11institutetext: Université Paris-Saclay, CNRS, Institut d’Astrophysique
Spatiale, 91405 Orsay, France 22institutetext: Littoral, Environnement et
Sociétés, Université de La Rochelle, and CNRS (UMR7266), La Rochelle, France
33institutetext: Instituto de Astrofísica de Canarias, E-38205 Tenerife, and
University of La Laguna, E-38206 Tenerife, Spain 44institutetext: Laboratoire
de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne
Université, Université Paris Cité, F-75005 Paris, France 55institutetext:
Tartu Observatory, Tartu University, Observatooriumi 1, 61602 Tõravere,
Tartumaa, Estonia

# Dissecting a miniature universe:
A multi-wavelength view of galaxy quenching in the Shapley supercluster

N. Aghanim<EMAIL_ADDRESS>T. Tuominen 11 V. Bonjean 2233 C.
Gouin 11 T. Bonnaire 44 M. Einasto 55

Multiple-cluster systems, i.e. superclusters, contain large numbers of
galaxies assembled in clusters inter-connected by multi-scale filamentary
networks. As such, superclusters are a smaller version of the cosmic web and
can hence be considered as miniature universes. In addition to the galaxies,
superclusters also contain gas, hot in the clusters and warmer in the
filaments. Therefore, they are ideal laboratories to study the interplay
between the galaxies and the gas. In this context, the Shapley supercluster
(SSC) stands out since it hosts the highest number of galaxies in the local
universe with clusters interconnected by filaments. In addition, it is
detected in both X-rays and via the thermal Sunyaev-Zel’dovich (tSZ) effect,
making it ideal for a multi-wavelength study of the gas and galaxies. Applying
for the first time a filament-finder based on graphs, T-REx, on a
spectroscopic galaxy catalogue, we uncovered the 3D filamentary network in and
around SSC. Simultaneously, we used a large sample of photometric galaxies
with information on their star formation rates (SFR) in order to investigate
the quenching of star formation in the SSC environments which we define as a
function of the gas distribution in the Planck tSZ map and the ROSAT X-ray
map.
With T-REx, we confirm filaments already observed in the distribution of
galaxies of the SSC, and detect new ones. We observe the quenching of star
formation as a function of the gas contained in the SSC. We show a general
trend of decreasing SFR where the tSZ and X-ray signals are the highest,
within the high density environments of the SSC. Within these regions, we also
observe a rapid decline of the number of star-forming galaxies, coinciding
with an increasing number of transitioning and passive galaxies. Within the
SSC filaments, the fraction of passive galaxies is larger than outside
filaments, irrespective of the gas pressure. Our results suggest the zone of
influence of the SSC, in which galaxies are pre-processed and quenched, is
well defined by the tSZ signal that combines the density and temperature of
the environments.

###### Key Words.:

Cosmology: large-scale structure of Universe, Galaxies: clusters: individual:
Shapley, Galaxies: evolution

##  1 Introduction

The cosmic web is an entangled structure made of nodes (galaxy groups and
clusters) at the intersection of filaments surrounded by walls and separated
by voids. In the cosmic web, galaxy superclusters are defined as the high-
density regions in the distribution of galaxies or galaxy groups/clusters
(e.g., Einasto et al., 1997; Liivamägi et al., 2012; Chon et al., 2013; Chow-
Martínez et al., 2014; Sankhyayan et al., 2023a, b). Superclusters occupy only
1% of the volume of the Universe; however they host around 15% of galaxies
including all very rich and luminous galaxy clusters which reside in
superclusters or in their high-density cores (e.g., Einasto et al., 2022b,
2024). Furthermore, numerical simulations show that the progenitors of the
present-day galaxy superclusters are already seen in the very early Universe
(Park et al., 2022; Einasto et al., 2023). Several studies have shown that
galaxy superclusters or their high-density cores are the largest objects which
are either collapsing now or which will collapse in the future (e.g., Dünner
et al., 2006; Kopylova & Kopylov, 2007; Luparello et al., 2011; Chon et al.,
2015; Einasto et al., 2016, 2021, 2022b). This property has further been used
to define superclusters as in Luparello et al. (2011) and Chon et al. (2015).
In their study, Einasto et al. (2022b) compared different definitions of
superclusters based on their sizes and masses. They showed that the largest
collapsing cores are associated with the richest superclusters, such as the
Shapley and the Corona Borealis supercluster in the local Universe, or the
BOSS Great Wall at redshift $z=0.47$. These cores have sizes up to
approximately $10-12$ h-1 Mpc and masses up to $10^{16}M_{\mathrm{sun}}$.

Superclusters embed galaxies, groups, and clusters connected by galaxy
filaments, which may extend to their surrounding cosmic web. Supercluster
environment is known to impact the evolution of galaxies within them. This was
shown in seminal studies (e.g., Einasto & Einasto, 1987) and in detailed
analyses of a few nearby superclusters (e.g., Luparello et al., 2013; Pearson
et al., 2014; Lietzen et al., 2016; Lacerna et al., 2016; Einasto et al.,
2018, 2020, 2021; Castignani et al., 2022; Heinämäki et al., 2022). They
conclude that galaxies in groups within superclusters have older stellar
populations, suggesting that groups in superclusters formed differently from
groups in other environments (see e.g., Einasto et al., 2023, for a recent
study) with their galaxies impacted via a stage of pre-processing before they
fall in the clusters. In addition to their galaxy content, simulations (e.g.,
Flores-Cacho et al., 2009) show that superclusters contain large quantities of
hot ionised gas which should be observed via the thermal Sunyaev-Zel’dovich
(tSZ) signal (Sunyaev & Zeldovich, 1970). As a matter of fact, evidence for
hot ionised gas in superclusters was found either in individual cases (e.g.,
Battistelli et al., 2006), for a few selected objects (e.g., Heinämäki et al.,
2022) or via the stacking of hundreds of superclusters (Tanimura et al., 2019)
or directional stacking (Lokken et al., 2022). This gas was also observed in a
few cases in the X-ray domain (e.g., Kull & Böhringer, 1999; Reiprich et al.,
2021; Veronica et al., 2022). The interplay between gas and galaxies in
clusters is one of the main drivers of galaxy evolution and as such it has
been extensively studied. This interplay intervenes at different redshifts and
masses, it is quite complex, and it takes very diverse forms (such as ram
pressure stripping, evaporation, etc., see e.g., Gunn & Gott, 1972; Cowie &
Songaila, 1977; Larson et al., 1980; Nulsen, 1982, for early studies). In
addition to the impact of the local overdensity, those physical processes
actually shape the galaxy properties and their star formation activity.

In the present study, we investigate the relation between the hot gas in a
supercluster and the galaxy properties. To do so, we determine the
supercluster’s structure and examine how the star-formation rate of the galaxy
populations evolves with the Compton $y$ parameter tracing the hot gas
distribution.
For our analysis, we focus on the extended cosmic-web structure that contains
the largest concentration of galaxies and rich Abell clusters (34 in the
catalogue of Einasto et al., 1997) in the local Universe, namely the Shapley
supercluster (SSC, Shapley, 1930). This miniature Universe extends over
$\approx 260$ Mpc2 and covers a redshift range from 0.033 to 0.06 (with a mean
redshift $z=0.048$). Its core region, with the right ascension ranging between
R.A. = 198 and 204 degrees and declination ranging between -34 and -29
degrees, includes 11 clusters and groups (A3552, A3554, A3556, A3558, A3559,
A3560, A3562, AS0724, AS0726, SC1327-312, SC1329-313) with masses in the range
$M_{500}\approx 1-6\times 10^{14}\,M_{\mathrm{sun}}$. Among these, A3558 and
A3528 are merging X-ray clusters which form two complex structures in the
centre and in the outskirts of SSC (Bardelli, 2004). The high-density core of
the Shapley supercluster is probably the largest among the collapsing cores of
superclusters in the local Universe (Reisenegger et al., 2000) with a mass and
radius of $M\approx 1.3\times 10^{16}\,M_{\mathrm{sun}}$ and radius
$12.4\,h^{-1}\,$Mpc. Our choice of the SSC as a case study is not only due to
its exceptional nature; it is also triggered by the wealth of data available
for a multi-wavelength analysis. Indeed, the SSC was lengthly observed and
studied in the optical and nearIR (e.g., Quintana et al., 1995, 1997; Mercurio
et al., 2006; Merluzzi et al., 2015). It was observed in the X-rays (Kull &
Böhringer, 1999; Merluzzi et al., 2016) and it is seen in the ROSAT survey.
Finally, Shapley’s hot ionised gas is clearly observed via tSZ in the Planck
data (Planck Collaboration et al., 2014; Tanimura et al., 2022).
The paper is organised as follows. In Sect. 2, we describe the photometric and
spectroscopic data used to study the structure of SSC and the galaxy
properties, together with the data tracing the hot ionised gas. In Sect. 3, we
present the results we obtained from our different analyses. We start by
addressing the SSC structure as revealed by the detection of filaments with a
state-of-the-art technique. We continue with the distribution of the galaxy
populations in the SSC field. Finally, we exhibit the relation between the
star-formation rate in galaxies and the Compton $y$ parameter and investigate
its modification in the environment defined by the SSC filamentary pattern. We
discuss our results in Sect. 4 and conclude in Sect. 5. In the paper, we used
$H_{0}=70$km/s/Mpc.

Figure 1: Image, centred on Shapley Super Cluster, within a redshift range of
$0.03<z<0.083$. White stars indicate known clusters from (Proust et al.,
2006a). The colour scale represents the galaxy number density, normalised by
the median density in each pixel. The outer orange solid contours and inner
black dashed contours correspond to Compton $y$ parameters values of
$4.4\times 10^{-6}$ and $1.1\times 10^{-5}$, respectively, in the tSZ
reconstructed map from the Planck all-sky survey. The outer and inner grey
contours correspond to X-ray signal of 2000 counts s${}^{-1}\,$arcmin-2 and
$10^{4}$ counts s${}^{-1}\,$arcmin-2, respectively, in the ROSAT all-sky
survey map.

##  2 Data

###  2.1 Photometric galaxy catologue

The photometric galaxy catalogue used in this study was specifically designed
to the analysis of the Shapley supercluster, namely covering the large sky
area and including key galaxy properties such as star-formation rate and
stellar masses. It is an optimised version of the value added catalogue
constructed using machine learning following Bonjean et al. (2019) from the
WISExSCOS photometric redshift catalogue (Bilicki et al., 2016), for the faint
galaxies, combined with 2MASSxSCOSxWISE for the bright galaxies. The approach
followed by Bonjean et al. (2019), based on the training of a Random Forest
(RF) algorithm, shows that estimated star-formation rate (SFR) and stellar
masses ($\mathrm{M}_{\star}$) of both passive and star-forming galaxies can be
derived accurately, i.e. with reduced scatter and are unbiased with respect to
redshift in the range of the training sample (see Bonjean et al., 2019, for
comparison with the literature).

By construction, the accuracy of the RF-based estimates of SFR and
$\mathrm{M}_{\star}$ depends on the learned-model, i.e. on the training sample
and more specifically its redshift range. Therefore, we have defined a
redshift range encompassing the Shapley supercluster ($z<0.15$) and applied
the approach of Bonjean et al. (2019). Using the redshift estimates from the
two catalogues (WISExSCOS and 2MASSxSCOSxWISE), the SCOS magnitudes in the R
and B bands, and the WISE magnitudes in the bands W1 and W2, we estimated the
star-formation rate and stellar masses for the 83,700 galaxies in the range
$z<0.15$. Following, Bonjean et al. (2019), we have used the distance to the
main sequence on the SFR-$\mathrm{M}_{\star}$ diagram (d2ms, hereafter), which
estimates the star-formation activity of galaxies, as a criterion to define
three baseline populations of galaxies, namely star-forming (0.0 ¡ d2ms ¡
0.6), transitioning (0.8 ¡ d2ms ¡ 1.3), and passive (1.5 ¡ d2ms ¡ 2.0). The
ranges were chosen such that each population is clearly distinct from the
other two (as displayed in Fig. 2). In the redshift range $0.03<z<0.08$
including the Shapley supercluster complex 19195 galaxies are considered,
among them 12542 are star-forming, 1907 are transitioning, and 2115 passive
galaxies. The range of SFR and stellar masses of these populations are shown
in Fig. 3. We also show, as shaded areas covering the mass range use for their
estimates, the local main sequence scaling relations derived by Speagle et al.
(2014), in the range $9.7<$log($\mathrm{M}_{\star}$)$<11.1$, and by Leroy et
al. (2019), in the range $9.5<$log($\mathrm{M}_{\star}$)$<11$. We see the good
agreement between the different estimates in the local universe and those
obtained by the Machine learning techniques used here, confirming the already
noted agreement] between results in Bonjean et al. (2019) and those in Cluver
et al. (2014) and Wen et al. (2013) at higher redshift.

Figure 2: Left panel: Number of photometric galaxies in different populations,
as defined by their distance-to-main-sequence, d2ms, for the full Shapley
supercluster area shown in Fig. 1. Blue bars show all the galaxies while
orange bars indicate the number of galaxies within filaments. Right panel:
Same as left for the zoom-in region discussed in Sect. 3.2, with the number of
galaxies within the SSC core region (i.e. with a Compton-$y$ values
$y>2.2\times 10^{-6}$, see Fig 6) in green.

Figure 3: Left panel: SFR - M⋆ diagram of the galaxies from the value-added
photometric catalogue within the SSC field (Fig. 1). Blue dots correspond to
star-forming galaxies, green are transitioning while red dots are passive
galaxies, defined by their d2ms (see Fig. 2). Gray dots are galaxies not
clearly defined within any of the populations (between shaded areas in Fig.
2). The coloured lines correspond to scaling relations computed by (Speagle et
al., 2014, violet) and Leroy et al. (2019) from ZOMGS (turquoise) and GSWLC
(orange) galaxy catalogues, with reported scatters of 0.2, 0.36 and 0.31 dex,
respectively (shaded regions). The solid lines and shaded areas correspond to
the mass range used for computing the scaling relation
($9.5<\log(\mathrm{M}_{\star})<11$) Right panel: Same as left for the zoom-in
region discussed in Sect. 3.2.

###  2.2 Photometric galaxy maps

In the present study, we analyse the spatial distribution of the galaxies and
their properties as compared to the gas distribution. Hence based on the
added-value photometric galaxy catalogue described in Sect. 2.1 and following
Bonjean et al. (2020), we constructed full-sky maps of galaxy number density
in the redshift range $0.03<z<0.083$ chosen so that galaxies belong to the
Shapley supercluster, within the dispersion of the photometric redshifts
$\sigma_{z}=0.033$. Given this dispersion and the considered redshift range
($0.03<z<0.083$), it is not possible to define bins of redshifts; we hence
considered a single redshift slice with the coordinates of each galaxy on the
plane of sky given in the catalogue. We compute the galaxy number density on a
continuous grid by applying the Delauney Tesselation Field Estimator (DTFE,
Schaap, 2007) to the galaxy distribution.111The DTFE Python code developed by
V. Bonjean can be found at https://git.ias.u-psud.fr/ByoPiC/pydtfe We thus
obtain a two-dimensional density field which we smooth, with a Gaussian
smoothing kernel of radius $r\approx 0.04$ degrees, in order to reduce
possible edge effects induced by the tesselation.

In addition to the number density map of the whole galaxy population, we
compute in the same way the maps of the three different populations (star-
forming, transitioning and passive galaxies). We also produce the associated
SFR maps by computing the mean SFR within each pixel of the density maps.

We show, in Fig. 1, a $15\times 15$ square degree area centred on Shapley
where the colour map corresponds to the galaxy number density normalised by
the median density. We display groups and clusters of galaxies detected in the
SSC area in the X-rays, and listed in Higuchi et al. (2020), and in the
optical from Proust et al. (2006a). They are shown as white stars. For each
galaxy population (Fig. 6), we display the galaxy number density normalised by
the total galaxy number density. Thus, each map indicates the regions
predominantly dominated by star-forming, transitioning or passive galaxies.

###  2.3 Spectroscopic galaxies

We have used the Shapley Supercluster velocity Database. This is a publicly
available and comprehensive catalogue of velocities in the area of about $300$
square degrees centred on SSC compiled by Quintana et al. (2020). The dataset
includes 18,146 velocity measurements with proper photometry and astrometry
for 10,719 galaxies. We have restricted our analysis to the velocities ranging
between 9,000 and 18,900 km/s, i.e. within a redshift range of $0.03<z<0.063$
corresponding to the spectrospic redshifts of galaxies belonging to the
Shapley supercluster similarly to Quintana et al. (2020) (see also Fig. 4).
Furthermore following Quintana et al. (2020) assessment of the reliability of
the photometric selection, we also used only the galaxies for which R2
magnitudes222Derived from the SuperCOSMOS scans of photographic Schmidt survey
plates http://www-wfau.roe.ac.uk/sss/index.html, data cover BRI bands, with
the R represented at two epochs R1 and R2. are brighter than 18. This amounts
to a total of 5,553 galaxies.

In order to account for the complex filamentary structures in the 3D velocity
distribution, we need to correct for effects such as Fingers of God (FoG,
Jackson, 1972) due to clusters and groups of galaxies (see Fig. 4 upper panel)
that represent stretched distribution of galaxies which could be mistaken for
actual filaments of the cosmic web. We therefore implemented a method to
statistically correct for these redshift distortions present in the selected
sample of spectroscopic galaxies which we use in Sect. 3 to identify three-
dimensional filamentary web around Shapley.

The correction of FoG effect proceeds in two steps, first identifying the
groups and clusters of galaxies and second compressing the elongated
structures caused by FoG. The procedure we used to identify the groups and
clusters follows the group finding algorithm described in Duarte & Mamon
(2014) and references therein. First, we identify galaxies within the same
bound structures using a Friend-of-Friend (FoF) algorithm which depends on two
linking lengths normalised to the mean nearest neighbour separation of field
galaxies, along line-of-sight, los, ($b_{\mathrm{los}}=1.0$) and in the plane
of the sky ($b_{\mathrm{plan}}=0.2$). Subsequently, we correct for the FoG
effect. Namely, the radial distances of galaxies, identified as members of the
structures by the FoF algorithm, are redistributed so that the redshift-
distortion elongation along the los is compressed around the centre of the
structure. We assume that the distribution of galaxies inside groups and
clusters is symmetrical both perpendicularly and along the los (see, e.g.,
Tegmark et al., 2004; Tempel et al., 2012; Hwang et al., 2016). The
compression factor is computed from the ratio between the rms of galaxies
distance, w.r.t. the centre of the group or cluster, perpendicular and along
the los. As a result, the correction to the FoG distortions slightly modifies
the redshift range which is reduced to $0.03<z<0.058$.

Figure 4: Upper panel: Each black dot corresponds to a spectroscopic galaxies
selected from Quintana et al. (2020) such that $R2<18$ mag and
$9,000<v<18,900$ km/s. Lower panel: Same galaxies after correcting for the FoG
effect following Sect. 2.3.

###  2.4 Gas tracers

In addition to the galaxy distribution in the area of Shapley, we also used
two tracers of the hot gas in SSC, namely the X-ray emission and the thermal
Sunyaev-Zel’dovich (tSZ) signal (Sunyaev & Zeldovich, 1970).

For the X-ray emission, we used the publicly available data from the ROSAT
survey (Snowden et al., 1997) which include count rates over the whole sky.
The X-ray maps333https://www.jb.man.ac.uk/research/cosmos/rosat/ in HEALpix
format (Górski et al., 2005) are provided in six standard energy bands
covering $0.1-2$ keV. For the present work, we used the three higher energy
bands covering $0.56-2$ keV. For the tSZ signal, we made use of the new full-
sky Compton parameter map ($y$-map) reconstructed by Tanimura et al. (2022)
from the Planck multi-frequency channel maps, between 100 and 857 GHz, within
the Planck data release 4 (Planck Collaboration et al., 2020).

In both full-sky maps, we extracted a patch of $15\times 15$ square degrees
centred on Shapley and corresponding to the whole field. We display, in Fig.
1, contours illustrating inner and outer regions of the SSC in the tSZ and
X-ray signals. The outer and inner contours of the tSZ signal correspond to
Compton $y$ parameters values of $4.4\times 10^{-6}$ and $1.1\times 10^{-5}$,
respectively. The outer and inner contours in the X-ray signal correspond to
2000 counts s${}^{-1}\,$arcmin-2 and $10^{4}$ counts s${}^{-1}\,$arcmin-2,
respectively.

##  3 Analysis

Figure 5: 3D visualisation of the T-ReX filaments around SSC, with a
probability above 0.5 (left), defined as our baseline for reliable filaments,
and a lower probability of 0.2 (right). The green dots correspond to the
clusters from Proust et al. (2006a).

Figure 6: Upper left: Same as Fig. 1, with T-ReX filaments shown in gray
areas. Main detected filaments are indicated with cyan ellipses. Upper right:
Zoom-in region around the SSC system with normalised number density of star-
forming galaxies. lower right and left: Same as upper right for transitioning
and passive galaxies, respectively. The white areas correspond to normalised
number density values such that
$n_{\mathrm{population}}/n_{\mathrm{all/galaxies}}<0.1$. White stars
correspond to known clusters, projected 3D filaments are indicated by gray
areas, while orange and turquoise contours correspond to the tSZ and X-ray
signals, respectively.

Figure 7: Same as lower left panel in Fig. 6, with the blue-end transitioning
galaxies (lower d2ms hence more star-forming) on the left and the red-end
transitionning galaxies (higher d2ms hence more passive) on the right. The
colour bar is adjusted to better highlight the differences. As in previous
figures, white stars are known clusters and the gray areas correspond to
detected filaments.

###  3.1 Filament detection

Elongated structures connecting galaxy clusters were seen in the observations
of Shapley supercluster (e.g., Quintana et al., 2020; Higuchi et al., 2020,
and references therein). In this study, we use for the first time an actual
filament detection technique to identify the filaments in the SSC area. We
perform the filament detection both in 3D, using the spectroscopic galaxy
sample corrected for the FoG effects, and in 2D, using the galaxies from the
WISExSCOS photometric redshift catalogue. The detection in 3D provides the
actual filaments connecting the clusters of the SSC area. The detection in 2D
shows what is accessible when limited by the precision of the photometric
redshifts.

Several web-finder algorithms have been developed to identify the environments
of the cosmic web (voids, walls, nodes, and filaments, see, e.g., review by
Libeskind et al., 2018). Here, we choose to use the Tree-based Ridge Extractor
(T-REx) algorithm (Bonnaire et al., 2020, 2021) in order to detect the
filamentary network in the SSC area, (see Bonnaire et al., 2020, for a
comparison with other filament finders applied on simulations). T-REx models
the filamentary pattern as a graph structure and outputs a smooth version of
the minimum spanning tree using a Gaussian mixture model to describe the
spatial distribution of the galaxies. Hence, one of the advantages of T-REx is
that it directly estimates the filament spines from the galaxy distribution
without resorting to the construction of smooth density field. Moreover by
using graphs to trace interconnected galaxies, T-REx does not assume any shape
or width for the filaments that can rather be learnt during the optimisation.

In order to extract a reliable 3D filamentary network from the galaxy
distributions, it is essential to use the radial distances of the galaxies. We
thus used the distances from the spectroscopic galaxies sample corrected for
FoG effects (see Sect. 2.3). The output of T-REx is filaments represented by
graph ridges and indicating one particular path linking graph nodes together,
hence only one possible spine, without providing any idea of uncertainty of
the linking graph. In order to estimate the reliability of the detected
filaments, we follow the approach of Bonnaire et al. (2020) who introduced a
robust representation that takes into account the possible variations in the
input node distribution by defining and analysing random subsamples of the
input distribution. In a similar fashion as in bootstrap approaches, we
perform 100 iterations of the filament extraction. In practice, the input data
is divided into 100 randomly selected subsamples, each containing $75\%$ of
the galaxies from the original sample as shown in Bonnaire et al. (2020). In
that way, each subsample traces one specific linking path, that is, a specific
set of filaments. Subsequently, we construct a 3D probability grid based on
the number of times a given cell is crossed by a realisation of a filament.
This probability is represented by a fractional value between 0-1, with 0 for
no filament out of 100 samples detected in a given cell, and increasing
probability of detecting filaments from individual realisations up to a value
of one for a cell where every realisation has recovered a filament. The
significance of the detected filaments can be defined by setting a threshold
value between 0 and 1. A conservative limit, close to 1, may result in
filaments that appear disconnected, while a lower limit, close to 0, may
include spurious filaments (see Fig. 5 for a comparison between two threshold
probabilities 0.2 and 0.5). In the following we trade reliability and
completeness, out of all the realisations of the filamentary pattern detected
by T-REx we focus only on the reliable ones, namely we select the cells with a
probability above 0.5 (see Fig. 5 left panel). A projection of the 3D cells
containing these reliable filaments is shown as a gray area in Figs. 6, and 8.

Despite the large uncertainties on the photometric redshifts, we also applied
the T-ReX algorithm to the subset of passive galaxies, which trace the
filaments (Bonjean et al., 2020), from the photometric galaxies sample
described in Sect. 2.1. This provided us with a catalogue of filaments
projected on the sky. Within the SSC region, the 2D and 3D filamentary
patterns are overlaid (Fig. 8) showing the overall agreement between the 3D
and 2D structures of SSC.

####  3.1.1 The SSC structure

The overall filamentary structure of the SSC as traced by the galaxy
overdensity has already been presented and discussed in details by Proust et
al. (2006b) and Quintana et al. (2020) and references therein. In the
following, we present the results of a blind detection of the filamentary
pattern by the T-REx algorithm applied on FoG corrected galaxy positions. We
show how our results, when considering reliable filaments only (probability
above 0.5), compare with those of previous studies and how they provide a
renewed view of the SSC global structure.

  * •

Applying the web-finder, T-REx, on the spectroscopic galaxy sample, we clearly
detect an extended and reliable (probability above 0.5) filamentary pattern
(Figs. 5 and 8) relating the central region of the SSC as defined in Quintana
et al. (2020) and references therein, namely the groups and clusters of
galaxies A3552, A3554, A3556, A3558, A3559, A3560, AS0724, AS0726, SC1327-312,
SC1329-313. With T-REx, we identify very large scale filaments. We identify
the filament in the North connecting the core region of SSC to the cluster
A3559 (via Filament 1, labelled F1 in Figs. 5 and 6). This elongated structure
extends even further. We find a filament extending from the core of SSC beyond
A3559 in the overall direction of A1736 to which it is connected with lower
reliability filament identified with T-REx. We clearly note the T-REx high
reliability filament in the South of SSC relating the core of Shapley and the
clusters of galaxies A3560 (via Filament 3, noted F3), A3562 (via Filament 4,
F4), and 3554 (via Filament 2, F2). An elongated structure extends towards
A3566 to which it is connected with lower reliability filament.

  * •

Foreground galaxies form “Front Eastern Wall” identified in Quintana et al.
(2020) which extends to the east and in front of SSC, composed of a bridge of
galaxies, groups and clusters. With T-REx, we confirm the detection of such a
very large complex with filaments connecting A3578 in the North to A3537 in
the South and linking the groups and clusters A3571, A3575, S0744, and S0736
(Fig. 5). Considering slightly lower reliability filaments detected with
T-REx, the complex network includes the groups and clusters SC1336-314 A3570,
and S0748.

  * •

We also detect with T-REx and hence confirm the large scale structure in the
North West of the SSC core made of the clusters of galaxies A3528, A3530 and
the filaments connecting them, in addition to a lower reliability T-REx
filament connected to A3532. The web-finder algorithm identifies several
realisations of filaments bridging between this structure and the SSC.
However, only a portion of the filaments pass our reliability threshold
(probability above 0.5).

Figure 8: Same as Fig. 1, with the filaments overplotted on the galaxy density
map. The filaments were obtained in 2D from the passive population in the
WISExCOSMOS added value catalogue (cyan) and in 3D from the spectroscopic
catalogue (brown areas). The 2D and 3D filaments have a probability above 0.5,
as given by the T-ReX algorithm. The black stars correspond to clusters from
Proust et al. (2006a).

###  3.2 Galaxy populations in the SSC environment

We examine the spatial distribution of the galaxy types in the SSC region. We
compare it against the spatial distribution of the hot ionised gas, traced by
the tSZ and X-ray signals. We also identify a zoom-in region of $7\times 6$
deg2 centred in the Shapley core in order to avoid the foreground structures
from the SSC larger field (see Fig. 5). In Fig. 6, we display the quantitative
fractions of galaxies from each population and overlay the contours of the tSZ
and X-ray signals together with the areas defined by the projected 3D
filaments.

As expected from the quenched nature of galaxies in clusters (see Dressler,
1980, for a seminal study), we clearly observe that the passive galaxies
occupy the densest environments of SSC corresponding to clusters and groups
where the tSZ signal is the largest. This is particularly well seen in Fig. 6
(also in Fig. 1) for example at the positions of isolated clusters of galaxies
in the field such as A3554, A3556, A3558, A3560, A3562, A3566 or A1736 where
we observe consequently at the same positions that theses regions are devoid
of star-forming and transitioning galaxies. All over these regions, the
fraction of the smoothed number densities of passive galaxies is above 0.4 as
compared to values below 0.2 in the background region. In the very same
regions, the fraction of star-forming and transitioning galaxies remains below
approximately 0.2. (see Dressler, 1980, for a seminal study).
Not all the clusters in the SSC seem to have reached a fully quenched galaxy
stage. In the very core of the SSC where the tSZ signal is the highest, we
additionally observe a large density of star-forming and transitioning
galaxies, in addition to the passive population as seen in the right panel of
Fig. 2.. This observation is the signature of a significant star-formation
activity that could be triggered by gas supplied in the filaments or by
cluster interactions or by nearby groups or field galaxies. For example,
extended tSZ emission in the region North SC1329-314 and SC1327-312 is filled
with transition galaxies with contribution from star-forming galaxies and just
very few passive galaxies (see also Fig. 7). This observation is coherent with
the observations on the clusters in the very core region of SSC. Indeed,
Merluzzi et al. (2015) states that A3558 is considered as a late merger-stage
cluster while Quintana et al. (2020) proposes that the groups SC1329-314 and
SC1327-312 could be associated to the in-fall of matter along the line of
site.
Outside the core region of SSC, we also find clusters dominated by a
population of transitioning galaxies, as in the case of A3559, or clusters
with the core dominated by passive galaxy population and surrounding shells of
transitioning and star-forming galaxies, such as AS 0726 or A1736. In this
latter case, the overdensity of transitioning galaxies at the north side of
the cluster is overlaping with the peaks of the X-ray and tSZ signals.

Focusing on the large-scale spatial distribution of hot gas as traced by the
tSZ contours in Fig. 6, we clearly observe an extended tSZ signal north of
A3558 associated with the location of an overdensity of transitioning
galaxies. In this region where a filament was detected with T-REx, the
fraction of the smoothed number density of passive galaxies exceeds a value of
0.5 (see lower left panel in Fig. 6), while there is no significant excess of
star-forming or of passive galaxies. This region, dominated by transitioning
galaxies, is remarkably well delineated by the outer tSZ contour in the South
and the projected T-REx filament in the West. This would imply that galaxies
are impacted by the filament and the supercluster, and being quenched by the
higher density and the gas temperature in these environments. Moreover, we
found that the transitioning galaxies with lower d2ms values (i.e., the most
star-forming galaxies among the transitioning population) are pressed towards
the filament, while the galaxies with higher d2ms (i.e., the most passive
galaxies among the transitioning population) are closer to the tSZ contour
(see Fig. 7). Indeed, in this latter region we also find a significant
fraction of passive galaxies. This spatial distribution suggests that either
the supercluster environment is more efficient at quenching the galaxy star
formation, or this quenching started earlier closer to the SSC than to the
filament. Similarly, the extended regions of tSZ signal west of A3556 and
north of A3562 seem associated with overdensities of transitioning galaxies,
situated along the filaments detected with T-REx, with the passive galaxies
being at the locations of the cluster centers.

Figure 9: SFR and Compton $y$ relation for star-forming (upper panel),
transitioning (middle panel) and passive galaxies (lower panel) in the zoom-in
region of SSC. The colour scale indicates the number of pixels for each
combination of SFR and $y$, while the dots and bars are the median and 68%
distribution, respectively. Vertical black lines correspond to the same tSZ
outer (orange solid, $y_{\mathrm{outer}}=2.2\times 10^{-6}$) and inner (black
dashed, $y_{\mathrm{inner}}=1.1\times 10^{-5}$) contours in Fig. 6.

###  3.3 SFR-tSZ relation

The results, presented in Sect. 3.2, illustrate the interplay between galaxy
evolution and the environment (clusters, filaments) in which they are located.
The latter not only contains the galaxies but is also filled with gas,
presumably hot ($T_{\mathrm{e}}>10^{6}$ K), traced by tSZ or X-ray signals. In
the rest of the analysis, we investigate the environmental effects within the
filamentary pattern of SSC on star formation in galaxies, traced by the SFR.
On the one hand, we make use of the SFR maps constructed for passive,
transitioning and star-forming galaxies (described in Sect. 2.2). On the other
hand, we use the tSZ map providing us via the Compton $y$ parameter values a
measure of the pressure of the gas in the SSC field and hence defining in a
single quantity, which combines both density and temperature, the environment
in which galaxies evolve. Focusing on the zoom-in region of $7\times 6$ square
degrees shown in Fig. 6, we compute the SFR in the pixel maps for each of the
galaxy populations and display this quantity against the Compton $y$ value of
the tSZ map (see Fig. 9). To avoid background noise in the tSZ map we consider
only pixels above a threshold value of $y=10^{-7}$. The vertical lines, from
left to right at $y_{\mathrm{outer}}\approx 2.2\times 10^{-6}$ ($\log
y_{\mathrm{outer}}\approx-5.66$) and $y_{\mathrm{inner}}\approx 1.1\times
10^{-5}$ ($\log y_{\mathrm{inner}}\approx-4.96$), indicate the Compton
parameter values associated with tSZ signal contours delimiting the outer
region, i.e. where tSZ is dominated by background, and the inner core region
of the SSC, i.e. dominated by the tSZ signal from hot gas. In Fig. 9, the
colour indicates the number pixels with the corresponding SFR and $y$. The
orange dots and associated error-bars indicate the median SFR at a given $y$
and the 68% dispersion around the median, respectively.
As expected, we find that the star-forming galaxies have a larger median SFR
($\approx 0.46$ M⊙ $y^{-1}$) than the transitioning ($\approx 0.23$ M⊙
$y^{-1}$) which are more star-forming that the passive galaxies ($\approx
0.06$ M⊙ $y^{-1}$). Turning to the slopes of the SFR-$y$ relations, deviations
from a zero slope indicate that the SFR is impacted by the tSZ signal from hot
gas. In the region defined by the outer contours ($y<2.2\times 10^{-6}$)
independently of the galaxy type, we observe no departure from zero-slope
suggesting that there is no impact of the tSZ signal on the SFR in galaxies
apart from the value of the median SFR. In the SSC region defined by the tSZ
contours ($y>2.2\times 10^{-6}$), the transitioning galaxies show mostly a
zero-slope relation whereas star-forming galaxies experience an increase of
their SFR above a Compton parameter value $y_{q}>3.4\times 10^{-6}$ ($\log
y_{q}>-5.46$, where the SFR-$y$ slope $>0$). This could be explained by
enhanced gas compression triggering an increase of star formation activity, as
suggested in previous studies (e.g., Rawle et al., 2014; Castignani et al.,
2020). This increase coincides with a small decrease of the SFR as a function
of $y$ in the passive galaxies. We show in Table 1 the results of the Spearman
test run over the pixels of the maps (sample size $\approx 10,000$) for the
correlations between Compton $y$ parameter and SFR and galaxy number density.
All $p$ values were found smaller than $10^{-6}$.

Figure 10: Left panel: Median SFR values for all three galaxy populations
(star forming, transitioning and passive) as a function of the tSZ $y$
parameter. Right panel: Distribution of the median SFR weighted by the
fraction of galaxy-density of a given population w.r.t. total as a function of
the tSZ $y$ parameter. In both panels, error bars indicate the 68%
distribution around the median. Vertical solid lines correspond to the tSZ
outer ($y_{\mathrm{outer}}=2.2\times 10^{-6}$) and inner
($y_{\mathrm{inner}}=1.1\times 10^{-5}$) contours. Vertical dashed lines
represent Compton parameter values at which the slopes of the SFR-tSZ relation
significantly change (see text).

The number density of galaxies of different types are different. Hence in
order to take this into account in our interpretation of the star-formation
activity vs tSZ in Fig. 10 (left panel), we compute the SFR weighted by the
fraction of galaxy of a given type relative to the total number of galaxies
(see Fig. 6 for the associated maps). We display the results in Fig. 10 (right
panel) where we also show the full galaxy sample in black. We observe, as
expected, that it is the sum of the contributions from the three galaxy
populations relative to their number density. We can focus on the different
regimes of tSZ signal defined by the contours of the Compton $y$ map.

Table 1: Spearman correlation coefficients relating Compton $y$ to SFR, upper
part of the Table (Fig. 9); and Compton $y$ to galaxy number density lower
part of the Table (Fig 11), for the full range of $y$-values and for
$\hat{y}_{q}<\log y<\hat{y}_{\mathrm{inner}}$ (with $\hat{y}_{q}=\log
y_{q}=-5.46$ and $\hat{y}_{\mathrm{inner}}=\log y_{\mathrm{inner}}=-4.96$).
All $p$ values were found smaller than $10^{-6}$. $\log y$ versus SFR
---
$y$ range | Star-forming | Transitioning | Passive
$\log y>-7$ | 0.08 | -0.06 | -0.07
$\hat{y}_{q}<\log y<\hat{y}_{\mathrm{inner}}$ | 0.25 | -0.12 | -0.3
$\log y$ versus number density
$y$ range | Star-forming | Transitioning | Passive
$\log y>-7$ | -0.37 | 0.23 | 0.36
$\hat{y}_{q}<\log y<\hat{y}_{\mathrm{inner}}$ | -0.45 | 0.21 | 0.48

In the tSZ outer-contour region ($y<2.2\times 10^{-6}$), background regime, we
observe no impact of the tSZ effect on the SFR whatever the galaxy type. In
the intermediate zone between the outer tSZ contours and the innermost
contours ($2.2\times 10^{-6}<y<1.1\times 10^{-5}$), we notice a transition in
the SFR-$y$ relation for all populations. At the Compton parameter value
$y_{q}\approx 3.4\times 10^{-6}$, the weighted SFRs of the total population
and star-forming galaxies drop, while the weighted SFRs of transitioning and
passive galaxies increase, already starting from the outer tSZ contour
($y>2.2\times 10^{-6}$). The transition observed for the star-forming
population suggests that the galaxies become quenched, at $y_{q}$, which
translates in an increase of the number density of transitioning and passive
galaxies at the expense of the star-forming galaxies. This increase is more
significant given the slight decrease in SFR for transitioning and passive
galaxies beyond $y_{q}$ (Fig. 10, left panel). By contrast for the star-
forming galaxies and as seen in Fig. 10 (left panel), the $y_{q}$ value
coincides with an increase in the SFR. This suggests that while a fraction of
star-forming galaxies may be quenched, the remaining galaxies undergo a boost
of star formation. We discuss, in Sect. 4, the possible scenarii leading to
this observation.
In the inner region of the tSZ signal where the Compton-$y$ is highest
($y>1.1\times 10^{-5}$), we observe another change of regime in the weighted
SFR (Fig. 10, right panel). At Compton parameter $y_{\mathrm{int}}\approx
2.\times 10^{-5}$ ($\log y_{\mathrm{int}}\approx-4.7$) the weighted SFR of
transitioning galaxies decreases slightly, in parallel we observed that the
passive galaxies reach the same weighted SFR values. Since the intrinsic SFR
is considerably lower for the passive galaxies, this indicates that their
number density is considerably larger. Moreover above $y_{\mathrm{int}}$, we
note that the SFR of the transitioning galaxies increases once again, the flat
weighted SFR suggesting that the number density of transitioning decreases. At
the same $y_{int}$ value, the weighted SFR of the star-forming galaxies does
not change with $y$. Given that the SFR of these star-forming galaxies
increases (Fig. 10, left panel), this zero-slope relation is compensated by a
decrease in the number density of star-forming galaxies. This suggests that
the drop seen in the weighted SFR is a combination of a strong decrease in the
number of galaxies to compensate for the correlation between SFR and $y$. To
complete these interpretations, we display, in Fig. 11 (left panel), the
relative fraction of passive, transitioning, and star-forming galaxies as
function of the tSZ signal. In the left panel, we observed that galaxy SFR is
strongly affected by the hot gas environment, with a dominant fraction of
star-forming galaxies laying outside the outer contours of the tSZ signal
($y<2.2\times 10^{-6}$) and passive galaxies dominating within the inner tSZ
regions ($y>1.1\times 10^{-5}$). The intermediate zone between the outer tSZ
contours and the innermost contours ($2.2\times 10^{-6}<y<1.1\times 10^{-5}$),
marks the transition from a fraction of galaxies dominated by star-forming to
a fraction dominated by passive galaxies.

Figure 11: Left panel: Fraction of galaxy number density per population as a
function of tSZ. Indicates the values by which the left panel in Fig. 10 was
weighted to obtain the right panel in the same Figure. Right panel: Same as
left, but for galaxies inside and outside filaments, corresponding to Fig. 13

###  3.4 SFR–X-ray relation

By contrast with tSZ that traces extended region of hot gas around the SSC,
the X-ray emission being proportional to the electron density squared traces
the cluster cores of the SSC. Indeed as seen in Fig. 1, the inner contours of
the tSZ signal at $5\sigma$ level ($y_{\mathrm{inner}}\approx 1.1\times
10^{-5}$) correspond to the outer contours of the X-ray emission at $1\sigma$
level (count rate (CR) such that CR${}_{\mathrm{inner}}\approx$ 2000 counts
s${}^{-1}\ \mathrm{arcmin}^{-2}$). The inner X-ray contours at 5$\sigma$
level, defined by a count rate of CR${}_{\mathrm{outer}}=10^{4}$ counts
s${}^{-1}\ \mathrm{arcmin}^{-2}$, are situated well within the core where
Compton$-y$ values are the highest.

We take advantage from the fact that X-ray emission traces essentially the
cluster cores in the very central regions of the SSC to investigate the
relation between star-formation activity and hot ionised gas. Considering the
zoom-in region within $7\times 6$ square degrees around the SSC, we repeat the
analysis in Sect. 3.3 and show in Fig. 12 (left panel) the median SFR of all
the galaxies as well as for each population (star forming, transitioning and
passive) as a function of the X-ray count rates.
In the regime dominated by the background (CR¡CRouter), the median SFR remains
flat independent of the X-ray emission as observed in the SFR-$y$ relation
(left panel in Fig. 10). From the X-ray outer contours inwards, the general
trend for all galaxies is a decreasing median SFR. The latter remains
unchanged with increasing X-ray count rates all the way to the highest values,
both for passive and transitioning galaxies. The star-forming galaxies,
however, exhibit an increase in their median SFR which flattens out a first
time, in the region CR${}_{\mathrm{outer}}<$CR$<$CRinner, and second time in
the very core region defined by CR$>$CRinner.

Figure 12: Left panel: Median SFR values for all three populations (star
forming, transitioning and passive) as a function of the ROSAT X-ray count
rates. Right panel: Distribution of the median SFR weighted by the fraction of
galaxy-density of a given population w.r.t. total as a function of the ROSAT
X-ray count rates. In both panels, the vertical lines correspond to the X-ray
outer (CR${}_{\mathrm{outer}}\approx 2000$ counts s${}^{-1}\
\mathrm{arcmin}^{-2}$) and inner (CR${}_{\mathrm{outer}}\approx 10^{4}$ counts
s${}^{-1}\ \mathrm{arcmin}^{-2}$) contours (see also text).

To account for the impact of galaxy-number densities on the median SFR, we
computed the SFR weighted by the fraction of each galaxy population with
respect to the total galaxy density (right panel in Fig. 12, similarly to Fig.
7). For all galaxy types, the weighted median SFR remains mostly unchanged
(albeit a slight increase for the passive galaxies) for count rates below the
outer X-ray contour. At larger count rates, the weighted median SFR of passive
and transitioning galaxies increases with increasing X-ray emission. This is
expected, since high count rates trace dense environments, within clusters, in
which the number density of galaxies greatly increases. While this increase is
very mild for the transitioning galaxies, the passive galaxies experience a
rapid increase of the weighted median SFR up to the inner contour, after which
it flattens out and reaches the same value as that of the transitioning
galaxies. This behaviour is similar to the trend observed in the tSZ analysis
where passive and transitioning galaxies had comparable value above
$y_{\mathrm{int}}$. By contrast, the weighted median SFR of the star-forming
galaxies gradually decreases with the X-ray count rate above CRouter. These
observations may hint to the fact that, in the regions probed by the X-ray
emission denser than those associated with the tSZ signal, most of the star-
forming galaxies turn to passive (see Fig. 11, left panel). Hence, this would
suggest that the fast quenching channel dominates in the environment traced by
X-rays.

###  3.5 Star formation activity in the SSC environment

With the same relations computed in Sect. 3.3, namely SFR vs $y$ and galaxy-
density weighted SFR vs $y$ to account for the variation of galaxy density of
different types, we investigate the impact on the SFR-$y$ relation of
environmental effects within and outside filaments. To do this, we compare the
SFR (and weighted SFR) relations within and outside the area defined by the
projected 3D filaments detected in Sect. 3.1. It is worth noting that the
regions containing the highest Compton$-y$ values are all associated with the
clusters and the connecting filaments in the very core region of SSC, i.e.
inside filaments. This explains that the data-points outside filaments, in
Fig. 13, do not extend to the highest $y$ values. Also throught this section,
we focus solely on the tSZ signal given that all the regions defined by the
outer X-ray contours are imbeded in the densest/core areas of the filaments.

For passive galaxies, we see that the SFR-$y$ relation (Fig. 13, left panel,
yellow and red crosses) is the same inside and outside filaments for the whole
range of $y$ values, with a small deviation (decrease of SFR) from a zero-
slope relation at $y_{q}$.
In the case of the transitioning galaxies, the SFR-$y$ relation (Fig. 13, left
panel, green and magenta triangles) is also the same inside and outside
filaments up to $y_{q}$, where the SFR outside filaments becomes slightly
larger than inside filaments. In the region defined by the tSZ inner contours
($y>y_{inner}=1.1\times 10^{-5}$), the SFR-$y$ relation has a zero slope but
the overall median SFR values are smaller indicating that the the star-
formation activity has decreased in the high-Compton parameter region, due to
quenching.
The star-forming galaxies inside (blue dots) and outside (pink dots) filaments
exhibit the same median SFR values, independently of $y$ (Fig. 13, left
panel). It is as expected larger than the two other populations. Beyond
$y_{q}\approx 3.4\times 10^{-6}$, the SFR-$y$ relation inside and outside
differs with an increase of SFR inside filaments, while it remains flat
outside. In the regions delimited by the inner tSZ contours and where the
Compton parameter values are the largest, we witness at
$y>y_{\mathrm{inner}}=1.1\times 10^{-5}$ a steepening of the SFR vs $y$ slope
and the median SFR reaches larger values indicating a significant star
formation activity.

A complementary view is provided by the analysis of the SFR weighted by the
number density of galaxies for each population (Fig. 13, right panel). We can
see in particular that the star-forming galaxies inside (blue dots) and
outside (pink dots) filaments share the same slopes and median SFR values up
to $y_{\mathrm{outer}}\approx 2.2\times 10^{-6}$ where they start departing
from each other. Beyond this value, the weighted SFR inside filaments (blue
dots) gradually decreases with $y$ due to the decrease in the number density
while the weighted star formation outside filaments (pink dots) increases. In
the very core region of SSC $y>y_{\mathrm{inner}}=1.1\times 10^{-5}$, the
number-density weighted SFR decreases slightly due to the combined effect of
reduced star formation and number of galaxies.
Focusing on the weighted SFR-$y$ relation for transitioning galaxies displayed
in Fig. 13 (right panel), we observe that the SFR of galaxies outside (green
triangles) filaments do not vary with $y$ while for galaxies inside (magenta
triangles) filaments there is a gradual and slow increase up to $y_{q}$. At
this Compton parameter value, the weighted SFR outside filaments gradually
increases with $y$. On the other hand within filaments, the SFR slightly
decreases between $y_{q}<y<y_{\mathrm{int}}$, after which it starts increasing
again.
In parallel, we see that the weighted SFR of passive galaxies follow a similar
evolution with $y$, albeit larger median SFR inside the filaments (yellow
crosses) than outside (red crosses). Indeed, we observe a slight increase in
the SFR for Compton parameter values $y>2.2\times 10^{-6}$ (within the outer
tSZ contour). At $y_{\mathrm{int}}\approx 1.62\times 10^{-5}$, the weighted
median SFR in passive galaxies reaches that of the transitioning galaxies.
This indicates that the number density of passive galaxies is much larger than
of transitioning galaxies, compensating for the SFR of the former which is
much lower (left panel in Fig. 13). This larger number of passive galaxies is
likely the result of an increased number of transitioning galaxies turning
passive or star-forming turning directly passive. These interpretations are in
line with the variation of the relative fraction of passive, transitioning,
and star-forming galaxies as a function of the tSZ signal inside and outside
filaments shown in Fig. 11 (right panel).

Figure 13: Same as Fig. 10, but considering separately the regions within
filaments (defined by the projection of the 3D T-REx filaments) and those
outside the filaments.

##  4 Discussion

  * $\bullet$

We derived the large scale structure of the SSC using a state-of-the-art web-
finder algorithm, T-REx, applied both on 2D and 3D galaxy distributions. Our
results agree very well with those of Quintana et al. (2020). Not only we
confirm with a blind detection technique the main structure of the filamentary
pattern; but we also identify reliable filaments connecting the SSC central
region to the clusters surrounding it. Additionally, we detect the filaments
within the large complexes of galaxies in the foreground and background of
SSC. T-REx outputs an associated probability to the detected filaments which
allows us to estimate their reliability. We found that low-reliability
filaments connect the SSC region to the two, foreground and background, galaxy
complexes. We have compared our results with those of Higuchi et al. (2020) on
the DM distribution in 23 square degrees around the SSC from a weak lensing
(WL) analysis based on the data from Merluzzi et al. (2015) and Haines et al.
(2018). Higuchi et al. (2020) show internal (within Shapley core) and external
filaments in the reconstructed projected mass distribution in the r and g
photometric bands. The overall agreement with our results, based on T-REx, is
very good in the core region of Shapley. In the outskirt notably, we clearly
detect quantitatively with T-REx applied on the 3D galaxy distribution, the
filament that relates A3558 and A3559. This structure was also seen as a
stream of galaxies by Haines et al. (2018). We find a good overlap between
this stream and a 2D filament detected with T-REx. Comparing with the 3D
filament, the stream in Haines et al. (2018) connects the two clusters more
towards the eastern side, while T-REx 3D filament is directly to the north.
However, it is worth noting that the T-REx filaments quoted here are
identified as reliable when their probability is greater than 0.5. Hence, the
difference between our two results may be due to the presence of a lower
probability filament traced in Haines et al. (2018). In addition, it was
hinted by the WL analysis performed in the r band (see Fig. 4 in Higuchi et
al., 2020) but given the low density contrast no definitive conclusion was
made. In addition to these filaments, we also detect quantitatively with T-REx
the two filaments relating, on the one hand, Shapley core with A3554 and, on
the other hand, Shapley core with A3560.

  * $\bullet$

The SSC area is a large and complex concentration of galaxies. Its analysis
using the T-REx filament-finder technique permits us to investigate several
aspects of the connection of clusters to their large-scale cosmic web
environment. For instance, the number of filaments connected to clusters, i.e.
the connectivity, has been the subject of different studies in simulation
(Aragón-Calvo et al., 2010; Codis et al., 2018; Gouin et al., 2021; Kraljic et
al., 2022; Malavasi et al., 2023; Galárraga-Espinosa et al., 2023b, a) and
observations (Darragh Ford et al., 2019; Sarron et al., 2019; Malavasi et al.,
2020; Einasto et al., 2020, 2021). In particular, Gouin et al. (2021) have
used T-REx technique on simulations and shown that the connectivity relates to
mass assembly in clusters and hence their mass and dynamical state; and that
it impacts observational properties such as their shapes, etc. (see also Gouin
et al., 2022). Our analysis of the Shapley field identified the filaments
connecting the galaxy clusters in the central part of the supercluster. It
also showed that Shapley’s central region is connected to five reliable
filaments. Four of them, shown in Figs. 5 and 6, were already hinted in
previous studies (see Sect. 3.1.1), the fifth is a filament on the western
side of the SSC. This connectivity is coherent with that of supercluster
A2142, estimated to 6-7 filaments according to Einasto et al. (2020), or that
of Corona Borealis estimated to seven (Einasto et al., 2021). As shown in the
analysis of numerical simulations (Gouin et al., 2021) these high values of
the connectivity are representative of massive systems still ongoing mass
accretion, i.e. still forming, as suggested by Chon et al. (2015) for the
Shapley supercluster.

Filaments of the cosmic web not all have the same nature (e.g., Feldbrugge &
van de Weygaert, 2023). In addition, Galárraga-Espinosa et al. (2020) showed
that two extreme populations of filaments trace different environments and
have different physical and thermodynamical properties (Galárraga-Espinosa et
al., 2021; Tuominen et al., 2021; Galárraga-Espinosa et al., 2023a). Short
filaments ($\approx 10$ Mpc) trace dense environments relating massive galaxy
clusters and are filled with hot gas. In the very central region of Shapley,
we clearly detect this type of filaments, connecting A3558 to A3562, and
emitting in the X-rays (Kull & Böhringer, 1999; Merluzzi et al., 2016). This
very central region with the highest density of matter filled with hot gas
that also shows the largest tSZ signal ($y>10^{-5}$) seen in the Planck data
(Planck Collaboration et al., 2014).

  * $\bullet$

The impact of the filaments detected in the cosmic web on galaxy properties,
in particular star-formation, has been shown by many analyses both in
simulations and in observations (e.g., Poudel et al., 2017; Laigle et al.,
2018; Bonjean et al., 2020; Malavasi et al., 2022; Bulichi et al., 2023;
Herzog et al., 2023; Ramsøy et al., 2021; Galárraga-Espinosa et al., 2023b).
It was also observed in the outskirts of clusters out to several virial radii,
again both in simulations and observations (e.g., Salerno et al., 2019; Sarron
et al., 2019; Gouin et al., 2020; Kuchner et al., 2020; Spérone-Longin et al.,
2021; Cornwell et al., 2023). One of the major impacts is the pre-processing
process by which star formation is quenched before galaxies fall in clusters,
with the observation in the cluster outskirts at large virial radii that the
density of star-forming galaxies does not reach the level of the field star-
forming galaxies. In our study when considering all the galaxies in the SSC
field, there is a much larger number of star-forming than passive galaxies and
we also find that the outer regions of the SSC have similar fractions of star-
forming galaxies than the field (see Fig. 2). However within regions defined
by the detected filaments, the number of passive and star-forming galaxies is
comparable. This indicates that the population of galaxies within filaments is
quenched, suggesting that galaxies are pre-processed in the filaments and the
groups therein (in agreement with e.g., Aragon Calvo et al., 2019; Lopes et
al., 2023).
In parallel to the decrease of the weighted SFRs of star-forming galaxies
(Fig. 10), our results also show that both weighted SFRs of passive and
transitioning galaxies increase when getting closer to the inner regions of
the SSC, until a $y$ threshold beyond which passive and transitioning galaxies
reach the same weighted median SFR. This confirms the impact of the dense
environment in the SSC core in quenching the star formation. It may also
indicate that the two quenching channels, fast and slow, discussed in Moutard
et al. (2018) are at play in the Shapley supercluster quenching the star-
forming galaxies and therefore increasing in parallel the number of
transitioning and passive galaxies. A similar scenario may also be at play in
the Virgo superclusters, where Chung et al. (2021) showed that about half the
galaxies in the VirgoIII filament are transitional dwarf galaxies,
transforming into quiescent dwarf early-type galaxies. By nature of the
Bremsstrahlung emission, the regions of the SSC probed by the X-ray emission
correspond to denser environments than those traced by the tSZ signal. In
these regions, we observe a milder evolution of the weighted median SFR with
X-ray count rates both for star-forming and transitioning galaxies while it
increases more sharply for passive galaxies. This may hint to the fact that
most of the star-forming galaxies turn to passive via the fast quenching
channel proposed in (e.g., Moutard et al., 2018).

  * $\bullet$

The environment of galaxies (in other words the cosmic web structures, in
particular clusters and filaments) is known to impact galaxies by triggering
or quenching star formation via many interlinked and different physical
processes (galaxy encounters or mergers, ram-pressure stripping, gas
evaporation, etc.) (e.g., Alberts & Noble, 2022, and references therein). The
local density of galaxies has long been identified as a main driver of the
quenching/star-formation processes (Einasto et al., 2022a, and references
therein). Consequently, galaxy environments are traditionally defined by their
local density and can also be defined by the luminosity density (e.g.,
Liivamägi et al., 2012; Kuutma et al., 2020). However, the gas properties of
the environments in which galaxies are located, in particular the temperature,
are also known to impact galaxies (e.g., Gabor & Davé, 2015).
In our study, we define the environment in which galaxies evolve combining
both density and gas temperature. This is conveniently captured by the Compton
parameter, which measure the integrated gas pressure. We hence use the $y$
parameter, which measures the amplitude of the tSZ signal, as a proxy of the
zone of influence of the cosmic web matter content both in clusters and
filaments. Moreover rather than a commonly used distance-centric definition,
we define the zone of influence of the environment via the contours of the $y$
parameter amplitude.
Therefore, we analysed the impact of the environment on the star-formation
activity as a function of the Compton parameter. We observed that, beyond a
given $y$ value equivalent to $2\sigma$ (where $\sigma$ defines the background
tSZ signal), the median SFR decreases with increasing tSZ signal in particular
in the very central core of the Shapley supercluster. In agreement with
Bonjean et al. (2020), we also find that the regions of SSC which are filled
with hot gas, traced by the tSZ signal, contain mostly low star-forming or
transitioning galaxies. In Bonjean et al. (2020), the authors performed a
study of the distribution of quiescent galaxies w.r.t. the filament spines
that they compared to observed tSZ signal in the filaments from Tanimura et
al. (2020). Their result suggested that the hot gas around filaments has a
non-negligible role in quenching star formation. The observed absence of blue
late-type spirals together with the shaping of the galaxy luminosity
functions, by Mercurio et al. (2006), also hinted towards the role of
mechanisms related to the gas such as galaxy harassment or ram-pressure
stripping in reducing or stopping star formation. In our study, we find a
similar trend (see Sects. 3.3 and 3.5). Certainly at the very highest $y$
values, the fraction of passive galaxies in the SSC dominates over both star-
forming and transitioning populations. Moreover for the star-forming galaxies,
we identify a threshold Compton parameter value, $y_{q}$, that coincides with
an increase in the SFR suggesting that while a large fraction of star-forming
galaxies may be quenched, the remaining galaxies undergo a boost of star
formation.

As suggested by Singh et al. (2020), this could be the result of condensation
of intra-filamentary gas into the filament galaxies fuelling star formation;
or it could be the result of interactions between filament galaxies due to
increased number density of galaxies near the filament spines. In this case,
mergers convert star forming spirals into passive ellipticals, while
interactions stir the ISM to enhance star formation. So at the same time star-
forming galaxies are less numerous but star-formation is very efficient.
Merger-induced star formation has been observed in other cases (e.g.,
Johnston-Hollitt et al., 2008). In our analysis, the observed increase of the
median SFR above $y_{q}=3.4\times 10^{-6}$ takes place mainly in the core
region of Shapley and its connected filaments, recognised as undergoing
gravitational collapse Reisenegger et al. (2000); Ragone et al. (2006); Chon
et al. (2015), which would indeed suggest merger-driven star formation. The
associated decrease of weighted median SFR for the star-forming galaxies,
observed at $y_{q}$, could thus be explained by the competition between on the
one hand the effect of merging/interactions, increasing the SFR, and on the
other hand the higher gas pressure inside the core region of Shapley,
stripping off the cold gas from galaxies and thus preventing star formation.
This could be comparable to the findings of Castignani et al. (2022), in the
case of Virgo, where they conclude that gas is depleted in filaments before
the quenching processes, depending mostly on the local density. In the Shapley
supercluster field and particularly at the connection and within the very core
of SSC, the filamentary network is likely made of prominent, short filaments
tracing the densest surroundings (e.g., Galárraga-Espinosa et al., 2020;
Feldbrugge & van de Weygaert, 2023, for a definition of short filaments) and
expected to be filled with gas at temperature $>10^{6}$ K or larger (Gheller
et al., 2015, 2016; Gheller & Vazza, 2019; Martizzi et al., 2019; Galárraga-
Espinosa et al., 2021; Tuominen et al., 2021; Gouin et al., 2022; Vurm et al.,
2023). An analysis of the thermal properties of gas in prominent filaments in
hydrodynamical numerical simulations by Zhu et al. (2022) shows that about
half the gas, located in relatively highly overdense regions, is hotter than
$10^{6}$ K. Zhu et al. (2022) propose that this hot gas could suppress the
supply of cold gas to halos before they enter clusters. This physical process
could hence explain the quenching of the star formation in the galaxies
located in the Shapley supercluster’s environment, triggering the relation we
observed between median SFR and Compton-$y$ parameter. Hydrodynamical
simulations also suggest that gas accretion of galaxies decreases closer to
filaments, due to the vorticity at the edges of filaments (Song et al., 2021).
This could act as an additional source of quenching.

##  5 Conclusions

The present analysis focuses on the study of the Shapley supercluster in its
large-scale environment with two main goals. First, we aimed at identifying
quantitatively the large-scale filamentary network to which the Shapley
multiple-cluster system is connected. Then, we aimed at investigating how the
environment defined by the SSC, together with the filaments attached to it,
modifies the star-formation activity of the galaxies located inside and
outside Shapley and its filamentary network.

We investigated the structure of the whole Shapley supercluster system based
on the 2D photometric and 3D spectroscopic galaxy distributions within
$15\times 15$ square degrees. By applying a dedicated filament-finder method
based on graphs, T-REx, to the 2D and 3D galaxies, we traced in a quantitative
manner the filamentary network in the SSC and around it. Our filament finder
quantifies the reliability of the detected filaments by computing an
associated probability to their detection. We detected all the filaments found
or hinted in previous studies confirming their reliability. We also detected
new filaments which were not previously observed, connecting the SSC central
region to the clusters surrounding it. We found that the Shapley core region
connecting A3558 to A3562 has a connectivity of five as expected for a system
ongoing collapse. In addition, we detected the filamentary network of large
complexes of galaxies in the foreground and background of SSC.

Focusing on the star-formation rate in star-forming, transitioning and passive
galaxies in a zoom-in region of $7\times 6$ square degrees centred on the SSC
core, we exhibited the impact of the SSC environment. Within the areas defined
by the detected filaments, we find that the number of passive and star-forming
galaxies is comparable while it is the opposite in the outer regions of SSC
indicating that the population of galaxies within filaments is pre-processed
and quenched.

Both the density and the gas properties, in particular temperature, of the
environments affect star-formation activity. The amplitude of the tSZ effect,
i.e. Compton $y$ parameter, measures the integrated gas pressure that is a
combination of density and temperature. Therefore, we defined environment of
the SSC and its filamentary network based on the amplitude of the tSZ effect,
as a proxy of the zone of influence of both the clusters and the filaments. We
then analysed the impact of the environment on the star-formation rate of
galaxy population as a function of the Compton $y$ parameter reconstructed
from the Planck data. We found that the zone of influence of the supercluster
on the galaxy properties extends beyond the core region of Shapley. As
expected, we showed that the star formation rate decreases significantly with
increasing tSZ signal in particular in the very central core of SSC which
contains mostly passive or transitioning galaxies. However, we also identified
a threshold Compton $y$ value where the median SFR of star-forming galaxies
increases. This can be explained by the fact that while a large fraction of
star-forming galaxies are quenched, potentially via both slow and fast
channels, the remaining ones undergo a boost of star formation probably
induced by the interactions and mergers in the SSC core region. All these
results were confirmed by our analysis of the star-formation rate as a
function of the X-ray emission in the SSC field, from ROSAT, with the main
difference being that galaxies seem to be quenched mainly via the fast
channel, that is, directly from star forming to passive. This could be
explained by the denser regions probed by X-rays not allowing for a slow,
gradual transition to passivity.

The analysis of the relation between the median star-formation rate of galaxy
populations and the integrated pressure of the gas, contained in the clusters
and the filaments connected to them, indicates that both the distribution of
galaxy types inside and outside the SSC filamentary network and the star-
formation activity are the result of a competition between the effects of
merging/interactions, increasing the SFR, and the higher gas pressure inside
the SSC structure, preventing star formation. In this context, the use of the
tSZ signal to define the zone of influence of the cosmic-web structures is a
novel way of identifying the environment of galaxies. The combination and
comparison of data from existing and future tSZ surveys, such as those of the
Atacama Cosmology Telescope444https://act.princeton.edu/, the Simons
Observatory555https://simonsobservatory.org/, or the South Pole
Telescope666https://pole.uchicago.edu/public/Home.html, and X-ray surveys such
as eROSITA777https://erosita.mpe.mpg.de/, with those of the large galaxy
surveys, e.g. Euclid888https://www.euclid-ec.org/, Dark Energy Spectroscopic
Instrument999https://www.desi.lbl.gov/, etc., should allow us to address in a
systematic and statistical manner the complex topic of galaxy evolution across
all cosmic web environments.

###### Acknowledgements.

This research was supported by funding for the ByoPiC project from the
European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation program grant number ERC-2015-AdG 695561. T.B.
acknowledges funding from the French government under management of Agence
Nationale de la Recherche as part of the “Investissements d’avenir” program,
reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute). The authors thank D.
Eckert and M. Douspis for comments together with the members of the ByoPiC
team101010https://byopic.eu/team for useful discussions. They also thank an
anonymous referee for their comments and suggestions.

## References

  * Alberts & Noble (2022) Alberts, S. & Noble, A. 2022, Universe, 8, 554
  * Aragon Calvo et al. (2019) Aragon Calvo, M. A., Neyrinck, M. C., & Silk, J. 2019, The Open Journal of Astrophysics, 2, 7
  * Aragón-Calvo et al. (2010) Aragón-Calvo, M. A., van de Weygaert, R., & Jones, B. J. T. 2010, MNRAS, 408, 2163
  * Bardelli (2004) Bardelli, S. 2004, in IAU Colloq. 195: Outskirts of Galaxy Clusters: Intense Life in the Suburbs, ed. A. Diaferio, 71–77
  * Battistelli et al. (2006) Battistelli, E. S., De Petris, M., Lamagna, L., et al. 2006, ApJ, 645, 826
  * Bilicki et al. (2016) Bilicki, M., Peacock, J. A., Jarrett, T. H., et al. 2016, ApJS, 225, 5
  * Bonjean et al. (2020) Bonjean, V., Aghanim, N., Douspis, M., Malavasi, N., & Tanimura, H. 2020, A&A, 638, A75
  * Bonjean et al. (2019) Bonjean, V., Aghanim, N., Salomé, P., et al. 2019, A&A, 622, A137
  * Bonnaire et al. (2020) Bonnaire, T., Aghanim, N., Decelle, A., & Douspis, M. 2020, A&A, 637, A18
  * Bonnaire et al. (2021) Bonnaire, T., Decelle, A., & Aghanim, N. 2021, arXiv e-prints, arXiv:2106.09035
  * Bulichi et al. (2023) Bulichi, T.-E., Dave, R., & Kraljic, K. 2023, arXiv e-prints, arXiv:2309.03282
  * Castignani et al. (2022) Castignani, G., Combes, F., Jablonka, P., et al. 2022, A&A, 657, A9
  * Castignani et al. (2020) Castignani, G., Jablonka, P., Combes, F., et al. 2020, A&A, 640, A64
  * Chon et al. (2013) Chon, G., Böhringer, H., & Nowak, N. 2013, MNRAS, 429, 3272
  * Chon et al. (2015) Chon, G., Böhringer, H., & Zaroubi, S. 2015, A&A, 575, L14
  * Chow-Martínez et al. (2014) Chow-Martínez, M., Andernach, H., Caretta, C. A., & Trejo-Alonso, J. J. 2014, MNRAS, 445, 4073
  * Chung et al. (2021) Chung, J., Kim, S., Rey, S.-C., & Lee, Y. 2021, ApJ, 923, 235
  * Cluver et al. (2014) Cluver, M. E., Jarrett, T. H., Hopkins, A. M., et al. 2014, ApJ, 782, 90
  * Codis et al. (2018) Codis, S., Pogosyan, D., & Pichon, C. 2018, MNRAS, 479, 973
  * Cornwell et al. (2023) Cornwell, D. J., Aragón-Salamanca, A., Kuchner, U., et al. 2023, MNRAS, 524, 2148
  * Cowie & Songaila (1977) Cowie, L. L. & Songaila, A. 1977, Nature, 266, 501
  * Darragh Ford et al. (2019) Darragh Ford, E., Laigle, C., Gozaliasl, G., et al. 2019, MNRAS, 489, 5695
  * Dressler (1980) Dressler, A. 1980, ApJ, 236, 351
  * Duarte & Mamon (2014) Duarte, M. & Mamon, G. A. 2014, MNRAS, 440, 1763
  * Dünner et al. (2006) Dünner, R., Araya, P. A., Meza, A., & Reisenegger, A. 2006, MNRAS, 366, 803
  * Einasto et al. (2023) Einasto, J., Hütsi, G., Liivamägi, L.-J., et al. 2023, MNRAS, 523, 4693
  * Einasto et al. (2020) Einasto, M., Deshev, B., Tenjes, P., et al. 2020, A&A, 641, A172
  * Einasto & Einasto (1987) Einasto, M. & Einasto, J. 1987, MNRAS, 226, 543
  * Einasto et al. (2024) Einasto, M., Einasto, J., Tenjes, P., et al. 2024, A&A, 681, A91
  * Einasto et al. (2018) Einasto, M., Gramann, M., Park, C., et al. 2018, A&A, 620, A149
  * Einasto et al. (2022a) Einasto, M., Kipper, R., Tenjes, P., et al. 2022a, A&A, 668, A69
  * Einasto et al. (2021) Einasto, M., Kipper, R., Tenjes, P., et al. 2021, A&A, 649, A51
  * Einasto et al. (2016) Einasto, M., Lietzen, H., Gramann, M., et al. 2016, A&A, 595, A70
  * Einasto et al. (1997) Einasto, M., Tago, E., Jaaniste, J., Einasto, J., & Andernach, H. 1997, A&AS, 123, 119
  * Einasto et al. (2022b) Einasto, M., Tenjes, P., Gramann, M., et al. 2022b, A&A, 666, A52
  * Feldbrugge & van de Weygaert (2023) Feldbrugge, J. & van de Weygaert, R. 2023, J. Cosmology Astropart. Phys., 2023, 058
  * Flores-Cacho et al. (2009) Flores-Cacho, I., Rubiño-Martín, J. A., Luzzi, G., et al. 2009, MNRAS, 400, 1868
  * Gabor & Davé (2015) Gabor, J. M. & Davé, R. 2015, MNRAS, 447, 374
  * Galárraga-Espinosa et al. (2020) Galárraga-Espinosa, D., Aghanim, N., Langer, M., Gouin, C., & Malavasi, N. 2020, A&A, 641, A173
  * Galárraga-Espinosa et al. (2021) Galárraga-Espinosa, D., Aghanim, N., Langer, M., & Tanimura, H. 2021, A&A, 649, A117
  * Galárraga-Espinosa et al. (2023a) Galárraga-Espinosa, D., Cadiou, C., Gouin, C., et al. 2023a, arXiv e-prints, arXiv:2309.08659
  * Galárraga-Espinosa et al. (2023b) Galárraga-Espinosa, D., Garaldi, E., & Kauffmann, G. 2023b, A&A, 671, A160
  * Gheller & Vazza (2019) Gheller, C. & Vazza, F. 2019, MNRAS, 486, 981
  * Gheller et al. (2016) Gheller, C., Vazza, F., Brüggen, M., et al. 2016, MNRAS, 462, 448
  * Gheller et al. (2015) Gheller, C., Vazza, F., Favre, J., & Brüggen, M. 2015, MNRAS, 453, 1164
  * Górski et al. (2005) Górski, K. M., Hivon, E., Banday, A. J., et al. 2005, ApJ, 622, 759
  * Gouin et al. (2020) Gouin, C., Aghanim, N., Bonjean, V., & Douspis, M. 2020, A&A, 635, A195
  * Gouin et al. (2021) Gouin, C., Bonnaire, T., & Aghanim, N. 2021, A&A, 651, A56
  * Gouin et al. (2022) Gouin, C., Gallo, S., & Aghanim, N. 2022, A&A, 664, A198
  * Gunn & Gott (1972) Gunn, J. E. & Gott, J. Richard, I. 1972, ApJ, 176, 1
  * Haines et al. (2018) Haines, C. P., Busarello, G., Merluzzi, P., et al. 2018, MNRAS, 481, 1055
  * Heinämäki et al. (2022) Heinämäki, P., Teerikorpi, P., Douspis, M., et al. 2022, A&A, 668, A37
  * Herzog et al. (2023) Herzog, G., Benítez-Llambay, A., & Fumagalli, M. 2023, MNRAS, 518, 6305
  * Higuchi et al. (2020) Higuchi, Y., Okabe, N., Merluzzi, P., et al. 2020, MNRAS, 497, 52
  * Hwang et al. (2016) Hwang, H. S., Geller, M. J., Park, C., et al. 2016, ApJ, 818, 173
  * Jackson (1972) Jackson, J. C. 1972, MNRAS, 156, 1P
  * Johnston-Hollitt et al. (2008) Johnston-Hollitt, M., Sato, M., Gill, J. A., Fleenor, M. C., & Brick, A. M. 2008, MNRAS, 390, 289
  * Kopylova & Kopylov (2007) Kopylova, F. G. & Kopylov, A. I. 2007, Astronomy Letters, 33, 211
  * Kraljic et al. (2022) Kraljic, K., Laigle, C., Pichon, C., et al. 2022, MNRAS, 514, 1359
  * Kuchner et al. (2020) Kuchner, U., Aragón-Salamanca, A., Pearce, F. R., et al. 2020, MNRAS, 494, 5473
  * Kull & Böhringer (1999) Kull, A. & Böhringer, H. 1999, A&A, 341, 23
  * Kuutma et al. (2020) Kuutma, T., Poudel, A., Einasto, M., et al. 2020, A&A, 639, A71
  * Lacerna et al. (2016) Lacerna, I., Hernández-Toledo, H. M., Avila-Reese, V., Abonza-Sane, J., & del Olmo, A. 2016, A&A, 588, A79
  * Laigle et al. (2018) Laigle, C., Pichon, C., Arnouts, S., et al. 2018, MNRAS, 474, 5437
  * Larson et al. (1980) Larson, R. B., Tinsley, B. M., & Caldwell, C. N. 1980, ApJ, 237, 692
  * Leroy et al. (2019) Leroy, A. K., Sandstrom, K. M., Lang, D., et al. 2019, ApJS, 244, 24
  * Libeskind et al. (2018) Libeskind, N. I., van de Weygaert, R., Cautun, M., et al. 2018, MNRAS, 473, 1195
  * Lietzen et al. (2016) Lietzen, H., Tempel, E., Liivamägi, L. J., et al. 2016, A&A, 588, L4
  * Liivamägi et al. (2012) Liivamägi, L. J., Tempel, E., & Saar, E. 2012, A&A, 539, A80
  * Lokken et al. (2022) Lokken, M., Hložek, R., van Engelen, A., et al. 2022, ApJ, 933, 134
  * Lopes et al. (2023) Lopes, P. A. A., Ribeiro, A. L. B., & Brambila, D. 2023, MNRAS[arXiv:2309.11578]
  * Luparello et al. (2011) Luparello, H., Lares, M., Lambas, D. G., & Padilla, N. 2011, MNRAS, 415, 964
  * Luparello et al. (2013) Luparello, H. E., Lares, M., Yaryura, C. Y., et al. 2013, MNRAS, 432, 1367
  * Malavasi et al. (2020) Malavasi, N., Aghanim, N., Tanimura, H., Bonjean, V., & Douspis, M. 2020, A&A, 634, A30
  * Malavasi et al. (2022) Malavasi, N., Langer, M., Aghanim, N., Galárraga-Espinosa, D., & Gouin, C. 2022, A&A, 658, A113
  * Malavasi et al. (2023) Malavasi, N., Sorce, J. G., Dolag, K., & Aghanim, N. 2023, A&A, 675, A76
  * Martizzi et al. (2019) Martizzi, D., Vogelsberger, M., Artale, M. C., et al. 2019, MNRAS, 486, 3766
  * Mercurio et al. (2006) Mercurio, A., Merluzzi, P., Haines, C. P., et al. 2006, MNRAS, 368, 109
  * Merluzzi et al. (2016) Merluzzi, P., Busarello, G., Dopita, M. A., et al. 2016, MNRAS, 460, 3345
  * Merluzzi et al. (2015) Merluzzi, P., Busarello, G., Haines, C. P., et al. 2015, MNRAS, 446, 803
  * Moutard et al. (2018) Moutard, T., Sawicki, M., Arnouts, S., et al. 2018, MNRAS, 479, 2147
  * Nulsen (1982) Nulsen, P. E. J. 1982, MNRAS, 198, 1007
  * Park et al. (2022) Park, C., Lee, J., Kim, J., et al. 2022, ApJ, 937, 15
  * Pearson et al. (2014) Pearson, D. W., Batiste, M., & Batuski, D. J. 2014, MNRAS, 441, 1601
  * Planck Collaboration et al. (2014) Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2014, A&A, 571, A29
  * Planck Collaboration et al. (2020) Planck Collaboration, Akrami, Y., Andersen, K. J., et al. 2020, A&A, 643, A42
  * Poudel et al. (2017) Poudel, A., Heinämäki, P., Tempel, E., et al. 2017, A&A, 597, A86
  * Proust et al. (2006a) Proust, D., Quintana, H., Carrasco, E. R., et al. 2006a, A&A, 447, 133
  * Proust et al. (2006b) Proust, D., Quintana, H., Carrasco, E. R., et al. 2006b, The Messenger, 124, 30
  * Quintana et al. (1997) Quintana, H., Melnick, J., Proust, D., & Infante, L. 1997, A&AS, 125, 247
  * Quintana et al. (2020) Quintana, H., Proust, D., Dünner, R., Carrasco, E. R., & Reisenegger, A. 2020, A&A, 638, A27
  * Quintana et al. (1995) Quintana, H., Ramirez, A., Melnick, J., Raychaudhury, S., & Slezak, E. 1995, AJ, 110, 463
  * Ragone et al. (2006) Ragone, C. J., Muriel, H., Proust, D., Reisenegger, A., & Quintana, H. 2006, A&A, 445, 819
  * Ramsøy et al. (2021) Ramsøy, M., Slyz, A., Devriendt, J., Laigle, C., & Dubois, Y. 2021, MNRAS, 502, 351
  * Rawle et al. (2014) Rawle, T. D., Altieri, B., Egami, E., et al. 2014, MNRAS, 442, 196
  * Reiprich et al. (2021) Reiprich, T. H., Veronica, A., Pacaud, F., et al. 2021, A&A, 647, A2
  * Reisenegger et al. (2000) Reisenegger, A., Quintana, H., Carrasco, E. R., & Maze, J. 2000, AJ, 120, 523
  * Salerno et al. (2019) Salerno, J. M., Martínez, H. J., & Muriel, H. 2019, MNRAS, 484, 2
  * Sankhyayan et al. (2023a) Sankhyayan, S., Bagchi, J., Tempel, E., et al. 2023a, arXiv e-prints, arXiv:2309.06251
  * Sankhyayan et al. (2023b) Sankhyayan, S., Bagchi, J., Tempel, E., et al. 2023b, arXiv e-prints, arXiv:2309.06251
  * Sarron et al. (2019) Sarron, F., Adami, C., Durret, F., & Laigle, C. 2019, A&A, 632, A49
  * Schaap (2007) Schaap, W. E. 2007, PhD thesis, University of Groningen, Netherlands
  * Shapley (1930) Shapley, H. 1930, Harvard College Observatory Bulletin, 874, 9
  * Singh et al. (2020) Singh, A., Mahajan, S., & Bagla, J. S. 2020, MNRAS, 497, 2265
  * Snowden et al. (1997) Snowden, S. L., Egger, R., Freyberg, M. J., et al. 1997, ApJ, 485, 125
  * Song et al. (2021) Song, H., Laigle, C., Hwang, H. S., et al. 2021, MNRAS, 501, 4635
  * Speagle et al. (2014) Speagle, J. S., Steinhardt, C. L., Capak, P. L., & Silverman, J. D. 2014, ApJS, 214, 15
  * Spérone-Longin et al. (2021) Spérone-Longin, D., Jablonka, P., Combes, F., et al. 2021, A&A, 654, A69
  * Sunyaev & Zeldovich (1970) Sunyaev, R. A. & Zeldovich, Y. B. 1970, Ap&SS, 7, 3
  * Tanimura et al. (2020) Tanimura, H., Aghanim, N., Bonjean, V., Malavasi, N., & Douspis, M. 2020, A&A, 637, A41
  * Tanimura et al. (2019) Tanimura, H., Aghanim, N., Douspis, M., Beelen, A., & Bonjean, V. 2019, A&A, 625, A67
  * Tanimura et al. (2022) Tanimura, H., Douspis, M., Aghanim, N., & Salvati, L. 2022, MNRAS, 509, 300
  * Tegmark et al. (2004) Tegmark, M., Blanton, M. R., Strauss, M. A., et al. 2004, ApJ, 606, 702
  * Tempel et al. (2012) Tempel, E., Tago, E., & Liivamägi, L. J. 2012, A&A, 540, A106
  * Tuominen et al. (2021) Tuominen, T., Nevalainen, J., Tempel, E., et al. 2021, A&A, 646, A156
  * Veronica et al. (2022) Veronica, A., Su, Y., Biffi, V., et al. 2022, A&A, 661, A46
  * Vurm et al. (2023) Vurm, I., Nevalainen, J., Hong, S. E., et al. 2023, A&A, 673, A62
  * Wen et al. (2013) Wen, X.-Q., Wu, H., Zhu, Y.-N., et al. 2013, MNRAS, 433, 2946
  * Zhu et al. (2022) Zhu, W., Zhang, F., & Feng, L.-L. 2022, ApJ, 924, 132