# The Way to Quench: Galaxy Evolution in A2142

ChengGong Qu  Department of Astronomy, Beijing Normal University, Beijing
100875, China  Heng Yu  Department of Astronomy, Beijing Normal University,
Beijing 100875, China  Antonaldo Diaferio  Dipartimento di Fisica, Università
di Torino, Via P. Giuria 1, I-10125 Torino, Italy  Istituto Nazionale di
Fisica Nucleare (INFN), Sezione di Torino, Via P. Giuria 1, I-10125 Torino,
Italy  Jubee Sohn  Astronomy Program, Department of Physics and Astronomy,
Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of
Korea  Smithsonian Astrophysical Observatory, 60 Garden Street, Cambridge, MA
02138, USA  DengQi Liu  Department of Astronomy, Beijing Normal University,
Beijing 100875, China

###### Abstract

We show how the star formation activity of galaxies is progressively inhibited
from the outer region to the center of the massive cluster A2142. From an
extended spectroscopic redshift survey of 2239 galaxies covering a circular
area of radius $\sim 11$ Mpc from the cluster center, we extract a sample of
333 galaxies with known stellar mass, star formation rate, and spectral index
$D_{n}4000$. We use the Blooming Tree algorithm to identify the substructures
of the cluster and separate the galaxy sample into substructure galaxies, halo
galaxies and outskirt galaxies. The substructure and halo galaxies are cluster
members, whereas the outskirt galaxies are only weakly gravitationally bound
to the cluster. For the cluster members, the star formation rate per stellar
mass decreases with decreasing distance $R$ from the cluster center.
Similarly, the spectral index $D_{n}4000$ increases with $R$, indicating an
increasing average age of the stellar population in galaxies closer to the
cluster center. In addition, star formation in substructure galaxies is
generally more active than in halo galaxies and less active than in outskirt
galaxies, proving that substructures tend to slow down the transition between
field galaxies and cluster galaxies. We finally show that most actively star
forming galaxies are within the cluster infall region, whereas most galaxies
in the central region are quiescent.

methods: data analysis-astronomical databases: catalogs-galaxies: structure-
galaxies: star formation-galaxies: evolution-galaxies: interactions

##  1 Introduction

According to the current model of the formation of cosmic structures, clusters
of galaxies form by gravitational instability from perturbations in the
initial matter density field. Small groups of galaxies flow along the
filaments of the cosmic web and contribute to the formation and evolution of
galaxy clusters. In hierarchical scenarios, increasingly massive clusters
form, on average, at increasingly later times (Neto et al. 2007; Boylan-
Kolchin et al. 2009).

Spectrophotometric properties of galaxies are correlated with the density of
the galaxy environment. For example, galaxies in the local universe show two
distinct distributions in the color-magnitude diagram: a red sequence, mostly
due to early-type galaxies, and a blue cloud, mostly due to star-forming late-
type galaxies (Strateva et al. 2001; Blanton et al. 2003). Galaxies on the red
sequence are generally located in the dense central regions of galaxy
clusters, whereas blue-cloud galaxies populate less dense
environments(Dressler 1980; Postman & Geller 1984; Balogh et al. 2004; Rawle
et al. 2013; Crone Odekon et al. 2018; Mishra et al. 2019). In the current
model of galaxy formation, late-type galaxies might evolve into early-type
galaxies through various processes, including galaxy merging, tidal stripping,
and ram pressure stripping (Bekki 1999; Taylor & Babul 2004). While falling
from the outskirts to the center of a massive galaxy cluster, galaxies are
likely to be affected by these types of interaction. Although the shock of the
hot intracluster medium (ICM) acting on the cold gas of the galaxy can
sometimes increase the star formation activity (Safarzadeh & Loeb 2019), this
ram pressure stripping mostly removes cold gas from the galaxy and inhibits
star formation (Gunn & Gott 1972; Balogh et al. 2000; Jablonka et al. 2013;
Peng et al. 2015; Deshev et al. 2020; Taylor et al. 2020). The timescale
associated with this starvation mechanism is $\sim 4$ Gyr (Peng et al. 2015),
generally longer than the timescale for ram pressure stripping of $\sim
0.5-4$Gyr.

In a cluster, the local galaxy density is correlated with the distance from
the cluster center, and the fraction of late-type galaxies increases with
clustrocentric distance, as happens, for example, in the Perseus cluster
(Meusinger et al. 2020). Similarly, in A2029, the spectral index $D_{n}4000$
of the cluster galaxies, an indicator of the age of their stellar population,
decreases with clustrocentric distance, suggesting younger stellar populations
in the outer galaxies, as expected for late-type galaxies (Sohn et al. 2019).

Most rich clusters exhibit some amount of substructure in the galaxy
distribution (Geller & Beers 1982; Wen & Han 2013). Since galaxies in
substructures have relative velocities comparable to the velocity dispersion
of stars in galaxies, the probability of galaxy mergers increases (Girardi et
al. 2015; Zarattini et al. 2016). Indeed, many early-type galaxies are in
substructures (Einasto et al. 2014), suggesting that galaxy mergers might have
already taken place before the galaxies were completely accreted by the
cluster. Because of the diversity of environments within a galaxy cluster and
its outer region, investigating the properties of cluster galaxies provides
crucial information on galaxy evolution.

A2142 is a massive galaxy cluster at redshift z $\sim$ 0.0898. It is located
at the center of a supercluster connected to the large-scale filamentary
structure (Einasto et al. 2020). The cold fronts of A2142 observed in X-rays
are probably the result of a sloshing cool core in the central region
(Markevitch et al. 2001; Tittley & Henriksen 2005; Owers et al. 2011). A
galaxy group that is undergoing ram pressure stripping is also observed near
the radius $R_{500}$ (Eckert et al. 2014). The outskirts of the cluster are
dominated by star-forming blue galaxies, unlike the inner region (Einasto et
al. 2018). Although the dense environment of the central region of the cluster
has an impact on the evolution of galaxies, many galaxies are within high-
density substructures flowing toward the cluster along filaments that surround
it. The relation between galaxy properties, clustrocentric distance, and local
environment is thus complicated by the presence of substructures.

The caustic method based on a hierarchical clustering algorithm (Yu et al.
2015) can be used to identify the substructures of clusters. The algorithm was
successfully applied to A85 (Yu et al. 2016) and A2142 (Liu et al. 2018). The
Blooming Tree algorithm is an updated version of the algorithm (Yu et al.
2018). Here, we plan to apply the Blooming Tree algorithm to identify the
substructures of A2142 and constrain the relation between galaxy properties
and local environment.

This paper is organized as follows. In Section 2, we present our data. In
Section 3, we separate our sample into three subsamples according to their
membership of the cluster, substructures, or outer region. We distinguish
star-forming galaxies from quiescent galaxies, and discuss the relation
between their physical properties and their environment. We summarize our
results in Section 4. Throughout this paper, we adopt a Wilkinson Microwave
Anisotropy Probe standard cosmological model with $\Omega_{m}$ = 0.272,
$\Omega_{\Lambda}$ = 0.728, and $H_{0}=70.4\,km\,s^{-1}\,Mpc^{-1}$ (Komatsu et
al. 2011). All the errors we mention are $1\sigma$.

##  2 Observational data

Liu et al. (2018) compiled a spectroscopic redshift survey of 2239 galaxies in
the field of view of A2142. Hereafter, we call these 2239 galaxies the
$z$-available galaxies. This catalog covers a circle of radius 0.∘56 from the
cluster center, whose celestial coordinates are R.A. = 239.∘5833 and decl. =
27.∘2334\. This angular radius corresponds to a radius of 10.8 Mpc at the
cluster redshift $z=0.09$. Figure 1 shows the redshift distribution of the
galaxies around this redshift. For the analysis of the structure of A2142, we
consider the 1186 galaxies with redshift in the range [0.06,0.12]. Hereafter,
we call these 1186 galaxies the $z$-slice galaxies. The redshift distribution
of the $z$-slice galaxies is shown by the gray bars in Fig. 1. The red solid
line is the Gaussian fit to this distribution obtained after 3$\sigma$
clipping.

The star formation rates(SFRs) and the stellar masses, $M_{\star}$, of the
$z$-slice galaxies are collected from the GALEX–SDSS–WISE Legacy Catalog
(GSWLC, Salim et al. 2018). This catalog is based on photometric data in
multiple bands, including UV data taken by the Galaxy Evolution Explorer
(GALEX, Martin et al. 2005) and optical data taken by the Sloan Digital Sky
Survey (SDSS, Abazajian et al. 2009).

Figure 1: Redshift distribution of the galaxies in the field of view of A2142.
The hollow bars show the distribution of the $z$-available galaxies. The gray
bars show the distribution of the $z$-slice galaxies, the 1186 galaxies in our
sample whose redshift is in the range $[0.06,0.12]$. The vertical dashed lines
indicate this redshift range. The red solid line is the Gaussian fit to the
distribution of the $z$-slice galaxies after 3$\sigma$ clipping.

We also consider the spectral index $D_{n}4000$, the ratio of the average flux
densities in the narrow continuum bands 3850-3950 Å and 4000-4100 Å (Balogh et
al. 1999). This spectral index correlates with the age of the stellar
population that contributes most of the electromagnetic emission in the
optical band (Bruzual et al. 1983; Poggianti & Barbaro 1997). The $D_{n}4000$
values are queried from the database of SDSS (Hopkins et al. 2003).

There are 333 galaxies, out of the 1186 $z$-slice galaxies, with SFRs, stellar
mass $M_{\star}$, and $D_{n}4000$ available. Hereafter, we call these 333
galaxies the data-available galaxies. The spectroscopic completeness of the
2239 $z$-available galaxies as a function of the Petrosian $r$-band magnitude
is shown by the blue line in the top panel of Fig. 2. The decrease in
spectroscopic completeness at magnitudes fainter than 18 mag is caused by the
Petrosian $r$-band magnitude limit $m_{r,Petro,0}<17.77$ of the spectroscopic
galaxy sample of SDSS (Balogh et al. 1999). The red dashed line indicates the
ratio between the 333 data-available galaxies and the 1186 $z$-slice galaxies.

Figure 2: Top panel: the spectroscopic completeness of the $z$-available
galaxies as a function of the Petrosian $r$-band magnitude (blue line). The
red dashed line shows the ratio between the number of data-available galaxies
and the number of $z$-slice galaxies. Bottom panel: the distribution of the
ratio between the number of data-available galaxies and the number of
$z$-slice galaxies on the sky. In this panel only galaxies with
$m_{r,Petro,0}<17.77$ are considered. The red circle shows a circle of radius
$0.^{\circ}$56 around the cluster center indicated by the red cross.

The bottom panel of Fig. 2 shows the spatial distribution of the ratio between
the number of data-available galaxies and the number of $z$-slice galaxies. We
limit the computation of this ratio to the galaxies with
$m_{r,Petro,0}<17.77$. We have 303 data-available galaxies and 319 $z$-slice
galaxies brighter than this magnitude limit. The two-dimensional map shown in
Fig. 2 has $10\times 10$ pixels for a squared field of view of $1.^{\circ}$12
on a side. The overall ratio is $303/319=0.95$ with a standard deviation
$0.286$. In the panel, the pixels outside the red circle contain no data.

##  3 Data analysis

In Sect. 3.1 we use the Blooming Tree algorithm to split our galaxy sample
into three subsamples: halo, substructure, and outskirt galaxies. In Sect. 3.2
we distinguish star-forming galaxies from quiescent galaxies; Sect. 3.3
discusses the relation between the star-formation rate per unit mass (the
specificSFR, or sSFR) and the spectral index $D_{n}4000$; Sect. 3.4 focuses on
the radial distribution of sSFR and $D_{n}4000$, and Sect. 3.5 discusses the
galaxy distribution in the $R$$-$$v$ diagram.

###  3.1 Halo, substructure, and outskirt galaxies

The Blooming Tree algorithm is a method for identifying substructure based on
the hierarchical clustering algorithm (Yu et al. 2018). It arranges all the
galaxies in the field of view into a tree, or dendrogram. The arrangement is
based on the pairwise projected binding energy, which is estimated from the
location of the galaxies on the sky and from their redshift (Diaferio 1999).
By adopting a proper density contrast parameter $\Delta\eta$, we can trim the
tree into distinct structures: $\Delta\eta$ is the difference between two
values of $\eta$, the former associated with the structure and the latter
associated with the surrounding background structure; $\eta$ combines the
line-of-sight velocity dispersion, the size, and the number of galaxies in the
structure; increasing values of $\Delta\eta$ identify increasingly dense
structures (see Yu et al. 2018, for further details).

We apply the Blooming Tree algorithm to the sample of 1186 $z$-slice galaxies.
By setting $\Delta\eta=5$, we identify 684 cluster galaxies. By increasing the
density contrast to $\Delta\eta=25$, we identify denser structures: we find 16
structures with more than five member galaxies. The basic properties of these
16 structures are listed in Table 1: $n_{\mathrm{g}}$ is the number of member
galaxies, $n_{\mathrm{d}}$ is the number of member galaxies with known SFR,
$M_{\star}$, and $D_{n}$4000, $z_{\mathrm{sub}}$ is the average redshift of
the structure, and $v_{\mathrm{disp}}$ is the velocity dispersion of the
structure. All the 480 members of the 16 structures, which are named sub1 to
sub16, belong to the 684 cluster galaxies identified with the contrast
parameter $\Delta\eta=5$. We associate the remaining 204 out of these 684
galaxies with a diffuse component indicated by grp0 in Table 1.

Table 1:  Properties of the galaxy structures. $n_{g}$ is the number of member galaxies, and $n_{d}$ is the number of member galaxies with known SFR, $M_{\star}$,and $D_{n}4000$. $z_{sub}$ is the average redshift of the structure and $v_{disp}$ is its velocity dispersion. GroupID | $n_{\mathrm{g}}$ | $n_{\mathrm{d}}$ | $z_{\mathrm{sub}}$ | $v_{\mathrm{disp}}(\mathrm{km}\,\mathrm{s}^{-1})$
---|---|---|---|---
cluster | 684 | 189 | 0.0898 | 912$\pm$11
grp0 | 204 | 66 | 0.0895 | 1059$\pm$10
sub1 | 178 | 43 | 0.0902 | 786$\pm$10
sub2 | 81 | 26 | 0.0884 | 477$\pm$10
sub3 | 41 | 10 | 0.0929 | 464$\pm$10
sub4 | 26 | 7 | 0.0870 | 303$\pm$10
sub5 | 22 | 3 | 0.0916 | 403$\pm$11
sub6 | 18 | 5 | 0.0888 | 266$\pm$10
sub7 | 17 | 8 | 0.0895 | 356$\pm$7
sub8 | 17 | 4 | 0.0960 | 318$\pm$14
sub9 | 12 | 1 | 0.0858 | 353$\pm$15
sub10 | 12 | 1 | 0.0892 | 283$\pm$11
sub11 | 12 | 2 | 0.0870 | 351$\pm$6
sub12 | 11 | 4 | 0.0897 | 334$\pm$6
sub13 | 10 | 3 | 0.0907 | 219$\pm$12
sub14 | 9 | 2 | 0.0946 | 304$\pm$10
sub15 | 7 | 4 | 0.0906 | 202$\pm$8
sub16 | 7 | 0 | 0.0887 | 347$\pm$6

The distribution of the $z$-slice galaxies on the sky is shown in Fig. 3,
where the 480 members of the structures are represented as colored squares;
the 204 cluster members associated with grp0 are represented as open
triangles; the remaining 502 $z$-slice galaxies which belong neither to the
cluster nor to any structure, are represented by black dots.

The galaxies are plotted on top of the map of Petrosian $r$-band luminosity
density. The density map is computed from the 1186 $z$-slice galaxies by
assuming that the $r$-band luminosity $L_{R}$ of each galaxy is smoothed with
a 2D Gaussian window of $2^{\prime}$ width. (see Wen & Han 2013, for details).
Figure 3 shows that the distribution of the luminosity density is generally
consistent with the distribution of the structures, as expected.

Figure 3: Distribution on the sky of the 1186 $z$-slice galaxies superimposed
on the distribution of their Petrosian $r$-band luminosity. The galaxy sample
separates into 382 halo galaxies and 302 substructure galaxies, totalling to
684 cluster members, and 502 outskirt galaxies. The open triangles show the
members of grp0, the orange squares show the members of the core sub1, the
other colored squares show the members of the structures from sub2 to sub16,
and the black dots show the outskirt galaxies. The two black dashed circles
have radius $R_{500}=1.408$ Mpc and $R_{200}=2.160$ Mpc at the cluster
redshift $z=0.09$ (Tchernin et al. 2016).

The structures from sub2 to sub16 are distinct components that we identify as
cluster substructures. The structure sub1 (orange squares in Fig. 3) is
located at the cluster center and we identify this structure with the cluster
core. We define halo galaxies to be the galaxies in the core and in the
structure grp0, substructure galaxies to be members of the structures from
sub2 to sub16, and outskirt galaxies to be the $z$-slice galaxies that are
neither halo nor substructure galaxies.

The 333 data-available galaxies, with known SFR, $M_{\star}$, and $D_{n}$4000,
separate into 109 halo galaxies (grp0 and sub1), 80 substructure galaxies
(sub2 to sub16), and 144 outskirt galaxies. In the following analysis and
discussion we focus on these three galaxy subsamples.

###  3.2 Star-forming and quiescent galaxies

Cluster galaxies at low redshift generally distributed into two distinct
groups in the plane of stellar mass versus star formation rate,
$M_{\star}-$SFR (Noeske et al. 2007; Peng et al. 2015): the two groups
distinguish the star-forming (SF) galaxies, with smaller values of the
spectral index $D_{n}4000$, and the quiescent galaxies, with larger values of
$D_{n}4000$. The 333 data-available galaxies in our sample show this bimodal
distribution, with most galaxies being massive and quiescent (Fig. 4). It is
worth noting that there are only star-forming galaxies when
$M_{\star}<10^{10.4}M_{\odot}$. To keep the completeness of our sample, we do
not remove them. However, our later results remain the same without these less
massive starforming galaxies.

Figure 4: The distribution of the 333 data-available galaxies in the
SFR$-M_{\star}$ plane. The red circles, blue squares, and black triangles
represent halo, substructure, and outskirt galaxies, respectively. The black
dotted line shows the specific SFR, sSFR = $10^{-11}$ yr-1, separating SF
galaxies from quiescent galaxies. S1 and S2 are the brightest galaxies of
substructures sub14 and sub3, respectively. BCG is the brightest galaxy of
A2142.

We consider the sSFR, defined as the SFR per unit stellar mass $M_{\star}$. We
separate the SF from the quiescent galaxies according to the threshold sSFR =
$10^{-11}$ yr-1 (McGee et al. 2011; Wetzel et al. 2012). The 333 data-
available galaxies separate into 93 SF galaxies and 240 quiescent galaxies.
Table 2 lists how these galaxies are distributed into halo, substructure, and
outskirt galaxy samples. The fraction of SF galaxies steadily increases from
the halo sample to the outskirt sample. This trend suggests that star
formation is progressively quenched from the outskirt galaxies to the
substructure and the halo galaxies. The larger fraction of SF galaxies in the
substructures than in the halo sample is also consistent with the scenario
where the substructure galaxies entered the cluster more recently than the
halo galaxies, and star formation in substructure galaxies is less inhibited
than in halo galaxies.

There are two SF galaxies with SFR larger than $10$ $M_{\odot}$yr-1. We label
these galaxies S1 and S2. S1, with
$\log[{\mathrm{SFR}/({\mathrm{M}}_{\odot}{\mathrm{yr}}^{-1})]}=1.866$, is the
brightest galaxy of the substructure sub14; S2, with
$\log[{\mathrm{SFR}/({\mathrm{M}}_{\odot}{\mathrm{yr}}^{-1})]}=1.156$, is the
brightest galaxy of the substructure sub3. Sub14 is a substructure falling
toward the center of the cluster at a high speed, as shown by Eckert et al.
(2014, 2017), and Liu et al. (2018). Ram pressure stripping might enhance the
star formation rate of S1 (Roberts et al. 2021). The image of S1 is also
disturbed, suggesting an ongoing galaxy merger (Liu et al. 2018). In contrast,
the large SFR of S2 might derive from its nature of grand-design spiral
galaxy, whose face-on image appears undisturbed.

Table 2:  Star-forming and Quiescent Data-available Galaxies.$n_{d}$ is the number galaxies with known SFR, $M_{\star}$, and $D_{n}4000$. Galaxy Sample | $n_{\mathrm{d}}$ | SF | Quiescent
---|---|---|---
Total | 333 | 93 (27.9%) | 240 (72.1%)
Halo | 109 | 10 (9.2%) | 99 (90.8%)
Substructure | 80 | 20 (25.0%) | 60 (75.0%)
Outskirt | 144 | 63 (43.8%) | 81 (56.3%)

The decreasing fraction of quiescent galaxies from the halo to the outskirt
sample is also apparent in the decreasing fraction of galaxies lying on the
red-sequence relation in the color-magnitude diagram (Fig. 5). The mean colors
of the quiescent galaxies are comparable in the three samples: 0.99 $\pm$
0.07, 0.95 $\pm$ 0.06, and 0.96 $\pm$ 0.06 for the halo, substructure, and
outskirt samples, respectively.

Figure 5: The color–magnitude ($m_{g}-m_{r}$)$-m_{r}$ diagram for the halo
galaxies (top), substructure galaxies (middle), and outskirt galaxies
(bottom). The magenta and cyan dots show the quiescent and SF galaxies,
respectively. The dashed line in each pane is the red-sequence fit to the
quiescent halo galaxies in the top panel: $m_{g}-m_{r}$ = $-0.0314m_{r}$ \+
$1.528$.

###  3.3 The sSFR$-D_{n}4000$ relation

Figure 6 shows the distributions of the spectral index $D_{n}4000$ and the
sSFR for the galaxies in our three samples. This figure also shows the
correlation between these two quantities. For the halo and substructures
galaxies, the distributions peak at small sSFR and large $D_{n}4000$, whereas
for the outskirt galaxies the distributions appear somewhat flat. This
different behavior indicates a correlation between the environment and the
galaxy properties.

Figure 6:  Top panel: the distribution of sSFR for the halo galaxies (red
histogram), the substructure galaxies (blue histogram), and the outskirt
galaxies (hollow histogram). Right panel: same as the top panel for
$D_{n}4000$. Bottom left panel: the relation between sSFR and $D_{n}4000$. The
two dotted lines are linear fits to the SF and quiescent galaxies separately.
For illustrative purposes, the entire galaxy sample is separated into bins of
fixed width on the $\log({\mathrm{sSFR/yr}^{-1}})$ axis: for each of these
bins, the shaded areas show the rms values of $D_{n}4000$ around the mean.
BCG, S1, and S2 are the central bright galaxies of A2142, sub14, and sub3,
respectively.

Our galaxy sample indeed confirms the expected anticorrelation between sSFR
and $D_{n}4000$ (Kauffmann et al. 2004): $D_{n}4000$ increases with the age of
the stellar population (Balogh et al. 1999) and is thus expected to increase
with decreasing sSFR if sSFR decreases with increasing age of the stellar
population (Duarte Puertas et al. 2022).

We separately fit the sSFR$-D_{n}4000$ relation for the SF galaxies and the
quiescent galaxies, and find
$D_{n}4000=-0.39\log({\mathrm{sSFR/yr^{-1}}})-2.24$ and
$D_{n}4000=-0.06\log({\mathrm{sSFR/yr^{-1}}})+1.17$ for the two samples,
respectively. The relation is steeper for the sample of SF galaxies than for
the quiescent galaxies, suggesting that the star formation activity gradually
decreases in increasingly denser environments.

###  3.4 The radial distribution of sSFR and $D_{n}4000$

The properties of cluster galaxies are closely related to the local galaxy
density, which, in turn, generally depends on the clustrocentric distance
(Odekon et al. 2018; Coccato et al. 2020; Meusinger et al. 2020). Figure 7
shows the dependence of the sSFR on the projected radius $R$ from the cluster
center for the entire galaxy sample (top panel) and for the three galaxy
samples separately (bottom panel). The data are divided into 10 equally spaced
radial bins. The median value of each bin is given. Their rms values are shown
with shading. Despite the large scatter, our entire sample shows that sSFR
increases with $R$. The substructure galaxies are mainly responsible for this
trend. Indeed, the outskirt galaxies show a flat relation, with larger sSFRs
than substructure galaxies, on average, and the halo galaxies show a slightly
decreasing relation.

Figure 7: The dependence of sSFR on the projected clustrocentric radius $R$.
Top panel: the entire galaxy sample with the rms values of sSFR around the
mean in each of the 10 evenly spaced radial bins (shaded area). The dots
indicate the median values of each bin. The dotted line shows the best linear
fit. The two vertical solid lines show the two radii $R_{500}=1.408$ Mpc and
$R_{200}=2.16$ Mpc. Bottom panel: same as the top panel for the three galaxy
subsamples separately: halo (red), substructure (blue), and outskirt galaxies
(black/gray).

Figure 8 shows the dependence of $D_{n}4000$ on $R$ (Balogh et al. 1999). It
mirrors the dependence of sSFR on $R$, because of the correlation between sSFR
and $D_{n}4000$ shown in Fig. 6: for the entire sample, $D_{n}4000$ decreases
with increasing $R$, similarly to the galaxies in A2029 (Sohn et al. 2019). As
in the sSFR-$R$ relation, this trend is mostly due to the substructure
galaxies, whereas halo and outskirt galaxies have shallower relations, with
the values of $D_{n}4000$ of the outskirt galaxies smaller, on average, than
those for the other two galaxy samples.

Figures 7 and 8 show that the average values of sSFR and $D_{n}4000$ of the
substructure galaxies in the cluster center are comparable to the values of
the halo galaxies. Similarly, at large radii, these quantities of the
substructure galaxies are comparable to the values of the outskirt galaxies.
This result suggests (1) that the substructure galaxies are sensitive to the
environment of their own substructure, and (2) that substructures tend to slow
down the transition from field galaxies to cluster galaxies. This scenario is
consistent with results of simulations, which suggest that orphan galaxies
that have lost their subhalos are more vulnerable to environmental effects
than those that still have them(Cora et al. 2018). Those orphan galaxies
belong to the diffuse halo galaxies here.

Figure 8: Same as Fig. 7 for the $D_{n}4000$$-$$R$ relation.

Considering the sSFR depends strongly on the stellar mass, the mass
segregation effect could bias our result. We check the distribution of radial
stellar mass log$M_{\star}$ of the three subsamples and find their median
masses are consistent at all radii, as Fig. 9 shows.

Figure 9: Same as Fig. 7 for the log$M_{\star}$$-$$R$ relation. The solid
black line indicates the median value in each bin.

###  3.5 The $R$$-$$v$ diagram

We know only three out of the six phase-space coordinates of each galaxy in
the field of view of A2142: the two celestial coordinates and the line-of-
sight velocity. This limited knowledge prevents us from grasping the full
dynamics of the cluster and its structure. Nevertheless, from the distribution
of galaxies in the $R$$-$$v$ diagram, namely the line-of-sight velocity versus
the projected distance from the cluster center, we can infer the global depth
of the gravitational potential well of the cluster, or, equivalently, the
escape velocity from the cluster (Diaferio & Geller 1997; Diaferio 1999; Serra
et al. 2011), and identify the galaxies that are members of the cluster (Serra
& Diaferio 2013). This information can be extracted for a large interval of
projected distances from the cluster center, from the central region to radii
much larger than the virial radius, in regions where the dynamical equilibrium
hypothesis does not hold and where the galaxies surrounding the cluster are
falling into it for the first time.

Figure 10 shows the $R$$-$$v$ diagram, or projected phase-space (PPS) diagram,
of our three galaxy samples. The blue dotted lines show the location of the
caustics derived in Sohn et al. (2020). The caustics are related to the escape
velocity from the cluster (Diaferio & Geller 1997; Diaferio 1999). According
to Serra & Diaferio (2013), the sample of galaxies within the caustics
contains $(95\pm 3)$% of the real members and is contaminated by $\sim 8$% of
interlopers within 3$R_{200}$. The caustic technique thus represents a valid
procedure to identify cluster members in real data.

Alternatively, Oman & Hudson (2016) adopt an approximate relation to identify
cluster members. Their relation is based on dark matter-only simulations. By
defining as interlopers those satellite dark matter halos with distance, in
real space, $r_{3d}>2.5r_{vir}$, with $r_{vir}$ the cluster virial radius,
they find that, in the $R$$-$$v$ diagram, the line
$v/\sigma_{3d}=-(4/3)R/r_{vir}+2$ roughly separates the region of the
$R$$-$$v$ diagram dominated by the cluster members from the region dominated
by interlopers. The black solid lines in Fig. 10 show the line of Oman &
Hudson (2016), where we set $\sigma_{3d}=\sqrt{3}\sigma_{cluster}$ and
$R_{200}/r_{vir}=0.73$. The black solid lines are roughly consistent with the
caustic location and thus appear to be a reasonable proxy for the caustics.
For the sake of simplicity, we adopt these black solid lines, rather than the
caustics, as the cluster boundaries.

Figure 10 shows two additional sets of black dashed lines: they have the same
slope as the black solid lines and cross the $v/\sigma_{cluster}=0$ axis at
$R_{200}$ and $R_{500}$, respectively. We adopt these lines in the $R$$-$$v$
diagram as the counterparts of $R_{200}$ and $R_{500}$ in real space.

The distribution of our galaxy samples in the $R$$-$$v$ diagram is generally
consistent with the identification of the cluster members derived in Sect.
3.1: most outskirt galaxies (triangles), which are not expected to be cluster
members, lie outside the regions identified by the caustics or the black solid
lines, whereas most halo and substructure galaxies, which are expected to be
cluster members, are within these regions.

Figure 10: The $R$$-$$v$ diagram of the 333 data-available galaxies of A2142.
The data-available galaxies consist of 80 substructure galaxies (squares), 109
halo galaxies (circles), and 144 outskirt galaxies (triangles). Cyan and
magenta symbols show SF and quiescent galaxies, respectively. The symbol size
is proportional to the specific SFR. The red square on the left is the BCG.
The blue dotted lines show the caustic location. The black solid and dashed
lines are described in the text.

We now investigate the star formation activities of the galaxies in the infall
region of the cluster. We define the infall region as the band of the
$R$$-$$v$ diagram between the black solid line and the black dashed line
crossing the point $(R_{200},0)$. We consider the specific SFR, sSFR, and the
spectral index $D_{n}4000$ as a function of the distance $\Delta d$ of each
galaxy from the black solid line: $\Delta d$ is thus the segment perpendicular
to the black solid line joining the galaxy and the black solid line. According
to the analysis of the orbits of galaxies falling into clusters in numerical
simulations (e.g., Yoon et al. 2017; Arthur et al. 2019), a galaxy that is
falling into the cluster traces a trajectory roughly parallel to the black
solid line in the $R$$-$$v$ diagram; the radial coordinate $R$ of this
trajectory clearly decreases during the galaxy infall. Therefore, larger
$\Delta d$ implies larger initial radial distance of the falling galaxy.

Figure 11 shows the $\Delta d$ distribution of the 93 SF galaxies, namely the
data-available galaxies with $\log(\mathrm{sSFR/yr}^{-1})>-11$. Out of these
93 galaxies, 30 are cluster members: specifically there are 20 substructure
galaxies and 10 halo galaxies. Out of these 20 and 10 galaxies, 17 and 8,
respectively, lie in the infall region, namely in the band between the black
solid line and the outer black dashed line in the $R$$-$$v$ diagram.
Therefore, 83% (25 out of 30) of the cluster members that are actively forming
stars are in the infall region. Our sample thus demonstrates, as expected,
that the dense intracluster medium within $R_{200}$ inhibits the star
formation activity. The only SF galaxy (LEDA 1801474) within $R_{500}$ is a
halo galaxy. The SDSS image of this galaxy suggests that its star formation
activity is triggered by an ongoing merger.

Figure 11: Top: relation between sSFR and $\Delta d$ for the 93 SF galaxies in
the data-available galaxy sample. Middle: the distribution of $\Delta d$ for
the full sample of 93 SF galaxies. Bottom: the distribution of $\Delta d$ for
the halo, substructure, and outskirt SF galaxies separately. The two vertical
black dotted lines indicate $R_{200}$ ($\Delta d$ = $-0.9$) and $R_{500}$
($\Delta d$ = $-1.2$), respectively. The vertical black solid line is the
boundary line $\Delta d=0$.

Figure 12 shows the $\Delta d$ distribution of the 82 galaxies with spectral
index $D_{n}4000<1.6$. We call these galaxies blue galaxies. Their
distribution is similar to the distribution of sSFR in Fig. 11. There are 26
(84%) out of 31 blue galaxies that are cluster members, namely either
substructure or halo galaxies, in the infall region. There are 17 out of 20
substructure blue galaxies, and 9 out of 11 halo blue galaxies. The only blue
galaxy within $R_{500}$ is a halo galaxy (SDSS J155827.26+271300.3). Its color
might be contaminated by a nearby blue object, which is only 4 arcsec away.

Figure 12: Same as Fig. 11 for the 82 blue galaxies with $D_{n}4000<1.6$.

Figures 11 and 12 show that the SF and blue galaxies that are cluster members
are concentrated in the infall region, namely in the PPS region located
between the black dashed line corresponding to $R_{200}$ and the black solid
line. This result indicates that the dense ICM environment substantially
inhibits the star formation activity of the galaxies once they enter the
region within $R_{200}$. In addition, the transition from star forming
galaxies to quiescent galaxies substantially ends at radii larger than
$R_{500}$.

##  4 Summary

We compiled a catalog of 333 galaxies from a spectroscopic redshift survey of
2239 galaxies in the field of view of the cluster A2142 (Liu et al. 2018). The
survey covers a circular area of radius $\sim 11$ Mpc from the cluster center.
Each of the 333 galaxies has measured stellar mass $M_{\star}$, SFR, and
spectral index $D_{n}$4000\. We use the Blooming Tree algorithm, an algorithm
for the identification of cluster substructure (Yu et al. 2018), to separate
our sample into three subsamples: the halo, the substructure, and the outskirt
galaxies. The halo and the substructure galaxies are cluster members. The
outskirt galaxies are still in the outer region of the cluster, but, according
to the Blooming Tree algorithm, their gravitational bond to the cluster is
weak.

We investigate the relation between the environment and the star formation
activity of the galaxies in these three subsamples. Our main conclusions are
as follows.

  * •

The specific SFR, sSFR=SFR/$M_{\star}$, is larger in the outskirt galaxies and
smaller in the halo galaxies. In addition, the sSFR increases, on average,
with increasing distance from the cluster center; similarly, the spectral
index $D_{n}4000$, which is an indicator of the age of the stellar population,
decreases with increasing distance from the cluster center. Both results show
that the star formation activity tends to be inhibited a high density
environment.

  * •

The sSFR of substructure galaxies is intermediate between the sSFR of halo
galaxies and that of outskirt galaxies; in addition, the sSFR depends on the
environment of the substructure of the galaxy, being smaller, on average, for
galaxies in substructures that are close to the cluster center, and larger for
galaxies in substructures that are in the outer region of the cluster. The
spectral index $D_{n}4000$ shows the same behavior. This result demonstrates
that substructures tend to slow down the transition between field galaxies and
cluster galaxies.

  * •

Galaxies that are actively forming stars mostly lie in the cluster infall
region, roughly between $R_{200}$ and the turn-around radius: star formation
is progressively inhibited while approaching $R_{200}$ and substantially
quenched within $R_{200}$.

Our analysis demonstrates the relevance of spectroscopic redshifts for
investigating the connection between the physical properties of galaxies and
their environment. For this goal, our Blooming Tree algorithm proves efficient
at associating the galaxies with the composite structures of a cluster. The
application of the Blooming Tree algorithm to data from future extensive
spectroscopic surveys, such as Euclid (Euclid Collaboration et al. 2022) or
LSST (Ivezić et al. 2019), is thus expected to greatly enhance our
comprehension of galaxy evolution in clusters.

## Acknowledgments

We thank the referee sincerely for his/her valuable comments and suggestions
in the report. This work was supported by Bureau of International Cooperation,
Chinese Academy of Sciences GJHZ1864. A.D. acknowledges partial support from
the INFN grant InDark.

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