# Examining transitional galaxies to understand the role of clusters and their
dynamical status in galaxy quenching

Douglas Brambila1, Paulo A. A. Lopes,1, André L. B. Ribeiro2, Arianna Cortesi1
1Observatório do Valongo, Universidade Federal do Rio de Janeiro, Ladeira do
Pedro Antônio 43, Saúde,
Rio de Janeiro, RJ 20080-090, Brazil –<EMAIL_ADDRESS>
2Laboratório de Astrofísica Teórica e Observacional – Departamento de Ciências
Exatas e Tecnológicas –Universidade Estadual de Santa Cruz,
45650-000, Ilhéus, BA, Brazil

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

In this work, we consider four different galaxy populations and two distinct
global environments in the local Universe (z $\leq 0.11$) to investigate the
evolution of transitional galaxies (such as star-forming spheroids and passive
discs) across different environments. Our sample is composed of 3,899 galaxies
within the R200 radius of 231 clusters and 11,460 field galaxies. We also
investigate the impact of the cluster’s dynamic state, as well as the galaxy’s
location in the projected phase space diagram (PPS). We found that although
the cluster environment as a whole influences galaxy evolution, the cluster
dynamical state does not. Furthermore, star-forming galaxies represent recent
cluster arrivals in comparison to passive galaxies (especially in the case of
early-types). Among the ETGs, we find that the D${}_{n}(4000)$ and Hδ
parameters indicate a smooth transition between the subpopulations. In
particular, for the SF-ETGs, we detect a significant difference between field
and cluster galaxies, as a function of stellar mass, for objects with Log
$M_{*}$/M${}_{\odot}>10.5$. Analyzing the color gradient, the results point
toward a picture where field galaxies are more likely to follow the monolithic
scenario, while the cluster galaxies the hierarchical scenario. In particular,
if we split the ETGs into lenticulars and ellipticals, we find that the
steeper color gradients are more common for the lenticulars. Finally, our
results indicate the need for galaxy pre-processing in smaller groups, before
entering clusters.

###### keywords:

galaxies: clusters: general – galaxies: clusters - galaxies: evolution -
galaxies: clusters: environment

††pubyear: 2022††pagerange: Examining transitional galaxies to understand the
role of clusters and their dynamical status in galaxy quenching–Examining
transitional galaxies to understand the role of clusters and their dynamical
status in galaxy quenching

##  1 Introduction

The existence of a bi-modality in different galaxy properties is well
established in the past years (Strateva et al., 2001; Kauffmann et al., 2003b;
Baldry et al., 2004; Balogh et al., 2004; Baldry et al., 2006). We can
separate galaxies into two main categories: blue cloud galaxies (BC) – mostly
blue star-forming spiral galaxies; and red sequence objects (RS) — mainly red
early-types with no significant star-formation activity. Despite that, we have
found galaxies that defy the simplistic view that elliptical galaxies are red
and dead while spiral galaxies are blue and lively (e.g., Wolf et al. 2009;
Masters et al. 2010; Cortese 2012; Crossett et al. 2014; Lopes et al. 2016;
Kuchner et al. 2017; Mahajan et al. 2018). We have also established the
existence of an intermediary region between the BC and the RS, called Green
Valley (GV), that works as a transitioning region between the BC and RS
(Martin et al., 2007; Salim et al., 2009; Mendez et al., 2011; Schawinski et
al., 2014). These two points together paint a clear scenario where galaxies
evolve from the BC to the RS as their life progresses. However, the mechanisms
responsible for this transformation are still open for debate.

Dressler (1980) showed that there is a relation between the galaxy morphology
and the environment where the galaxy inhabits (the Morphology-Density
Relation). Early-type galaxies (ETGs; the dominant morphology in the RS) show
a preference for inhabiting higher-density environments, and therefore are
primarily found in galaxy groups or clusters. On the contrary, late-type
galaxies (LTGs; the dominant morphology in the BC) show a preference for
inhabiting lower-density environments, being mainly found in the field or the
outskirts of groups and clusters. Alongside that relation, we also have
evidence that the fraction of blue galaxies inside clusters increases while
the fraction of red galaxies decreases when we go for higher redshift regimes
(Butcher & Oemler, 1984).

Different mechanisms impact a galaxy as it enters a cluster. Those can be
responsible for quenching the galaxy’s star formation or, at least,
accelerating this process. One of those effects is ram-pressure striping
(RPS), where the gas inside the galaxy is removed due to the pressure caused
by the hot intracluster medium (Gunn & Gott, 1972). Other ones are
strangulation and starvation — when the hot intracluster medium removes gas
from the galaxy halo and also prevents a new supply of gas from falling into
the galaxy (Larson et al., 1980). We also have events like mergers (when two
galaxies go into a fusion process and become one single entity — Toomre &
Toomre 1972), harassment (the accumulative effect of several fly-by encounters
of a galaxy with others — Moore et al. 1996; Moore et al. 1998), and tidal
force from the gravitational potential well of the cluster (capable of driving
gas to the center of the galaxy and triggering a center starburst and bar
instabilities — Byrd & Valtonen 2001; Łokas et al. 2016). All of those
processes are, in some way or another, capable of altering the gas content of
a galaxy inside or entering the cluster.

On the other hand, one cannot ignore that galaxies also evolve when found in
isolation in the Universe. This isolated evolution points toward a myriad of
processes happening inside those galaxies. This event falls under the umbrella
of mass quenching. In lower mass systems (M${}_{*}<10^{9}M_{\odot}$), stellar
and AGN feedback are capable of heating and, in some cases, even removing
galactic gas (e.g., Ponman et al. 1999), while for higher mass systems, the
importance of stellar feedback decreases, but the AGN one is still very
important (Larson, 1974; Dalla Vecchia & Schaye, 2008; Croton et al., 2006;
Fabian, 2012).

Several studies show that mass quenching and environmental quenching have
distinct effects on different galaxy types. According to Peng et al. (2010),
satellite galaxies are more likely to be quenched by environmental action,
whereas central galaxies are more likely to be quenched by mass-related
effects.

It is not an easy task to separate the influence of internal and external
mechanisms in galaxy evolution. Besides showing that mass and environmental
quenching have a distinct impact on different types of galaxies, Peng et al.
(2010) also verified that environmental quenching acts independently of the
mass and vice-versa.

A clear evidence of the cluster influence in galaxy evolution is presented by
Jaffé et al. (2015). The authors analyzed galaxies of the relaxed cluster
Abell $963$ (z $=0.203$) observed with the Blind Ultra Deep HI Environmental
Survey (BUDHIES). They showed that galaxies lose their gas content, down to
the BUDHIES detection limit, in their first passage into the cluster center.
The authors also encounter a significant fraction of galaxies that arrive at
the cluster already without gas content. This last result raises the question
of the role of the cluster in the gas removal of those galaxies.

In the present work, we try to shed some light on the role of clusters in
galaxy quenching, investigating the properties of different galaxy populations
and at different locations within clusters. We focus on the comparison of
transitional galaxies - such as the star-forming spheroids and red discs - to
the more regular populations. That is done in different locations in the
projected phase space diagram. We also investigate possible dependencies to
the cluster’s dynamical state and compare the cluster results to what is found
in the field.

The paper is organized as follows: In $\S 2$, we introduce our data,
describing the galaxy morphological and star-formation activity
classification, as well as the cluster dynamical state, while in $\S 3$, we
show our results. In$\S 4$, we have a discussion of the main results and our
conclusions. The cosmology assumed in this work is $\Omega_{\rm m}=0.3$,
$\Omega_{\lambda}=0.7$, and H${}_{0}=100$ $\rm h$ $\rm km$ $s^{-1}$ Mpc-1,
with $\rm h$ set to $0.7$.

##  2 Data

In this work, we consider galaxies from two very different environments, as we
have a sample of cluster galaxies and one of field objects. The cluster sample
is a combination of objects selected in different wavelengths. We have
clusters from the supplement version of the Northern Sky Optical Cluster
Survey (NoSOCS, Lopes et al. 2004, 2009a), the Cluster Infall Regions in the
SDSS (CIRS, Rines & Diaferio 2006), the HIghest X-ray FLUx Galaxy Cluster
Sample (HIFLUGCS, Reiprich & Böhringer 2002; Andrade-Santos et al. 2017), the
Planck Early Sunyaev-Zel’Dovich (ESZ, Planck Collaboration et al. 2011) and
the SPIDERS catalog (Kirkpatrick et al., 2021).

Figure 1: The distribution of Log M200 for the cluster samples considered for
the present work. In the top left we show the NoSOCS+CIRS clusters, in the top
right the HIFLUGCS objects are displayed, while in the bottom we have the
Planck ESZ (left) and SPIDERS (right) samples. The distributions are for the
original data sets, before we check for duplicates and remove them, but we do
consider the redshift and mass cuts described above ($z\leq 0.10$ and LOG
M${}_{200}/M_{\odot}\geq 13.5$). On each panel, we display objects with no
substructure in red (solid lines) and those with substructure in blue (dashed
lines). The number of systems with or without substructure is also listed in
the panels.

The NoSOCS clusters comprise the only optically selected catalog of those
listed above. HIFLUGCS is an X-ray cluster catalog. The CIRS and SPIDERS
samples are composed of X-ray selected clusters, with SDSS spectroscopic data.
The latter is actually based on an extensive follow-up effort of SDSS-IV. The
Planck ESZ catalog consists of clusters selected through the Sunyaev-
Zel’Dovich effect. All the clusters we use in the current work are within the
SDSS DR7 spectroscopic footprint, so that we can uniformly derive cluster
properties for these systems. We have previously worked with the NoSOCS+CIRS
clusters in Lopes et al. (2009a, b); Lopes et al. (2014); Lopes et al. (2016);
Lopes et al. (2017) and Ribeiro et al. (2013). In Lopes et al. (2018), we
compared substructure estimates and BCG properties of those clusters to the
ones from the HIFLUGCS and Planck ESZ lists (as provided by Andrade-Santos et
al. 2017). In the current paper, we combined all these catalogs with the
SPIDERS sample. Our goal is to minimize possible biases due to different
selection techniques and wavelengths. One bias example is related to the
substructure fraction, discussed in Andrade-Santos et al. (2017) and Lopes et
al. (2018), that can be found when comparing X-ray and SZ selected samples
(also seen when comparing to optically selected systems). However, in order to
have a more uniform data set we only consider systems at $z\leq 0.10$,
containing at least 10 members within R200 and with LOG
M${}_{200}/M_{\odot}\geq 13.5$ (membership, R200 and M200 estimates are
explained below). Doing so, we are able to work with a complete spectroscopic
sample from the SDSS DR7 main sample and derive reliable estimates of
membership and cluster physical parameters.

Figure 1 shows the distribution of Log M200 for each cluster sample mentioned
in the previous paragraph. The number of objects with (dashed line) or without
(solid line) substructure is also indicated. The distributions are for the
original data sets, before we check for duplicates and remove them (see
below), but we do consider the redshift and mass cuts described above ($z\leq
0.10$ and LOG M${}_{200}/M_{\odot}\geq 13.5$). This figure shows that the
combination of the samples is an important step towards a more complete
distribution according to the cluster mass. We are also able to mitigate the
impact of cluster catalogs heavily affected by substructure (such as the
Planck ESZ list). Note that systems with substructure generally have higher
masses in comparison to the more regular clusters, a result consistent to the
findings of Ribeiro et al. (2011).

All the clusters in our sample have the same redshift limits and had a minimum
number of member galaxies and cluster mass imposed. However, the main factor
that could still affect our results is the cluster mass cut, as we also
consider groups, or low mass clusters. We verified that applying a higher mass
cut (at LOG M${}_{200}/M_{\odot}=14$, instead of $13.5$) do not affect our
main results. For instance, the fractions of the galaxy populations displayed
in Table 1 (see below) do not show a large variation. Note also, that the
fraction of all galaxies within the groups (LOG M${}_{200}/M_{\odot}<14$) is
small ($23\%$). Hence, we decided to keep the analysis with all systems in our
sample, as described above (with LOG M${}_{200}/M_{\odot}\geq 13.5$).

For each cluster from the above catalogs, we used SDSS-DR7 photometric and
spectroscopic data to select members (and exclude interlopers), estimate the
velocity dispersion ($\sigma_{cl}$), physical radius (R500 and R200) and mass
(M500 and M200).

As in Lopes et al. (2009a) we select members and exclude interlopers after
applying the shifting gapper technique (Fadda et al., 1996) to all galaxies
with available redshifts around each cluster. We only use the members within
$2.5$ h-1 Mpc to derive an initial estimate of the velocity dispersion
($\sigma_{cl}$). Differently from what we did in previous works when we
estimated physical radius and cluster masses from a virial analysis (following
the approach of Girardi et al. 1998), we now follow the procedure described in
Ferragamo et al. (2020). First, we apply the corrections proposed by Ferragamo
et al. (2020) to the velocity dispersion estimate (initially derived within
$2.5$ h-1 Mpc). Next, we obtain an estimate of M200 adopting the equation 1
(listed below) of Ferragamo et al. (2020) (also see Munari et al. 2013). The
corrections considered by Ferragamo et al. (2020) to the mass estimate are
also employed.

$\frac{\sigma_{{\rm 1D}}}{{\rm
km~{}s^{-1}}}=A\left[\frac{h(z)M_{200}}{10^{15}~{}{\rm
M\odot}}\right]^{\alpha},$ (1)

where $A$ is $1777.0$ ${\rm km~{}s^{-1}}$ and $\alpha=0.364$.

R200 is assumed to be the radius at which the averaged mass density reached
$200$ times the critical mass density of the Universe at redshift $z$. Hence,
considering the mass $M_{200}=(4\pi/3)200\rho_{c}(z)R^{3}_{200}$ is the total
mass within R200, we can derive an estimate of R200 from the above mass
estimate. We then obtain a final mass estimate, but now considering only
members within R200 (instead of $2.5$ h-1 Mpc). Having this updated member
list we estimate again $\sigma_{cl}$ and the mass, using equation 1 of
Ferragamo et al. (2020); Munari et al. (2013). The corrections from Ferragamo
et al. (2020) are again applied both to $\sigma_{cl}$ and M200. R500 and M500
estimates are derived after assuming a NFW profile and interpolating to the
appropriate radius. For more details on the estimates above, we refer the
reader to Lopes et al. (2009a); Lopes et al. (2014); Lopes et al. (2018) and
Ferragamo et al. (2020).

Next, we eliminate common clusters from the different catalogs, arriving at a
cluster sample with 231 objects. They are between $0.018\leq z\leq 0.100$, and
have $13.5\leq$ LOG M${}_{200}/M_{\odot}\leq 15.13$. In order to keep a
cluster, we also impose a minimum number of 10 members within R200. The upper
redshift limit ($z=0.100$) corresponds to the completeness limit of the SDSS
main spectroscopic sample, limited at $r_{r}^{petro}=17.77$. That is
translated to an absolute magnitude limit of $M_{r}\sim M^{*}+1=-20.58$. We
call galaxies more luminous than this absolute magnitude limit as bright,
which are the ones studied in the current work. In total, we have $3899$
bright galaxies ($M_{r}\leq M^{*}+1$), inside R200 of those 231 galaxy
clusters, ranging between $0.015\leq z\leq 0.107$ and $10^{9.0}\leq
M_{*}/M_{\odot}\leq 10^{12}$. For all those galaxies, we have morphological
information from Domínguez Sánchez et al. (2018, hereafter DS18) or Huertas-
Company et al. (2011, hereafter HC11); see $\S$2.1. Although most of our work
based on the cluster sample considers only galaxies within R200, we still have
member galaxies up to 5$\times R_{200}$ (approximately the turn-around
radius). In total, we have $9931$ members within 5$\times R_{200}$ (which are
used in Fig. 11). It’s important to notice that our sample includes low-mass
galaxy systems (M${}_{200}<1\times 10^{14}$), which should be referred to as
groups. However, for ease of reading, we decided to call, in this paper, all
the objects in our sample as clusters. Groups correspond to $\sim 40\%$ of our
sample, containing $\sim 23\%$ of all the galaxies in our cluster sample.

The field sample was selected by comparing the photometric and spectroscopic
SDSS-DR7 data with a sample of about $15,000$ groups and clusters provided by
Gal et al. (2009), combined with our cluster sample described above. To select
field galaxies, we excluded any galaxy with a distance smaller than 4 Mpc and
with $\Delta z<0.06$ of any object from the combined cluster catalog. To
ensure a lower level of contamination from clusters and groups that eventually
are not present in the cluster comparison sample, we also remove galaxies with
a local galaxy density LOG$(\Sigma_{5})<-0.5$. The parameter $\Sigma_{5}$
(described in La Barbera et al. 2010; Lopes et al. 2014, 2017) is given by
$5/\pi d^{2}_{n}$, where $d_{n}$ was selected to be the projected distance of
the fifth-nearest galaxy with maximum velocity offset of $1,000~{}kms^{-1}$.
The total number of field galaxies selected according to the criteria above is
$55,842$ sources. Our sample was reduced to $\sim 30,000$ galaxies after we
impose redshift ($0.01\leq z\leq 0.11$), stellar mass ($10^{9.0}\leq
M_{*}/M_{\odot}\leq 10^{12}$) and luminosity cuts ($M_{r}<M^{*}+1$). Note that
we also require the galaxies to have morphological information provided by
DS18 (or HC11). Finally, we construct a sample of field galaxies that follows
the mass distribution of the cluster sample. To do so, we select a random
sample (of 3899 galaxies) from the $30,000$ field galaxies, forcing it to have
the same pattern of stellar mass distribution that the cluster sample has. We
then apply a Kolmogorov–Smirnov (KS) and Anderson-Darling (AD) test to check
if the samples are statistically similar. In this case, we keep the selection
and repeat the process, removing the already selected galaxies from the
$30,000$ pile. We repeat the process until the KS and AD return that the
sample is statistically distinct. In the end, we retain the largest sample of
field galaxies that has a similar stellar mass distribution to the cluster
sample, resulting in $11,460$ field objects. The $p-value$ is 0.13 and the AD
test has the confidence of $99.5\%$.

###  2.1 Galaxy morphology

Galaxy morphology was mainly extracted from DS18. They adopt a deep learning
technique to classify galaxies from the sample, described at Meert et al.
(2015, 2016). This data set was constructed from the SDSS-DR7 spectroscopic
main sample, taking into account redshift ($0.005<z<1.0$) and magnitude
($14<m_{r}^{petro}<17.77$) cuts. DS18 provides morphological information for
about 670,000 galaxies. The Convolutional Neural Network was trained to obtain
the T-type values and the probability of the galaxies containing certain
features like a disc, inclination (face/edge-on), bar signature, bulge
prominence, roundness, and mergers. They also provide the probability of a
galaxy having a lenticular morphology.

To create a robust classification, we combine the T-type information and the
probabilities provided by DS18 to have a morphological classification for
elliptical and lenticular galaxies. We proceed as below:

  * •

Elliptical (E):

    * –

T-type $<-1.5$

    * –

P${}_{bulge}>0.6$

    * –

P${}_{disk}<0.8$

  * •

Lenticular (S0):

    * –

$-1.5<$ T-type $<0.0$

    * –

P${}_{S0}>0.6$

    * –

P${}_{disk}<0.8$

Cluster sample
---
| Passive | GV | SF | GV+SF | Total
ETG | 2432 | 77 | 56 | 133 | 2565
| (94.81%) | (3.00%) | (2.18%) | (5.18%) | (65.79%)
Ellipticals (E) | 2003 | 39 | 24 | 63 | 2066
Lenticulars (S0) | 429 | 38 | 32 | 70 | 499
LTG | 827 | 116 | 391 | 507 | 1334
| (61.99%) | (8.7%) | (29.31%) | (38.01%) | (34.21%)
Total | 3259 | 193 | 447 | 640 | 3899
| (83.58%) | (4.95%) | (11.46%) | (16.41%) | (100%)
Field sample
| Passive | GV | SF | GV+SF | Total
ETG | 4385 | 378 | 715 | 1093 | 5478
| (80.05%) | (6.90%) | (13.05%) | (19.95%) | (47.80%)
Ellipticals (E) | 3461 | 188 | 239 | 427 | 3888
Lenticulars (S0) | 924 | 190 | 476 | 666 | 1590
LTG | 1596 | 827 | 3559 | 4386 | 5982
| (26.68%) | (13.82%) | (59.50%) | (73.32%) | (52.20%)
Total | 4386 | 1205 | 4274 | 4274 | 11460
| (52.19%) | (10.51%) | (37.29%) | (47.81%) | (100%)

Table 1: Morphological division for the galaxy cluster sample (top table) and
for the field sample (bottom table). We also show the division between
passive, green-valley, and star-forming galaxies (and also a combination of
the GV and SF populations). This separation was made using eqs. 1 and 2 (see
§2.2 for more details). Figure 2: Stellar mass vs. SFR diagram. In red, we
have the plot for the cluster sample and in blue we have the field sample. In
both, the dashed lines are equations (1) and (2) of Trussler et al. 2020
(equations 2 and 3 here), delineating the passive and the star-forming
regions. This figure already gives a good indication of the predominance of
passive galaxies in the cluster sample, and the bi-modality observed for the
field sample in Table 1.

We combined E and S0 galaxies into one class, which we named Early-type
Galaxies (ETGs). Objects that are not ETGs are called Late-type Galaxies
(LTGs). When morphological information was not obtainable through DS18, we
supplemented the data with the classification provided by HC11. HC11 provided
morphological information gathered for the SDSS-DR7 spectroscopic sample (up
to $z=0.25$) via a Machine Learning technique (in their case, using a Support
Vector Machine). HC11 gives probabilistic information to classify galaxies as
ellipticals, early Spirals (ab), and late Spirals cd. From the $11460$ field
galaxies, only $13$ ($\sim 0.1\%$) were absent from the DS18 sample and
required HC11 information. From the $3899$ cluster galaxies, only $38$ ($\sim
1\%$) do not have DS18 information and were classified using HC11 data. For
these $51$ sources, we utilize the HC11 as follows:

  * •

E:

    * –

Prob(E) $>0.8$

  * •

S0:

    * –

Prob(S0) $>0.8$

We added the morphological classification from HC11 as it is based on a
similar data set (also built from the SDSS-DR7 spectroscopic main sample) and
it is a classification provided by the same research group as in DS18.
Nonetheless, it is important to mention that we consider less than $1\%$ of
galaxies from HC11, and removing those galaxies does not affect our main
conclusions.

###  2.2 Separation of passive and star-forming galaxies

Galaxy properties such as star formation rate (SFR) and stellar masses were
calculated by the Max Planck Institute for Astrophysics and the Johns Hopkins
University group (MPA-JHU), following the methods of Brinchmann et al. (2004),
Kauffmann et al. (2003a), and Tremonti et al. (2004). The MPA-JHU sample
provides this information for over $1,800,000$ galaxies up to $z\sim 0.3$ for
the SDSS-DR8 release.

Figure 2 shows, in the left panels, the M∗ vs. SFR plane for our cluster
sample (top) and field sample (bottom). The dashed lines in each of the panels
are the visual construction of the equations (1) and (2) of Trussler et al.
(2020) (equations 2 and 3 here). Equation 2 gives the boundary between star-
forming (SF) and green-valley (GV) galaxies, and Equation 3 gives the boundary
between GV and passive (Pas) galaxies:

$log(SFR)=0.70~{}log(M_{*})-7.52$ (2) $log(SFR)=0.70~{}log(M_{*})-8.02$ (3)

Using the above equations, we separate our data sets (cluster and field
galaxies) in different subpopulations, regarding morphology and star-formation
activity. Table 1 summarizes the result of this separation.

To illustrate the impact of environment and morphology on the star formation
activity, we also display in Figure 2 the stellar mass (central panels) and
SFR distributions (right panels) of ETGs (red lines) and LTGs (blue lines).
The distributions for all galaxies are shown by the black-filled histograms.
As before, the cluster results are in the top panels, while the field results
are shown at the bottom. The LTG distributions show fewer massive galaxies (in
comparison to the ETGs), both for clusters and the field. However, this
difference does not look very large. Despite that, the SFR distributions of
LTGs are remarkably different from the ETGs, and those differences are
enhanced with the environment (if we compare the cluster and field results).
Note the LTG distribution of SFR is very different between the cluster and
field datasets. We can also detect an increase of SF ETGs when comparing the
cluster and field distributions.

###  2.3 Cluster dynamical state

To investigate the possible impact of the cluster’s dynamical state on the
galaxy properties, we also separated the clusters according to their degree of
substructures. Objects with no significant substructure are named relaxed,
while the others (with strong signs of substructure) are named non-relaxed. To
perform this classification, we applied the Dressler $\&$ Shectman test
(Dressler & Shectman 1988). For more details, we refer the reader to Pinkney
et al. (1996); Lopes et al. (2006); Lopes et al. (2009b, 2018).

In our cluster sample, within R200, we have a total of $2878$ galaxies in
$197$ relaxed clusters and $1021$ galaxies in $34$ non-relaxed clusters. A
summary of the different galaxy populations found within the relaxed and
disturbed systems is given in Table 2.

| Passive | GV | SF | GV+SF | Total
---|---|---|---|---|---
Relaxed cluster sample
ETG: | 1864 | 62 | 45 | 107 | 1971
| (94.17%) | (3.15%) | (2.28%) | (5.57%) | (68.49%)
Ellipticals | 1542 | 29 | 21 | 50 |
Lenticulars | 322 | 33 | 24 | 57 |
LTG: | 544 | 89 | 274 | 363 | 907
| (59.98%) | (9.81%) | (30.21%) | (40.02%) | (31.51$)
Non-relaxed cluster sample
ETG: | 568 | 15 | 11 | 26 | 594
| (95.62%) | (2.53%) | (1.85%) | (4.37%) | (58.18%)
Ellipticals | 461 | 10 | 3 | 13 |
Lenticulars | 107 | 5 | 8 | 13 |
LTG: | 283 | 27 | 117 | 144 | 427
| (66.28%) | (6.32%) | (27.40%) | (33.72%) | (41.48%)
Total | 3259 | 193 | 447 | 640 | 3899
| (83.58%) | (4.95%) | (11.46%) | (16.41%) |

Table 2: Division for the $3899$ bright galaxies ($M_{r}\leq M^{*}+1$) in our
cluster sample according to the cluster dynamical state, galaxy morphology,
and star-formation activity.

##  3 Results

Figure 3: Projected phase-space diagrams for ETGs in relaxed clusters (left
side panels) and non-relaxed clusters (right side panels). Rhee et al. (2017)
regions are delineated by the dashed black lines, and as mentioned in Rhee et
al. (2017) is an indication of different times since infall. From top to
bottom, we show passive (Pas), green valley (GV), star-forming (SF), and a
combination of GV and SF galaxies, respectively. Figure 4: Projected phase-
space diagrams for LTGs in relaxed clusters (left side panels) and non-relaxed
clusters (right side panels). Rhee et al. (2017) regions are delineated by the
dashed black lines, and as mentioned in Rhee et al. (2017) is an indication of
different times since infall. From top to bottom, we show passive (Pas), green
valley (GV), star-forming (SF) and a combination of GV and SF galaxies,
respectively.

The environmental dependence of galaxy populations is clear from Table 1. As
expected, the ETGs dominate within clusters ($\sim 66\%$ of all galaxies).
Different results are found for the field galaxies. LTGs comprise $\sim 52\%$
of all objects in this environment. As for the star-formation activity, we
have the following. Inside clusters, the ETGs are overwhelmingly dominated by
passive galaxies ($\sim 95\%$). In the field, we found this fraction to be
reduced to $\sim 80\%$. For the LTGs, we have a similar trend, but with
different values. Within clusters, we found that $\sim 62\%$ of all LTGs are
passive, while in the field, this fraction decreases to $\sim 27\%$. This
behavior is a strong indication of the environmental influence, despite the
morphological classification. In order to have further information about these
results, we investigated the location of the galaxies within the projected
phase-space (PPS) diagram. We also compare the cumulative distributions of
different galaxy properties.

###  3.1 Location in the Phase-Space Diagram and the impact of the dynamical
state

As discussed by many authors (e.g., Mahajan et al. 2011, Oman et al. 2013,
Rhee et al. 2017, Pasquali et al. 2019, Pasquali et al. 2019), the projected
phase-Space diagram (PPS) can be utilized as a good indicator of the cluster
assembly process. Hence, we can use it to estimate how long a galaxy is inside
a cluster. Based on a cosmological hydrodynamic simulation, Rhee et al. (2017)
verified that although the positions of galaxies in the PPS are not as precise
as would be the case for the real phase-space diagram, it is still possible
and reliable to utilize the PPS as an indicator of the infall time. The
authors created a PPS from mock data and divided the diagram into five regions
(A to E). These regions are divided to be dominated by four major groups:
first infallers (A), recent infallers (B, C), intermediate infallers (D), and
ancient infallers (E). Fig. 6 of Rhee et al. (2017) gives good visual support
to the understanding of these regions. Each one of these categories has a time
interval for the time since infall:

Comparison between Relaxed vs. Non-relaxed samples
---
| ETGs
| M∗ | $\Sigma_{5}$ | D${}_{n}(4000)$ | H$\delta$ | sSFR |  $\nabla$(g - i)
Pasrelax vs. Pasnon-relax | $0.1111$ | $0.3895$ | $0.0773$ | $0.1412$ | $0.5596$ | $0.0095$
GVrelax vs. GVnon-relax | $0.8694$ | $0.6954$ | $0.8962$ | $0.6241$ | $0.4852$ | $0.6167$
SFrelax vs. SFnon-relax | $0.4086$ | $0.5502$ | $0.7534$ | $0.3111$ | $0.3588$ | $0.8341$
GV$+$SF${}^{relax}vs.GV$+$SF^{non-relax}$ | $0.7525$ | $0.6059$ | $0.7130$ | $3.539e-5$ | $0.8588$ | $0.8218$
| LTGs
| M∗ | $\Sigma_{5}$ | D${}_{n}(4000)$ | H$\delta$ | sSFR |  $\nabla$(g - i)
Pasrelax vs. Pasnon-relax | $0.4322$ | $0.6392$ | $0.7693$ | $0.081$ | $0.5906$ | $0.0343$
GVrelax vs. GVnon-relax | $0.0415$ | $0.6340$ | $0.5264$ | $0.7919$ | $0.3132$ | $0.4825$
SFrelax vs. SFnon-relax | $0.2021$ | $0.0446$ | $0.9502$ | $0.5258$ | $0.9744$ | $0.1652$
GV$+$SF${}^{relax}vs.GV$+$SF^{non-relax}$ | $8.839e-3$ | $0.080$ | $0.3160$ | $6.625e-5$ | $0.4629$ | $0.1711$
Comparison between Cluster vs. Field samples
| ETGs
| M∗ | $\Sigma_{5}$ | D${}_{n}(4000)$ | H$\delta$ | sSFR |  $\nabla$(g - i)
Pascluster vs. Pasfield | $2.978e-6$ | $1.163e-10$ | $6.661e-15$ | $1.110e-16$ | $1.110e-16$ | $4.219e-15$
GVcluster vs. GVfield | $0.078$ | $0.000$ | $0.4692$ | $1.331e-4$ | $0.9039$ | $8.523-8$
SFcluster vs. SFfield | $0.2319$ | $1.110e-16$ | $0.0554$ | $0.0159$ | $0.073$ | $0.0132$
GV$+$SF${}^{cluster}vs.GV$+$SF^{field}$ | $0.087$ | $3.331e-16$ | $4.806e-6$ | $1.489e-20$ | $1.521e-7$ | $4.922e-8$
| LTGs
| M∗ | $\Sigma_{5}$ | D${}_{n}(4000)$ | H$\delta$ | sSFR |  $\nabla$(g - i)
Pascluster vs. Pasfield | $1.228e-6$ | $2.109e-15$ | $1.631e-6$ | $2.109e-15$ | $2.109e-15$ | $5.815e-38$
GVcluster vs. GVfield | $7.741e-5$ | $9.992e-16$ | $0.012$ | $0.6756$ | $0.014$ | $2.781e-7$
SFcluster vs. SFfield | $5.551e-16$ | $5.551e-16$ | $5.145e-6$ | $0.016$ | $8.978e-5$ | $7.923e-10$
GV$+$SF${}^{cluster}vs.GV$+$SF^{field}$ | $2.442e-15$ | $3.331e-16$ | $7.488e-4$ | $1.196e-6$ | $0.003$ | $4.108e-15$

Table 3: P-values for the KS tests comparing our different sub-samples. The
first batch of tests compares galaxies inside relaxed clusters with galaxies
inside non-relaxed clusters (comparing stellar mass, the local galaxy density
($\Sigma_{5}$), $4000$ Å break, H$\delta$, specific star formation rate, and
color gradient). The second batch of tests compares galaxies in the combined
cluster sample (relaxed+non-relaxed clusters) with galaxies in the field.
Consider that $\leq 0.05$ the null hypothesis is refuted with $2\sigma$
significance (distinguishable sample $-$ red background), and for p-value,
$>0.05$ the null hypothesis is accepted with $2\sigma$ significance
(indistinguishable sample $-$ green background).

  * •

First Infallers (A): Not fallen yet

  * •

Recent Infallers (B and C): $0.00<t_{inf}<3.63Gyr$

  * •

Intermediate Infallers (D): $~{}3.63<t_{inf}<6.45Gyr$

  * •

Ancient Infallers (E): $~{}~{}~{}~{}~{}~{}~{}~{}~{}6.45<t_{inf}<13.7Gyr$

In Figures 3 and 4, we show the PPS of our data, for ETGs and LTGs,
respectively. The data is divided into relaxed (left side panels) and non-
relaxed clusters (right side panels), and also subdivided into the
subpopulations present for each morphology: Pas (first row), GV (second row),
and SF (third row). We further added a combination of GV and SF galaxies
(fourth row). The dashed lines in each diagram delimit the regions introduced
by Rhee et al. (2017).

Figure 3 shows the differences in the distributions of ETGs in the PPS as a
function of their star-formation activity. Pas-ETGs have a higher
concentration in the E region (dominated by galaxies in the ancient infall
time interval). On the contrary, the GV-ETGs and SF-ETGs tend to avoid this
region. These galaxies are predominantly found in the regions labeled C and D
(dominated by galaxies in the recent/intermediate infall time interval). The
tendency is also present when we compare the Pas-ETGs with the combined sample
of GV$+$SF-ETGs.

The distinction present in Figure 3 indicates that Pas and GV and/or SF-ETGs
inhabit different regions of the PPS, thus having distinct times since infall:
shorter periods for GV/SF-ETGs in comparison to the Pas-ETGs counterparts. As
those galaxies have the same morphology but different infall times and
different levels of star-formation activity, we can formulate some hypotheses:
(i) the GV/SF-ETGs enter the clusters as such, and we are witnessing their
residual star-formation; (ii) the GV/SF-ETGs are going through a new star-
formation event, bringing them back from the passive phase $-$ rejuvenation
process that could be triggered by gas infusion (Yi et al., 2005; Marino et
al., 2009; Kaviraj et al., 2009, 2011).

Figure 5: Cumulative Distribution Functions of the local galaxy density
($\Sigma_{5}$) comparing the cluster subpopulations of ETGs and LTGs. In the
first row of panels, the cluster ETGs are the ones being compared. In this
instance, red is Pas-ETGs, green is GV-ETGs, orange is SF-ETGs and salmon is
GV+SF-ETGs. In the second row of panels, cluster LTGs are the ones being
compared. In this instance, in blue are the Pas-LTGs, in green are the GV-
LTGs, in purple are the SF-LTGs, and finally, in salmon the combined GV+SF-
LTGs. Since the p-value for the local density parameter in Table 1 shows that
the distribution of log ($\Sigma_{5}$) is drawn from the same distribution for
all subpopulations in the relaxed and non-relaxed samples (with an exception
for SF-LTGs), the present plot was made by combining the subpopulation from
the relaxed sample with their counterpart in the non-relaxed sample. The
numbers in the top part of the CDF plots are the p-values for those properties
(see Table 3).

Another aspect worth noticing here is the apparent absence of similar behavior
for the LTGs in Figure 4. There is a large spread in the distribution of LTGs
in the PPS for the three subpopulations (Pas, GV, and SF). The regions they
occupy are similar (mainly C and D), pointing to similar infall times. It is
also interesting to note that these regions are similar to those occupied by
the GV and SF-ETGs. That could indicate the GV and SF ETGs and LTGs could be
subject to similar environmental effects, despite their morphology. On the
other hand, the similar location of the passive and GV/SF-LTGs may indicate
that the former did not have time yet to go through a morphological
transformation but may have already quenched their star formation. Note that
although the GV and SF-LTG subpopulations occupy similar regions in the PPS to
the Pas-LTGs, they do have small distinctions. For instance, we find different
fractions of Pas/GV/SF-LTGs in region E. In the case of relaxed clusters, the
Pas-LTGs have $35.85\%~{}\pm~{}2.06\%$ of its galaxies inside region E, while
the SF-LTGs have $24.82\%~{}\pm~{}2.61\%$. For the non-relaxed clusters, the
scenario is similar, Pas-LTGs have $33.92\%~{}\pm~{}2.81\%$, and the SF-LTGs
have $23.08\%~{}\pm~{}3.90\%$.

Besides the location in the PPS in Figures 3 and 4, in Figure 5 we compare the
local density parameter ($\Sigma_{5}$). We do so to investigate if the cluster
action in the GV and SF-ETGs is a more local influence than a global one. For
ETGs in clusters, the passive galaxies inhabit the same environment as the GV
counterpart, while being statistically distinct from the SF counterpart. But,
the GV and the SF seem to inhabit the same environment. Pas-LTGs occupy
regions with higher local densities than SF-LTGs and GV+SF-LTGs. For the Pas-
LTGs and GV-LTGs, the distinctions are not so strong, with the KS and AD tests
very close to the confidence level. That could indicate that these passive
objects may have been inside the clusters for slightly longer periods compared
to the GV and SF galaxies, especially for ETGs. Another possibility is that
these passive galaxies have been already pre-processed in less massive groups
before infalling into the clusters (Jaffé et al., 2012, 2015; Haines et al.,
2015; Mahajan, 2013).

Despite that, for the cluster sample, the results point towards a transition
of environments where the GV galaxies are in a local environment very similar
to the Pas ones (but not quite identical since the KS test and AD test give
values close to the confirmation of the null hypothesis), and the SF galaxies
are located in a less dense environment than both of them. Figures 3 and 4
already hint in this direction by showing that Pas-ETGs preferentially inhabit
the central regions of the cluster more than their SF counterparts, where the
local density is higher than the outer parts of the cluster.

Figure 6: Cumulative distribution function for stellar masses. The top panels
compare the cluster ETGs (continuous lines), while the bottom panels compare
the field ETGs (dashed lines). In both cases, red tones correspond to Pas-
ETGs, green tones are GV-ETGs, orange tones are SF-ETGs, and salmon tones the
combine GV+SF ETGs. The numbers in the top part of the CDF plots are the
p-values for those properties (see Table 3).

Having established that the infall time of the passive galaxies (even more for
Pas-ETGs, but also true for Pas-LTGs) is different from the other populations
and that there may be small differences among the latter, we then proceed to
investigate the distributions of different galaxies and environmental
properties. To do so, we compare different properties by applying the
Kolmogorov-Smirnov (KS) test to our sample (Table 3). The $p-value$ obtained
by comparing the different subpopulations in the relaxed and non-relaxed
samples (displayed in Table 3) indicates that the dynamical state of the
cluster bears no significant influence on the properties studied in this work
(with few exceptions that can be observed in the Table). This result is also
supported by Table 2. Although Table 2 shows a small discrepancy in the GV and
SF fractions of galaxies in relaxed and non-relaxed clusters, it is not a
major difference, even more, because the number of galaxies in the non-relaxed
clusters is much smaller than available in the relaxed sample. The indication
provided by the p-values obtained with the KS test points to a scenario where,
if the cluster environment influences the galaxy evolution, the conditions for
this influence exist independent of the cluster dynamical state.

In order to give more confidence to this result, we also made the same
comparison shown in Table 3 using the Anderson-Darling test. The Anderson-
Darling test is a variation of the KS test that gives more weight to the tails
of the distribution than the KS test (more centrally focused). The results
were almost identical, at a $5\%$ significance level, to the ones obtained
from the KS test. For the ETGs, the only divergence was for the
D${}_{n}(4000)$ when comparing Pas-ETGs in the relaxed and non-relaxed cluster
where the KS test gives a p-value for the samples being drawn from the same
distribution, but the AD test does not. For the LTGs, the discrepancy is
present in three cases. First, in the comparison for stellar mass between GV-
LTGs in relaxed and non-relaxed samples, the KS test rejects the null
hypothesis, but the AD test accepts it. The second discrepancy for LTGs is for
the local density for the comparison between GV+SF-LTGs in relaxed and non-
relaxed, where the KS test accepts the null hypothesis, but the AD test does
not. The third discrepancy in LTGs is for the color gradient in the comparison
between Pas-LTGs in relaxed and non-relaxed samples, where the KS rejects the
null hypothesis and the AD test accepts.

Figure 6 shows the distribution of stellar mass for the cluster sample in the
top panels (considering different subpopulations of ETGs). Since the KS test
indicates that the samples are statistically similar, we combine both relaxed
and non-relaxed samples to compare the mass distribution of each one of the
subpopulations. For the cluster sample, we can see that the GV and SF galaxies
(also GV+SF galaxies) are systematically less massive than their passive
counterparts.

Two caveats should be considered when looking at the comparisons in Figures 3
to 6. The first is the large time intervals for each of the Rhee et al. (2017)
regions. Naturally, a finer tune in those regions would give a better grasp of
the galaxies’ infall intervals and their preferred locations in the PPS as a
function of morphology and star-formation activity. The second is that when we
compare galaxies in clusters with different dynamical states, we have to be
careful since in a few cases we have just a few objects (especially for the GV
and SF-ETGs in non-relaxed clusters), leading to small statistic confidence.
In this sense, it would also be possible that we are only ruling out only
large distinctions, not the subtle ones. Taking these caveats into account, it
seems that the positioning of different galaxy populations in the PPS could
point to small differences between the relaxed and non-relaxed clusters, but a
larger sample is needed in order to reach definitive conclusions.

To further investigate the influence of the cluster environment in the galaxy
evolution, in the next section, we compare the cluster and field samples.

Figure 7: D${}_{n}(4000)$ vs. M∗ (top left panel) and $H\delta$ vs. M∗ (top
right panel) planes. The contour curves illustrate the cluster distribution.
The dots are the median value for the binned mass for clusters, while the
triangles are the median value for the binned mass for the field sample. As
can be seen, for fixed stellar mass, the median values of D${}_{n}(4000)$
(H$\delta$) for GV and SF galaxies are always lower (bigger) than for Pas. The
same behavior for the SF in comparison to GV is observed. In what regards the
cluster vs. field comparison, small distinctions are observed in this plane.
In the bottom panels, we show the Gaussian fit for each of the distributions.
The distribution shows clearly a distinction between the Pas, GV, and SF-ETGs.
On the other hand, when comparing cluster vs. field, for the D${}_{n}(4000)$
the distinction is nonexistent for GV and SF-ETGs (but present for Pas-ETGs).
While, for H$\delta$, they are all distinct from each other. This result is
given by the p-value of the KS test.

###  3.2 The impact of the global environment – cluster vs. field

Figure 8: Distribution of $\nabla(g-i)$ for each of the subpopulations in the
cluster (continuous lines) and field (dashed lines) samples. Red tones
represent Pas-ETGs, green tones GV-ETGs, and orange tones SF-ETGs. The numbers
in the legend are the mean value of the Gaussian fit, while the top right
numbers are the p-values for the comparison between the cluster and field
subpopulations. As can be easily seen, the color gradient distributions are
different when we compare Pas, GV, and SF ETGs between themselves, and also
when we compare the cluster populations with their counterparts in the field.
Figure 9: Distributions of the color gradient for the ETGs, split into
elliptical (thin black dashed lines) and S0 (thin gray dashed lines) galaxies.
The colored histograms represent the distribution for the whole sample. The
top panels present the distribution for cluster ETGs, and the bottom panels
present the distribution for field ETGs. The vertical lines represent the
median values (listed in all panels) of the Gaussian fit for each
distribution.

On the contrary direction from the comparison between the relaxed and non-
relaxed environments, the comparison between cluster and field samples bears
significant differences (also Table 3. When we compare the galaxies in the
field with those in the combined cluster sample (a combination of the relaxed
and non-relaxed samples), the great majority of the p-values for the KS test
have values below $0.05$ (displayed in the bottom of Table 3). There are some
cases where the p-value is $>0.05$, and it is important to highlight them $-$
the stellar mass for GV, SF, and GV+SF-ETGs accept the null hypothesis, the
same occurs for the D${}_{n}(4000)$ and sSFR for the GV and SF-ETGs
comparisons. Overall, field and cluster samples are distinguishable between
themselves. We applied the Anderson-Darling test to these samples to confirm
the results obtained by the KS test. At a $5\%$ significance level, the great
majority of the KS tests are confirmed by the AD test, with four discrepancies
for the ETGs and one for the LTGs. The discrepancies for the ETGs occur for
M∗, both for the GV-ETGs and the GV+SF-ETGs, as well as for D${}_{n}(4000)$
and sSFR in the case of the SF-ETGs. For the LTGs, the discrepancy occurs for
the sSFR of GV galaxies. While the KS test refuses the null hypothesis, the AD
test accepts it. Besides the summary displayed in Table 3, we also show the
comparison of some properties between the field and cluster populations in
Figures 7 and 8.

Figure 10: Comparison of CDFs for Asymmetry and Smoothness for all
subpopulations. As in previous figures, continuous lines represent cluster
samples, and dashed lines represent field galaxies. Pas-ETGs are in red (first
column), SF-ETGs in orange (second column), GV-ETGs in green (third column),
and GV+SF-ETGs in salmon (fourth column). The top numbers show the p-value of
the KS test and the statistic and critical value for the $95\%$ confidence
level for the Anderson-Darling test (the null hypothesis is accepted when
$stats~{}<~{}C_{value}$). Figure 11: Star-forming fractions variations with
clustercentric distance (normalized by R200). The continuous black line shows
the variation of the overall fractions of star-forming galaxies without
morphological distinction. In this figure, we are considering as SF galaxies
the combination of GV and SF galaxies. The orange dashed curve only considers
SF-ETGs, and the purple dashed line displays the results for SF-LTGs. The gray
square in the extreme right part of the figure is the fraction for all star-
forming galaxies in the field. We have also indicated the field values for SF-
ETGs and SF-LTGs, with the orange and purple squares, respectively. The error
bars indicate the standard error for proportions.

Of the properties shown in Table 3, two of them give us a clue about the star-
formation history of the galaxies. They are the D${}_{n}(4000)$ and H$\delta$
parameters. In this case, we are using the MPA-JHU DR7 (Kauffmann et al.
2003a) calculation of the H$\delta$ Lick index, and the D${}_{n}(4000)$ (also
from the MPA-JHU catalog), considering the Balogh et al. (1999) definition. In
both cases, the calculation was done taking into account corrections for
emission lines. D${}_{n}(4000)$ is a measurement of the $4000$ Å break, while
H$\delta$ is a measurement of the Balmer absorption. The first is related to
how long ago the galaxy stopped the star formation (a big break indicates a
longer time). This is the case since the break is created due to photon
absorption by metals in the stellar atmosphere, and in hot massive stars, the
metals are ionized, so the absorption does not happen. The second, H$\delta$,
measures bursts of star formation that ended in an interval of $0.1-1~{}Gyr$.
After a star formation burst, the galaxy’s light is dominated by O and B stars
that have weak Balmer absorption. Once their main sequence lifetime is
completed, the galaxy light becomes dominated by A-F stars, that have
prominent Balmer absorption. It is important to keep in mind that both indexes
depend on metallicity, but that is relevant only for old ages (more than
$10^{9}yr$ after the burst, Kauffmann et al. 2003a). The authors also verified
that when those indexes are used together, they provide a powerful probe of
the recent star formation history of a galaxy. Hence, we can use both indexes
to discriminate between young and old stellar populations. Galaxies with
D${}_{n}(4000)$ $<1.55$ and H$\delta>2.0$ are characterized by young stellar
populations, while the opposite is true for old stellar populations (see
Kauffmann et al. 2003b).

In Figure 7 we display the distributions of those two parameters in the bottom
panels, while at the top we show their variation with stellar mass. The left
panels contain the results regarding D${}_{n}(4000)$, while on the right we
have the results for H$\delta$. The analysis is displayed for ETGs, classified
as passive, GV, or SF, located in the field and clusters. Independent of the
environment, we can see a clear variation from the SF to the Pas population,
with the GV in the middle. That suggests the Pas ETGs stopped their star
formation longer ago, showing no signs of recent activity. The opposite is
true for the SF-ETGs, according to their D${}_{n}(4000)$ and H$\delta$ values.
In between, we have the GV population, with residual star formation. On what
regards the field vs cluster comparison, we can see that for the transitional
galaxies (GV and SF ETGs) there is a small difference in the D${}_{n}(4000)$
values, but a significant offset in the H$\delta$ vs M∗ plane. That reinforces
the scenario of strong(residual) recent activity for the SF(GV) ETGs, which is
reduced according to their global environment. However, it is important to
notice the field H$\delta$ distributions (bottom right panel, with no mass
distinction) always show higher values than the cluster ones. These results
are confirmed by the KS-test, (the p-values are listed on the right side of
the bottom panel, or in Table 3). Regarding the Pas ETG, although there is a
significant difference in the distributions in the two environments (field and
cluster), they are consistent with quenched galaxies, that stopped their star
formation long ago. And, as shown by Kauffmann et al. (2003b), for older
stellar populations, the metallicity starts to be an important factor. So, for
passive galaxies, it is difficult to know if the distinction between the
cluster and field samples is driven by age or metallicity (or both).

Another important aspect we detect in the top panels of Figure 7 is the
variation with stellar mass. As pointed out by Kauffmann et al. (2003b), there
is a strong dependence of D${}_{n}(4000)$ and H$\delta$ with M∗, with a clear
distinction at M${}_{*}\sim 3\times 10^{10}~{}$M⊙. We see that is true in our
case, for all the populations shown. However, the effect becomes stronger
according to the population, being steeper for the SF-ETGs, especially for
H$\delta$. On what regards the environment, we can see that for low mass (Log
M${}_{*}/$M${}_{\odot}<10.5$) SF-ETGs, there is no environmental distinction.
That appears for the higher mass galaxies. For the most massive SF-ETGs, we
actually find that cluster objects have no sign of recent activity (according
to H$\delta$), but that is not the case for the field counterparts.

We have also investigated the distributions of the color gradient (provided by
the KIAS catalog $-$ Choi et al. 2010), which gives the color variation inside
the galaxy. Although there is a degeneracy between age and metallicity in
regard to color, some authors believe that the main driver of the color
gradient is the metallicity gradient inside the galaxy (e.g., Peletier et al.
1990; Saglia et al. 2000; Tamura et al. 2000; Tamura & Ohta 2000; Kobayashi
2004). In any case, the nature of the formation of the color gradient is not
up for debate in the current work, as the important aspect here is the
existence of the color gradient per se. It is important because we can use the
color gradient as a proxy to identify the different types of formation and
evolution regimes: monolithic vs. hierarchical. In a monolithic scenario, the
potential well of the galaxy’s central region acts as a retainer of gas. The
accumulation of gas in the inner part causes a greater enrichment in the
region, leading to a more negative gradient. While, in a hierarchical
scenario, due to the mixture and infusion of gas related to merger processes,
there is a dilution of the chemical content, causing a less steep gradient
(Tortora et al., 2010; Kobayashi, 2004). In the case where the age is the main
factor in the formation of the color gradient in galaxies, the scenario
depicted above is still valid. The center of the galaxy will be older than the
outskirts in the monolithic scenario, and in the hierarchical scenario, the
infusion of new gas will lead to new star-formation, equalizing the color
gradient in the same manner we observe in the case where metallicity is the
main factor for the color gradient formation.

Figure 8 displays the distribution of the color gradient for our ETG sample.
As in other figures, the continuous lines give the distribution of cluster
samples, while the dashed lines show the distribution of field samples. The
red tones represent the Pas-ETGs, the green tones the GV-ETGs, and the orange
tones the SF-ETGs. This figure shows that GV and SF-ETGs have systematically
more negative values of $\nabla(g-i)$ than Pas-ETGs, for both environments.

From Figure 8 it is also possible to compare the different ETGs subpopulations
according to the environment, cluster vs. field. In all cases, the
distribution of $\nabla(g-i)$ for field galaxies displays systematically more
negative values than for cluster galaxies. This result indicates that the
environment in which galaxies inhabit acts as a regulator of their
evolutionary paths. Field ETGs are more likely to experience monolithic
evolution, while cluster ETGs probably have their evolution explained by the
hierarchical scenario. Of course, the evolution probably does not follow
exclusively one of the scenarios, being more likely that the evolution of
galaxies needs both of them to explain all of their properties. However, the
distinction in the color gradient can indicate a higher likelihood that the
galaxies in a more recent past had been evolving monotonically or
hierarchically.

The same trends demonstrated in Figure 8 for ETGs are observed for LTGs. The
comparison of $\nabla$(g - i) between cluster and field LTGs is displayed in
Table 3. As for the ETGs, the GV and SF-LTGs (and the combined sample) have
more negative color gradient values than Pas-LTGs. We also found that field
LTGs have more negative values than their cluster counterparts.

In Figure 9 we still show the $\nabla$(g - i) distributions for the ETGs
inside clusters and in the field. However, now we distinguish between
elliptical (black lines) and lenticular (gray lines) galaxies. For Pas-ETGs in
clusters, the distributions of ellipticals and S0s are very similar,
displaying only a small difference in the median value of the distributions. A
similar behavior is observed for the Pas-ETGs in the Field, but the median
values of the distributions show a slightly larger difference. For the GV, SF,
and GV+SF-ETGs, the scenario is quite different. For each of these
subpopulations, the lenticulars and elliptical galaxies show distinct
distributions, having different peaks. In the field, the separation is even
larger.

Figure 9 demonstrates that lenticular galaxies are responsible for the
systematical shift in the distribution of $\nabla$(g - i) or the GV, SF, and
GV+SF-ETGs subpopulations in relation to the Pas-ETGs. It also shows that most
of the shift observed in the comparison between cluster and field ETGs is due
to the lenticular galaxies having a stronger tail in the field compared to
clusters. That indicates that the likelihood of elliptical and lenticular
galaxies following a similar evolutionary path in both environments is small.

In Figure 10 we follow up the discussion of hierarchical vs. monolithic
scenario observed in Figures 8 and 9, by comparing the distributions of
Asymmetry (A) and Smoothness (S) of our sub-samples (measured by Barchi et al.
2020). A is a measurement of how symmetrical a galaxy is, in general, spiral
galaxies present higher values of asymmetries than elliptical galaxies
(Conselice, 2003). Recent merger remnants may (especially major mergers)
present the highest values of asymmetries (Palmese et al., 2017), and the
value would decrease with time, while the merger remnant reaches a new
dynamical equilibrium. On the other hand, smoothness, S is a measurement of
how much of the galaxy’s light is contained in small clumps (Conselice, 2003).
Therefore, smoothness is higher for unperturbed early-type galaxies. Figure 10
shows the CDFs of these two properties, comparing the cluster (solid lines)
and the field (dashed lines) samples. The red tones are for Pas-ETGs, the
green tones are for GV-ETGs, the orange tones are for SF-ETGs, and the salmon
tones are for GV+SF-ETGs. Figure 10 indicates a subtle but statistically
significant difference in the value of A between cluster and field ETGs, for
both passive and star-forming ones - confirmed by the KS and the Anderson-
Darling tests in a $95\%$ confidence level - but not for the GV-ETGs. For this
case, the null hypothesis is accepted. That is also true for S. These results
indicate that cluster ETGs are more asymmetrical and have a less smooth light
distribution than field objects.

Due to the nature of the hierarchical formation, it is expected that the
galaxies will tend to be more asymmetric and have the light more concentrated
in small pockets across the galaxy (consequently, less smooth). This will
cause higher values of A and lower values of S. Thus, the results observed in
Figure 10 partially support the scenario where cluster early-type galaxies
have a higher likelihood of having followed a hierarchical formation scenario
in comparison to those in the field by showing that cluster ETGs are more
asymmetrical and less smooth (i.e., more clumpy).

We reinforce here that these statements are purely based on galaxy
morphological parameters, which might be biased by the object’s apparent
magnitude (i.e. mass) and apparent size, as well as being affected by the
presence of companions (i.e. the environment they live in). More detailed
galaxy maps are needed to put stronger constraints on the galaxy’s
evolutionary paths and its relation with the environment. In a follow-up
study, we intend to apply this study to IFU data, to retrieve the spatially
resolved star-formation history.

To further attest the cluster environmental influence on galaxy evolution, we
display in Figure 11 the variation of the fractions of star-forming galaxies
with normalized clustercentric distance, up to 5$\times$R200. As mentioned in
§2 we have 9931 cluster members within 5$\times$R200. In this case, we
consider as SF all galaxies above the Eq. 3 that separate the passive from the
green-valley galaxies in Figure 2. The black continuous curve describes the
fractional variation of all star-forming galaxies without morphological
distinction. The purple dashed curve displays the results for the SF-LTGs,
while the orange dashed curve shows the SF-ETGs sample. The field fraction
(for each case) is displayed by the squares on the right side of the figure,
for comparison. We can see a positive variation of the fraction of star-
forming cluster galaxies up to $\sim 3\times$R200 (reaching a plateau to
larger distances). As the SF fractions within clusters are always smaller than
the field fractions (even when we go to large distances), these results
suggest that galaxies are pre-processed in smaller units (groups) before being
accreted by large clusters (Haines et al., 2015).

##  4 Discussion and Conclusions

One of the main goals of the present work is to use transitional galaxies,
such as GV and SF-ETGs as a proxy for galaxies migrating from the BC to the RS
and investigate the influence of different environments in this transition. In
general, we expect early-type galaxies to be red and dead objects.
Nonetheless, several works have been showing that this is not the whole truth.
The presence of SF-ETGs objects needs to be accounted for (Lee et al., 2006;
Kannappan et al., 2009; Schawinski et al., 2009). To do so, we have analyzed a
sample of $3,899$ cluster galaxies and $11,460$ field galaxies in the local
Universe. We further divided the cluster sample between galaxies belonging to
relaxed clusters ($2,878$ galaxies) and non-relaxed clusters ($1,021$
galaxies).

Hence, a proper understanding of these populations can shed some light on the
evolutionary path of galaxies. According to Vulcani et al. (2015), SF-ETGs
comprise about 6$\%$ of the general field ETG population. Kaviraj et al.
(2011) point out that ETGs account for around half the stellar mass budget in
the local Universe. They also state that SF-ETGs contribute to $\sim$14
percent of the cosmic star-formation budget.

We have shown in Figure 3 that the SF-ETGs arrived at the cluster in a later
epoch than Pas-ETGs (for both relaxed and non-relaxed clusters). This is also
true for the GV-ETGs and for the combined GV+SF-ETG sample. They also have an
infall period similar to the one observed in the late-type population (star-
forming or quenched). While the GV and SF-ETGs are dominated by galaxies with
recent or intermediate time since infall (same for the LTGs), the Pas-ETGs are
dominated by galaxies with ancient infall time. This behavior is consistent
with other results in the literature (Jaffé et al., 2015; Jaffé et al., 2016;
Lotz et al., 2019), that indicate that the interstellar gas of the galaxies is
removed after the first passage into the center of the cluster, preventing
further star-formation activity to happens.

While the segregation in the PPS according to the star-formation activity is
clear for ETGs, that is not the case for LTGs. Figure 4 indicates small
differences between the location of Pas, GV, SF, and GV+SF-LTGs in the PPS. We
find the fractions of galaxies inside the E region are higher for Pas-LTGs, in
comparison to what was observed for GV-LTGs, for the SF-LTGs, and for the
GV+SF-ETGs (Figure 3). As we saw for the ETGs, this result indicates that the
Pas-LTGs may have been within clusters for slightly longer periods than the
other LTG subpopulations.

We also show in §3.1 that the dynamical state of the cluster does not have a
major influence on the properties studied in this work (Table 3). This result
agrees with the findings of Sampaio et al. (2021), that using a different
methodology to classify the dynamical state of clusters with
M${}_{200}>10^{14}M_{\odot}$, found that the investigated properties are
globally similar in both environments. Although, the galaxies’ infall rate of
non-relaxed clusters is larger than the one for relaxed clusters.

Unlike what was obtained in §3.1, we have shown in the subsection 3.2
(comparison of cluster and field galaxies) that the cluster environment
influences most of the galaxies’ properties. As shown in Table 3, for LTGs the
scenario is very clear. With exception to the H$\delta$, all the comparisons
made in Table 3 rejected the null hypothesis that the samples were drawn from
the same distribution. On the other hand, for the ETGs, the scenarios are more
complex, especially for the D${}_{n}(4000)$ and for the sSFR. According to the
KS test, the GV and the SF-ETGs from the cluster and the field are drawn from
the same distribution, meaning that stellar population age and the star-
formation taking place at the cluster and field GV/SF-ETGs are similar.
However, when the comparison considers the combined sample (GV+SF-ETGs), the
scenario changes. For this enlarged sample, all the properties are distinct
between cluster and field (except only for stellar mass). The difference is
probably mostly due to the reduced number of galaxies in the individual GV and
SF-ETGs samples, yielding low statistics for the individual comparison. This
result indicates that the combined cluster sample of GV+SF-ETGs has an older
stellar population - given by the D${}_{n}(4000)$, a more relevant recent
star-formation (given by H$\delta$), and a more suppressed ongoing star-
formation (given by the sSFR). Since their stellar masses are statistically
similar, we can’t tribute this difference to a mass effect. This result is in
line with several works that have pointed out that different phenomena impact
infalling galaxies, affecting their star formation activity (Haines et al.,
2013; Zinger et al., 2018; Wang et al., 2018; Lotz et al., 2019).

In Figure 7, we show evidence for a combination of the environment and mass
action to quench the star formation activity. We see that for SF-ETGs the
environment matters above Log M${}_{*}/$M${}_{\odot}\sim 10.5$. The recent
star formation activity (indicated by H$\delta$) shows different results,
between the field and cluster, only above this mass. In general, the SF-ETGs
reduce their activity as they grow in mass, but this process is accelerated
for cluster galaxies.

Another result suggested by Table 3 and demonstrated by Figures 8 and 9, is
the difference in the color gradient distributions, related to the galaxy
environment. As previously argued, the color gradient can give clues to the
formation scenario followed by a galaxy. We interpret the results from these
two figures (8 and 9) as an indication that cluster galaxies show a higher
likelihood of having followed the hierarchical formation scenario, while field
galaxies are more likely to follow the monolithic scenario. On top of that,
the results from Figure 10 (regarding the Asymmetry and Smoothness parameters)
suggest that pre-processing of galaxies is an important step before they enter
the cluster environment. Before a galaxy becomes a cluster member, it could be
part of a galaxy group, and as a group member, the galaxy can suffer similar
processes to the ones in the cluster environment (e.g., starvation, fly-byes,
mergers, harassment, and others; Haines et al. 2015). Due to the high-velocity
dispersion, it’s less likely that galaxies go through mergers inside clusters
(within R$200$). Thus, it is more probable the results we are observing are
the result of mergers that took place before the galaxies become cluster
members, where the velocity dispersion is lower than the observed in the
interior of the cluster (Hickson, 1997). In our subsequent project, we intend
to investigate the regions where such influences occur by extending our
investigation to several R$200$. Preliminary confirmation of the pre-
processing effect is displayed here, in Figure 11.

Figure 9 offers an attempt to answer the reasoning that the field and cluster
samples have different distributions of the color gradient, especially for
star-forming ETGs. The bulk of the distinction comes from what we classified
as lenticular galaxies. According to this classification, lenticular galaxies
are pulling the distribution of field samples to a stronger negative color
gradient, indicating a preference for monolithic formation. Our result
diverges from other recent works in the literature, like the one of Coccato et
al. (2020); Coccato et al. (2022). In both papers, using IFU data, the authors
investigate the different formation scenarios that lenticular galaxies can
evolve from. Using the kinematic information obtained by the IFU data, they
point out the existence of two types of lenticular galaxies: rotationally-
supported and pressure-supported ones. They interpreted each of these types as
an indication of the formation processes. Rotationally-supported lenticular
would have formed through fast processes that consume their gas (like ram-
pressure and starvation). On the contrary, pressure-supported lenticular
galaxies would have formed through minor-mergers processes that modified their
kinematic characteristics. The authors found an environmental dependency for
each of the different types of lenticular galaxies: cluster lenticulars are
more rotationally-supported, while field lenticulars are more pressure-
supported (Coccato et al., 2020). Furthermore, as pointed out in Coccato et
al. (2022), "faded spiral" pathway is the most efficient channel to produce
S0s, and it becomes more efficient as the mass of the group or cluster or
local density of galaxies increases. The merger pathway is also a viable
channel, and its efficiency becomes higher with decreasing local density or
environment mass.. It is important to consider that the morphology
classification used in Coccato et al. (2020); Coccato et al. (2022) is not the
same for the present work. Also, their stellar mass and luminosity intervals
are more constrained to higher luminosity/stellar masses. Furthermore, in
Coccato et al. (2020); Coccato et al. (2022), the authors do not distinguish
the lenticular galaxies into passive and star-forming galaxies as we did in
the present work. This consideration is relevant when comparing both works
since, as was demonstrated in Figures 8 and 9, the distinction observed for
the evolutionary paths (according to the color gradient distributions) is
connected to the star-formation level of the galaxies.

The combination of the results obtained with the color gradient (Figures 8 and
9), the Asymmetry and Smoothness (Figure 10), and the star-forming/passive
fraction variation with clustercentric distance (Figure 11) offer strong
argumentation to the need for pre-processing of galaxies before they enter the
cluster. The same argument was pointed out by Haines et al. (2015), where the
authors investigate a sample of star-forming galaxies coming from 30 massive
clusters in a redshift interval of $0.15<z<0.30$. The authors found that the
fraction of star-forming galaxies increases with cluster-centric radii, but
remains below the field value even at 3R200. This result can not be reproduced
by a scenario where star-formation suppression only occurs in infalling field
galaxies, justifying the need for the galaxies to suffer pre-processing before
the cluster infall.

As we have shown, the cluster environment has important consequences for the
evolution of galaxies, but is not the only one responsible for the differences
observed within the galaxy population. The pre-processing of galaxies must be
taken into account when studying galaxy evolution. We intend to give sequence
to this work by extending the present analysis into the outer parts of
clusters.

## Acknowledgements

This work would not be possible without the funding of Coordenação de
Aperfeiçoamento de Pessoal de Nível Superior (CAPES), which supported DB with
a Ph.D. fellowship. PAAL thanks the support of CNPq, grants 433938/2018-8 e
312460/2021-0. ALBR thanks the support of CNPq, grant 316317/2021-7, and
FAPESB INFRA PIE 0013/2016. AC acknowledges the FAPERJ grant E$\\_$40/2021 -
Apoio ao Jovem Pesquisador Fluminense sem vínculo EM ICTS do Estado do RJ -
2021 - E-26/200.607 and 210.371/2022(270993). We acknowledge the anonymous
referee for the very helpful suggestions.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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