# The Evolving Effect Of Cosmic Web Environment On Galaxy Quenching

Farhanul Hasan Department of Astronomy, New Mexico State University, Las
Cruces, NM 88003, USA  Joseph N. Burchett Department of Astronomy, New Mexico
State University, Las Cruces, NM 88003, USA  Alyssa Abeyta  Department of
Astronomy, New Mexico State University, Las Cruces, NM 88003, USA  Douglas
Hellinger  Department of Physics, University of California, Santa Cruz, CA
95064, USA  Nir Mandelker Centre for Astrophysics and Planetary Science, Racah
Institute of Physics, The Hebrew University, Jerusalem 91904, Israel  Joel R.
Primack Department of Physics, University of California, Santa Cruz, CA 95064,
USA  S. M. Faber University of California Observatories and Department of
Astronomy and Astrophysics,
University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064,
USA  David C. Koo University of California Observatories and Department of
Astronomy and Astrophysics,
University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064,
USA  Oskar Elek Department of Computational Media, University of California,
1156 High Street, Santa Cruz, CA 95064, USA  Daisuke Nagai Department of
Physics, Yale University, New Haven, CT 06520, USA Farhanul Hasan
<EMAIL_ADDRESS>
(Received 2023 Mar 13; Revised 2023 Apr 21; Accepted 2023 Apr 23)

###### Abstract

We investigate how cosmic web structures affect galaxy quenching in the
IllustrisTNG (TNG100) cosmological simulations by reconstructing the cosmic
web within each snapshot using the DisPerSE framework. We measure the comoving
distance from each galaxy with stellar mass
${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!8}$ to the nearest node
($d_{\mathrm{node}}$) and the nearest filament spine ($d_{\mathrm{fil}}$) to
study the dependence of both median specific star formation rate
($\langle\mathrm{sSFR}\rangle$) and median gas fraction ($\langle
f_{\mathrm{gas}}\rangle$) on these distances. We find that the
$\langle\mathrm{sSFR}\rangle$ of galaxies is only dependent on cosmic web
environment at $z<2$, with the dependence increasing with time. At $z\leq
0.5$, ${8\\!\leq\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!9}$ galaxies
are quenched at ${d_{\mathrm{node}}}\lesssim 1$ Mpc, and have significantly-
suppressed star formation at ${d_{\mathrm{fil}}}\lesssim 1$ Mpc, trends driven
mostly by satellite galaxies. At $z\leq 1$, in contrast to the monotonic drop
in $\langle\mathrm{sSFR}\rangle$ of
${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!10}$ galaxies with decreasing
$d_{\mathrm{node}}$ and $d_{\mathrm{fil}}$,
${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!10}$ galaxies – both centrals
and satellites – experience an upturn in $\langle\mathrm{sSFR}\rangle$ at
${d_{\mathrm{node}}}\lesssim 0.2$ Mpc. Much of this cosmic web dependence of
star formation activity can be explained by an evolution in $\langle
f_{\mathrm{gas}}\rangle$. Our results suggest that in the past $\sim$10 Gyr,
low-mass satellites are quenched by rapid gas stripping in dense environments
near nodes and gradual gas starvation in intermediate-density environments
near filaments. At earlier times, cosmic web structures efficiently channeled
cold gas into most galaxies. State-of-the-art ongoing spectroscopic surveys
such as SDSS and DESI, as well as those planned with the Subaru Prime Focus
Spectrograph, JWST, and Roman, are required to test our predictions against
observations.

Cosmic web (330), Large-scale structure of the universe (902), Galaxy
quenching (2040), Galaxy evolution (594), Intergalactic filaments (811),
Magnetohydrodynamical simulations (1966)

##  1 Introduction

In the standard cosmological model, structure formation in the universe occurs
at vastly different scales. Galaxies form stars within tens of kpc and grow
inside dark matter (DM) halos that can be two orders of magnitude larger. At
even larger scales, galaxies and their DM halos are embedded within an
intricate network of strand-like filaments, diffuse sheets, dense nodes, and
underdense voids, which is termed the “cosmic web” (e.g., Bond et al., 1996;
Springel et al., 2005). While the cosmic web has been studied on both
theoretical and observational grounds for decades, it remains one of the major
outstanding questions in astrophysics whether and how the large-scale cosmic
web environment influences the formation and evolution of galaxies.

A chief question in galaxy evolution is how star formation activity proceeds
in galaxies and how it ceases, i.e., how quenching occurs. It has long been
known that quenching depends on internal mechanisms characterized by the
stellar mass $M_{\ast}$ or halo mass $M_{\mathrm{vir}}$ (e.g., Brinchmann et
al., 2004; Cattaneo et al., 2006; Williams et al., 2009; Peng et al., 2010;
Darvish et al., 2016), such that galaxy-scale processes, including supernovae
(SNe) and Active Galactic Nuclei (AGN) feedback, can regulate and curtail star
formation activity. A widely adopted theoretical viewpoint posits that
galaxies in halos with mass
$\log(M_{\mathrm{vir}}/{\mathrm{M}_{\odot}})\gtrsim 11.5-12$ can form stable
virial accretion shocks and, therefore, a hot, hydrodynamically stable
circumgalactic medium (CGM) that suppresses accretion of cold gas to the
interstellar medium (ISM) necessary for star formation (e.g., Dekel &
Birnboim, 2006; Kereš et al., 2005, 2009; Dekel et al., 2009; Stern et al.,
2020, 2021). Lower-mass galaxies (typically with
$\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!10$), especially at high
redshifts ($z\\!\gtrsim\\!2$), lack this ability to form a stable hot CGM and
“self-quench” (e.g., Croton et al., 2006; Gabor & Davé, 2012).

External processes as characterized by their environment have also emerged as
crucial factors in determining how galaxies quench (e.g., Elbaz et al., 2007;
Peng et al., 2012; Eardley et al., 2015; Moutard et al., 2018; Bluck et al.,
2020). However, the exact nature of the relationship between quenching and
environment, and what physical mechanisms manifest this relationship, is a
topic of widespread debate. In the hot, dense halos of galaxy groups and
clusters, hydrodynamical interactions between the halo medium and satellite
galaxies – most notably ram pressure stripping (e.g., Bahé & McCarthy, 2015;
Boselli et al., 2022) – or tidal interactions between separate galaxies or
between galaxies and the halo (e.g., Boselli & Gavazzi, 2006; Marasco et al.,
2016) can remove the star-forming ISM of a galaxy. Over longer timescales, gas
accretion onto the ISM can be halted, either due to lack of accretion from the
intergalactic medium (IGM) to the CGM or from the CGM to the ISM via
strangulation or starvation (e.g., Larson et al., 1980; Balogh & Morris, 2000;
Peng et al., 2015).

The cosmic web itself has also been invoked in models of galaxy quenching.
Aragon Calvo et al. (2019) proposed that “cosmic web detachment,” wherein
galaxies are detached from cold gas-supplying primordial filaments, can
explain much of the observed quenching phenomena across time. Song et al.
(2021) suggested that close to the edges of filaments there is coherent, high
angular momentum supply of gas to the outer parts of halos, which prevents an
efficient transfer of gas from the outer halo to galactic centers – ultimately
quenching these galaxies (see also Peng & Renzini, 2020; Renzini, 2020). Pasha
et al. (2022) found that cosmological accretion shocks at $z\\!\sim\\!2-5$ can
produce a hot ($T\\!>\\!10^{6}$ K) IGM at the edge of sheets, which can quench
low-mass centrals at these epochs, as shocks around filaments, groups, and
clusters can at lower redshifts (e.g., Birnboim et al., 2016; Zinger et al.,
2018; Li et al., 2023).

Studies of the connection between galaxy quenching and the cosmic web in the
past decade have yielded mixed results. While many observational studies have
found that passive or quenched galaxies are typically located near nodes and
filaments (e.g., Kuutma et al., 2017; Kraljic et al., 2018; Laigle et al.,
2018; Winkel et al., 2021), some have shown that proximity to cosmic web
filaments can also enhance star formation in galaxies (e.g., Darvish et al.,
2014; Vulcani et al., 2019). Cosmological hydrodynamical simulations have also
provided an inconclusive picture. In the IllustrisTNG simulations (Nelson et
al., 2019a), Malavasi et al. (2022) found that the specific star formation
rate ($\mathrm{sSFR}\\!=\\!\mathrm{SFR}/{M_{\ast}}$) of galaxies is generally
reduced with proximity to nodes and filaments at $z\\!=\\!0$. Xu et al. (2020)
found in the EAGLE simulations (Schaye et al., 2015) a characteristic stellar
mass ($\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\sim\\!10.5$) below which
galaxies have lower sSFR in nodes than in filaments and above which this
dependence vanishes. Both Kotecha et al. (2022) and Zheng et al. (2022)
reported evidence, instead, of filaments increasing star formation activity or
at least delaying quenching. Therefore, consensus is yet to be reached on the
impact of cosmic web environment on galaxy quenching and how this varies with
stellar mass and redshift.

In this paper, we employ the IllustrisTNG cosmological simulations to study
the impacts of cosmic web environment, particularly the proximity to filaments
and nodes, on star formation and gas content in galaxies across cosmic time.
We reconstruct the cosmic web in IllustrisTNG using the topologically-
motivated DisPerSE framework (Sousbie, 2011; Sousbie et al., 2011). This is
the first study of the dependence of star formation quenching on the cosmic
web in the TNG100-1 run across many different redshift snapshots. Malavasi et
al. (2022) performed a similar analysis of the TNG300-1 run at $z=0$.

This paper is organized as follows. In Section 2, we describe the simulation
data used in this work and methods of reconstructing the cosmic web. We
present our results in Section 3. We discuss the physical interpretations of
our results and propose observational tests in Section 4, and conclude in
Section 5. We adopt the Planck 2015 cosmology (Planck Collaboration et al.,
2016), with $H_{0}=67.74$ $\,{\rm km\,s}^{-1}~{}{\rm Mpc}^{-1}$,
$\Omega_{\mathrm{M},0}=0.3089$, and $\Omega_{\Lambda,0}=0.6911$. All distances
are quoted in comoving units, unless stated otherwise.

##  2 Data and Methods

###  2.1 TNG Simulations

We analyzed outputs from the IllustrisTNG magneto-hydrodynamical cosmological
simulations, which use the AREPO moving-mesh hydrodynamics code (Springel,
2010) to simulate the evolution of gas, stars, DM, and black holes (BH) from
the early universe ($z=127$) to the present day ($z=0$). The public data
release of the simulations was presented in Nelson et al. (2019a), while
introductory results were presented in Pillepich et al. (2018), Nelson et al.
(2018), Springel et al. (2018), Marinacci et al. (2018), and Naiman et al.
(2018). In particular, we make use of TNG100-1, the highest resolution run of
the TNG100 simulation, which has a box size of $\sim$110.7 comoving Mpc per
side, minimum baryonic and DM particle mass of
$\sim\\!1.4\\!\times\\!10^{6}~{}{\mathrm{M}_{\odot}}$ and $\sim
7.5\\!\times\\!10^{6}~{}{\mathrm{M}_{\odot}}$ respectively, a Planck 2015
cosmology (Planck Collaboration et al., 2016), and $1820^{3}$ initial DM
particles. While TNG300-1 provides greater statistics of galaxies and cosmic
structures with $\approx\\!20$ times the volume of TNG100-1, it has
$\approx\\!1/8$ the particle mass resolution. On the other hand, TNG50-1
provides $\approx\\!16\times$ greater particle mass resolution than TNG100-1,
but has $\approx\\!1/10$ the volume.

We obtain galaxy data for all 100 snapshots of the TNG100-1 simulation
(hereafter TNG) from the online data repository111https://www.tng-
project.org/data/ (Nelson et al., 2019a). In each snapshot, “Group” catalogs
are constructed using the friends-of-friends (FoF) substructure identification
algorithm, while the Subfind algorithm and searches for gravitationally bound
objects in each FoF group representing either subhalos or the main (host) halo
(Springel et al., 2001; Dolag et al., 2009). We make use of both the group and
subhalo catalogs to identify halos and galaxies, respectively.

Figure 1: 2D visual representation of galaxies in the TNG100 simulation and
cosmic web structures identified by DisPerSE at $z=0$ (left), $z=1$ (middle),
and $z=2$ (right). In each panel, filament spines are represented by black
curves, and nodes are represented by semi-transparent grey circles, while
galaxies are represented by scatter points sized by the stellar mass and
color-coded by specific star formation rate. The same x-y projection of a
slice 37 Mpc thick ($\sim 1/3$ of the total box width) is shown for each
redshift. The global star formation activity declines considerably from higher
to lower redshift. Quiescent galaxies at lower redshifts appear to be
clustered closer to nodes and filaments.

For each snapshot, we set a minimum stellar mass of
$\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!=\\!8$, which corresponds to a
typical minimum observable stellar mass of galaxies in the (nearby) universe
and also ensures that the galaxies are well-resolved with at least about 100
stellar particles in them. Similarly, we set a minimum halo mass –
corresponding to the mass enclosed in a sphere whose mean density is 200 times
the critical density of the Universe – of
$\log({M_{\mathrm{200,c}}}/{\mathrm{M}_{\odot}})\\!=\\!9$ to ensure that each
of the galaxies in our catalog resides inside halos that are well-resolved
with at least 100 DM particles. These criteria yielded $\sim$50,000 galaxies
at $z\\!=\\!0$ and $\sim$11,000 galaxies at $z\\!=\\!5$. From these catalogs,
we obtained the galaxy comoving position, star formation rate (SFR), stellar
mass ($M_{\ast}$), halo mass ($M_{\mathrm{200,c}}$), halo virial radius
($R_{\mathrm{200,c}}$; comoving radius at which $M_{\mathrm{200,c}}$ is
calculated), and mass of all gas gravitationally bound to a subhalo
($M_{\mathrm{gas}}$). Hereafter, we refer to subhalos as galaxies and groups
as halos.

###  2.2 Reconstructing the Cosmic Web with DisPerSE

Next, we apply the Discrete Persistent Structures Extractor (DisPerSE)
algorithm (Sousbie, 2011; Sousbie et al., 2011) to find cosmic web filaments
and nodes in each TNG snapshot where at least 10,000 galaxies matched our
selection criteria above. DisPerSE identifies the topology of space in any
given volume based on an input distribution of discrete tracers, which in our
case are the spatial locations of all galaxies matching our selection criteria
above. To do this, it computes the density field from the inputs, using the
Delaunay Tessellation Field Estimator (DTFE; Schaap & van de Weygaert, 2000),
wherein the entire volume is divided into tetrahedrons, with the positions of
individual galaxies as vertices. During the tessellation, the density field at
the position of each vertex of the tessellation is smoothed by averaging it
with its two nearest neighbors. This is done in order to minimize
contamination by shot noise and the detection of small-scale spurious features
(see, e.g., Malavasi et al., 2022). DisPerSE calculates the gradient of the
density field and identifies critical points where the gradient is zero. These
correspond to the voids (minima), saddle points, and nodes (maxima) of the
density field. Filaments consist of a series of segments connecting maxima to
other critical points.

For each topologically significant pair of critical points, DisPerSE computes
the persistence, which is defined as the ratio of the density value at the two
critical points. Persistence is a simple measure of how robust topological
structures, i.e., the identified critical points and filament segments, are to
local variations, in this case, of the density field measured from input
galaxy positions. This sets the effective significance level of the detected
filaments and allows us to quantify the effect of shot noise in the input
data. For our fiducial run, we choose a persistence threshold of $3\sigma$,
which has been known to eliminate most spurious filamentary features in the
TNG simulations (e.g., Galárraga-Espinosa et al., 2020). By experimenting with
cuts of $4\sigma$ and $5\sigma$, we find that these miss fainter structures,
but, nonetheless, do not significantly alter our results.

In addition, we choose to apply a smoothing to the position of the segments of
the filamentary skeleton by averaging the initial positions of the extrema of
a segment with those of the extrema of contiguous segments. In essence, the
skeleton is smoothed by keeping the critical points fixed and averaging the
coordinates of each point along a filament with that of its two neighbors.
This is done to reduce sharp and/or unphysical shapes of filament segments
caused by shot noise We apply one level of smoothing and find that increasing
the amount of smoothing by one level or removing this smoothing does not have
a significant effect on our statistical results.

Furthermore, we experimented with varying the minimum stellar mass cut of our
galaxy catalog and cosmic web reconstruction, using cuts of
$\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!9$ and
${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!10}$. These are more
realistic minimum masses to compare to large observational surveys such as the
Sloan Digital Sky Survey (SDSS; e.g., Strauss et al., 2002) DR17 (see, e.g.,
Wilde et al. (2023), and Section 4.3 of this paper). However, the sharp drop
in the number of galaxies in TNG with these higher masses yielded increasingly
fewer input tracers for DisPerSE, which resulted in far fewer identified
filaments and nodes than in our fiducial
${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!8}$ cut, and particularly
very few short filaments (with length $<$1 Mpc). These higher mass cuts could
therefore bias our results towards more prominent cosmic web features and
longer filaments. In practice, varying the minimum $M_{\mathrm{200,c}}$ cut
was mostly degenerate with varying the minimum $M_{\ast}$ cut.

A 2D visual representation of the DisPerSE-identified filaments and nodes
superimposed on the distribution of galaxies in TNG is shown in Fig. 1. The
three panels show $x-y$ projections in a 37 Mpc thick slice (corresponding to
$\sim 1/3$ of the total thickness) at $z\\!=\\!0$ (left), $z\\!=\\!1$
(middle), and $z\\!=\\!2$ (right). In each panel, the filament spines and
nodes are represented by black curves and grey circles, respectively, while
galaxies are represented by scatter points, with sizes proportional to
$M_{\ast}$ and color-coding by sSFR.

From this visualization, we can qualitatively assess the spatial distribution
of star formation activity in galaxies with respect to cosmic web nodes and
filaments. At any redshift, higher sSFR galaxies are located throughout the
volume, whereas lower sSFR galaxies are almost always located close to a
filament spine or a node. From higher to lower redshift (right to left panel),
there is a clear decline in global star formation activity which reflects the
decline in cosmic star formation rate density after the so-called “cosmic
noon” thoroughly chronicled in observations (e.g., Madau & Dickinson, 2014).
The number of massive quiescent galaxies increases considerably from
$z\\!=\\!2$ to $z\\!=\\!1$ and even more prominently from $z\\!=\\!1$ to the
present day. A rough qualitative visual check showed that virtually all
$\mathrm{SFR}\\!=\\!0$ galaxies at low redshift, regardless of mass, live near
nodes and/or filaments (we quantify a galaxy’s proximity to these cosmic web
structures below).

###  2.3 Defining Distances

To quantitatively study the relationship between the physical properties of a
galaxy and its cosmic web environment, we measure two different distances for
each galaxy at each snapshot: $d_{\mathrm{node}}$ – the comoving Euclidean
distance from the center of a galaxy to the center of the nearest identified
node, and $d_{\mathrm{fil}}$ – the comoving transverse distance from the
center of a galaxy to the nearest identified filament spine. We chose these
cosmic web-centric distance characterizations as they are similar to those of
Welker et al. (2020) and Malavasi et al. (2022), among others. Depending on
the physical mechanisms affecting star formation quenching, use of physical
distances or other parameters such as local gas density, pressure, angular
momentum, etc. are also viable options for the study of the dependence of
galaxy properties on the cosmic web environment. In the following, we
investigate how star formation quenching and gas reservoirs of TNG galaxies
depend on $d_{\mathrm{node}}$ and $d_{\mathrm{fil}}$ at different masses and
redshifts.

##  3 Results

###  3.1 Star Formation And Cosmic Web Environment

We first investigate the relationship between star formation activity in
galaxies and their proximity to cosmic web structures. In each snapshot, we
divide galaxies into three different stellar mass ranges –
${8\\!\leq\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!9}$,
${9\\!\leq\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!10}$, and
${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!10}$ – and into seven bins of
the distances $d_{\mathrm{node}}$ and $d_{\mathrm{fil}}$. These bins are
chosen such that each has an equal number of galaxies. We measure the median
sSFR, $\langle\mathrm{sSFR}\rangle$, for each bin of $d_{\mathrm{node}}$ and
$d_{\mathrm{fil}}$. Experimenting with different numbers of bins, we find the
overall results to be insensitive to the number of bins.

The results of these binned statistics are presented in Fig. 2, the top row
showing $\langle\mathrm{sSFR}\rangle$ as a function of $d_{\mathrm{node}}$ and
the bottom row $\langle\mathrm{sSFR}\rangle$ as a function of
$d_{\mathrm{fil}}$, and each column represent a different mass range. The
$\langle\mathrm{sSFR}\rangle$ are color-coded by redshift; vertical error bars
represent $\pm 1\sigma$ bootstrapped errors on $\langle\mathrm{sSFR}\rangle$
in each $d_{\mathrm{node}}$ or $d_{\mathrm{fil}}$ bin, and horizontal error
bars represent the width of the bin. Dotted curves represent simple spline
interpolations to the $\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{node}}$ and
$\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{fil}}$ relations. For a finer look
at some intermediate redshifts, each panel also contains an inset showing a
color contour plot for each snapshot between $z\\!=\\!0.5$ and $z\\!=\\!3$.
For certain bins, we show an upper limit on $\langle\mathrm{sSFR}\rangle$,
corresponding to SFR$=\\!10^{-2.5}~{}{\mathrm{M}_{\odot}~{}\mathrm{yr}^{-1}}$,
which is the minimum resolvable SFR (averaged over 200 Myr) in TNG due to
stochastic star formation with a minimum star particle mass (see Terrazas et
al., 2020). For example, for
${8\\!\leq\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!9}$ galaxies, the
maximum upper limit in sSFR is $10^{-11.5}~{}\mathrm{yr}^{-1}$, considering
the most massive galaxies in this mass range.

Figure 2:  The median sSFR as a function of distance to the nearest node (top
row) and filament spine (bottom row) for galaxies with
${8\\!\leq\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!9}$ (left panels),
${9\\!\leq\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!10}$ (middle panels),
and ${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!10}$ (right panels). The
data points and curves are color-coded by redshift as indicated by the
discrete color-bars on the right. Each panel contains an inset which is a
continuous color contour plot showing the
$\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{node}}$ or
$\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{fil}}$ relationship for a larger
number of intermediate redshifts, to help locate the redshift at which a
distance-dependence disappears (see text). Only galaxies with
${d_{\mathrm{node}}}>1$ Mpc are included for the filament-centric
relationships to mitigate the potential halo-centric effects of nearby
clusters and groups. Note that some points are shown as upper limits on
$\langle\mathrm{sSFR}\rangle$. Star formation activity is dependent on
$d_{\mathrm{node}}$ and (to a lesser extent) on $d_{\mathrm{fil}}$ only at
lower redshifts, while this dependence disappears at $z\geq 2$.

In order to separate the effect of nearby nodes from that of filaments alone
(because many galaxies that are close to filament spines are also close to
nodes), we only considered galaxies that are ${d_{\mathrm{node}}}\\!>\\!1$ Mpc
away from the nearest node for the bottom row of Fig. 2. The choice of 1 Mpc
is motivated by two considerations. 1) This is slightly higher than the virial
radius $R_{\mathrm{200,c}}$ of the most massive galaxy cluster in TNG100.
Therefore, this ensures that we remove possible halo-centric effects of nearby
clusters and groups (which reside in nodes) and isolates the effect of nearby
filaments. 2) This is four times the scale radius of the number density
profile of galaxies in filaments derived for TNG300 by Galárraga-Espinosa et
al. (2020) and corresponds to the width containing almost all of the matter
inside of filaments. We vary this cut to be ${d_{\mathrm{node}}}\\!>\\!0.5$,
$1.5$, and $2$ Mpc as well and find that only galaxies at $z\\!\lesssim 1\\!$
with ${d_{\mathrm{fil}}}\\!<\\!1$ Mpc show noticeable changes to our
quantitative results, while the qualitative results described below remain
unchanged. In essence, this $d_{\mathrm{node}}$ cut ensures that only galaxies
at intermediate to high, rather than extremely high local densities, are
considered for the $d_{\mathrm{fil}}$ analysis (see Burchett et al. (2020) for
an example of how cosmic matter densities relate to different filamentary
environments).

First, examining the node-centric relationships, we find that
$d_{\mathrm{node}}$ is strongly correlated with quenching of star formation in
galaxies of all masses at low redshifts ($z\\!\lesssim\\!0.5$). For
${8\\!\leq\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!9}$ galaxies at
$z\\!\leq\\!0.5$, $\langle\mathrm{sSFR}\rangle$ vanishes at
${d_{\mathrm{node}}}\\!\lesssim\\!1$ Mpc. The increase from low to high
$d_{\mathrm{node}}$ is much more gradual at $\\!z=\\!1$ ($\approx\\!3\times$
from $\langle{d_{\mathrm{node}}}\rangle\\!\sim\\!0.2$ Mpc to
$\langle{d_{\mathrm{node}}}\rangle\\!\sim\\!15$ Mpc). At $z\\!\geq\\!2$
however, there is virtually no dependence of $\langle\mathrm{sSFR}\rangle$ on
$d_{\mathrm{node}}$. We note that our results at $z\\!=\\!0$ are broadly in
agreement with those of Geha et al. (2012), who found that in SDSS DR8, almost
all quenched galaxies with $7\leq\log(M_{\ast}/\mathrm{M}_{\odot})\leq 9$ are
found within $\sim$1.5 Mpc of a massive host.

For intermediate-mass
${9\\!\leq\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!10}$ galaxies, the
trends are similar in that there is a large $\sim$1 dex rise in
$\langle\mathrm{sSFR}\rangle$ from the lowest to the highest
$d_{\mathrm{node}}$ bin at $z\\!=\\!0$, a much smaller rise at $z\\!=\\!0.5$,
and effectively no $d_{\mathrm{node}}$ dependence at $z\\!\geq\\!1$. The lack
of $d_{\mathrm{node}}$-dependence of $\langle\mathrm{sSFR}\rangle$ at
$z\\!>\\!1$ is also seen for high-mass
${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!10}$ galaxies, but,
interestingly, these galaxies do not show a monotonic increase in
$\langle\mathrm{sSFR}\rangle$ with $d_{\mathrm{node}}$ at lower redshifts. In
fact, following a decline with decreasing $d_{\mathrm{node}}$ at
${d_{\mathrm{node}}}\\!\gtrsim\\!0.2$ Mpc, there is an upturn in
$\langle\mathrm{sSFR}\rangle$ at ${d_{\mathrm{node}}}\\!\lesssim\\!0.2$ Mpc.

Figure 3:  $\langle\mathrm{sSFR}\rangle$ in bins of $d_{\mathrm{node}}$ (top
two rows) and $d_{\mathrm{fil}}$ (bottom two rows) for central galaxies (1 and
3 row) and satellite galaxies (2 and 4 row) at different redshifts. Star
formation in central galaxies is less dependent on cosmic web environment than
that in satellite galaxies which are significantly quenched at low
$d_{\mathrm{node}}$ and $d_{\mathrm{fil}}$ at low redshifts. Neither centrals
nor satellites exhibit a cosmic web dependence of star formation activity at
$z\geq 2$. Insets are not included where no significant relationships between
cosmic web environment and sSFR are seen.

Considering the filament-centric relationships, we find both differences and
similarities with the node-centric relationships. For low-mass galaxies at
$z=0$, there is a sizeable $\sim 5\times$ increase in
$\langle\mathrm{sSFR}\rangle$ from
$\langle{d_{\mathrm{fil}}}\rangle\\!\sim\\!0.3$ Mpc to
$\langle{d_{\mathrm{fil}}}\rangle\\!\sim\\!15$ Mpc, however, the rise in
$\langle\mathrm{sSFR}\rangle$ with $d_{\mathrm{fil}}$ is much smaller at $z=0$
($\lesssim 2\times$) and negligible at $z\geq 1$. For the intermediate mass
range, there is effectively no gradient of $\langle\mathrm{sSFR}\rangle$ with
$d_{\mathrm{fil}}$ at any redshift. For high-mass galaxies at $z=0$, we do not
see an upturn in $\langle\mathrm{sSFR}\rangle$ at the lowest
$d_{\mathrm{fil}}$ (unlike at low $d_{\mathrm{node}}$) but rather a somewhat
smooth rise by a factor of a few times in $\langle\mathrm{sSFR}\rangle$ with
$d_{\mathrm{fil}}$ from low to high $d_{\mathrm{fil}}$. At $z>0.5$, the
relationship between $\langle\mathrm{sSFR}\rangle$ and $d_{\mathrm{fil}}$ is
very weak. Thus, only low-mass and high-mass galaxies at low redshifts are
preferentially quenched near filaments, whereas galaxies of all masses are
impacted near nodes.

One of the most striking findings on the star formation-cosmic web connection,
seen in both the filament- and node-centric analyses, is the disappearance of
a dependence of star formation on distance to cosmic web structures at higher
redshifts. The color contour insets included in Fig. 2 show the
$\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{node}}$ and
$\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{fil}}$ relationships for many
snapshots at $0.5\\!\leq\\!z\\!\leq\\!3$. These contours flatten out past a
certain redshift for all three mass ranges, indicating that star formation
activity is essentially independent of proximity to the cosmic web prior to
this epoch. The independence of star formation on cosmic web node-centric
distance occurs at $z\sim 1.3$ for
${9\\!\leq\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!10}$ galaxies and
$z\sim 2$ for ${8\\!\leq\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!9}$ and
${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!10}$ galaxies. The
$d_{\mathrm{fil}}$-independence of star formation occurs at $z\sim 1$ for low-
mass and high-mass galaxies, while the star formation in moderate-mass
galaxies does not show any significant $d_{\mathrm{fil}}$-dependence at any
redshift. From our analysis, it can be deduced that the cosmic web environment
began affecting star formation activity during the latter stages of, or
immediately after, the so-called “cosmic noon” of star formation when the star
formation rate density in the universe peaked (ending around $z\sim 1.5$;
e.g., Madau & Dickinson, 2014).

###  3.2 Central And Satellite Galaxies

We separate our galaxy samples into central and satellite galaxies to
investigate how star formation depends on cosmic web environment for both
galaxy types. At each redshift, we identify the most massive galaxy in a halo
as the central galaxy and the rest as satellite galaxies and then repeat the
analysis in Section 3.1. The $\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{node}}$
and $\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{fil}}$ relationships are shown
for central and satellite galaxies in Fig. 3. We only include the color
contour inset plots in the panels where any significant relationship between
cosmic web environment and star formation is seen.

In general, we find that at low redshifts, the star formation in satellite
galaxies is much more strongly connected to cosmic web environment than that
of central galaxies. At $z\\!<\\!1$, there is a very modest rise in
$\langle\mathrm{sSFR}\rangle$ of low-mass centrals with $d_{\mathrm{node}}$
and in intermediate-mass centrals, there is no dependence of
$\langle\mathrm{sSFR}\rangle$ on $d_{\mathrm{node}}$. In contrast, star
formation is effectively quenched close to nodes in low-mass satellites at
$z\\!\leq\\!0.5$, and in intermediate-mass satellites at $z\\!=\\!0$.

High-mass centrals show a strong correlation between
$\langle\mathrm{sSFR}\rangle$ and $d_{\mathrm{node}}$ at low redshifts. While
the rise in $\langle\mathrm{sSFR}\rangle$ with $d_{\mathrm{node}}$ is mostly
monotonic at $z\\!=\\!0$, we see an upturn in $\langle\mathrm{sSFR}\rangle$ at
low $d_{\mathrm{node}}$ (${d_{\mathrm{node}}}\\!\lesssim\\!0.1$ Mpc) at
$z\\!\sim\\!0.5-1$, similar to that found for the full galaxy population at
the lowest redshifts (Fig. 2). This upturn is also seen in high-mass
satellites at $z\\!=\\!0$, suggesting that the elevation of star formation
activity of high-mass galaxies very close to nodes is applicable for both
centrals and satellites (with the caveat that the errors for the satellite
relationships are larger). Beyond ${d_{\mathrm{node}}}\\!\sim\\!0.1$ Mpc,
there is a smooth rise in $\langle\mathrm{sSFR}\rangle$ with
$d_{\mathrm{node}}$ for satellites at $z\\!\leq\\!0.5$ and for centrals at
$z\\!\leq\\!1$.

With respect to filaments, there is negligible dependence of
$\langle\mathrm{sSFR}\rangle$ on $d_{\mathrm{fil}}$ in centrals of any mass
across cosmic time. Both low-mass and high-mass satellites are effectively
quenched at low $d_{\mathrm{fil}}$ at $z\\!=\\!0$, while the rise in
$\langle\mathrm{sSFR}\rangle$ with $d_{\mathrm{fil}}$ is more modest in
intermediate-mass satellites. However the small-number statistics of the high-
mass satellite population prevents us from drawing strong conclusions about
their star formation dependence. While satellites appear to drive much of the
dependence of star formation on proximity to cosmic web filaments and nodes at
low redshifts, there is no statistically significant dependence of star
formation on cosmic web environment at $z\\!\geq\\!2$ for either centrals or
satellites.

###  3.3 Gas Fraction And Cosmic Web Environment

Figure 4:  The median gas fraction, $\langle f_{\mathrm{gas}}\rangle$, as a
function of $d_{\mathrm{node}}$, for all galaxies (top row), centrals (middle
row), and satellites (bottom row), at redshifts $z=0$, 1, 2, and 4. The
general cosmic web dependence of star formation follows from the available gas
supply. Satellites drive the gas fraction trends for lower mass galaxies while
both centrals and satellites drive the high-mass trends.  Figure 5:  Same as
Fig. 4, but in bins of $d_{\mathrm{fil}}$. Satellites drive the dependence of
$\langle f_{\mathrm{gas}}\rangle$ on $d_{\mathrm{fil}}$ more than centrals.

To further investigate the star formation-cosmic web connection, we examine
the available gas content in galaxies relative to nodes and filaments. To this
end, we measure the gas fraction,

${f_{\mathrm{gas}}}=\frac{{M_{\mathrm{gas}}}}{{M_{\mathrm{gas}}}+{M_{\ast}}}\,,\vspace{-5pt}$
(1)

which is the ratio of gas mass to the sum of gas and stellar mass bound to a
galaxy. We calculate the median gas fraction, $\langle
f_{\mathrm{gas}}\rangle$, for all galaxies, centrals and satellites, in the
same bins of $d_{\mathrm{node}}$ and $d_{\mathrm{fil}}$ for the same mass
ranges and redshifts as above. The $\langle
f_{\mathrm{gas}}\rangle$-$d_{\mathrm{node}}$ and $\langle
f_{\mathrm{gas}}\rangle$-$d_{\mathrm{fil}}$ relationships are presented in
Figures 4 and 5, respectively. For clarity of presentation, we only include
four redshift bins, $z=0,1,2,$ and $4$ in these plots. As in Fig. 2, the $\pm
1\sigma$ bootstrapped error-bars on the medians are shown.

Fig. 4 shows that for the full galaxy population, there is a strong dependence
of $\langle f_{\mathrm{gas}}\rangle$ on $d_{\mathrm{node}}$ at lower
redshifts. At $z\\!=\\!0$, low-mass galaxies at
${d_{\mathrm{node}}}\\!\lesssim\\!1$ Mpc are completely devoid of gas, which
explains why they are quenched in these environments. This is mostly driven by
satellite galaxies, as low-mass centrals only see a drop of a few percent in
$\langle f_{\mathrm{gas}}\rangle$ from higher to lower $d_{\mathrm{node}}$. In
intermediate-mass galaxies, $\langle f_{\mathrm{gas}}\rangle$ drops by an
order of magnitude from the highest to the lowest $d_{\mathrm{node}}$ bin at
$z\\!=\\!0$, which is commensurate with the $\sim$1 dex drop in
$\langle\mathrm{sSFR}\rangle$ in Fig. 2. This is again primarily driven by a
dramatic decline in gas fraction of satellites while centrals only exhibit a
modest decline.

In high-mass galaxies, we find a minimum in $\langle f_{\mathrm{gas}}\rangle$
at ${d_{\mathrm{node}}}\\!\approx\\!0.7$ Mpc followed by a steep rise at lower
$d_{\mathrm{node}}$. This dramatic upturn in gas fraction helps explain the
upturn in star formation at low $d_{\mathrm{node}}$ at low redshifts, but this
turnover is a) much more pronounced in $\langle f_{\mathrm{gas}}\rangle$ than
in $\langle\mathrm{sSFR}\rangle$ and b) persists out to $z=4$ for $\langle
f_{\mathrm{gas}}\rangle$ while it only exists out to $z\sim 1$ for
$\langle\mathrm{sSFR}\rangle$. The relationship between $\langle
f_{\mathrm{gas}}\rangle$ and $d_{\mathrm{node}}$ in high-mass galaxies is
largely dictated by central galaxies, which have large gas fractions close to
nodes across cosmic time. This, however, does not result in highly enhanced
star formation in low-redshift centrals at low $d_{\mathrm{node}}$, possibly
implying a lack of star formation efficiency in these environments – possibly
due to central AGN heating the gas in these galaxies and suppressing star
formation (see discussion below). High-mass satellites also exhibit a small
upturn in $\langle f_{\mathrm{gas}}\rangle$ at
${d_{\mathrm{node}}}\\!\lesssim\\!0.1$ Mpc at $z\\!\leq\\!3$. Unlike with star
formation activity, the gas fraction in all
${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!10}$ galaxies depends on the
proximity to nodes even at $z\\!=\\!4$.

Proximity to filaments is less strongly correlated with $\langle
f_{\mathrm{gas}}\rangle$ than proximity to nodes, as shown in Fig. 5. At low
redshifts, a monotonic rise in $\langle f_{\mathrm{gas}}\rangle$ with
$d_{\mathrm{fil}}$ in low and intermediate-mass galaxies is caused mostly by
the steep rise in the satellite population, but this dependence disappears
with increasing redshift. Centrals of all masses show virtually no
$d_{\mathrm{fil}}$-dependence on $\langle f_{\mathrm{gas}}\rangle$ with at any
redshift, consistent with a lack of dependence of star formation activity on
distance to filaments.

We also note that the declining availability of gas in galaxies should not
immediately result in reduced star formation activity; instead, there should
be a time lag between the reduction in gas and the reduction in star
formation. This is generally consistent with our results: $\langle
f_{\mathrm{gas}}\rangle$ decreases at small $d_{\mathrm{node}}$ and
$d_{\mathrm{fil}}$ at higher redshift than does $\langle\mathrm{sSFR}\rangle$
for any given stellar mass range. In satellites and even high-mass centrals, a
correlation between $\langle f_{\mathrm{gas}}\rangle$ and $d_{\mathrm{node}}$
exists out to $z\\!=\\!4$ while star formation is independent of
$d_{\mathrm{node}}$ at $z\\!\geq\\!2$. Alternatively, these results can also
be explained by star formation being less efficient further from nodes than
closer to nodes at earlier times.

Our results in this section suggest the following. 1) Star formation quenching
near cosmic web structures is typically preceded by a scarcity of gas, 2) the
gas fraction in satellite galaxies is more significantly affected by cosmic
web environment than that in central galaxies and drive the general cosmic web
dependence of gas fraction, and 3) at later times, high-mass galaxies,
including both satellites and centrals, are more gas-rich near centers of
nodes than at the outskirts, leading to increased star formation closer to
nodes.

##  4 Discussion

###  4.1 Physical Interpretations

Here, we interpret our results in terms of physical mechanisms governing the
evolution of galaxies and large-scale structure. Perhaps the most puzzling
result is that the star formation activity of galaxies in TNG does not depend
on their large-scale cosmic web environment at $z\\!\geq\\!2$, in contrast
with later times when significant dependence occurs. At face value, this seems
to suggest a rising importance of quenching driven by environment with cosmic
time and, indeed, several recent works have found varying degrees of evidence
for a lack of small or large-scale environmental dependence of star formation
at higher redshifts – in both observations (e.g., Moutard et al., 2018; Chang
et al., 2022; Momose et al., 2022) and simulations (e.g., Xu et al., 2020).

####  4.1.1 The Cosmic web dependence After Cosmic Noon

The low-redshift dependence of star formation activity on $d_{\mathrm{node}}$
and $d_{\mathrm{fil}}$ can generally be explained by the variation of gas
fraction with these distances. In lower mass galaxies at low redshifts, the
monotonic descent in $\langle\mathrm{sSFR}\rangle$ towards nodes and filaments
is consistent with the corresponding descent in $\langle
f_{\mathrm{gas}}\rangle$. On average, low-mass galaxies that are within
several hundred kpc of a node or filament effectively stop forming new stars
at $z\\!=\\!0$, most likely because they have very little to no gas available
to do so, a behavior largely driven by satellites.

This points to a picture where dwarf galaxies that accrete onto the halos of
more massive centrals are quenched in overdense environments where their gas
supplies are depleted. Dwarf satellites located in galaxy clusters and groups
are subjected to harsh gaseous environments dominated by warm and hot gas with
high densities and long cooling times. In these environments, a combination of
physical processes can act together on the gas reservoirs of dwarf satellites.

Gas may be removed by ram pressure stripping when these galaxies move through
the group/cluster medium or by gravitational (tidal) interactions between the
satellites and the central/other satellites or the halo itself. These
processes, while often identified as the likely culprits for gas stripping and
quenching of low-mass satellites in clusters/groups, typically act on
relatively short timescales of $\lesssim$500 Myr (e.g., Bahé & McCarthy, 2015;
Marasco et al., 2016). Here, we find that low-mass satellites close to nodes
are already quenched at $z\\!=\\!0.5$ and have greatly reduced gas fractions
at $z\\!=\\!1$, meaning that the quenched satellites in the local universe had
been quenched much earlier. In fact, Donnari et al. (2021) found that in TNG,
a large fraction of $z\\!=\\!0$
$\log(M_{\ast}/{\mathrm{M}_{\odot}})\\!\lesssim\\!10$ satellites in groups and
clusters were members of other halos whence they experienced environmental
quenching before falling into their final host – a phenomenon dubbed “pre-
processing” (see also, e.g., Fujita, 2004; Hou et al., 2014).

AGN feedback from massive central galaxies in groups and clusters may also
play an important role in quenching star formation in satellites. The TNG
model allows for both “ejective” feedback whereby BHs expel star-forming gas
from a galaxy and “preventative” feedback whereby BHs heat up the gas and
prevent star formation on longer timescales (Zinger et al., 2020). Both these
modes of AGN feedback have been observed in galaxies near and far (e.g.,
Fabian, 2012; King & Pounds, 2015). In particular, Martín-Navarro et al.
(2019) showed that stronger BH feedback produces hotter group/cluster media
that makes quenching more efficient in satellites. While beyond the scope of
this work, it would be valuable to understand how central BH properties such
as mass and accretion rate might relate to the cosmic web dependence of star
formation.

Satellites at close filament-centric distances and
${d_{\mathrm{node}}}\\!>\\!1$ Mpc would reside in more intermediate density
environments than those at close node-centric distances. In either of these
types of environments, fresh gas accretion onto the ISM can be stopped by
strangulation/starvation such that star formation quenches over longer
timescales of $\sim$few Gyr (e.g., Peng et al., 2015; Zinger et al., 2018). In
a comprehensive analysis of nearby galaxies, Trussler et al. (2020) found that
starvation is likely to be the initial prerequisite for quenching across
virtually all masses but the remaining cold ISM gas needs to be heated or
ejected to complete the quenching process. Low-mass centrals, on the other
hand, exhibit a modest cosmic web dependence on gas fraction and consequently,
star formation. For these galaxies, so-called “mass quenching” via internal
processes (such as feedback) may dominate over environmental effects (e.g.,
Peng et al., 2010).

In our investigation, we considered the total content of all gas
gravitationally bound to a galaxy, without regards to the physical conditions
or location of the gas. For instance, we did not measure the fraction of cool
gas which would in principle be a more direct measure of gas supply available
for star formation. Regardless, we find that the gas fraction of low-mass
satellites declines dramatically from $z\\!=\\!1$ to $z\\!=\\!0$ at small
$d_{\mathrm{node}}$ and to a lesser, but still significant, extent at small
$d_{\mathrm{fil}}$, indicating a lack of accretion from the IGM to the CGM.
Many hydrodynamical simulations indeed show that accretion of cold gas from
the IGM becomes increasingly inefficient over time (e.g., Anglés-Alcázar et
al., 2017; Hafen et al., 2020). Furthermore, gas in the CGM may be heated
substantially or even ejected by SNe (e.g., Pandya et al., 2022) or AGN (as
discussed above) to prevent accretion onto the ISM.

In low-redshift ${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!10}$
galaxies, a minimum in gas fraction and star formation activity occurs at
${{d_{\mathrm{node}}}\\!\sim\\!0.2}$ Mpc, following an unexpected rise at
smaller $d_{\mathrm{node}}$. This upturn in $f_{\mathrm{gas}}$ and sSFR close
to nodes persists out to $z\\!=\\!2$, but manifests in an analogous
relationship between star formation and proximity to nodes at $z\\!\leq\\!1$.
When we limit our sample to even higher mass galaxies, this effect is further
accentuated, implying that the highest mass galaxies are primarily
responsible. The effect of enhanced star formation very close to nodes is
stronger in satellites than in centrals at $z\\!=\\!0$ while the converse is
true at $z\\!=\\!0.5-1$. The fact that both $\langle\mathrm{sSFR}\rangle$ and
$\langle f_{\mathrm{gas}}\rangle$ are lowest at
${d_{\mathrm{node}}}\\!\sim\\!0.2$ Mpc implies that massive galaxies falling
into groups/clusters from the outskirts are more gas-poor and passive relative
to galaxies at the center.

It is conceivable that some/much of the gas removed from low-mass satellites
in rich groups and clusters ends up in higher mass galaxies, enabling the
massive galaxies to form stars at higher rates near the centers of these
halos. The cores of many groups and clusters have been observed to be abundant
in cold gas, which may temporarily trigger star formation near the center
(e.g., McDonald et al., 2012; Olivares et al., 2019). However, this gas is
also hypothesized to feed central AGN activity and eventually curtail star
formation (see Donahue & Voit, 2022, and references therein). Heating from the
central AGN could explain why the rise in star formation at small
$d_{\mathrm{node}}$ is not as dramatic as the rise in gas fraction in high-
mass galaxies.

The enhancement of star formation in dense environments is not typically
observed in statistical studies of the cosmic web-galaxy connection (e.g.,
Kraljic et al., 2018; Winkel et al., 2021). But there is evidence – both in
observations (e.g., Roediger et al., 2014) and in simulations (e.g., Nelson et
al., 2018) – of galaxies in groups/clusters enjoying brief episodes of star
formation via compression of gas from ram pressure, mergers or other
processes, a phenomenon sometimes called “rejuvenation.” However, these events
are rare in TNG, with only $10\%$ of
$\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!>\\!11$ galaxies and $6\%$ of all
galaxies at $z\\!=\\!0$ ever having experienced them (Nelson et al., 2018). An
analysis of satellite galaxies by Martín-Navarro et al. (2021) showed that AGN
outflows can clear out the CGM of massive halos, which reduces ram pressure
and preserves star formation in satellites along the direction of the outflows
(the minor axis of the central). These phenomena of positive AGN feedback can
potentially boost star formation in dense environments such as those close to
nodes.

It is also possible that the high-density upturn in star formation is a result
of some additional mechanism in the simulations funnelling too much gas into
galaxies, over-cooling the gas, or otherwise reducing the efficiency of
quenching at the highest density environments. Donnari et al. (2021) report
that TNG galaxies in dense environments have diverse histories and quenching
pathways that may complicate the interpretation of how and when they quench.
Moreover, the AGN-driven gas expulsion in TNG is known to be so efficient that
there are very few galaxies with intermediate sSFR (i.e., Green Valley
galaxies; e.g., Schawinski et al., 2014), creating tension with observations
(Terrazas et al., 2020).

####  4.1.2 No Cosmic web dependence Before Cosmic Noon?

There is now a growing body of evidence suggesting that cosmological accretion
shocks from the formation of cosmic web structures, similar to those around
massive halos, can affect galaxy formation. Birnboim et al. (2016) showed that
in filaments with a specific linear mass density, the accretion shocks are
unstable. These structures can efficiently siphon cool gas into
$10\\!\lesssim\\!\log({M_{\mathrm{200,c}}}/{\mathrm{M}_{\odot}})\\!\lesssim\\!13$
halos at $z=3$ and
$12\\!\lesssim\\!\log({M_{\mathrm{200,c}}}/{\mathrm{M}_{\odot}})\\!\lesssim\\!15$
halos at $z\\!=\\!0$ (see their Fig. 5). According to the stellar-to-halo-mass
relations at these redshifts (e.g., Behroozi et al., 2019), this means that
unstable filaments can potentially enhance star formation in galaxies of
virtually all masses we studied at higher redshifts, while at lower redshifts
only the most massive galaxies would see an increase in star formation via
this channel. This phenomenon is a possible pathway for early galaxies close
to filaments and nodes to have their sSFR elevated to levels comparable to
those far from filaments and nodes.

This explanation necessitates an environmental dependence of overall star
formation activity at high $z$ instead of specifically quenching. The net
trend of constant sSFR with distance from the cosmic web could be naively
interpreted as quenching processes being environment-independent at high $z$.
As noted in Section 3.3, we find evidence of star formation in satellites
close to nodes being more efficient than that in galaxies further away at
early times ($z\\!\geq\\!2$). A plausible scenario for this is that gas is
more efficiently channelled into the centers of nodes, and eventually
galaxies, via cold streams at high redshift (e.g., Dekel et al., 2009).

Cosmological accretion shocks can also suppress star formation in galaxies.
Zinger et al. (2018) showed that accretion shocks at the outskirts of galaxy
clusters can quench satellites, which likely impacts galaxies near nodes in
our analysis. In TNG, Li et al. (2023) found that shock-induced stripping of
the ISM and CGM can quench low-mass satellites inside clusters at
$z\\!<\\!0.11$. Recently, Pasha et al. (2022) found that
$5.5\\!<\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!8.5$ central galaxies
at $z\\!=\\!2-5$ can be quenched by shock-heated cosmic sheets (which
eventually collapse into filaments and nodes; e.g., Bond et al. (1996)). These
shocks directly raise the ambient gas temperature in the vicinity of the
sheets and suppress gas accretion and star formation in surrounding galaxies.

The impact of accretion shocks in filaments and nodes on galaxy quenching, as
a function of both stellar mass and redshift, may be central to interpreting
the results of this paper and therefore deserves detailed investigation. In a
follow-up study, we will address this problem by analyzing the gaseous
conditions of filaments and nodes – with particular emphasis on accretion
shock signatures – in tandem with properties of the galaxies residing within
them across cosmic time. This analysis will also allow us to characterize
filaments and nodes in more detail and account for the fact that not all
filaments or nodes will have the same effect on galaxy formation (e.g.,
Galárraga-Espinosa et al. 2020 found short and long filaments in TNG to be
statistically different populations).

####  4.1.3 Other Important Physical Considerations

Angular momentum is another important aspect of galaxy formation which may
shed additional light on how quenching is affected by the cosmic web. From
their analysis of quenching timescales in TNG, Walters et al. (2022) suggested
that low angular momentum gas accretion leads to galaxies quenching faster
than high angular momentum accretion. In the cosmic web framework, galaxies
form in the vorticity-rich regions of filaments, acquire angular momentum, and
drift to the nodes (e.g., Dubois et al., 2014; Codis et al., 2015).
Simulations have predicted for many years that at $z\\!\gtrsim\\!1.5$, gas and
angular momentum are funnelled through cold filamentary streams into the
centers of galaxies (e.g., Dekel et al., 2009; Pichon et al., 2011). Over
time, as these streams disappear due to heating or other processes, the
efficiency of galaxy formation at the centers of filaments and nodes may also
decline, potentially explaining the difference in star formation activity in
these regions between low and high redshift. Additionally, galactic properties
such as mass and sSFR have been found to be correlated with the acquisition of
angular momentum from the cosmic web (e.g., Kraljic et al., 2019; Welker et
al., 2020). Thus, a complete understanding of how the cosmic web affects
quenching needs to account for angular momentum acquisition in galaxies in
tandem with proximity to cosmic web structures.

Many of the relationships between star formation and cosmic web environment
may result from the assembly of DM halos. Subhalo abundance matching
predictions from $\Lambda$CDM cosmology are found to agree with observed SDSS
galaxy distributions, implying that the local density dependence of galaxy
properties stems from the corresponding density dependence of halo properties
(Dragomir et al., 2018). In the Bolshoi-Planck simulations, Lee et al. (2017)
found that for $\log({M_{\mathrm{200,c}}}/{\mathrm{M}_{\odot}})\lesssim 12$
halos, halo accretion is higher in low-density environments at $z\lesssim 1$
and in high-density environments at $z\\!\gtrsim\\!1$. However, some $N$-body
simulations have shown that DM halo properties are independent of cosmic web
location at fixed overdensities (e.g., Goh et al., 2019). A detailed analysis
of the dependence of halo mass accretion with cosmic web environment in TNG is
necessary to disentangle the effect of halo mass growth from baryonic effects
in determining the galaxy quenching-cosmic web connection.

###  4.2 Other Caveats

We consider certain other aspects of our methodology that may affect the
robustness of our results as well as the conclusions we draw. The first is how
numerical resolution in the simulation may affect our results. Galárraga-
Espinosa et al. (2021) showed that despite the $\sim$8 times difference in
resolution between TNG300-1 and TNG300-2, there are only minor differences in
the distribution (including the DisPerSE reconstruction) and properties of
filaments. The large scales of the cosmic web are likely to be well-resolved
with any of the TNG runs, but the smaller scales of galaxy formation are more
sensitive to resolution. Thus, it would be interesting to compare our results
for TNG100-1 with those of TNG50-1, which has $\sim$16 times the particle mass
resolution of TNG100-1 (e.g., Nelson et al., 2019b, 2020).

The input physics model is another potential source of uncertainty for
theoretical galaxy evolution studies. Galárraga-Espinosa et al. (2020) found
that different baryonic physics implemented in different simulations result in
somewhat different matter distribution around filaments but that gravity is
still the dominant driver. Xu et al. (2020) investigated the sSFR of galaxies
in filaments, nodes, sheets, and voids in the EAGLE simulation which uses
somewhat different hydrodynamics and feedback prescriptions from the TNG model
(see Schaye et al., 2015). They found that at $z\\!<\\!1$, galaxies with
$\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\lesssim\\!10.5$ are less star-
forming in nodes than other cosmic web environments, while for more massive
galaxies there is virtually no cosmic web dependence, the latter finding being
at odds with our results. At $z\\!>\\!1$, they found no statistical dependence
of sSFR on the cosmic web environment, consistent with our findings. In a
separate study, Rosas-Guevara et al. (2022) found that the star-forming
fraction of $\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!>\\!9$ galaxies in EAGLE
decreases with distance to the nearest void at $z\\!=\\!0$. It would be
interesting to apply our methodology to investigate the evolving cosmic web
dependence of star formation in other hydrodynamical cosmological simulations
such as SIMBA (Davé et al., 2019) and Horizon-AGN (Dubois et al., 2014). Such
comparisons might help illuminate the effect of uncertain baryonic processes
such as AGN feedback on the relationship between galaxy formation and the
cosmic web.

Another crucial check on our results is the cosmic web reconstruction itself.
As mentioned in Section 2.2, we experimented with DisPerSE parameter choices
such as persistence and smoothing of the filamentary skeleton. The latter did
not have any significant effect on our results and varying the former affected
the frequency of identified structures but did not affect any qualitative
conclusions. Overall, we consider our results to be robust to parameter
choices. There are several other cosmic web reconstruction techniques that
have been employed for cosmic web studies, which have advantages and
disadvantages over the DisPerSE framework (see Libeskind et al., 2018, for a
detailed comparison of many of these methods). We are currently applying a new
state-of-the-art cosmic web reconstruction algorithm called the Monte Carlo
Physarum Machine (MCPM), inspired by the Physarum Polycephalum (slime mold)
organism (Elek et al., 2021, 2022), to compare to the local density estimation
and global cosmic web characterization from DisPerSE. This method produces
continuous cosmic matter densities (as opposed to discrete DTFE densities at
the locations of galaxies) and has been applied successfully to both
theoretical and observational datasets (e.g., Burchett et al., 2020; Simha et
al., 2020; Wilde et al., 2023).

We also assess the importance of local galaxy overdensity in shaping the star
formation-cosmic web connection. We repeat our analyses in Section 3 by only
considering galaxies with local DTFE galaxy overdensity (as computed by
DisPerSE) within $\pm 1\sigma$ of the mean. We find that the resulting
relationships with respect to $d_{\mathrm{node}}$ and $d_{\mathrm{fil}}$ look
strikingly similar to those we report without filtering out galaxies by
overdensity, implying that the effect of cosmic web environment on star
formation persists beyond just the highest density regions of the universe.
However, we stress that local overdensity and global cosmic web environment
are necessarily related to each other and it is therefore not trivial to
disentangle the effects of one from the other. We defer a detailed
characterization of the dependence of $d_{\mathrm{fil}}$ and
$d_{\mathrm{node}}$ on overdensity across different redshifts in TNG100 to a
future work (see Malavasi et al., 2022, for an in-depth mapping of overdensity
to cosmic web proximity in TNG300).

Finally, in our interpretations, we neglected the effect of pseudo-evolution
of filaments and nodes, i.e., the evolution of the reference density (in our
case, the DTFE mean density) instead of a true physical density. Such pseudo-
evolution is known to strongly drive the mass-evolution in DM halos,
especially at lower redshifts (Diemer et al., 2013), and we defer a detailed
investigation of this effect to future work.

###  4.3 Testing Predictions with Observations

The predictions presented herein from the TNG100 simulation establish clear
objectives for observational studies. First, we identified a point in cosmic
time where galaxies’ star formation activity begins to depend on their
location relative to the large-scale cosmic web environment. Confronting this
prediction with observations will necessitate wide-field galaxy surveys
capable of characterizing the large-scale structure over a large range of
redshifts, out to at least $z\\!=\\!2$. Second, a common theme we observed in
both sSFR and gas fraction was an increase at small node-centric distances for
high-mass galaxies. This will require both the extensive survey data necessary
for finding, and perhaps even more challenging, measuring the gas contents of,
these galaxies. Spectroscopic galaxy surveys both underway and planned for the
next several years should make serious headway towards at least the first
element of this challenging observational experiment.

The current gold standard for wide-field spectroscopic surveys is SDSS, which
can provide the lowest redshift anchor point for such a comparison. The quoted
SDSS spectroscopic completeness limit of $m_{r}\\!=\\!17.7$ would correspond
to a redshift limit of $z\\!\sim\\!0.01$ for the lowest mass galaxies studied
here ($10^{8}~{}\mathrm{M}_{\odot}$). Even at $z\\!\sim\\!0.1$, SDSS is only
complete to $\sim 10^{10}~{}\mathrm{M}_{\odot}$, covering the most massive bin
we study. Thus, SDSS, in principle, is capable of yielding measurements
comparable with the dark blue data points in Figures 2 and 3. Although an
independent analysis of observational datasets with our methodology is beyond
the scope of this paper, we refer the reader to the work of Kuutma et al.
(2017), Crone Odekon et al. (2018), and Winkel et al. (2021), who explore
similar relationships with SDSS. Also of note is Kraljic et al. (2018) who
employ the Galaxy and Mass Assembly (GAMA) survey, which goes two magnitudes
deeper than SDSS, albeit over a much smaller volume. Still, this does not push
completeness to the $z\\!>\\!1$ transition point in cosmic web dependence we
report here.

Constraining the higher redshifts will be more difficult, although the various
Dark Energy Spectroscopic Instrument (DESI) surveys should enable cosmic web
reconstructions at intermediate redshifts. Initial data and results from the
Survey Validation phase are beginning to be released now, showing promising
prospects for mapping the large-scale structure to $z\\!\sim\\!0.5$ for the
Bright Galaxy Survey, $z\\!\sim\\!1.1$ for the Luminous Red Galaxies (LRGs),
$z\\!\sim\\!1.6$ for Emission Line Galaxies (ELGs), and possibly beyond (Lan
et al., 2023, and references therein). However, each of these samples is
likely to contain highly biased tracers of the underlying structure; e.g., the
LRGs are by definition passive galaxies and will preferentially reside in the
most massive halos, likely tracing nodes. Conversely, the ELGs, being
vigorously star-forming, might bias against these very environments.
Nevertheless, neither of these samples will suitably represent the full
diversity in star formation exhibited by the general population. Deep follow-
up surveys with more agnostic selection criteria will be necessary for a fair
comparison with our results.

The Subaru Prime Focus Spectrograph (PFS) also offers great promise for
mapping out the galaxy-cosmic web connection at higher redshifts (Takada et
al., 2014). In particular, the PFS Galaxy Evolution program will observe up to
half a million galaxies at redshifts $0.7\\!\lesssim\\!z\\!\lesssim\\!7$
(Greene et al., 2022). The largest survey of this program is expected to yield
$>\\!10^{5}$ continuum-selected galaxies down to a stellar mass limit of
$\log(M_{\ast}/\mathrm{M}_{\odot})\\!\approx\\!10.5$ over a comoving survey
volume of $\sim\\!0.1~{}\mathrm{Gpc}^{3}$ ($\sim$100 times the TNG100 volume)
at $0.7\\!\lesssim\\!z\\!\lesssim\\!2$. Stellar masses, SFRs, and gas
properties will be measured for the vast majority of these galaxies. This
sample will be complemented by a smaller number of LBGs and Lyman Alpha
Emitters (LAE) out to $z\\!\sim\\!7$ which would be more biased tracers of the
cosmic web as discussed above.

Spectroscopic surveys with JWST and, eventually, the Nancy Grace Roman Space
Telescope will yield galaxy datasets ripe for placing in context with the
cosmic web mapped by DESI and Subaru PFS. Roman, which will map 1700 deg2 of
the sky at infrared wavelengths via the High Latitude Spectroscopic Survey
(Wang et al., 2022), should reveal the cosmic web over scales of $\sim$1 Gpc
as well as the galaxies within to $z\\!\sim\\!2$. In the shorter term, JWST,
through programs such as JADES (Cameron et al., 2023), will yield galaxy
spectra to $z>5$ albeit over much smaller fields of view (the JWST Micro-
shutter Assembly will map scales $\sim 1$ Mpc across in a single pointing). An
amalgamation of several such deep fields will be necessary to mitigate cosmic
variance.

##  5 Conclusion

In this study, we investigated the IllustrisTNG simulations to understand how
the star formation activity of galaxies depends on their cosmic web
environment. We used all ${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!8}$
galaxies to reconstruct the cosmic web in the TNG100 snapshots using the
DisPerSE framework. We measured the median sSFR and median $f_{\mathrm{gas}}$
of galaxies as functions of distance to the nearest cosmic web node
($d_{\mathrm{node}}$) and filament spine ($d_{\mathrm{fil}}$). Our main
results are as follows:

  1. 1.

The $\langle\mathrm{sSFR}\rangle$ of galaxies at any mass only depends on
$d_{\mathrm{node}}$ or $d_{\mathrm{fil}}$ at redshifts $z\\!\lesssim\\!2$; the
median star formation is independent of cosmic web environment at
$z\\!\geq\\!2$. This holds true also for central and satellite galaxies
separately.

  2. 2.

In ${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!10}$ galaxies,
$\langle\mathrm{sSFR}\rangle$ increases monotonically with $d_{\mathrm{node}}$
at $z\\!\leq\\!1$, with
${8\\!\leq\\!\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!<\\!9}$ galaxies being
completely quenched at ${d_{\mathrm{node}}}\\!<\\!1$ Mpc at $z\\!\leq\\!0.5$.
$\langle\mathrm{sSFR}\rangle$ has a shallower increase with $d_{\mathrm{fil}}$
at these redshifts. These trends are almost entirely driven by satellites.

  3. 3.

In ${\log({M_{\ast}}/{\mathrm{M}_{\odot}})\\!\geq\\!10}$ galaxies, the
$\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{node}}$ relationship inverts at
${d_{\mathrm{node}}}\\!\lesssim\\!0.2$ Mpc up to $z\\!=\\!1$, while the
$\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{fil}}$ relation does not. The
$\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{node}}$ inversion is driven by both
satellites and centrals, but the
$\langle\mathrm{sSFR}\rangle$-$d_{\mathrm{fil}}$ relationship is due to
satellites.

  4. 4.

Most of these star formation-cosmic web relationships can be explained by the
cosmic web dependence of gas fraction in galaxies, although there is evidence
of $\langle f_{\mathrm{gas}}\rangle$ depending more strongly on cosmic web
environment than $\langle\mathrm{sSFR}\rangle$ in some cases.

Our results point to a picture where the influence of the cosmic web
environment on quenching galaxies is first established at $z\\!\sim\\!2$. In
the last $\sim$10 Gyr, low-mass dwarf satellites are quenched by their star-
forming gas supplies being depleted either on short timescales (e.g., via ram
pressure stripping or outflows) or on longer timescales (e.g., via
starvation), while star formation in low-mass centrals is far less affected by
cosmic web environment. At this epoch, high-mass galaxies at the centers of
nodes are more gas-rich and star-forming than their counterparts at the
outskirts, which could be due to temporary rejuvenation events, positive AGN
feedback, and/or a consequence of the TNG model itself. In the earlier
universe ($>$10 Gyr ago), cosmic web structures likely aided star formation
more than they suppressed it, possibly via unstable filaments feeding cold gas
to galaxies or cold streams efficiently funnelling initially high angular
momentum gas to the central regions of filaments and nodes.

In a follow-up study, we will investigate how the gaseous physical conditions
of filaments and nodes affect galaxy formation in TNG100, in particular how
accretion shocks around filaments and nodes affect star formation.
Furthermore, we will compare the cosmic web reconstruction from DisPerSE with
that from the novel MCPM algorithm (Elek et al., 2021, 2022) to obtain more
fine-grained insights into the global and local environmental dependence of
star formation across cosmic time. The results of this work provide important
predictions to test against ongoing large spectroscopic surveys such as SDSS
and DESI, as well as those ongoing and planned with Subaru PFS, JWST and
Roman.

We are very grateful to N. Luber and Z. Edwards for help with setting up
DisPerSE. We thank the anonymous referee for helpful comments that improved
the quality of this manuscript. We thank attendees of the 2022 Santa Cruz
Galaxy Workshop and the 2023 KITP Cosmic Web Conference, including F. van den
Bosch, J. Woo, H. Aung, J. Powell, C. Pichon, U. Kuchner, C. Welker, S. Simha,
K-G. Lee, and R. Momose, for stimulating and interesting conversations on this
work. FH, JNB, and AA are supported by the National Science Foundation LEAPS-
MPS award $\\#2137452$. OE is supported by an incubator fellowship of the Open
Source Program Office at UC Santa Cruz funded by the Alfred P. Sloan
Foundation (G-2021-16957). DN is supported by NSF (AST-2206055) and NASA
(80NSSC22K0821 & TM3-24007X) grants.

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