# Star Formation and Dust in the Cosmic Web

Massimiliano Parente SISSA, Via Bonomea 265, I-34136 Trieste, Italy  INAF,
Osservatorio Astronomico di Trieste, via Tiepolo 11, I-34131, Trieste, Italy
Cinthia Ragone-Figueroa Instituto de Astronomía Teórica y Experimental (IATE),
Consejo Nacional de Investigaciones Científicas y Técnicas de la
República Argentina (CONICET), Universidad Nacional de Córdoba, Laprida 854,
X5000BGR, Córdoba, Argentina  INAF, Osservatorio Astronomico di Trieste, via
Tiepolo 11, I-34131, Trieste, Italy  Pablo López Instituto de Astronomía
Teórica y Experimental (IATE), Consejo Nacional de Investigaciones Científicas
y Técnicas de la
República Argentina (CONICET), Universidad Nacional de Córdoba, Laprida 854,
X5000BGR, Córdoba, Argentina  Observatorio Astronómico, Universidad Nacional
de Córdoba, Laprida 854, X5000BGR, Córdoba, Argentina  Héctor J. Martínez
Instituto de Astronomía Teórica y Experimental (IATE), Consejo Nacional de
Investigaciones Científicas y Técnicas de la
República Argentina (CONICET), Universidad Nacional de Córdoba, Laprida 854,
X5000BGR, Córdoba, Argentina  Observatorio Astronómico, Universidad Nacional
de Córdoba, Laprida 854, X5000BGR, Córdoba, Argentina  Andrés N. Ruiz
Instituto de Astronomía Teórica y Experimental (IATE), Consejo Nacional de
Investigaciones Científicas y Técnicas de la
República Argentina (CONICET), Universidad Nacional de Córdoba, Laprida 854,
X5000BGR, Córdoba, Argentina  Observatorio Astronómico, Universidad Nacional
de Córdoba, Laprida 854, X5000BGR, Córdoba, Argentina  Laura Ceccarelli
Instituto de Astronomía Teórica y Experimental (IATE), Consejo Nacional de
Investigaciones Científicas y Técnicas de la
República Argentina (CONICET), Universidad Nacional de Córdoba, Laprida 854,
X5000BGR, Córdoba, Argentina  Observatorio Astronómico, Universidad Nacional
de Córdoba, Laprida 854, X5000BGR, Córdoba, Argentina  Valeria Coenda
Instituto de Astronomía Teórica y Experimental (IATE), Consejo Nacional de
Investigaciones Científicas y Técnicas de la
República Argentina (CONICET), Universidad Nacional de Córdoba, Laprida 854,
X5000BGR, Córdoba, Argentina  Observatorio Astronómico, Universidad Nacional
de Córdoba, Laprida 854, X5000BGR, Córdoba, Argentina  Facundo Rodriguez
Instituto de Astronomía Teórica y Experimental (IATE), Consejo Nacional de
Investigaciones Científicas y Técnicas de la
República Argentina (CONICET), Universidad Nacional de Córdoba, Laprida 854,
X5000BGR, Córdoba, Argentina  Observatorio Astronómico, Universidad Nacional
de Córdoba, Laprida 854, X5000BGR, Córdoba, Argentina  Gian Luigi Granato
INAF, Osservatorio Astronomico di Trieste, via Tiepolo 11, I-34131, Trieste,
Italy  Instituto de Astronomía Teórica y Experimental (IATE), Consejo Nacional
de Investigaciones Científicas y Técnicas de la
República Argentina (CONICET), Universidad Nacional de Córdoba, Laprida 854,
X5000BGR, Córdoba, Argentina  IFPU - Institute for Fundamental Physics of the
Universe, Via Beirut 2, 34014 Trieste, Italy  Andrea Lapi SISSA, Via Bonomea
265, I-34136 Trieste, Italy  IFPU - Institute for Fundamental Physics of the
Universe, Via Beirut 2, 34014 Trieste, Italy  INFN-Sezione di Trieste, via
Valerio 2, 34127 Trieste, Italy  INAF/IRA, Istituto di Radioastronomia, Via
Piero Gobetti 101, 40129 Bologna, Italy  Rien van de Weygaert  Kapteyn
Astronomical Institute, University of Groningen,PO Box 800, 9747 AD,
Groningen, The Netherlands

###### Abstract

The large-scale environment of the cosmic web is believed to impact galaxy
evolution, but there is still no consensus regarding the mechanisms. We use a
semi-analytic model (SAM) galaxy catalog to study the star formation and dust
content of local galaxies in different cosmic environments of the cosmic web,
namely voids, filaments, walls, and nodes. We find a strong impact of the
environment only for galaxies with $M_{\rm stars}\lesssim
10^{10.8}\,M_{\odot}$: the less dense the environment, the larger the star
formation rate and dust content at fixed stellar mass. This is attributed to
the fact that galaxies in less dense environments typically feature younger
stellar populations, a slower evolution of their stellar mass and a delayed
star formation compared to galaxies in denser environments. As for galaxies
with $M_{\rm stars}\gtrsim 10^{10.8}\,M_{\odot}$ differences among
environments are milder due to the disc instability (DI) driven supermassive
black hole (SMBH) growth implemented in the SAM, which makes SMBH growth, and
thus galaxy quenching, environment insensitive. We qualitatively test our
predictions against observations by identifying environments in the SDSS-DR16
using dust masses derived from the GAMA survey. The agreement is encouraging,
particularly at ${\rm log}\,M_{\rm stars}/M_{\odot}\gtrsim 10.5-11$, where
sSFRs and dust masses appear quite environment-insensitive. This result
confirms the importance of in situ growth channels of SMBHs.

Galaxy evolution (594) — Cosmic web (330) — Galaxy environments (2029) —
Interstellar medium (847) — Interstellar dust (836) — Galaxy quenching (2040)
— Supermassive black holes (1663)

††software: astropy (Astropy Collaboration et al., 2013, 2018), TOPCAT
(Taylor, 2005), L-Galaxies (Henriques et al., 2020).

##  1 Introduction

Extensive redshift galaxy surveys, such as 2dFGRS (Colless et al., 2001), SDSS
(York et al., 2000), GAMA (Driver et al., 2011) eBOSS (Alam et al., 2017), DES
(Abbott et al., 2018), have revealed that galaxies define a large scale cosmic
web structure, ranging from vast low-density regions known as cosmic voids to
higher-density regions such as walls, filaments, groups, and galaxy clusters.
This pattern is also present in the distribution of halos (Bond et al., 1996;
Cautun et al., 2014) in cosmological simulations, e.g. EAGLE (Schaye et al.,
2015; Crain et al., 2015), MultiDark (Klypin et al., 2016), IllustrisTNG
(Pillepich et al., 2018). The cosmic web results from the gravity-driven
evolution of primordial density perturbations. Hence, it embodies a large
amount of information which may be exploited to test different cosmological
models (e.g. Bos et al., 2012; Paillas et al., 2021; Bonnaire et al., 2022).
On the other hand, the properties of galaxies and their dependence on the
cosmic web are crucial for understanding their formation and evolution. It is
well established that galaxy local environment ($\lesssim 5\,{\rm Mpc}$)
strongly affects their star formation activity, colors and morphology (e.g.
Dressler, 1980; Balogh et al., 2004; Kauffmann et al., 2004; Bamford et al.,
2009; Peng et al., 2010; Woo et al., 2013; Old et al., 2020). These works show
that galaxies tend to be less star-forming, redder and more elliptical as
local density increases. On the other hand, galaxies and their local
environments are embedded in different large-scale environments ($\gtrsim
10-100\,{\rm Mpc}$) of the cosmic web (like cosmic voids, walls, filaments).
However, the role of such environments on galaxy formation and evolution
remains a matter of debate (e.g. Alfaro et al., 2022; Rodríguez-Medrano et
al., 2023; Wang et al., 2023). In this work, we employ the term environment to
denote the large-scale environment, unless stated otherwise.

The densest regions of the cosmic web are nodes and filaments. The most
massive nodes host galaxy clusters, which represent the largest entities in
the Universe that exist in a state of quasi-virial equilibrium. They feature a
deep gravitational potential well permeated by an intra-cluster medium (ICM)
of hot ionized gas. In this dense and possibly hostile environment, multiple
mechanisms influence galaxy evolution. Some of them, such as ram pressure
stripping, strangulation and tidal stripping, trigger gas depletion, leading
to the quenching of star formation (see e.g. Abadi et al. 1999; Vijayaraghavan
& Ricker 2015; Steinhauser et al. 2016; Peng et al. 2015; Gnedin 2003). Due to
these processes and frequent interactions, clusters of galaxies host galaxies
often characterized by red colours and elliptical morphologies (e.g. Dressler,
1980; Whitmore et al., 1993; Domínguez et al., 2001; Bamford et al., 2009;
Paulino-Afonso et al., 2019).

Nodes are connected by filaments, elongated structures which have undergone
gravitational collapse along two principal axes. They represent a kind of
bridges along which matter flows to accrete into nodes. Filaments are the
predominant visual features within the cosmic web and host galaxies which tend
to exhibit a larger mass, a redder color, and earlier-type morphologies
compared to their counterparts in less dense environments (Chen et al., 2017;
Laigle et al., 2018; Kraljic et al., 2018; Kuutma et al., 2017).

In contrast to high-density regions, large voids represent the extremely low-
density environment characterized by reduced galaxy mergers and interactions
compared to the field or groups. Cosmic voids represent a unique and pristine
environment where galaxies are unaffected by the transformation processes
typical of over-dense galaxy systems, like clusters and groups. Thus, they
allow to study galaxy evolution as a result of nature only, without nurture.

Numerous studies have focused on galaxies in cosmic voids and found that they
appear to have significantly different properties than field galaxies. The
luminosity function of galaxies in voids (e.g. Hoyle et al. 2005) shows a
fainter characteristic magnitude. However, the relative importance of faint
galaxies is similar to that found in the field. Spectroscopic and photometric
properties of void galaxies have also been studied in detail (Rojas et al.,
2005; Hoyle et al., 2005, 2012; Kreckel et al., 2012). These results indicate
that galaxies inside voids have higher star formation rates and bluer colours
than galaxies in denser regions and are still forming stars at a rate
relatively closer to the past one. Statistical studies using observational
data report that void galaxies are smaller, bluer, later-type morphology and
more star-forming than those in average density environment (Grogin & Geller,
2000; Rojas et al., 2004; Hoyle et al., 2005; Patiri et al., 2006; Park et
al., 2007; Wegner & Grogin, 2008; Kreckel et al., 2011; Liu et al., 2015;
Tavasoli et al., 2015; Moorman et al., 2016; Beygu et al., 2017; Ceccarelli et
al., 2021; Jian et al., 2022). Finally, we mention the relevant result
recently presented by Domínguez-Gómez et al. (2023), within the context of
CAVITY project. The authors of the latter work performed a spectral analysis
on a sample of nearby galaxies in voids, filaments and walls, and clusters.
They find a clear correlation between the density of the large-scale
environment and the star formation history (SFH), namely galaxies in less
dense environments feature a slower SFH, that is, void galaxies assemble their
stellar mass slower.

On the theoretical side, both hydrodynamic simulations and semi-analytic
models (SAMs) have been used to shed light on the influence of the large-scale
environment on galaxy evolution. Kreckel et al. (2011) identified higher star
formation rates and younger stellar ages in void galaxies through their
hydrodynamic simulation. Rieder et al. (2013) studied the formation of
(sub)structures in the halo distribution in voids, within the context of the
Cosmogrid simulation. Habouzit et al. (2020) employed the Horizon-AGN
simulation (Dubois et al., 2014), coupled to the VIDE void finder (Sutter et
al., 2015), in order to investigate the black hole population within cosmic
voids. They reported no significant variations in black hole growth in voids
compared to more dense environments. Rosas-Guevara et al. (2022) studied
central galaxies located within and near voids using the EAGLE simulation
(Schaye et al., 2015; Crain et al., 2015) and the spherical voids catalog by
Paillas et al. (2017). They analyzed in detail the star formation,
metallicity, morphology and assembly history of galaxies as a function of
their stellar mass and environment. Alfaro et al. (2020, 2021) studied the
Halo Occupation Distribution (HOD) in cosmic voids and Future Virialized
Structures (FVS). Making use of the semi-analytic catalog MDPL2-SAG (Knebe et
al., 2018; Cora et al., 2018) and the hydrodynamic simulation TNG300
(Pillepich et al., 2018), they found a lower(higher) than average HOD and
formation redshift in voids(FVS). Finally, Jaber et al. (2023) exploited the
SAGE SAM (Croton et al., 2016) and the Spine-Web algorithm (Aragón-Calvo et
al., 2010) to study the large-scale dependence of the metallicity and stellar-
to-halo mass ratio. Their results indicate the presence of a threshold mass
(respectively $M_{\rm halo}\simeq 10^{12}\,M_{\odot}/h$ and $M_{\rm
stars}\simeq 10^{10}\,M_{\odot}/h$) below which the stellar-to-halo ratio and
metallicity are enhanced in dense environments.

Despite the substantial achievements of these studies, we still need a
complete understanding of how galaxy properties correlate with the large-scale
environment. The distinct underlying physical models within different
simulations and the lack of a single, clear-cut definition for large-scale
environments hinder a direct comparison of results. Furthermore, such
complexities make it challenging to establish the relative impact of different
physical mechanisms on galaxy evolution in distinct environments.

In this work, we study the dependence on the large-scale environment of the
star formation and, for the first time, the dust content of local galaxies. We
use a galaxy catalog obtained from a SAM, and different methods are adopted to
identify cosmic environments, namely voids, walls, filaments, and nodes. The
primary advantage of our approach lies in the computational efficiency of the
SAM method, enabling us to simulate relatively large volumes. This capability
is essential for obtaining a reliable statistical representation of large-
scale cosmic environments. Furthermore, the simplicity of running the SAM, and
the subsequent ability to test various physical models, makes easier the
identification of the role of different physical processes in shaping the
environmental dependence of galaxies properties. Also, adopting multiple
methods to define environments enhances the reliability of our results and
mitigates the inherent arbitrariness in defining large-scale structures.

In order to check our results, we compare them with observations. We use the
Sloan Sky Digital Survey (SDSS-DR16) for environmental classification, stellar
mass and star formation rates. At the same time, for a subset of galaxies, we
utilize dust mass measurements from the GAMA and H-ATLAS surveys. Our
qualitative comparison yields highly encouraging results, highlighting the
significance of the in situ supermassive black hole (SMBH) growth mechanism,
specifically secular accretion during disc instabilities (DIs) in our case. In
a broader context, our work underscores the importance of investigating galaxy
evolution in diverse environments as a possible way to assess the relative
significance of in situ and ex situ processes.

The paper is organized as follows. The adopted SAM and the observational data
are briefly described, respectively, in Sec. 2 and 3. In Sec. 4 we describe
the process of environment classification in both the simulated and observed
samples. The star formation and dust content of simulated galaxies in
different large-scale environments, as well as their evolution, are
investigated in Sec. 5.1 and 5.2, while Sec. 5.3 focuses on the impact of the
DI-driven SMBH growth. In Sec. 6 we compare the SAM results with observations,
and finally we draw our conclusions, after summarizing the work, in Sec. 7.

##  2 The semi-analytic model

SAMs are valuable tools for studying galaxy evolution, owing to their
exceptional capability to simulate extensive volumes while providing a
comprehensive albeit simplified representation of numerous physical processes
that shape the properties of galaxies (e.g. White & Frenk, 1991; Cole et al.,
2000). SAMs provide simplified descriptions of baryonic processes shaping
galaxy populations within Dark Matter (DM) halos merger trees. These processes
include gas inflow, cooling, star formation, SMBH growth and feedback effects.
The assumed sequence begins with gas collapse, forming rotation-supported gas
disks with mild star formation. Spheroidal galaxies result from mergers and
instabilities, potentially leading to starbursts. Also, environmental effects,
e.g. ram pressure and tidal forces, are often considered. These baryonic
processes are modeled through approximate and motivated relationships to
evolve the galaxy population over time.

In this work we adopt the last public release111The source code is available
at
https://github.com/LGalaxiesPublicRelease/LGalaxies_PublicRepository/releases/tag/Henriques2020
of the Munich galaxy formation model, L-Galaxies (Henriques et al., 2020),
along with the updates introduced and discussed in Parente et al. (2023),
hereafter P23. In the latter work we implemented a detailed treatment of dust
grains formation and evolution, as well as an updated treatment of disc
instabilities (DIs). The dust model (Sec. 2.1 of P23) includes two sizes
(large and small grains, with radii $0.05$ and $0.005\,\mu{\rm m}$) and two
chemical compositions (silicate and carbonaceous, MgFeSiO4 and C) of grains.
Briefly, grains are produced in AGB stars envelopes and type-II SNe ejecta,
thus ejected into the surrounding gaseous medium. Here, the model takes into
account different processes, which affect the mass (grains accretion,
destruction in SNe shocks, thermal sputtering) and the size (shattering,
coagulation) evolution of grains. These processes depend on the physical
properties of the galaxy as provided by the SAM (e.g. molecular gas fraction,
gas temperature, metallicity). As for the new treatment of DIs (Sec. 2.2 of
P23), we now consider the instability of the combined gas+stars disc (only the
stellar disc was considered in Henriques et al., 2020). The unstable stellar
component is transferred into the bulge component, while the unstable gas is
allowed to make a starburst and a fraction $f_{\rm BH,\,DI}$ accretes the
central SMBH.

These modifications allow our SAM to reproduce a broad range of galaxy
properties concerning dust, in particular the cosmic evolution of the galactic
dust abundance, and the local fraction of elliptical galaxies, still
reproducing several crucial properties of the galaxy population (e.g. cosmic
star formation, mass functions). Among the modifications introduced, the SMBH
growth during DIs is particularly relevant since it actively operates to
reduce star formation in the most massive objects due to the radio-mode AGN
feedback, and it turns out to be very relevant for the results presented here
(see extended discussion in Sec. 5.3). For this reason, along with the
standard fiducial (FID) version of P23, in the following we will often discuss
results obtained by switching off the SMBH growth channel during DIs ($f_{\rm
BH,\,DI}=0$)222This means setting $f_{\rm BH}=0$ in Eq. 23 of P23..

Finally, regarding environmental processes, the adopted version of the
L-Galaxies models tidal stripping, ram-pressure stripping, and tidal
disruption, all processes that shape the properties of satellite galaxies. A
detailed overview of these processes is available in the supplementary
material of Henriques et al. (2020, but see also  for an improved treatment of
environmental processes within the L-Galaxies framework).

The SAM is run on top of the Millennium merger trees (Springel et al. 2005,
box size $500{\rm Mpc}/h$, $2160^{3}$ particles), and a Planck cosmology333The
cosmology originally adopted in the Millennium simulation has been scaled
according to Angulo & White (2010) and Angulo & Hilbert (2015). (Planck
Collaboration et al., 2014) is assumed throughout this work ($h=0.673$,
$\Omega_{\rm m}=0.315$, $\Omega_{\rm b}=0.0487$, $\sigma_{8}=0.829$). A
Chabrier (2003) initial mass function (IMF) is adopted. We analyse galaxies
with a stellar mass content of at least $\log(M_{\rm stars}/M_{\odot})\geq 9$,
which approximately corresponds to the resolution limit of the underlying DM
simulation (e.g. Guo et al., 2011).

##  3 Observational Data

We exploit different data sets to test our model predictions concerning the
star formation and dust content of galaxies in different environments. We use
the Sloan Digital Sky Survey (SDSS) Data Release DR16 (Ahumada et al., 2020)
to identify cosmic environments. We use galaxies with $r-$band apparent
magnitudes $r<17.77$ (completeness limit) and in the redshift range
$0.02<z<0.1$. We take stellar masses and star formation rates from the MPA-JHU
catalog (Kauffmann et al., 2003).

As for dust masses, we exploit the results presented in Beeston et al. (2018),
who studied the local ($z<0.1$) dust mass function for galaxies in the
GAMA/H-ATLAS surveys. Specifically, the physical properties of these galaxies
(including dust mass) were obtained by Driver et al. (2018) using a spectral
energy distribution (SED) fitting procedure.

##  4 Environmental classification

We employ various methods to identify cosmic environments within the simulated
and observed large-scale structures. We categorize environments in two
fundamental ways: one involves employing a single and homogeneous method,
NEXUS+, to segment the cosmic web into voids, walls, filaments and nodes; the
other approach utilizes multiple independent methods for identifying specific
environments (voids and walls, filaments, and groups). The former is
exclusively applied to the simulation, while the latter is employed in both
the observed and simulated galaxy catalogs. We emphasize that the objective of
our study is not to compare the performances of different identification
algorithms. Indeed, no tuning of their parameters has been made to match
environments extracted from NEXUS+ to those extracted from the void, filament,
and group finders (see Fig. 1). Instead, our focus is on examining the
consistency and reliability of our results concerning the influence of the
environment on galaxy properties, regardless of the method used to identify
the different environments.

In the following sections, we introduce each specific environment we focus on
and a comprehensive overview of each identification method adopted.

###  4.1 Cosmic web segmentation: NEXUS+

For the segmentation of the simulated cosmic web into its distinct structural
environments we use the Multiscale Morphology Filter (MMF)/NEXUS pipeline,
specifically its NEXUS+ version (Cautun et al., 2013, 2014). It is the highest
dynamic range version of the library of routines for pattern classification
based on the MMF/NEXUS formalism (Aragón-Calvo et al., 2007, 2010; Cautun et
al., 2013, 2014; Aragon-Calvo et al., 2014, see also Libeskind et al. 2018 for
a short review). This formalism represents a scale adaptive framework that
classifies the matter distribution on the basis of local spatial variations in
either the density field, velocity field or gravity field. Subsequently, a set
of morphological filters is used to classify the spatial matter distribution
into three basic components, the clusters, filaments and walls that constitute
the cosmic web. The remaining volume elements are classified as part of voids.
The end product of the pipeline is a a map in which for each location in the
analyzed volume the morphological identity is specified.

In practice, NEXUS+ takes as input a regularly sampled density field, which we
obtain by projecting the halo distribution to a regular grid using the cloud-
in-cell interpolation scheme. In a first step, the input field is Gaussian
smoothed using a Log-density filter that is applied over a set of scales from
$1$ to $11h^{-1}\mathrm{Mpc}$. It results in a map of $1024^{3}$ cells,
corresponding to a cellsize of $0.472h^{-1}\mathrm{Mpc}$. Then, for each
smoothing scale, the resulting density is used to calculate the Hessian matrix
and its corresponding eigenvalues, whose values and signs determine the
environment response at each location, i.e. grid cell. In the last step,
NEXUS+ combines the environmental signature of all the scales to obtain a
scale-independent value. In this work, roughly $79.3\%$ of the total volume of
the box corresponds to cells located in voids, $14.5\%$ is classified as a
belonging to a walls, $6.0\%$ as located in filaments and a mere $0.2\%$
correspond to nodes. Assigning to each halo the environment of it hosting
cell, we find that, out of the total DM mass within the box, $9.5\%$ resides
in voids, $16.9\%$ in walls, $34.5\%$ in filaments and $39.1\%$ in the cluster
nodes of the cosmic web.

###  4.2 Spherical voids identification

We use the spherical void finder algorithm presented in Ruiz et al. (2015);
Ruiz et al. (2019) as an alternative method to construct our voids catalog.
This method aims at identifying the largest and non-overlapping spherical
regions that satisfy that the number density of tracers inside them is less
than 10 percent of the mean:

$\Delta(R_{\rm void})\leq-0.9,$ (1)

where $\Delta(r)$ is the integrated density contrast at scale $r$ and $R_{\rm
void}$ is the void radius.

We use the DM halos as structure tracers when applying this algorithm to our
SAM galaxies. We adopt $M_{\rm halo}\geq 10^{12}h^{-1}{\rm{M_{\odot}}}$ as
halo mass cut, obtaining 2729 voids. After constructing the voids catalog, we
define void galaxies as those residing within $r/r_{\rm void}\leq 1$ and void
wall galaxies as those located immediately outside the voids with $1<r/r_{\rm
void}\leq 1.2$.

The same algorithm is adopted to identify voids on top of the observational
catalog. Details about the algorithm application to observational samples are
provided in Ruiz et al. (2019). Specifically, in this work the void
identification is the same as in Rodríguez-Medrano et al. (2023, see their
Sec. 2.1). Voids are identified in a volume complete sample with limiting
redshift $z=0.1$ and maximum absolute magnitude in the r band $M_{\rm r}-5{\rm
log}h=-20$ extracted from the main SDSS region. In our analysis, we have
discarded voids close to the edge of the catalog, namely, void centers at
distances smaller than $1.8r_{\rm void}$. Starting from this voids catalog we
then define void ($r/r_{\rm void}\leq 1$) and void wall galaxies ($1<r/r_{\rm
void}\leq 1.2$).

###  4.3 Filaments and groups identification

As for the more dense environments, we also identify galaxy groups and
filaments with an alternative approach. Galaxy groups are identified with FOF
haloes in our SAM catalog. As for observed galaxies, we utilize the groups
catalog presented by Rodriguez et al. (2022), which is derived from the SDSS-
DR16 using the algorithm introduced in Rodriguez & Merchán (2020). This method
initially applies the FOF algorithm to identify galaxy systems that are
gravitationally bound and have at least one bright galaxy with an r-band
absolute magnitude brighter than -19.5. Subsequently, a halo-based algorithm
(Yang et al., 2005, 2007) is applied. A three-dimensional density contrast is
calculated in redshift space using a characteristic luminosity calculated with
the potential FOF galaxy members. The estimation procedure considers the
incompleteness caused by the observational catalog’s limiting magnitude. Next,
by abundance matching on luminosity, the mass of each group is assigned.
Assuming that galaxies populate the DM halos following a Navarro, Frenk &
White (1997) profile and using the assigned mass, the three-dimensional
density contrast is calculated to associate galaxies to the groups. With this
last assignment of members, the procedure recalculates the characteristic
luminosity and iterates until it converges. This algorithm showed excellent
results in purity and completeness (Rodriguez & Merchán, 2020).

Once galaxy groups are identified, they are used to build a catalog of
filaments in the large scale structure. They are cylinders linking groups of
galaxies. Our approach is similar to the filament identification carried out
by Taverna et al. (2023), which, in turn, is based on the original algorithm
by Martínez et al. (2016). Starting from the group sample, we search for all
pairs of groups more massive than a selected mass cut-off $M_{\mathrm{min}}$
that are separated (in redshift space in the case of the observations) by a
comoving distance smaller than a given threshold $\Delta_{\mathrm{max}}$. For
each pair of groups thus selected, we compute the numerical overdensity of
galaxies in a cylinder of radius $R$ that extends between the two groups. The
overdensity in this volume is obtained by the ratio between the number of
galaxies that lie in the cylinder, and the number of points within the same
cylinder from an unclustered homogeneous distribution of points. This
homogeneous distribution of points mimics the selection function of galaxies
while being 100 times denser in order to reduce shot noise in the overdensity
computation. We require the numerical overdensity of galaxies in the cylinder
to be greater than unity in order to consider a pair of groups are linked by a
filament. Galaxies in these cylindric regions are considered to be galaxies in
filaments.

In this work we use $M_{\mathrm{min}}=10^{13.5}\,M_{\odot}$,
$\Delta_{\mathrm{max}}=20\ $Mpc, which is the correlation length of groups
more massive than $M_{\mathrm{min}}$ according to Zandivarez et al. (2003),
and $R=2.2\ $Mpc (see Taverna et al. 2023). For the SDSS-DR16 groups and
galaxies, our unclustered homogeneous distribution of points mimics the
selection function of SDSS-DR16 galaxies in terms of angular coverage and
redshift distribution.

##  5 Properties of galaxies across cosmic environments

Figure 1: A $25\,{\rm Mpc}/h$ slice of our simulation box showing the outcomes
of the environments identification process. Each point represents a DM halo,
and is color-coded according to the assigned environment. The left panel shows
the results obtained by NEXUS+, which categorizes each DM halo of the
simulation as belonging to a void, wall, filament, or node. On the right panel
we show the combination of the specific identifiers for distinct environments
(R19+T23+FOF), i.e. spherical voids and their walls, cylindric filaments, and
massive groups ($M_{\rm group}>10^{13.5}\,M_{\odot}$). It is important to note
that, in this case, a DM halo may not necessarily belong to a specific
environment.

This section examines various physical properties of our simulated galaxies in
different environments. Namely, we look at the star formation and dust
content. The environmental dependence of dusty properties, such as the Dust-
to-Gas (DTG) ratio, the size and chemical composition of dust grains, is
discussed in App. B.

In the following analysis, we show the results for the NEXUS+ environments
(voids, walls, filaments and nodes), as well as for the other environments
definitions adopted in this work, namely spherical voids and their associated
walls, cylindrical filaments and massive groups ($M_{\rm
group}>10^{13.5}\,M_{\odot}$). The combination of the latter environments,
obtained by means of specific identifiers, will be often dubbed as
R19+T23+FOF. A visual representation of the environments identification in our
simulated box can be appreciated in Fig. 1 for both the aforementioned
methods.

###  5.1 Star Formation and Dust

The environment selection introduces a mass bias, namely, more massive
galaxies are associated with more clustered environments (App. A). To avoid
this issue, we could study the properties of galaxies with identical stellar
mass distribution in different environments. The procedure of selecting
samples with the same mass distribution as in voids certainly removes the mass
bias, however, since void galaxies are typically less massive than the whole
population, this analysis may not be representative of the full range of
$M_{\rm stars}$. For this reason, in this section we analyze galaxy properties
in different environments at fixed stellar mass.

We show in Fig. 2 the specific Star Formation Rate (sSFR) and dust mass as a
function of stellar mass. In the range $9\leq{\rm log}\,M_{\rm
stars}/M_{\odot}\lesssim 10.8$ we observe a clear trend with the environment,
regardless of the environment definitions adopted. Namely, at fixed stellar
mass, the less dense is the environment, the more star-forming and dust-rich
are the galaxies. Above this stellar mass value, we observe no clear trend
with the environment for the sSFR. As for the dust mass, differences among
environments are strongly reduced. This result suggests that the environmental
dependence of dust and star formation properties is suppressed in galaxies
above the stellar mass threshold. We will discuss this point at length in the
following.

We note that our finding of higher star formation in voids is in keeping with
some observational results which pointed out that void galaxies are typically
more SF and gas-rich than non-void ones (e.g. Rojas et al. 2005; von Benda-
Beckmann & Müller 2008; Kreckel et al. 2014; Beygu et al. 2016; Moorman et al.
2016; Florez et al. 2021). The same has also been found in numerical
simulations (e.g. Cen 2011; but see also Rosas-Guevara et al. 2022, who found
different environmental trends in different stellar mass regimes). Our
findings are also consistent with Martínez et al. (2016) particularly in
relation to the sSFR of filament galaxies. These rates are intermediate
falling between those observed in groups and those in less dense environments.
They additionally find indications that variations among environments are less
pronounced when considering high mass galaxies.

Figure 2: Specific SFR (left panel) and dust mass (right panel) as a function
of stellar mass for simulated galaxies in different environments. We report
the results for NEXUS+ environments (voids, walls, filaments and nodes, top
panels), as well as for the other environments definitions adopted in this
work, namely spherical voids and their walls, cylindrical filaments and
massive groups (R19+T23+FOF, bottom panels). Solid lines represent median
trends, with the typical $16-84$th percentile dispersion shown as a gray
shaded area.

###  5.2 Galaxy evolution across environments

Figure 3: Mass-weighted stellar populations age as a function of stellar mass
for simulated galaxies in different environments, as detailed in Fig. 2.

The scenario depicted above may be understood if galaxies undergo a slower
evolutionary process in less dense environments. This idea is corroborated by
the mass-weighted age of stellar populations, displayed in Fig. 3, which
suggests the existence of a relationship between age and environment for
$M_{\rm stars}\lesssim 10^{10.8}\,M_{\odot}$. Voids galaxies are the youngest
and nodes (or massive groups) galaxies exhibit the oldest ages. Walls and
filaments galaxies fall in between, with filament galaxies systematically
displaying older ages compared to wall galaxies. We devote this section to
further investigation of this point. In particular, we aim to understand the
differences in the evolution of galaxies with equal stellar mass at $z=0$, but
residing in different environments.

We thus inspect the stellar mass444Normalized to the $z=0$ value., SFR, and
dust mass evolution for galaxies with $M_{\rm stars}^{z=0}/M_{\odot}\simeq
10^{9},\,10^{10},\,10^{10.5},\,{\rm and}\,10^{11}$ in Fig. 4. The figures
indicate that the denser is the environment, the faster is the evolution for
$M_{\rm stars}^{z=0}\leq 10^{10.5}\,M_{\odot}$, in the sense that the SFR
peaks at earlier epochs, and consequently the evolution of the stellar mass is
more rapid. This holds true irrespective of the chosen environments
definition. As for the dust mass evolution, it reaches a maximum more recently
than the SFR, suggesting that the time of the maximum dust content of a galaxy
does not correspond to the time of the maximum of its star formation activity.
We argue that this is due to the fact that the dust budget is determined not
only by the production of dust by stars but also by its evolution, and by
grains accretion in particular555The efficiency of the accretion process is
delayed with respect to the dust production by stars also on a cosmic scale,
as can be appreciated in Fig. 11 of P23.. We also note that the peak of the
dust abundance occurs later in lower density environments and in lower $M_{\rm
stars}^{z=0}$ objects. This maximum has yet to be reached in voids and wall
galaxies of the less massive $M_{\rm stars}^{z=0}$ bin. This is consistent
with the slower evolution of galaxies in lower density environments.

The slower stellar assembly in less dense environments has already been
pointed out by other works based on hydrodynamical simulations (Artale et al.,
2018; Alfaro et al., 2020; Habouzit et al., 2020; Rosas-Guevara et al., 2022),
and recently confirmed through observations by Domínguez-Gómez et al. (2023).

As for the most massive stellar bin under examination, galaxies with
$M^{z=0}_{\rm stars}\simeq 10^{11}M_{\odot}$ show no notable distinctions
across diverse environments. The lack of differences in the evolution of these
high-mass galaxies aligns with the findings discussed in Sec. 5.1, which
suggest the existence of a certain stellar mass threshold ($\simeq
10^{10.8}\,M_{\odot}$) above which the influence of the large-scale
environments becomes less relevant.

Interestingly, the observational study of Domínguez-Gómez et al. (2023) found
smaller disparities in the assembly time of massive galaxies (log $M_{\rm
stars}/M_{\odot}\simeq 10.5-11$) belonging to different environments in
comparison to those reported for less massive galaxies (their Fig. 4a and 4d).

Figure 4: Stellar mass (top panels), SFR (middle panels), and dust mass
(bottom panels) evolution for galaxies with different values of the present-
day stellar mass, namely (from left to right) $M_{\rm
stars}^{z=0}/M_{\odot}\simeq 10^{9},\,10^{10},\,10^{10.5},\,{\rm
and}\,10^{11}$. For each quantity, we report the results for galaxies residing
at $z=0$ in different NEXUS+ environments (voids, walls, filaments and nodes),
as well as for the other environments definitions adopted in this work, namely
spherical voids and their walls, cylindrical filaments and massive groups
(R19+T23+FOF). Colors are as in previous figures. For each environment, we
randomly selected $\sim 10^{3}$ objects with $M_{\rm stars}^{z=0}$ in a narrow
range ($0.1\,{\rm dex}$) around the reported value, and traced their
evolutionary paths along the merger tree back in time. Solid lines represent
median trends, with the $16-84$th percentile dispersion shown as a shaded
area.

###  5.3 The impact of in situ SMBH growth on isolated galaxies evolution

Figure 5: Mean number of mergers (left panel) and ex situ fraction of the
total stellar mass (right panel) as a function of stellar mass for simulated
galaxies. We report the results for galaxies residing at $z=0$ in different
NEXUS+ environments (voids, walls, filaments and nodes, top panels), as well
as for the other environments definitions adopted in this work, namely
spherical voids and their walls, cylindrical filaments and massive groups
(R19+T23+FOF, bottom panels). Results from both the fiducial (solid) and
$f_{\rm BH,\,DI}=0$ (dotted) SAM are shown.

The latter result(s) is quite interesting. It suggests that the environmental
dependence of galaxy evolution is important up to some characteristic mass
(log $M_{\rm stars}/M_{\odot}\simeq 10.8$ in our model). Above this threshold,
galaxies in different large-scale environments and the same stellar mass
feature very similar properties.

This outcome is due to the treatment of SMBH growth and feedback, the main
channel of massive galaxies quenching in our SAM. More in detail, in our
model, SMBHs can grow during mergers, by hot gas accretion, and during disc
instabilities (DIs). The latter channel has been introduced in P23666The other
two channels are left as in the public L-Galaxies release (Henriques et al.,
2020). and has a profound impact on the results discussed in this work.

We demonstrate this by comparing the results obtained by our fiducial (FID)
SAM and a version in which the SMBH growth in DIs is switched off ($f_{\rm
BH,\,DI}=0$). In particular, Fig. 5 displays the number of mergers experienced
up to $z=0$ and the fraction of stellar mass assembled ex situ (i.e. in
mergers) for galaxies in distinct environments for both models. In the $f_{\rm
BH,\,DI}=0$ model there are evident differences across environments for ${\rm
log}\,M_{\rm stars}/M_{\odot}\gtrsim 10.8$, namely the denser the environment,
the larger the number of mergers experienced at $z=0$, and consequently the
fraction of stellar mass assembled ex situ. However, these differences are not
present in the FID model. At first glance, this is quite surprising since we
would expect the number of mergers to be independent of the baryonic physics
implemented within the model, as it is determined by the adopted DM halos
merger tree777Actually, the number of mergers experienced by a galaxy up to a
certain redshift also depends on the time a galaxy need to merge once its
associated DM subhalo merged. In our SAM, such a merging time is estimated
with the dynamical friction timescale (Binney & Tremaine, 1987), as detailed
in Sec. S1.16.1 of the supplementary material of Henriques et al. (2020)..

The reason why our novel888We clarify that the SMBH growth during DIs is not a
novelty in the panorama of SAMs, since it has been adopted by the community
for a long time (e.g. Croton et al., 2016; Lacey et al., 2016; Lagos et al.,
2018), also in the context of the same L-Galaxies model (Irodotou et al.,
2019; Izquierdo-Villalba et al., 2020). The wording novel adopted here has to
be intended as novel with respect to the public release of the L-Galaxies SAM
(Henriques et al., 2020). in situ SMBH growth channel produces such
differences may be understood in the following picture. The DI-driven SMBH
growth enhances the quenching of the most massive objects (P23), thus only
galaxies that can accumulate a significant mass fraction through mergers are
capable of reaching large stellar masses (${\rm log}\,M_{\rm
stars}/M_{\odot}\gtrsim 10.8$), since the in situ star formation is suppressed
by the instability-driven SMBH growth. This effect is particularly pronounced
in galaxies located in less dense environments, which generally undergo fewer
merger events. This is the reason why also the fraction of stellar mass formed
through mergers, i.e. acquired ex situ, is influenced by our DI model (Fig.
5).

In other words, according to our fiducial SAM, only galaxies which acquire a
substantial stellar mass from mergers can reach large $M_{\rm stars}\,(\gtrsim
10^{10.8}\,M_{\odot})$.

Concluding this section, it is worth remarking that our DI model significantly
modifies the in situ evolution of galaxies999Nonetheless, we note that our
model still reproduces many crucial properties of the galaxy population,
including the Stellar Mass Function, which is only mildly affected by the DI
model (Sec. 3.1 P23)., particularly impacting the environmental dependence of
certain properties. This is not surprising, considering mergers’ prominent
role in shaping galaxy evolution within SAM frameworks. Consequently, we
speculate that a thorough (also observational) study of galaxy properties in
different cosmic environments could serve as an effective test bench for
assessing the relative significance of the in situ and ex situ processes
implemented within SAMs. We perform a step in this direction in Sec. 6, where
we compare the specific SFR and dust content for the FID and $f_{\rm
BH,\,DI}=0$ models across different large-scale environments with
observations.

Finally, it is noteworthy that Jaber et al. (2023), using the SAGE SAM,
observed a significant increase in metallicities for galaxies located in the
densest environments compared to the entire sample. However, similar to our
findings, the influence of the environment disappears for galaxies with
stellar masses exceeding $\simeq 10^{10}M_{\odot}/h$. It is notable that their
model also utilizes unstable cold gas to fuel the growth of central black
holes, although they do not attribute the observed result to this mechanism.

###  5.4 Convergence mass and SMBH growth

Figure 6: Convergence mass for different runs where the parameter ruling the
DI-driven SMBH growth ($f_{\rm BH,\,DI}$) is modified by a constant factor,
specifically $f_{\rm BH,\,DI}$ x $0.2,\,0.5,\,2,\,5,\,{\rm and}\,10$. The
convergence mass is the stellar mass above which the $M_{\rm stars}-{\rm
sSFR}$ relation show no discernible differences among galaxies belonging to
different environments, at fixed stellar mass. We report the results obtained
with NEXUS+ environments (purple crosses) as well as for the other
environments definitions adopted in this work, namely spherical voids and
their walls, cylindrical filaments and massive FOF groups (green circles,
R19+T23+FOF).

Based on the previous discussion, it becomes clear that there is a stellar
mass threshold beyond which no noticeable distinctions exist among galaxies in
various environments, given a constant stellar mass. In our reference model,
this convergence mass may exhibit slight variations depending on the property
under consideration and the method used to identify the different
environments. However, it is approximately $M_{\rm
conv}\simeq{10^{10.8}}M_{\odot}$ for both the sSFR and dust mass (Fig. 2). In
Sec. 5.3 we have shown that this behaviour is due to the DI-driven SMBH growth
channel. This process is regulated by the parameter $f_{\rm BH,\,DI}$,
representing the fraction of unstable gas that undergoes accretion onto the BH
during episodes of DIs ($f_{\rm BH,\,unst}$ in Eq. 23 P23). Here we assess the
stability of the convergence mass to changes in $f_{\rm BH,\,DI}$ when using
different environments identifiers: NEXUS+ on one hand; or specific
identifiers for distinct environments $-$ spherical voids, cylindrical
filaments and massive halos $-$ on the other hand (R19+T23+FOF).

To this aim, we operationally define the convergence mass as follows. We
calculate the median trends of the $M_{\rm stars}-{\rm sSFR}$ relation101010A
similar approach can be applied to the $M_{\rm stars}-{M_{\rm dust}}$
relation. for all the environments, as reported in Fig. 2. We employ stellar
mass bins of $0.1\,{\rm dex}$. The convergence mass $M_{\rm conv}$ is
identified as the smallest $M_{\rm stars}$ value where the median ${\rm sSFR}$
for all environments falls within a range of $0.2\,{\rm dex}$. We compute
$M_{\rm conv}$ for different runs in which we modify only the $f_{\rm
BH,\,DI}$ parameter by a constant factor, specifically $f_{\rm BH,\,DI}$ x
$0.2,\,0.5,\,2,\,5,\,{\rm and}\,10$. The results for the convergence mass
obtained in these experiments are reported in Fig. 6.

The general trend suggests that, regardless of the environment classification
process, the convergence mass decreases as the efficiency of the DI-driven
SMBH growth increases. This is because higher values of $f_{\rm BH,\,DI}$ lead
to more efficient and rapid SMBH growth, enabling these objects and their
associated feedback to be relevant in less massive systems. A departure of a
factor of 2 from the fiducial x1 value implies a variation of approximately
$0.2\,{\rm dex}$ in $M_{\rm conv}$.

It is important to note that the parameters defining $f_{\rm BH,\,DI}$ allow
our model to reproduce the local SMF and the fractions of quenched galaxies at
different masses (Sec. 3.1 of P23, ) and were not further adjusted in the
present work. Interestingly, as will be seen in Sec. 6, the convergence mass
also manifests in observed galaxy samples.

##  6 Comparison with observations

|  |  | Number of galaxies
---|---|---|---
Environment | Algorithm | Criterion | SDSS | GAMA/H-ATLAS
|  |  | catalog | sample
Voids | Ruiz et al. (2015); Ruiz et al. (2019) | $r/r_{\rm void}\leq 1$ | 9367 | 95
Walls | Ruiz et al. (2015); Ruiz et al. (2019) | $1<r/r_{\rm void}\leq 1.2$ | 16863 | 138
Filaments | Taverna et al. (2023) | $M_{\rm nodes}\geq 10^{13.5}\,M_{\odot}$ | 12556 | 395
Massive groups | Rodriguez & Merchán (2020) | $M_{\rm groups}\geq 10^{13.5}\,M_{\odot}$ | 35161 | 380
Table 1: Details on the environment identification performed on the SDSS-DR16
catalog (see Sec. 4). For each environment (voids, walls, filaments, and
massive groups), we report the identification method adopted and the number of
galaxies identified in the SDSS catalog and GAMA/H-ATLAS sample.

In this section, we compare observations with our SAM predictions. As for our
simulated galaxies, in order to highlight the importance of the in situ, DI-
driven, SMBH growth channel, we compare the predictions obtained from our
fiducial version of the SAM with the aforementioned scenario where SMBH
accretion during DIs is switched off ($f_{\rm BH,\,DI}=0$).

Our goal is to compare the environments identified in the simulated and
observed samples as fairly as possible, exploiting the identification methods
detailed in Sec. 4. Specifically, here we focus on four different
environments, ranging from low to high large-scale density:

  * •

Voids In both the observed and simulated catalogs we take galaxies residing
within the spherical voids as identified by the Ruiz et al. (2015); Ruiz et
al. (2019) algorithm (Sec. 4.2).

  * •

Walls This category includes galaxies in the proximity $(1<r/r_{\rm void}\leq
1.2)$ of the aforementioned spherical voids.

  * •

Filaments Galaxies within filaments are identified using the Taverna et al.
(2023) algorithm, as applied to both the observed and simulated galaxy samples
(Sec. 4.3).

  * •

Massive groups These are galaxies belonging to groups more massive than
$M_{\rm group}>10^{13.5}M_{\odot}$. In the observational catalog the group
mass is estimated by the Rodriguez & Merchán (2020) algorithm, while in our
SAM we take the virial mass of the FOF halo (Sec. 4.3). We take these galaxies
as representative of the densest regions of the large-scale
structure111111This is reasonable since, in our model, galaxies in groups with
$M_{\rm group}/M_{\odot}>10^{13.5}$ are associated with the densest
environments identified by NEXUS+: the $\sim 96\%$ of the mass of massive
groups belongs to nodes, the $\gtrsim 99.7\%$ to filaments and nodes as
identified by NEXUS+..

The criteria employed and the number of objects identified in each environment
within the observed galaxies catalog are summarized in Table 1.
We emphasize that our purpose is not to conduct a one-to-one comparison
between environments in observations and simulations. Instead, our main
interest is comparing trends among the environments of the two samples.

###  6.1 Star formation

Figure 7: Specific star formation rate distributions for galaxies in different
stellar mass bins, namely (from left to right) ${\rm log}\,{M_{\rm
stars}/M_{\odot}}\in(9.5-10),\,(10-10.5),\,(10.5-11),\,(11-11.5)$. Results for
different cosmic environments are shown, namely (from top to bottom): voids in
blue, walls in green, filaments in orange, and massive groups ($M_{\rm
group}>10^{13.5}\,M_{\odot}$) in magenta. We report our model predictions
obtained with both the fiducial (FID) and $f_{\rm BH,\,DI}=0$ version of our
SAM (respectively solid and dotted lines). In each panel we compare with SDSS
data, shown as filled histograms. Environmental classification in both the
observed and simulated catalog is performed as detailed in Sec. 6 (see also
Table 1).  Figure 8: Fraction of passive galaxies (${\rm sSFR}<10^{-11}\,{\rm
yr}^{-1}$; top panel) and sSFR (bottom panel) as a function of stellar mass in
voids, walls, filaments and massive groups ($M_{\rm
group}>10^{13.5}\,M_{\odot}$). Colors are as in Fig. 7. We report our model
predictions obtained with both the fiducial (FID) and $f_{\rm BH,\,DI}=0$
version of our SAM (respectively solid and dotted lines). Filled circles refer
to observations (SDSS data). We also report the mean standard error associated
with observations as vertical lines and the typical $14$-$86$th dispersion of
our model predictions as a grey shaded rectangle in the right side of the
bottom panel.

In Fig. 7 we show the sSFR distributions for galaxies in different stellar
mass bins and cosmic web environments. As widely discussed in literature (e.g.
Katsianis et al., 2021), this distribution typically features a bimodal
behaviour, which corresponds to the superposition of a star-forming (${\rm
sSFR}\simeq 10^{-10}\,{\rm yr}^{-1}$) and a passive population (${\rm
sSFR}\simeq 10^{-12}\,{\rm yr}^{-1}$) at $z=0$.

From the reported observations it is clear that the larger the stellar mass
is, the larger is the prevalence of the passive population in each
environment. This pattern is even more evident when examining the fraction of
passive galaxies $f_{\rm passive}$ (defined as those featuring ${\rm
sSFR}<10^{-11}\,{\rm yr}^{-1}$) and the sSFR as a function of stellar mass,
both displayed in Fig. 8. The observed $f_{\rm passive}$(sSFR)
increases(decreases) with the density of the environment at fixed stellar mass
for $M_{\rm stars}\lesssim 10^{11}\,M_{\odot}$.

Our fiducial model displays similar trends, that is an increase of $f_{\rm
passive}$ and a decrease of the sSFR with stellar mass and, for $M_{\rm
stars}\lesssim 10^{10.8}-10^{11}\,M_{\odot}$, with the density of the
environment. Differences between the FID and $f_{\rm BH,\,DI}=0$ outcomes are
particularly evident at large $M_{\rm stars}$ and for low density
environments. In the two most massive stellar mass bins reported in Fig. 7,
the $f_{\rm BH,\,DI}=0$ model tends to predict more star forming galaxies than
the FID one in both voids and walls. The same holds true when inspecting Fig.
8. Voids galaxies in the $f_{\rm BH,\,DI}=0$ model exhibit a too large(small)
sSFR($f_{\rm passive}$) with respect to observations at large $M_{\rm stars}$.
Instead, the FID model aligns well with SDSS observations in this mass regime.
Thus the impact of the SMBH growth during DIs is particularly relevant for
star formation quenching in such isolated galaxies.

Also, the passive fraction (and the sSFR, to some extent) of the $f_{\rm
BH,\,DI}=0$ model exhibits a clear trend with the environment at any stellar
mass. This behaviour contrasts with observations, where the environmental
trend is observed only up to $M_{\rm stars}\lesssim 10^{11}M_{\odot}$.
Conversely, the fiducial model predicts a lack of environmental dependence at
large $M_{\rm stars}\,(\gtrsim 10^{10.8}-10^{11}\,M_{\odot})$, in keeping with
the observed pattern.

We conclude that the SMBH growth mechanism adopted by the $f_{\rm BH,\,DI}=0$
model is not sufficient to shut down the star formation in massive, isolated
galaxies.

###  6.2 Dust mass

Figure 9: Dust $-$ stellar mass relation in different large scale
environments: voids in blue, walls in green, filaments in orange, and massive
groups ($M_{\rm group}>10^{13.5}\,M_{\odot}$) in magenta. The results obtained
from our SAM are shown as lines, which refer to medians, while the typical
$14$-$86$th dispersion is shown as a grey shaded rectangle in the upper left
of the plot. Solid lines refer to our fiducial SAM, while results from the
$f_{\rm BH,\,DI}=0$ model are shown as dotted lines. Observations from the
GAMA/H-ATLAS sample (Beeston et al., 2018) are shown as filled points which
represent the mean dust mass in stellar mass bins of $0.3\,{\rm dex}$ width,
while the whole sample of observations is shown in the background as low
opacity circles. We also report the mean standard error associated with each
environment as vertical lines in the upper left side of the figure.
Environments and groups in this figure are identified as detailed at the
beginning of Sec. 6 (see also Table 1).

Fig. 9 compares model predictions on dust masses in local galaxies, as a
function of stellar mass and environment, to available observations. The data
reported in this section are obtained by matching the SDSS-DR16 catalog and
the GAMA/H-ATLAS sample, thus the final number of objects is much smaller than
the number of SDSS objects shown in the previous section (see Table 1). We
focus on the mean trends of data, which feature a large dispersion, keeping in
mind the limited sample size.

For $M_{\rm stars}\lesssim 10^{10.5}\,M_{\odot}$, observations suggest that at
fixed stellar mass galaxies are generally more dust rich in less dense
environments, with void galaxies featuring a mean dust content $5-10$ times
larger than massive groups objects. The median trends and the environmental
differences in this mass range predicted by the fiducial run of our SAM are
consistent with observations.
At larger stellar masses ($M_{\rm stars}\gtrsim 10^{10.5}\,M_{\odot}$ in
observations and $M_{\rm stars}\gtrsim 10^{10.8}\,M_{\odot}$ in our model)
dust masses appear to be nearly environment-independent both in observations
and in the fiducial model. By converse, in the $f_{\rm BH,\,DI}=0$ model, the
objects residing in low density environments feature a far too large median
$M_{\rm dust}$. This is consistent with the discussion in Sec. 6.1, according
to which the fraction of highly star forming massive galaxies (likely gas and
dust rich) is suppressed in low density environments by the novel in situ SMBH
growth.

Although a direct comparison between the convergence mass (Sec. 5.4) in the
SAM and observations is not straightforward121212This would need to identify
environments in mock catalogues from the simulated galaxy sample in the same
way as we do in the observed sample. Also, due to the lower number of objects
in the observed catalog the accuracy of its calculation in observations is
somewhat unreliable., we note that for observed $M_{\rm dust}$ curves,
convergence occurs around ${\rm log}{M_{\rm stars}/M_{\odot}}\sim 10.5-11$,
which is in nice agreement with the results obtained from SAM galaxies.

##  7 Summary and conclusions

In this work, we study the dependence of local galaxy properties, mainly
specific Star Formation Rate (sSFR) and dust, on the large-scale environment,
at fixed stellar mass. We adopt the simulated galaxy catalog produced by the
semi-analytic model (SAM) introduced in Parente et al. (2023), which is an
extension of the L-Galaxies SAM (Henriques et al., 2020). We identify cosmic
web environments from the underlying DM simulation exploiting different
methods. We employ NEXUS+ (Cautun et al., 2013) as a comprehensive method to
dissect the cosmic web into voids, walls, filaments, and nodes. This approach
provides us with a unified framework to identify different cosmic
environments. In contrast, we also utilize specific algorithms tailored for
distinct environments: the method introduced by Ruiz et al. (2015); Ruiz et
al. (2019) for identifying spherical voids and associated walls, the approach
outlined in Taverna et al. (2023) for detecting cylindrical filaments, and the
well-known FOF halo finder to pinpoint massive groups ($M_{\rm
group}>10^{13.5}\,M_{\odot}$), representing the most dense environments.

First, we study galaxy properties as a function of $M_{\rm stars}$ to
highlight the role of the environments (Sec. 5.1). For galaxies with $M_{\rm
stars}\lesssim 10^{10.8}\,M_{\odot}$ we find a clear and systematic trend: at
fixed stellar mass, galaxies in less dense environments feature a larger
specific SFR and dust abundance. Contrarily, differences among environments
are much less evident in more massive objects.

We interpret these results in light of the evolution of galaxies with the same
$z=0$ stellar mass, but residing in different environments (Sec. 5.2). At
$M^{z=0}_{\rm stars}\leq 10^{10.5}\,M_{\odot}$, the less dense is the
environment, the slower is the stellar mass evolution. At a given
$M^{z=0}_{\rm stars}$, galaxies in less dense environments feature a SFR peak
at more recent times, ending up with a larger SFR and dust content.
Contrarily, galaxies in more dense environments are in the declining phase of
their SF activity. Thus void galaxies host, on average, younger stellar
populations, are more star-forming and dust rich with respect to galaxies
located in other environments with the same $M^{z=0}_{\rm stars}$. Relevant
differences in the stellar mass assembly are not observed instead for more
massive galaxies $(M^{z=0}_{\rm stars}\gtrsim 10^{10.8}\,M_{\odot})$, and this
is in keeping with the environment-insensitivity of star formation and dust
for massive objects already discussed. This finding is remarkably robust,
irrespective of the variety of methods for environments identification adopted
in this work.

The picture resulting from our model suggests that galaxy properties are
affected by the large-scale environment up to a certain threshold mass. The
key to interpreting this finding stands in the supermassive black hole (SMBH)
growth channel during disc instabilities (DIs), which is adopted in our model.
This channel enables the growth of SMBHs even in isolated galaxies, allowing
them to halt star formation through AGN radio mode feedback. In the absence of
this channel, the growth of SMBHs in isolated objects is significantly
discouraged, as the other prominent growth channel in our SAM occurs during
merger events. This in situ SMBH growth tends to erase differences among
galaxies that exceed a specific stellar mass ($M_{\rm stars}\simeq
10^{10.8}\,M_{\odot}$, mass above which the SMBH driven quenching becomes
relevant in our model) residing in different environments.

Finally, we test our results against observations (Sec. 6). We identify
different environments in the SDSS-DR16, namely spherical voids, their
associated walls, cylindrical filaments, and massive groups $(M_{\rm
group}\gtrsim 10^{13.5}\,M_{\odot})$ using the algorithms by Ruiz et al.
(2015), Taverna et al. (2023), and Rodriguez & Merchán (2020). This is
conceptually similar to the identification process in our SAM catalog,
allowing us to compare the results. The fraction of passive galaxies $({\rm
sSFR}<10^{-11}\,{\rm yr}^{-1})$ with $M_{\rm stars}\lesssim
10^{10.5}-10^{11}\,M_{\odot}$ increases with the increasing density of the
environment, in both the SAM and SDSS catalog. As for the most massive objects
$(M_{\rm stars}\gtrsim 10^{10.5}-10^{11}\,M_{\odot})$, in both our model and
observations, we do not find any sign of a prominent star-forming population
in any environment. This is a direct consequence of the DI-driven SMBH growth
adopted in our model. Without this channel ($f_{\rm BH,\,DI}=0$), our model
would produce a prominent star forming population among massive voids
galaxies, and this is not present in the observed sample (Figg. 7 and 8).

We perform a similar comparison between our model and observations (combining
the SDSS-DR16 and GAMA/H-ATLAS surveys) in the $M_{\rm stars}-M_{\rm dust}$
plot (Fig. 9). We find a good match, namely the less dense is the environment,
the larger is the dust content of galaxies with $M_{\rm stars}\lesssim
10^{10.5}\,M_{\odot}$ in observations ($M_{\rm stars}\lesssim
10^{10.8}\,M_{\odot}$ in our model). The $\sim 0.5-1\,{\rm dex}$ difference in
the mean dust mass of voids and massive groups galaxies is not observed above
this mass. Again, this confirms the importance of the SMBH growth channel in
DIs, without which too dust-rich void galaxies would be predicted.

We draw two main conclusions from this work. First, we confirm the relevance
of the secular process of SMBH growth during DIs in our SAM, since it causes
quenching of galaxies in isolated environments. The importance of this growth
channel has been pointed out also by recent observational and simulation-based
investigations, whose claim is that secular processes dominate over mergers in
growing the central SMBH (e.g. Martin et al., 2018; Smethurst et al., 2019).
The second conclusion concerns our approach more than our results.
Investigating the properties of galaxies in different large-scale environments
may be a useful tool for constraining the relevance of in situ and ex situ
processes in shaping galaxy evolution.

The method outlined here can be improved in various ways, for example, by
striving for a more accurate match between the environments identified in
simulations and observations. A possible way to achieve this may be to
identify environments from mock catalogs derived from the SAM (or from
hydrodynamical simulations as well) to mimic the identification process
performed on the observed catalog as closely as possible.

In any case, besides any possible improvement, the role of future
observational surveys such as Euclid (Laureijs et al., 2011), DESI (DESI
Collaboration et al., 2016) and LSST (Ivezić et al., 2019), is crucial. They
will substantially advance our knowledge of the large-scale structure and,
concomitantly, deepen our insight into the evolution of galaxies within
distinct cosmic environments.

We aknowledge Agustín M. Rodríguez Medrano for sharing the observed catalog of
voids, and Angus H. Wright for directing us to the GAMA catalogue. We thank
Robert M. Yates for carefully reading the manuscript and providing
constructive comments. MP is grateful to Lumen Boco for his stimulating
comments and to Meriem Behiri for the help in dealing with observational
catalogs. This project has received funding from the European Union’s HORIZON-
MSCA-2021-SE-01 Research and Innovation programme under the Marie Sklodowska-
Curie grant agreement number 101086388 - Project acronym: LACEGAL, from
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) (PIP-2021
11220200102832CO, PIP-2022 11220210100064CO) and from the Ministerio de
Ciencia, Tecnología e Innovación (PICT-2020 03690) de la República Argentina.
Simulations have been carried out at the computing centre of INAF (Italia). We
acknowledge the computing centre of INAF-Osservatorio Astronomico di Trieste,
under the coordination of the CHIPP project (Bertocco et al., 2019; Taffoni et
al., 2020), for the availability of computing resources and support.

##  Appendix A Environments Stellar Mass Function and satellites fraction

Figure 10: Stellar Mass Function (left panels) and number fraction of simulated galaxies of type 0 (centrals, green), type 1 (satellites, purple), and type 2 (orphans, pink) (right panels) at $z=0.0$ for different environments. The top panels shows the predictions for environments as identified by NEXUS+ (voids, walls, filaments and nodes), while the bottom panels report the other environments definitions adopted in this work, namely spherical voids and their walls, cylindrical filaments and massive groups (R19+T23+FOF). The SMF of the whole sample of galaxies is also shown as a dashed gray line for reference. Environment | ${\rm log}\,{\mathcal{M}}_{*}/M_{\odot}$ |  |  | Environment | ${\rm log}\,{\mathcal{M}}_{*}/M_{\odot}$
---|---|---|---|---|---
Voids | $10.66$ |  |  | Sph Voids | $10.59$
Walls | $10.84$ |  |  | Sph Voids Walls | $11.02$
Filaments | $10.92$ |  |  | Filaments (T23) | $11.02$
Nodes | $11.64$ |  |  | Massive groups | $11.67$
Table 2: Characteristic mass, derived with a Schechter fit, for the SMFs of
the different environments discussed in the main text. SMFs are shown in Fig.
10.

Here we present the Stellar Mass Function (SMF) and the number abundance of
type $0,\,1,\,{\rm and}\,2$ galaxies (respectively centrals, satellites and
orphans131313Orphan galaxies are objects that have already lost their DM halo,
but still have a baryonic component. in the L-Galaxies framework) for
different cosmic environments at $z=0$. We report the cosmic environments we
focus on in the paper: voids, walls, filaments and nodes as identified by
NEXUS+, as well as spherical voids and their associated walls, cylindrical
filaments and massive groups (R19+T23+FOF). Results are shown in Fig. 10. We
also perform a fit of the SMFs with a Schechter function (Schechter, 1976):

$\phi(m)dm={\rm ln}(10)\phi^{*}10^{(m-m^{*})(1+\alpha)}{\rm
exp}(-10^{m-m^{*}})dm,$ (A1)

where $m={\rm log}\,M_{\rm stars}/M_{\odot}$ and $m^{*}={\rm
log}\,\mathcal{M_{*}}/M_{\odot}$. The latter is a parameter often referred to
as characteristic mass. We report this parameter of the SMFs of different
environments in Table 2.

As for the NEXUS+ SMF, the denser is the environment, the larger is the number
of massive galaxies (the same is observed for the Halo Mass Function; see e.g.
Fig. 17 of Cautun et al. 2013). The characteristic mass $\mathcal{M_{*}}$ of
the SMF as well increases with the density of the environment (Tab. 2). The
Nodes SMF exhibits a feature at log $M_{\rm stars}/M_{\odot}\simeq 11.5$. This
is due to one of the parameters required by NEXUS+, that is the minimum mass
for a cell to be classified as a node ($M_{\rm vir}\geq 2\cdot
10^{14}\,M_{\odot}$ here, about $M_{\rm stars}\gtrsim 2.5\cdot
10^{11}\,M_{\odot}$). For this reason, every cell containing objects which
meet this criterion will automatically be classified as a node.

Also, the relative fraction of central, satellites and orphan galaxies is
sensitive to the environment (top right panel of Fig. 10). The denser is the
environment, the smaller is the number of central (type $0$) galaxies. More
dense environments, particularly nodes, typically host more groups and
clusters of galaxies, and this explains the progressively larger number of
satellite (and orphan) galaxies.

A similar pattern is observed when comparing R19+T23+FOF environments (bottom
panels). We note that in this case walls galaxies are typically more massive
than filaments, and also host a lower fraction of central (type 0) galaxies.

##  Appendix B Dust properties across environments

Figure 11: Dust-to-Gas (left panel), Small-to-Large (middle panel), and
Silicate-to-Carbonaceous (right panel) ratio as a function of stellar mass, in
different cosmic web environments. We report the results for NEXUS+
environments (voids, walls, filaments and nodes, top panels), as well as for
the other environments definitions adopted in this work, namely spherical
voids and their walls, cylindrical filaments and massive groups (R19+T23+FOF,
bottom panels).

Here we analyze the dusty properties of galaxies in different environments.
Namely, we look at the Dust-to-Gas (DTG), Small-to-Large (S-to-L) and
Silicate-to-Carbonaceous (Sil-to-C) ratios as a function of stellar mass.
These quantities are particularly relevant as strongly dependent on the grains
accretion process in galaxies (e.g. Hirashita & Kuo, 2011; Aoyama et al.,
2017; Parente et al., 2022; Yates et al., 2023). In particular, in our model
the accretion process boosts the DTG ratio, as well as the silicate and small
grains abundance (the latter up to a certain mass when coagulation becomes
more efficient; see e.g. also Hou et al. 2019).

Results are shown in Fig. 11. Although to a lesser extent, the environment
still has an impact on these properties: at fixed $M_{\rm stars}$, the denser
is the environment, the larger are the DTG, S-to-L and Sil-to-C ratios at log
$M_{\rm stars}/M_{\odot}\lesssim 10.8$. This is particularly evident for
galaxies in nodes, which is the curve that deviates the most from the others.
However, this behaviour is mainly due to the contribution of satellite
galaxies, which are more abundant in dense environments, especially orphan
galaxies (see Fig. 10). Indeed, when looking at the same relations for central
galaxies only (type 0), differences among environments are strongly suppressed
(not shown here).

Thus the enhancement of DTG ratio at low masses (as well as of S-to-L and Sil-
to-C) towards denser environments is strictly related to the treatment of
satellites within the SAM. These objects are subject to hot gas stripping.
Moreover, orphan galaxies (type 2) have no hot gas at all. As a result, in
satellite galaxies, hot gas cooling is strongly (often totally) suppressed,
and consequently the cold gas metallicity is not diluted by the inflow of
(almost) pristine material. Thus the larger cold gas metallicity of these
objects enhances the grains accretion, and consequently DTG ratio, silicate
and small grains abundance.

At ${\rm log}\,M_{\rm stars}/M_{\odot}\gtrsim 10.8$ trends reverse, with
galaxies in denser environments featuring lower values of DTG, S-to-L and Sil-
to-C. The large majority of galaxies in this mass range are central galaxies
(type 0), which are quenched by the SMBH radio-mode feedback. Consequently, a
significant number of galaxies experience a substantial decrease in their
molecular gas fraction, inhibiting the grains accretion process and the
conversion of gas-phase metals into dust grains (a process that would lead to
a DTG increase). Importantly, the prevalence of galaxies with low molecular
gas fraction is linked to the environment, with approximately $\sim 95\%$ of
galaxies in Nodes (and $\sim 40\%$ in Voids) featuring $f_{\rm H_{2}}\lesssim
5\%$ for $M_{\rm stars}\gtrsim 10^{11}\,M_{\odot}$. Indeed, galaxies in denser
environments typically start to be quenched at earlier times, ending up to
$z=0$ with a lower gas, and H2, content. We observe this reversal of trends
also in the S-to-L and Sil-to-C trends, which are influenced as well by the
accretion process.

## References

  * Abadi et al. (1999) Abadi M. G., Moore B., Bower R. G., 1999, MNRAS, 308, 947
  * Abbott et al. (2018) Abbott T. M. C., et al., 2018, ApJS, 239, 18
  * Ahumada et al. (2020) Ahumada R., et al., 2020, ApJS, 249, 3
  * Alam et al. (2017) Alam S., et al., 2017, MNRAS, 470, 2617
  * Alfaro et al. (2020) Alfaro I. G., Rodriguez F., Ruiz A. N., Lambas D. G., 2020, A&A, 638, A60
  * Alfaro et al. (2021) Alfaro I. G., Ruiz A. N., Luparello H. E., Rodriguez F., Garcia Lambas D., 2021, Astronomy & Astrophysics, 654, A62
  * Alfaro et al. (2022) Alfaro I. G., Rodriguez F., Ruiz A. N., Luparello H. E., Lambas D. G., 2022, Astronomy & Astrophysics, 665, A44
  * Angulo & Hilbert (2015) Angulo R. E., Hilbert S., 2015, MNRAS, 448, 364
  * Angulo & White (2010) Angulo R. E., White S. D. M., 2010, MNRAS
  * Aoyama et al. (2017) Aoyama S., Hou K.-C., Shimizu I., Hirashita H., Todoroki K., Choi J.-H., Nagamine K., 2017, MNRAS, 466, 105
  * Aragón-Calvo et al. (2007) Aragón-Calvo M. A., Jones B. J. T., van de Weygaert R., van der Hulst J. M., 2007, A&A, 474, 315
  * Aragón-Calvo et al. (2010) Aragón-Calvo M. A., Platen E., van de Weygaert R., Szalay A. S., 2010, ApJ, 723, 364
  * Aragon-Calvo et al. (2014) Aragon-Calvo M. A., Neyrinck M. C., Silk J., 2014, arXiv e-prints, p. arXiv:1412.1119
  * Artale et al. (2018) Artale M. C., Zehavi I., Contreras S., Norberg P., 2018, MNRAS, 480, 3978
  * Astropy Collaboration et al. (2013) Astropy Collaboration et al., 2013, A&A, 558, A33
  * Astropy Collaboration et al. (2018) Astropy Collaboration et al., 2018, AJ, 156, 123
  * Ayromlou et al. (2021) Ayromlou M., Kauffmann G., Yates R. M., Nelson D., White S. D. M., 2021, MNRAS, 505, 492
  * Balogh et al. (2004) Balogh M. L., Baldry I. K., Nichol R., Miller C., Bower R., Glazebrook K., 2004, ApJ, 615, L101
  * Bamford et al. (2009) Bamford S. P., et al., 2009, MNRAS, 393, 1324
  * Beeston et al. (2018) Beeston R. A., et al., 2018, MNRAS, 479, 1077
  * Bertocco et al. (2019) Bertocco S., et al., 2019, arXiv e-prints, p. arXiv:1912.05340
  * Beygu et al. (2016) Beygu B., Kreckel K., van der Hulst J. M., Jarrett T. H., Peletier R., van de Weygaert R., van Gorkom J. H., Aragon-Calvo M. A., 2016, MNRAS, 458, 394
  * Beygu et al. (2017) Beygu B., Peletier R. F., van der Hulst J. M., Jarrett T. H., Kreckel K., van de Weygaert R., van Gorkom J. H., Aragon-Calvo M. A., 2017, MNRAS, 464, 666
  * Binney & Tremaine (1987) Binney J., Tremaine S., 1987, Galactic dynamics
  * Bond et al. (1996) Bond J. R., Kofman L., Pogosyan D., 1996, Nature, 380, 603
  * Bonnaire et al. (2022) Bonnaire T., Aghanim N., Kuruvilla J., Decelle A., 2022, A&A, 661, A146
  * Bos et al. (2012) Bos E. G. P., van de Weygaert R., Dolag K., Pettorino V., 2012, MNRAS, 426, 440
  * Cautun et al. (2013) Cautun M., van de Weygaert R., Jones B. J. T., 2013, MNRAS, 429, 1286
  * Cautun et al. (2014) Cautun M., van de Weygaert R., Jones B. J. T., Frenk C. S., 2014, MNRAS, 441, 2923
  * Ceccarelli et al. (2021) Ceccarelli L., Duplancic F., Lambas D. G., 2021, MNRAS, 509, 1805
  * Cen (2011) Cen R., 2011, ApJ, 741, 99
  * Chabrier (2003) Chabrier G., 2003, PASP, 115, 763
  * Chen et al. (2017) Chen Y.-C., et al., 2017, MNRAS, 466, 1880
  * Cole et al. (2000) Cole S., Lacey C. G., Baugh C. M., Frenk C. S., 2000, MNRAS, 319, 168
  * Colless et al. (2001) Colless M., et al., 2001, MNRAS, 328, 1039
  * Cora et al. (2018) Cora S. A., et al., 2018, MNRAS, 479, 2
  * Crain et al. (2015) Crain R. A., et al., 2015, MNRAS, 450, 1937
  * Croton et al. (2016) Croton D. J., et al., 2016, ApJS, 222, 22
  * DESI Collaboration et al. (2016) DESI Collaboration et al., 2016, arXiv e-prints, p. arXiv:1611.00036
  * Domínguez-Gómez et al. (2023) Domínguez-Gómez J., et al., 2023, Nature, 619, 269
  * Domínguez et al. (2001) Domínguez M., Muriel H., Lambas D. G., 2001, AJ, 121, 1266
  * Dressler (1980) Dressler A., 1980, ApJ, 236, 351
  * Driver et al. (2011) Driver S. P., et al., 2011, MNRAS, 413, 971
  * Driver et al. (2018) Driver S. P., et al., 2018, MNRAS, 475, 2891
  * Dubois et al. (2014) Dubois Y., et al., 2014, MNRAS, 444, 1453
  * Florez et al. (2021) Florez J., et al., 2021, ApJ, 906, 97
  * Gnedin (2003) Gnedin O. Y., 2003, ApJ, 582, 141
  * Grogin & Geller (2000) Grogin N. A., Geller M. J., 2000, AJ, 119, 32
  * Guo et al. (2011) Guo Q., et al., 2011, MNRAS, 413, 101
  * Habouzit et al. (2020) Habouzit M., Pisani A., Goulding A., Dubois Y., Somerville R. S., Greene J. E., 2020, MNRAS, 493, 899
  * Henriques et al. (2020) Henriques B. M. B., Yates R. M., Fu J., Guo Q., Kauffmann G., Srisawat C., Thomas P. A., White S. D. M., 2020, MNRAS, 491, 5795
  * Hirashita & Kuo (2011) Hirashita H., Kuo T.-M., 2011, MNRAS, 416, 1340
  * Hou et al. (2019) Hou K.-C., Aoyama S., Hirashita H., Nagamine K., Shimizu I., 2019, MNRAS, 485, 1727
  * Hoyle et al. (2005) Hoyle F., Rojas R. R., Vogeley M. S., Brinkmann J., 2005, ApJ, 620, 618
  * Hoyle et al. (2012) Hoyle F., Vogeley M. S., Pan D., 2012, MNRAS, 426, 3041
  * Irodotou et al. (2019) Irodotou D., Thomas P. A., Henriques B. M., Sargent M. T., Hislop J. M., 2019, MNRAS
  * Ivezić et al. (2019) Ivezić Ž., et al., 2019, ApJ, 873, 111
  * Izquierdo-Villalba et al. (2020) Izquierdo-Villalba D., Bonoli S., Dotti M., Sesana A., Rosas-Guevara Y., Spinoso D., 2020, MNRAS, 495, 4681
  * Jaber et al. (2023) Jaber M., Peper M., Hellwing W. A., Aragon-Calvo M. A., Valenzuela O., 2023, arXiv e-prints, p. arXiv:2304.14387
  * Jian et al. (2022) Jian H.-Y., et al., 2022, ApJ, 926, 115
  * Katsianis et al. (2021) Katsianis A., et al., 2021, MNRAS, 500, 2036
  * Kauffmann et al. (2003) Kauffmann G., et al., 2003, MNRAS, 341, 33
  * Kauffmann et al. (2004) Kauffmann G., White S. D. M., Heckman T. M., Ménard B., Brinchmann J., Charlot S., Tremonti C., Brinkmann J., 2004, MNRAS, 353, 713
  * Klypin et al. (2016) Klypin A., Yepes G., Gottlöber S., Prada F., Heß S., 2016, MNRAS, 457, 4340
  * Knebe et al. (2018) Knebe A., et al., 2018, MNRAS, 474, 5206
  * Kraljic et al. (2018) Kraljic K., et al., 2018, MNRAS, 474, 547
  * Kreckel et al. (2011) Kreckel K., Joung M. R., Cen R., 2011, ApJ, 735, 132
  * Kreckel et al. (2012) Kreckel K., Platen E., Aragón-Calvo M. A., van Gorkom J. H., van de Weygaert R., van der Hulst J. M., Beygu B., 2012, The Astronomical Journal, 144, 16
  * Kreckel et al. (2014) Kreckel K., van Gorkom J. H., Beygu B., van de Weygaert R., van der Hulst J. M., Aragon-Calvo M. A., Peletier R. F., 2014, Proceedings of the International Astronomical Union, 11, 591
  * Kuutma et al. (2017) Kuutma T., Tamm A., Tempel E., 2017, A&A, 600, L6
  * Lacey et al. (2016) Lacey C. G., et al., 2016, MNRAS, 462, 3854
  * Lagos et al. (2018) Lagos C., Tobar R. J., Robotham A. S. G., Obreschkow D., Mitchell P. D., Power C., Elahi P. J., 2018, MNRAS, 481, 3573
  * Laigle et al. (2018) Laigle C., et al., 2018, MNRAS, 474, 5437
  * Laureijs et al. (2011) Laureijs R., et al., 2011, arXiv e-prints, p. arXiv:1110.3193
  * Libeskind et al. (2018) Libeskind N. I., et al., 2018, MNRAS, 473, 1195
  * Liu et al. (2015) Liu C.-X., Pan D. C., Hao L., Hoyle F., Constantin A., Vogeley M. S., 2015, ApJ, 810, 165
  * Martin et al. (2018) Martin G., et al., 2018, MNRAS, 476, 2801
  * Martínez et al. (2016) Martínez H. J., Muriel H., Coenda V., 2016, MNRAS, 455, 127
  * Moorman et al. (2016) Moorman C. M., Moreno J., White A., Vogeley M. S., Hoyle F., Giovanelli R., Haynes M. P., 2016, ApJ, 831, 118
  * Navarro et al. (1997) Navarro J. F., Frenk C. S., White S. D. M., 1997, ApJ, 490, 493
  * Old et al. (2020) Old L. J., et al., 2020, MNRAS, 493, 5987
  * Paillas et al. (2017) Paillas E., Lagos C. D. P., Padilla N., Tissera P., Helly J., Schaller M., 2017, MNRAS, 470, 4434
  * Paillas et al. (2021) Paillas E., Cai Y.-C., Padilla N., Sánchez A. G., 2021, MNRAS, 505, 5731
  * Parente et al. (2022) Parente M., Ragone-Figueroa C., Granato G. L., Borgani S., Murante G., Valentini M., Bressan A., Lapi A., 2022, MNRAS, 515, 2053
  * Parente et al. (2023) Parente M., Ragone-Figueroa C., Granato G. L., Lapi A., 2023, MNRAS, 521, 6105
  * Park et al. (2007) Park C., Choi Y.-Y., Vogeley M. S., Gott J. Richard I., Blanton M. R., SDSS Collaboration 2007, ApJ, 658, 898
  * Patiri et al. (2006) Patiri S. G., Prada F., Holtzman J., Klypin A., Betancort-Rijo J., 2006, MNRAS, 372, 1710
  * Paulino-Afonso et al. (2019) Paulino-Afonso A., et al., 2019, A&A, 630, A57
  * Peng et al. (2010) Peng Y.-j., et al., 2010, ApJ, 721, 193
  * Peng et al. (2015) Peng Y., Maiolino R., Cochrane R., 2015, Nature, 521, 192
  * Pillepich et al. (2018) Pillepich A., et al., 2018, MNRAS, 475, 648
  * Planck Collaboration et al. (2014) Planck Collaboration et al., 2014, A&A, 571, A16
  * Rieder et al. (2013) Rieder S., van de Weygaert R., Cautun M., Beygu B., Portegies Zwart S., 2013, MNRAS, 435, 222
  * Rodriguez & Merchán (2020) Rodriguez F., Merchán M., 2020, A&A, 636, A61
  * Rodríguez-Medrano et al. (2023) Rodríguez-Medrano A. M., Paz D. J., Stasyszyn F. A., Rodríguez F., Ruiz A. N., Merchán M., 2023, MNRAS, 521, 916
  * Rodriguez et al. (2022) Rodriguez F., Merchán M., Artale M. C., 2022, MNRAS, 514, 1077
  * Rojas et al. (2004) Rojas R. R., Vogeley M. S., Hoyle F., Brinkmann J., 2004, ApJ, 617, 50
  * Rojas et al. (2005) Rojas R. R., Vogeley M. S., Hoyle F., Brinkmann J., 2005, ApJ, 624, 571
  * Rosas-Guevara et al. (2022) Rosas-Guevara Y., Tissera P., del P Lagos C., Paillas E., Padilla N., 2022, MNRAS, 517, 712
  * Ruiz et al. (2015) Ruiz A. N., Paz D. J., Lares M., Luparello H. E., Ceccarelli L., Lambas D. G., 2015, MNRAS, 448, 1471
  * Ruiz et al. (2019) Ruiz A. N., Alfaro I. G., Garcia Lambas D., 2019, MNRAS, 483, 4070
  * Schaye et al. (2015) Schaye J., et al., 2015, MNRAS, 446, 521
  * Schechter (1976) Schechter P., 1976, ApJ, 203, 297
  * Smethurst et al. (2019) Smethurst R. J., Simmons B. D., Lintott C. J., Shanahan J., 2019, MNRAS, 489, 4016
  * Springel et al. (2005) Springel V., et al., 2005, Nature, 435, 629
  * Steinhauser et al. (2016) Steinhauser D., Schindler S., Springel V., 2016, A&A, 591, A51
  * Sutter et al. (2015) Sutter P. M., et al., 2015, Astronomy and Computing, 9, 1
  * Taffoni et al. (2020) Taffoni G., Becciani U., Garilli B., Maggio G., Pasian F., Umana G., Smareglia R., Vitello F., 2020, arXiv e-prints, p. arXiv:2002.01283
  * Tavasoli et al. (2015) Tavasoli S., Rahmani H., Khosroshahi H. G., Vasei K., Lehnert M. D., 2015, ApJ, 803, L13
  * Taverna et al. (2023) Taverna A., Salerno J. M., Daza-Perilla I. V., Díaz-Giménez E., Zandivarez A., Martínez H. J., Ruiz A. N., 2023, MNRAS, 520, 6367
  * Taylor (2005) Taylor M. B., 2005, in Shopbell P., Britton M., Ebert R., eds, Astronomical Society of the Pacific Conference Series Vol. 347, Astronomical Data Analysis Software and Systems XIV. p. 29
  * Vijayaraghavan & Ricker (2015) Vijayaraghavan R., Ricker P. M., 2015, MNRAS, 449, 2312
  * Wang et al. (2023) Wang K., Avestruz C., Guo H., Wang W., Wang P., 2023, arXiv e-prints, p. arXiv:2309.15306
  * Wegner & Grogin (2008) Wegner G., Grogin N. A., 2008, AJ, 136, 1
  * White & Frenk (1991) White S. D. M., Frenk C. S., 1991, ApJ, 379, 52
  * Whitmore et al. (1993) Whitmore B. C., Gilmore D. M., Jones C., 1993, ApJ, 407, 489
  * Woo et al. (2013) Woo J., et al., 2013, MNRAS, 428, 3306
  * Yang et al. (2005) Yang X., Mo H. J., van den Bosch F. C., Jing Y. P., 2005, MNRAS, 356, 1293
  * Yang et al. (2007) Yang X., Mo H. J., van den Bosch F. C., Pasquali A., Li C., Barden M., 2007, ApJ, 671, 153
  * Yates et al. (2023) Yates R. M., Hendriks D., Vijayan A. P., Izzard R. G., Thomas P. A., Das P., 2023, MNRAS,
  * York et al. (2000) York D. G., et al., 2000, AJ, 120, 1579
  * Zandivarez et al. (2003) Zandivarez A., Merchán M. E., Padilla N. D., 2003, MNRAS, 344, 247
  * von Benda-Beckmann & Müller (2008) von Benda-Beckmann A. M., Müller V., 2008, MNRAS, 384, 1189