxies in denser environments
relative to the hot gas mass of field galaxies. In Fig. 8 we observe that,
regardless of stellar mass, the hot gas content of field galaxies grows
monotonically up to the present time (with a very slight decrease near $z=0$).
However, the hot gas mass of galaxies residing in clusters and in infall
regions increases monotonically only up to $z\sim 1$ for the former and up to
$z\sim 0.5$ for the latter, epochs in which their hot gas content begins to
decrease, on average. Besides, while at earlier epochs CG have more hot gas
than FRG and IRG, this trend is inverted during the decreasing stage, and the
rate of decrease becomes more pronounced as we consider IRG, FRG and CG, in
that order. These trends can be understood in terms of the number of central
and satellite galaxies among the progenitors of $z=0$ galaxies residing in
different environments, and the action of mass and environmental SF quenching
on these galaxy populations.

Fig. 9 shows the fraction of the main progenitors of CG, FRG, IRG and field
galaxies that are classified as satellites at different epochs ($F_{\rm
sat}$). Here, we do not separate the galaxies according to their $z=0$ stellar
mass since general patterns are similar for galaxies in any $z=0$ stellar mass
bin. The general trends observed for any of the environments considered is
that the number of satellites increases quite monotonically as we approach to
the present, simply indicating that galaxies that are satellites at a given
epoch where central galaxies at some time in the past, being the number of
satellites larger in denser environments at a given redshift. This general
behaviour is consistent with the structure growth in a $\Lambda$CDM cosmology.
Many satellites found in higher density regions have been probably satellites
of smaller accreted structures. This is supported by the results obtained by
Benavides et al. (2020) from the analysis of the cosmological hydrodynamical
simulation Illustris; they find that many surviving cluster galaxies at $z=0$
are accreted as part of groups, where the percentage depends on the
identification of group satellites, either given by the definition involved in
the halo finder ($\sim 38$ per cent) or by considering galaxies within the
virial radius of the infalling group ($\sim 20$ per cent). Thus, the large
rate of increment of $F_{\rm sat}$ in clusters shown in Fig. 9 is a result of
a combination of satellites accreted directly from the field (central
galaxies) and both central and satellite galaxies of accreted groups. Apart
from this general increasing trend of $F_{\rm sat}$ regardless of the
environment, we can see peaks and valleys at $z\lesssim 0.3$ for galaxies in
the infall regions. These features could be related to the definition of a
galaxy as satellite or central according to their gravitational binding energy
to a given structure (cluster, infalling group) in the outskirts of clusters
during the most recent stage of structure growth. We have discarded the
uncertainties related to the integration of the orbits of orphan galaxies as
being responsible of these variations of $F_{\rm sat}$, since the trends are
similar when we exclude them from the sample. Unravelling if the origin of
these variations have a physical origin or are related to definitions inherent
to the halo finder deserves a deeper study that is beyond the scope of this
work.

The values of $F_{\rm sat}$ at different redshifts globally characterise the
change in status of the progenitors of the $z=0$ galaxies from central to
satellites according to the dynamical evolution of their environments. The hot
gas of central galaxies is fed by the cosmological gas accretion during halo-
mass growth, a process that does not occur, by construction, in satellite
galaxies modelled by sag (and generally not taken into account in semi-
analytic models). Hence, while $F_{\rm sat}\lesssim 0.2$, it can be considered
that central galaxies dominate and, therefore, the median values of the hot
gas mass increase with decreasing redshift, thus explaining the quasi-
monotonic increase of the mean values of the hot gas content up to $z=0$ of
field galaxies and the change of regime at $z\sim 1$ for CG and $z\sim 0.5$
for FRG and IRG, when the hot gas mass start to decrease, as shown in Fig. 8,
according to the transformation of central galaxies in satellites. These
trends are a result of a competition of both internal and external processes
(the latter only act on satellite galaxies) and the dependence of their
efficiencies on stellar mass. The hot gas mass is reduced by gas cooling in
both central and satellite galaxies, a process regulated by the action of AGN
feedback. The implementation of AGN feedback in sag is limited to the so-
called ‘radio mode feedback’ (Croton et al., 2006), which is triggered by hot
gas accretion onto super massive black holes, generating jets and bubbles that
reduce or suppress gas cooling. Since this effect is stronger for more massive
galaxies, the median values of hot gas mass of galaxies in different
environments progressively increase as we consider more massive galaxies;
moreover, the amount of hot gas kept by the most massive galaxies is
considerably larger than that of less massive galaxies, and decreases in a
milder way towards $z=0$ for any environment. The relative difference of the
hot gas content of galaxies in different environments during the decreasing
phase can be explained by the action of RPS on satellite galaxies888The
environmental effects (as RPS) acting on satellites of infalling groups are
considered as pre-processing.. At a given redshift, the fraction of satellites
among the population of galaxy progenitors becomes larger as we consider IRG,
FRG and CG (see Fig. 9). The fact that RPS is milder for more massive
satellites explains the largest values of hot gas of the most massive
galaxies, since neither gas cooling nor RPS contribute significantly to their
decrement. Although reheated mass by supernova feedback can enhance the hot
gas reservoir of both central and satellite galaxies, these results show that
the evolution of hot gas is mainly determined by the relative role of AGN
feedback and RPS (see Cora et al., 2019, for a more detailed analysis and
discussion).

Figure 10:  Median values of the mass of cold gas in the disc as a function of
redshift for galaxies in the four selected environments in bins of stellar
mass as in Fig. 7. At the bottom of each panel, the differences between the
mass of cold gas of galaxies in denser environments relative to the mass of
cold gas of field galaxies are shown.

The way in which the cold gas content in the disc evolves is directly linked
to the evolution of the hot gas mass and can also be explained by the
dependence on stellar mass of RPS and AGN feedback. Fig. 10 is equivalent to
Fig. 8 but shows the evolution with redshift of the median values of the mass
of cold gas in the disc, $M_{\rm cold}$. The evolutionary patters of cold gas
mass for different environments follow the evolution of the hot gas mass shown
in Fig. 8 for the progenitors of galaxies with $z=0$ stellar mass ${\rm
log}M_{\star}/h^{-1}\,M_{\odot}\lesssim 10.3$ (first three stellar mass bins).
This is consistent with the fact that the gas cooling rate is larger for
higher available amounts of hot gas. However, this breaks down for the most
massive galaxies because the AGN feedback reduce the gas cooling rate and
prevents the cold gas reservoir from increasing despite the fact that there is
a large amount of hot gas. This is particularly evident for galaxies in the
field that experience a dramatic drop of their cold gas content since $z\sim
1$ which does not occur for galaxies with lower stellar mass. The significant
reduction or suppression of the gas cooling rate is also evident in the most
massive galaxies residing in more dense environments as the decrement of cold
gas content is more abrupt than the decrement of hot gas. On top of this, for
galaxies within any stellar mass range and in any environment, the cold gas
reservoir becomes progressively depleted by SF and feedback from supernova.

####  4.4.3 Evolution of the star formation rate

The evolution of the SFR predicted by sag is presented in Fig. 11, where each
point represents the median of $\log({\textup{SFR}})$ for the same stellar
mass bins as in Fig. 7; bottom panels show the excess of SFR of galaxies in
denser environments relative to those in the field. Since SF takes place from
the available cold gas, the features observed in the evolution of the SFR
closely follow those of the evolution of the cold gas (Fig. 10). Focusing
first on the general trends, we observe that, with the exception of field
galaxies and progenitors of FRG and IRG at $z\gtrsim 1$, the SFR of the
progenitors of galaxies currently residing in a given environment increase
with increasing redshift within the range of redshifts considered ($z\leq 2$),
which is consistent with observations where the highest values of SFR are at
$z\gtrsim 1.5$ (e.g. Lilly et al. 1996; Madau & Dickinson 2014).

The SF in progenitors of the most massive CG continuously falls as redshift
decreases. For the rest of the mass bins, the SFR of CG progenitors has little
change between redshift $\sim 2$ and $\sim 1$. After $z\sim 1$ and regardless
of the stellar mass, the SFR falls more steeply and do it faster than in the
infall regions. This behaviour indicate that the majority of the main
progenitors of objects classified as CG at $z=0$ inhabited environments
characterised by high levels of SF beyond $z\gtrsim 1$. The predictions of the
model are in agreement with the archaeological downsizing (Kodama et al. 2004;
Juneau et al. 2005), whereby more than $20-50$ per cent of the cosmic SF
occurred in the progenitors of CG at $z\sim 2$ (Madau & Dickinson 2014; Chiang
et al. 2017). The evolution of field galaxies shows a behaviour opposite to
those in clusters, going from being galaxies with the lowest SFR at $z\gtrsim
0.9$ to the highest one at $z\lesssim 0.8$. Finally, IRG and FRG show
intermediate values of SFR between galaxies in the field and in clusters, in
the entire redshift range. The SFR in the isotropic infall region and the
filamentary region are nearly indistinguishable from each other throughout the
redshift range analyzed, with the possible exception at low redshift
($z\lesssim 0.5$). More specifically, for $z\gtrsim 0.5$, galaxies in the
filamentary region systematically form slightly more stars than galaxies in
the isotropic infall region. This trend is reversed at lower redshifts, where
the difference becomes progressively larger.

It is worth noting that, for all the stellar mass bins, there is a small
redshift range where the SFR is similar for all the environments ($z\sim 0.7$
for the first three bins of stellar mass and $z\sim 1.1$ for the highest mass
bin). These redshifts represent a change in the relation between the SFR and
environment and is known as the reversal of the SFR-density relation999Effect
observed in surveys at high redshifts, where the SFR-density relation at
$z\sim 1$ shows an inverse behaviour compared to the well known relation at
$z\sim 0$. (Elbaz et al., 2007; Grützbauch et al., 2011; Popesso et al.,
2011). Besides, the way in which the values of SFR around $z\sim 0.7$
increases with increasing stellar mass is consistent with the main sequence
followed by star-forming galaxies observed by the ESA Herschel space
observatory (Pearson et al., 2018, see their fig. 5); the median values of SFR
predicted by the model are systematically lower because we are not restricting
the analysis to star-forming galaxies.

The trends followed by progenitors of $z=0$ galaxies residing in different
environments can be understood in terms of the evolution of the cold and hot
gas discussed in the previous section. These trends are a result of two
complementary aspects. On the one hand, the number of galaxies affected by RPS
is lower at higher redshifts since the number of satellites among CG
progenitors decrease with increasing redshifts (lower values of $F_{\rm sat}$
for higher $z$; Fig. 9). On the other hand, the values of ram pressure at
higher redshifts are lower because of the lower densities of the intergalactic
gas that permeates the overdensities of galaxies detected at higher redshifts
(like proto-clusters) (Tecce et al., 2010, see their fig. 5), producing less
stripping of hot gas (Dannerbauer et al. 2017, Cora et al. 2018). Thus, at
higher redshifts, galaxies have more hot gas available to feed the cold gas
reservoir for subsequent SF. The role of AGN feedback in reducing the gas
cooling rate gains relevance with the stellar mass growth of galaxy
progenitors. Besides, at a given redshift, some phenomena such as interaction
between galaxies can lead to enhance the SF efficiency in higher density
environments compared to lower-density ones (e.g. Moore et al. 1996;
Villalobos et al. 2014; Smith et al. 2015).

The levels of SFR at different redshifts determine the evolution of galaxy
colours, a quantity that can be directly compared with observational results,
contributing to their interpretation. The trends analysed in this Section
explain clearly the way in which $z=0$ galaxies in different environments have
achieved their colours, giving place to a larger fraction of red galaxies in
denser environments, as shown in Fig. 4. The larger values of $F_{\rm red}$
for more massive galaxies, also appreciated from this figure, is connected
with the steeper slopes in the decreasing trend of the SFR with decreasing
redshift as we consider more massive galaxies, both in clusters and in infall
regions. Thus, when the reduction of SFR is more pronounced, galaxies have
more time to become red, giving raise to larger values of $F_{\rm sat}$ at
$z=0$.

Figure 11: Median values of log(SFR) as a function of redshift for galaxies in
the four selected environments in bins of stellar mass as in Fig. 7. At the
bottom of each panel, the differences in the SFR for galaxies in denser
environments relative to field galaxies are shown.

##  5 Summary and Conclusions

In this work, we study the effects of the infall region on the quenching of
galaxies in the redshift range $z=[0,2]$. We use a sample of clusters and
galaxies from the semi-analytic model of galaxy formation and evolution sag
that uses DM haloes and subhaloes extracted from a MultiDark simulation. The
main goals are i) to quantify the model predictions of the relative
differences between the fractions of red galaxies in the different
environments considered and ii) to compare the trends of these fractions of
red galaxies with recent observational results.

We find that the fractions of red galaxies in the sag model are strongly
dependent on the stellar mass (Fig. 4). In addition, both the filamentary and
the isotropic infall regions show an intermediate behaviour between galaxies
in clusters and in the field. These main characteristics were reported in
observational works in the late Universe in M16 (left panel of their Fig. 7)
and in Paper 2 (left panel of their Fig. 3) and at intermediate and high
redshifts in Paper 2 (their Fig. 2). Sarron et al. (2019) also report similar
behaviours in the redshift range $0.15<z<0.7$.

We show that in the whole range of redshift analysed, the quenching of the SF
is stronger in the filamentary region than in the isotropic infall region. Our
results suggest that, at $z=0.85$ (right panels of Fig. 4), both the isotropic
and the filamentary regions are able to quench galaxies in nearly the whole
range of stellar mass. On the contrary, in Paper 2 the authors concluded that
only the filamentary region can pre-process galaxies. At intermediate
redshifts, observations and sag show a similar behaviour, that is, the red
fraction of both FRG and IRG are higher than the red fraction of field
galaxies, being the fraction of red FRG higher than that of IRG. It is
important to remark that in Paper 1 the authors performed an analysis on a
sample of galaxies in a broad redshift range, while in the present work we
analyse samples in narrower redshift ranges.

We also study the fraction of red galaxies, $F_{\textup{red}}$, as a function
of the normalised distance to the cluster centre in the local Universe. For
the low and intermediate stellar mass galaxies, and distances
$R/R_{\textup{200}}\lesssim 3$, $F_{\textup{red}}$ of IRG are similar to those
of FRG, while for radii $R/R_{\textup{200}}>3$, the fractions of red galaxies
in the filamentary region increases considerably. For high-mass galaxies, we
observe that from $R/R_{\textup{vir}}\sim 2$, the FRG are systematically more
quenched than IRG. It is important to emphasise that, regardless of stellar
mass, galaxies at $R/R_{\textup{200}}>3$ that are falling towards clusters
along filaments have been clearly more affected in their SF than those that
are infalling isotropically. In general terms, these predictions of the model
are in agreement with the observational results found by M16.

Additionally, we select a sample of post-starburst galaxies. PS have
${}^{0.1}(g-r)$ colours intermediate between red and blue galaxies. Our
results indicate that this type of objects are more likely to form in dense
environments, especially in clusters. The infall regions show intermediate
fractions between clusters and field, being the fraction of PS higher in the
filaments than in the isotropic region, in agreement with the observational
results of Paper 2. However, the percentages of PS galaxies in sag are
systematically lower than in Paper 2. This shift in the PS fractions could be
due to the different methods used to quantify the star-forming activity.

Finally, for the same set of environments, we have carried out a study on the
evolution of the properties of galaxies predicted by the semi-analytic model.
The results show that the main progenitors of galaxies at $z=0$ have different
evolutionary behaviours depending on the stellar mass and environment. The sag
model is able to reproduce the Lilly-Madau diagram (Lilly et al., 1996; Madau
& Dickinson, 2014), the reversal of SFR-density relation (Hwang et al. 2019;
Elbaz et al. 2007; Cooper et al. 2007), and the main sequence of galaxies
(Pearson et al., 2018). Comparing the evolution of the properties of the
progenitors of galaxies that, at $z=0$, have the same stellar mass, our
results show that the progenitors of galaxies that inhabit in clusters at
$z=0$ are the most efficient to form stars at $z\gtrsim 1.5$. In contrast,
field galaxies are the least efficient in that redshift range. This could be
attributed to the fact that in the progenitors of clusters (proto-clusters),
the ram-pressure is not an efficient mechanism to remove the gas (Dannerbauer
et al., 2017), while the frequent galaxy-galaxy interactions in a dense
environment tend to enhance the SF (e.g. Moore et al. 1996; Moore et al. 1999;
Gnedin 2003; Smith et al. 2015). Moreover, at high redshifts, the progenitors
of CG have the highest reservoirs of both hot and cold gas (Figs. 8 and 10,
respectively), since the number of satellites (which by construction of the
sag model are affected by RPS) among CG progenitors decreases with increasing
redshifts (Fig. 9), favouring the star formation in proto-clusters compared to
the other environments. Since clusters are the environments that first achieve
high levels of SFR, it is also expected they have the highest fractions of red
galaxies at for any stellar mass.

Regarding the evolution of galaxies in the infall regions, our results show
that the progenitors of galaxies with mass $\log(M_{\star}/h^{-1}\,{\rm
M}_{\odot})\lesssim 10.3$ that, at $z=0$, inhabit in the filamentary region
are slightly, but systematically, more massive than those in the isotropic
infall region. Regarding the SFR, the sag model predicts that FRG
systematically form slightly more stars than IRG for $z\gtrsim 0.5$. This
trend is reversed at lower redshifts, where the difference becomes
progressively larger. These differences are also appreciated in the reservoirs
of gas, that at low redshift decrease faster in FRG than in IRG. Even though
these differences in the stellar mass growth and SF histories should have
impacted in the evolution of the colour of galaxies, our results indicate that
the red fraction of the progenitors of FRG and IRG are nearly
indistinguishable from each other regardless of the redshift or the stellar
mass. Our findings allow us to conclude that the precursors of FRG and IRG at
$z=0$ began to differentiate from field galaxies long time before reaching the
cluster infall region, and that filamentary regions are more efficient in the
pre-processing of galaxies than the isotropic infall region.

In general agreement with the observational results, our analysis of the
predictions of the sag model shows that the infall region of clusters play an
important role in the pre-processing of galaxies along most of their
evolutionary history. Moreover, both model predictions and observational
results clearly show that the infall along filaments results in an extra SF
quenching in comparison with isotropic infall.

## Data availability

The raw data of the semi-analytic model of galaxy formation sag will be shared
on reasonable request to the corresponding author.

## Acknowledgements

The authors thank the referee for useful comments and suggestions that help to
greatly improve this manuscript. We would like to thank Héctor J. Martínez for
helpful discussions about the filament identification. This paper has been
partially supported with grants from Consejo Nacional de Investigaciones
Científicas y Técnicas (CONICET, PIP 11220130100365CO) Argentina, and
Secretaría de Ciencia y Tecnología, Universidad Nacional de Córdoba,
Argentina. This work used computational resources from
CCAD101010https://ccad.unc.edu.ar/ \- Universidad Nacional de Córdoba, which
are part of SNCAD - MinCyT, República Argentina. SAC acknowledges funding from
CONICET (PIP-2876), Agencia Nacional de Promoción de la Investigación, el
Desarrollo Tecnológico y la Innovación (Agencia I+D+i, PICT-2018-3743), and
Universidad Nacional de La Plata (G11-150), Argentina. CVM acknowledges
support from ANID/FONDECYT through grant 3200918, and he also acknowledges
support from the Max Planck Society through a Partner Group grant.

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