11institutetext: Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69,
53121, Bonn, Germany 22institutetext: National Centre for Nuclear Research,
Pasteura 7, 02-093 Warszawa, Poland 33institutetext: Institute of Space
Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona,
Spain 44institutetext: Astronomical Observatory of the Jagiellonian
University, Orla 171, 30-244 Kraków, Poland 55institutetext: Institute of
Physics, Jan Kochanowski University, ul. Swietokrzyska 15, 25-406 Kielce,
Poland 66institutetext: INAF - Osservatorio di Astrofisica e Scienza dello
Spazio, Via Piero Gobetti 93/3, I-40129 Bologna, Italy 77institutetext: INAF -
Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, via E. Bianchi
46, 23807 Merate, Italy

# The quiescent population at $0.5\leq z\leq 0.9$: Environmental impact on the
mass-size relation

M. Figueira The quiescent population at $0.5\leq z\leq 0.9$: Environmental
impact on the mass-size relationThe quiescent population at $0.5\leq z\leq
0.9$: Environmental impact on the mass-size relationThe quiescent population
at $0.5\leq z\leq 0.9$: Environmental impact on the mass-size relationThe
quiescent population at $0.5\leq z\leq 0.9$: Environmental impact on the mass-
size relation M. Siudek The quiescent population at $0.5\leq z\leq 0.9$:
Environmental impact on the mass-size relationThe quiescent population at
$0.5\leq z\leq 0.9$: Environmental impact on the mass-size relation A. Pollo
The quiescent population at $0.5\leq z\leq 0.9$: Environmental impact on the
mass-size relationThe quiescent population at $0.5\leq z\leq 0.9$:
Environmental impact on the mass-size relationThe quiescent population at
$0.5\leq z\leq 0.9$: Environmental impact on the mass-size relationThe
quiescent population at $0.5\leq z\leq 0.9$: Environmental impact on the mass-
size relation J. Krywult The quiescent population at $0.5\leq z\leq 0.9$:
Environmental impact on the mass-size relationThe quiescent population at
$0.5\leq z\leq 0.9$: Environmental impact on the mass-size relation D. Vergani
The quiescent population at $0.5\leq z\leq 0.9$: Environmental impact on the
mass-size relationThe quiescent population at $0.5\leq z\leq 0.9$:
Environmental impact on the mass-size relation M. Bolzonella The quiescent
population at $0.5\leq z\leq 0.9$: Environmental impact on the mass-size
relationThe quiescent population at $0.5\leq z\leq 0.9$: Environmental impact
on the mass-size relation O. Cucciati The quiescent population at $0.5\leq
z\leq 0.9$: Environmental impact on the mass-size relationThe quiescent
population at $0.5\leq z\leq 0.9$: Environmental impact on the mass-size
relation A. Iovino The quiescent population at $0.5\leq z\leq 0.9$:
Environmental impact on the mass-size relationThe quiescent population at
$0.5\leq z\leq 0.9$: Environmental impact on the mass-size relation

(Received 22/08/2023; accepted 02/04/2024)

###### Abstract

Context. How the quiescent galaxies evolve with redshift and the factors that
impact their evolution are still debated. It is still unclear what the
dominant mechanisms of passive galaxy growth are and what role is played by
the environment in shaping their evolutionary paths over cosmic time.

Aims. The population of quiescent galaxies is altered over time by several
processes that can affect their mean properties. Our aim is to study the mass-
size relation (MSR) of the quiescent population and to understand how the
environment shapes the MSR at intermediate redshift.

Methods. We used the VIMOS Public Extragalactic Redshift Survey (VIPERS), a
large spectroscopic survey of $\sim$90 000 galaxies in the redshift range
$0.5\leq z\leq 1.2$. We selected a mass-complete sample of 4786 passive
galaxies based on the NUVrK diagram and refined it using the $D_{n}4000$
spectral index to study the MSR of the passive population over $0.5\leq z\leq
0.9$. The impact of the environment on the MSR and on the growth of the
quiescent population is studied through the density contrast.

Results. The slope and the intercept of the MSR, $\alpha=0.62\pm 0.04$ and
$\textrm{log}(A)=0.52\pm 0.01$, agree well with values from the literature at
the same redshift. The intercept decreases with redshift,
$R_{e}(z)=8.20\times(1+z)^{-1.70}$, while the slope remains roughly constant,
and the same trend is observed in the low-density (LD) and high-density (HD)
environments. Thanks to the largest spectroscopic sample at $0.5\leq z\leq
0.9$, these results are not prone to redshift uncertainties from photometric
measurements. We find that the average size of the quiescent population in the
LD and HD environments are identical within $3\sigma$ and this result is
robust against a change in the definition of the LD and HD environments or a
change in the selection of quiescent galaxies. In the LD and HD environments,
$\sim$30 and $\sim$40% of the population have experienced a minor merger
process between $0.5\leq z\leq 0.9$. However, minor mergers account only for
30 to 40% of the size evolution in this redshift range, the remaining
evolution likely being due to the progenitor bias.

###### Key Words.:

Galaxies: elliptical and lenticular, cD - Galaxies: evolution - Galaxies:
formation - Galaxies: fundamental parameters - Galaxies: structure

##  1 Introduction

The formation and evolution of galaxies led to a wide variety of morphology
that are observed from the high redshift down to the local Universe:
elliptical, lenticular, spiral, barred spiral, and irregular. The first
evolutionary model, where elliptical or early-type galaxies (ETGs) were
thought to evolve into spiral or late-type galaxies (LTGs), was proposed by
Hubble (1936), and was known as the tuning fork diagram. Throughout the
increased efforts that were made during the past decades in that field, it has
nonetheless become clear that the evolutionary picture is far more
complicated.
These advances were made possible thanks to the multiple statistical
photometric and spectroscopic surveys from the local Universe and beyond that
were performed in the last two decades. Among them are the 2dF Galaxy Redshift
Survey (2dFGRS, $z\sim 0.1$, Colless et al. 2001, 2003), the Sloan Digital Sky
Survey (SDSS, $z\leq 0.3$, York et al. 2000; Ahn et al. 2014), the VIMOS
public extragalactic redshift survey (VIPERS, $0.4\leq z\leq 1.2$, Guzzo &
VIPERS Team 2013; Scodeggio et al. 2018), the Galaxy And Mass Assembly survey
(GAMA, $z<0.5$, Driver et al. 2016), or the Deep Extragalactic VIsible Legacy
Survey (DEVILS, $0.3<z<1.0$, Davies et al. 2018). Thrilling new results and
breakthroughs are also expected from the James Webb Space telescope (JWST)
Advanced Deep Extragalactic Survey (JADES, $2\leq z\leq 11$, Eisenstein et al.
2023) as well as from future observations with Euclid (Euclid Collaboration et
al., 2022) and the Rubin Observatory Legacy Survey of Space and Time (LSST).

One of the most interesting results unveiled in the field of galaxy evolution
is the fact that massive metal-rich ETGs ($\geq 10^{11}$ $M_{\odot}$) are more
compact at high redshift ($z\geq 2$) compared to the local Universe, with a
difference in stellar density reaching two orders of magnitude (e.g., Daddi et
al. 2005; Trujillo et al. 2006a, b; Zirm et al. 2007; van der Wel et al. 2008;
Cimatti et al. 2008; van Dokkum et al. 2008). At first sight, it appears that
ETGs have to undergo a substantial size evolution from $z\sim 2-3$ ($\sim
10-11$ Gyr ago) through different mechanisms (e.g., van Dokkum 2005; Trujillo
et al. 2006a, b; Franx et al. 2008; van der Wel et al. 2008; van Dokkum et al.
2008; Damjanov et al. 2011; Cimatti et al. 2012; Hamadouche et al. 2022) in
order to match observations performed in the local Universe. However, the size
evolution of ETGs is still debated and might not be required to explain the
mean properties of this population at $z=0$. For instance, Damjanov et al.
(2009) could not find a satisfactory size evolution mechanism at $z\sim 1.5$,
and Poggianti et al. (2013) find only a mild size increase from $z\sim 0.7$ to
$z\sim 0.05$. The number density evolution also seems to be inconsistent with
a strong size evolution (Poglitsch et al., 2010), the number density of
compact ETGs appears to be in agreement with local Universe observations in
clusters (Saracco et al., 2010), or to slightly decrease (Gargiulo et al.,
2016, 2017). In addition, the numbers of compact ETGs could be underestimated
in SDSS (Damjanov et al., 2009, 2011), leading to an apparent decrease in the
number density of those compact ETGs.

The change in size and mass that compact galaxies might experience over cosmic
time is imprinted on a fundamental plane known as the mass-size relation (MSR)
that is often used to quantify the evolution of galaxies, their assembly, or
the properties of their DM haloes (e.g., Shen et al. 2003; Cimatti et al.
2012; Ichikawa et al. 2012; Huertas-Company et al. 2013a; van der Wel et al.
2014; Faisst et al. 2017; Favole et al. 2018; Jiang et al. 2018; Mowla et al.
2019a, b; Damjanov et al. 2019; Barone et al. 2022; Afanasiev et al. 2023).
Several works have already shown that LTGs and ETGs are following their own
MSR (e.g., Shen et al. 2003; Ichikawa et al. 2012; van der Wel et al. 2014;
Faisst et al. 2017; Mowla et al. 2019a; Mosleh et al. 2020; Nedkova et al.
2021): while the size of galaxies increases with stellar mass ($M_{*}$), ETGs
show a steeper growth, but are on average smaller than LTGs at fixed $M_{*}$.
This gap in size disappears at the high-mass end ($M\sim 10^{11}$ $M_{\odot}$)
where the MSRs of the two populations are crossing (van der Wel et al., 2014;
Mowla et al., 2019a). These differences strongly suggest that these two
populations follow their own different evolutionary paths. Recent JWST
observations from The Cosmic Evolution Early Release Science Survey (CEERS)
show that star-forming and quiescent galaxies already have a different
morphology and different Sersic index at $z=5.5$ (Ward et al., 2024).

The size enhancement of ETGs observed with decreasing redshift may result from
one or several mechanisms with different weighted contributions, but those
processes are currently still debated. One of the most popular is the dry
(i.e., gas-poor) major and minor merger scenario (e.g., Cox et al. 2006;
Khochfar & Silk 2006; Naab et al. 2006; Bournaud et al. 2007; Naab & Ostriker
2009; Bezanson et al. 2009; Oser et al. 2010; Trujillo et al. 2011; Ferreras
et al. 2014; Oogi et al. 2016), where ETGs efficiently grow without
rejuvenation of star formation. An analysis of the Millenium Simulation Data
Base (Springel et al., 2005; De Lucia & Blaizot, 2007) by Oogi & Habe (2013)
reveals that major and minor mergers govern the evolution of ETGs, and several
observations have shown that major mergers could indeed impact the size growth
of massive early-type galaxies (e.g., Lin et al. 2008; López-Sanjuan et al.
2012; Oogi & Habe 2013; Ferreras et al. 2014). Growth through minor mergers
is, however, preferred since the growth in size is faster than the growth in
mass (Huertas-Company et al., 2013a), and major mergers would lead to more
massive galaxies than currently observed (e.g., López-Sanjuan et al. 2009) and
to a change in the MSR slope (e.g., Bernardi et al. 2011; Sweet et al. 2017).
Another mechanism proposed for the size growth of massive spheroidal galaxies
relies on an in situ process, where the quasi-adiabatic expansion is governed
by the ejection of matter from the central to the outer parts of the galaxy
due to AGN feedback, stellar winds, and supernovae explosions (Fan et al.,
2008, 2010; Williams et al., 2010; Ragone-Figueroa & Granato, 2011).
We previously mentioned that the mean size evolution does not automatically
imply that ETGs grow through time. Indeed star-forming galaxies can experience
quenching through tidal stripping (e.g., Łokas 2020), ram pressure stripping
(e.g., Joshi et al. 2020), or harassment (e.g., Bialas et al. 2015). As a
consequence, it is also possible that all these mechanisms listed above are of
minor importance, and what drives the observed mean size growth in a
population of ETGs is the incorporation of these recently quenched, and larger
than quiescent, star-forming galaxies into the passive population. This
effect, known as the progenitor bias, might be majorly responsible for the
observed size growth of the passive population (e.g., Carollo et al. 2013;
Belli et al. 2015; Gargiulo et al. 2016, 2017, 2019; Matteuzzi et al. 2022).

How galaxies evolve is further complicated by the environment that may impact
their evolutionary paths. Some properties, such as the star formation rate
(SFR), color, and morphology are known to depend on the environment. The
density-morphology relation (Dressler, 1980) shows that elliptical and spiral
galaxies are preferentially located in high-density (HD) and low-density (LD)
environments, respectively (e.g., Cooper et al. 2006, 2007; Capak et al. 2007;
Coil et al. 2008; Kovač et al. 2010b; Moutard et al. 2018; Paulino-Afonso et
al. 2019). In addition, since the color and star formation activity of
galaxies are correlated (e.g., Poggianti et al. 2008; Bait et al. 2017), an HD
environment also hosts more red quiescent galaxies, while blue star-forming
galaxies are found in LD environments. This indicates that ETG evolution may
not be identical in different environments. We may expect ETGs in HD
environments, such as those found inside groups and clusters, to undergo an
accelerated size growth through more numerous major and minor merger events,
or cluster-related processes compared to LD environments such as fields and
voids (e.g., Cavaliere et al. 1992; McIntosh et al. 2008; Fakhouri & Ma 2009;
Darg et al. 2010; Lin et al. 2008, 2010; Shankar et al. 2013; De Lucia et al.
2014; Yoon et al. 2017). At the same time, the merger rate in the highest
density environments may be reduced due to the higher peculiar velocities of
galaxies in these environments (e.g., Tran et al. 2008; Jian et al. 2012;
Matharu et al. 2019)

As a consequence, observations of galaxies in different environments might
reveal a difference in size growth, yet the works that have been done so far
lead to divergent results. For instance, several studies found the impact of
environment on ETGs to be negligible (e.g., Rettura et al. 2009; Weinmann et
al. 2009; Ferland et al. 2013; Cappellari 2013; Huertas-Company et al. 2013a,
b; Kelkar et al. 2015; Saracco et al. 2017; Zanisi et al. 2021), some found
ETGs to be larger in HD environments (e.g., Cimatti et al. 2008; Cooper et al.
2012; Papovich et al. 2012; Strazzullo et al. 2013; Bassett et al. 2013; Lani
et al. 2013; Cebrián & Trujillo 2014; Delaye et al. 2014; Mei et al. 2015;
Yoon et al. 2017; Chan et al. 2018; Huang et al. 2018; Wang et al. 2020;
Noordeh et al. 2021; Afanasiev et al. 2023), while other studies claim that
ETGs in HD environment are smaller (e.g., Raichoor et al. 2012; Poggianti et
al. 2013; Matharu et al. 2019). It is, therefore, not entirely clear whether
the environment has a measurable impact and how this impact, if any,
translates in term of galaxy sizes. Differences could also arise from the
methodology used to derive the stellar mass and the size, from the criterion
adopted to select passive galaxies, or from the methodology used to quantify
the environment.

The goals of the present paper are twofold. First, we study the MSR of
quiescent galaxies at $0.5\leq z\leq 0.9$ from the final release of VIPERS
(Guzzo & VIPERS Team, 2013; Garilli et al., 2014; Scodeggio et al., 2018), the
largest existing spectroscopic survey in the redshift range $0.4\leq z\leq
1.2$, with a statistically significant mass-complete sample of
spectroscopically measured galaxies. We then consider the impact of the
environment on the quiescent population of VIPERS through the density contrast
that was estimated for each galaxy (Cucciati et al., 2014, 2017) and on the
size growth in the redshift range $0.5\leq z\leq 0.9$.
The paper is organized as follows. In Section. 2 we describe VIPERS and the
derivation of associated physical parameters as well as the selection of the
mass-complete sample of quiescent galaxies. In Section. 3 we analyze the MSR
of the quiescent population and the impact of the environment. In Section. 4
we discuss the results, and present the conclusions of this work in Section.
5.
Throughout this work, we use $\Omega_{M}=0.3$, $\Omega_{\Lambda}=0.7$, and
$H_{0}=70$ km s-1 Mpc-1. All magnitudes are given in the AB system (Oke,
1974).

##  2 The VIPERS data

###  2.1 The survey

VIPERS (Guzzo & VIPERS Team, 2013; Garilli et al., 2014; Scodeggio et al.,
2018) is a spectroscopic survey based on the T005 release of the Canada-
France-Hawaii Legacy Survey Wide (CFHTLS-Wide, Goranova et al. 2009) catalog
toward a subarea of the W1 ($\sim$16 deg2) and W4 fields ($\sim$8 deg2). To
constrain the redshift range of target galaxies to $0.5\leq z\leq 1.2$, a
first selection was performed based on a limiting magnitude $i<22.5$ mag and
on a gri color-color selection. The half-light radius and reconstructed
spectral energy distribution (SED) from CFHTLS ugriz bands were used to
perform preliminary stellar decontamination. These selection criteria were
checked using two control samples from VVDS-Deep (Le Fèvre et al., 2005) and
VVDS-Wide (Garilli et al., 2008). Removing stars and galaxies outside the
redshift range of interest beforehand led to a much higher sampling rate
($\sim$47%) compared to previous surveys.

Observations were performed with the VIsible Multi-Object Spectrograph (VIMOS,
Le Fèvre et al. 2003), a four-channel imaging spectrograph with a 224 arcmin2
field of view at the ESO Very Large Telescope (VLT). Using the multiobject-
spectroscopic mode and the low-resolution red grism, the spectral coverage
goes from 5500 to 9500 Å in the observed frame with a resolution of $R=220$.
Using the EZ code (Garilli et al., 2010, 2014), a redshift ($z$), and a
redshift flag ($z_{flag}$) indicating the degree of confidence in the redshift
estimation and the agreement with the photometric redshift were assigned to
each spectrum. Both quantities were then independently and carefully checked
by two members of VIPERS.
In this work, we used the VIPERS PDR-2111http://vipers.inaf.it/ catalog
consisting of 91 507 sources and the updated T007 version of the photometric
catalog.

###  2.2 Morphological parameters

The morphological parameters of VIPERS galaxies were derived using the GALFIT
code (Peng et al., 2002) and are based on the CFHTLS-T006 images (Krywult et
al., 2017). A postage stamp centered around the galaxy was extracted from the
CFHTLS tile with adequate size to estimate the background accurately. Using
SExtractor (Bertin & Arnouts, 1996), all objects except the galaxy were
masked, and the estimated galaxy’s parameters were used as a first guess for
fitting a Sersic profile (Sérsic, 1963) with GALFIT. The Point Spread Function
(PSF) at the galaxy position used to convolve the Sersic profile is
represented by a Moffat profile (Moffat, 1969) whose parameters were estimated
from the isolated stars in each CFHTLS tile. The free parameters of the Sersic
profile estimated by GALFIT are the Sersic index ($n$), the semi-major axis
($a_{e}$), the axial ratio ($b/a$), the effective radius
($R_{e}=a_{e}\sqrt{b/a}$) of the galaxy, and the continuum background. Based
on the tests performed on the simulated galaxy images, the Sersic index $n$
and the effective radius $R_{e}$ are accurate to 33% and 12%, respectively,
for 95% of the VIPERS galaxies. More details can be found in Krywult et al.
(2017).
We note that different definitions of the galaxy size are used in the
literature, such as the effective radius (e.g., Damjanov et al. 2022, 2023),
the semi-major axis (e.g., van der Wel et al. 2014), a radius enclosing a
certain light fraction (20, 50 and 80, 90%, e.g., Ichikawa et al. 2012; Miller
et al. 2019; Mosleh et al. 2020) or sometimes using a mass fraction (e.g.,
Suess et al. 2019; Miller et al. 2023), which can lead to significantly
different results concerning the size evolution of galaxies (e.g., Miller et
al. 2023). In this work, we use the effective radius as the size of a galaxy.
Observations of galaxies at different rest-frame wavelengths also affect their
measured size, as different wavelengths trace different galaxy components. The
$i$-band observations, used to measure $R_{e}$, trace the (rest-frame)
emission at 5000 and 3950 Å at $z=0.5$ and $z=0.9$, respectively. To quantify
the color gradient, we follow the procedure of van der Wel et al. (2014) and
compute the effective radius of galaxies as if they were observed at 5000 Å,
$R_{\mathrm{5000\AA}}$, considering
$\Delta\textrm{log}\,R_{e}/\Delta\textrm{log}\,\lambda=-0.25$. The conversion
factor between $R_{e}$ and $R_{\mathrm{5000\AA}}$ decreases with redshift from
1 down to 0.96 and shows no strong dependence on stellar mass. Overall, the
correction is very weak for our sample of quiescent galaxies, being lower than
0.017 dex as the rest-frame $i$-band is close in wavelength to 5000 Å for the
redshift range studied in this work. We therefore do not expect the color
gradient to significantly affect the conclusions of this work and do not
perform any corrections.

###  2.3 The spectral break $D_{n}4000$

The spectral break $D_{n}4000$ is a discontinuity observed in the spectrum of
galaxies around 4000 Å due to the lack of emission from young and massive OB
stars and the apparition of absorption lines from ionized metals in the
stellar atmosphere of evolved stars. Consequently, $D_{n}4000$ has been widely
used as an evolutionary tracer of the galaxies’ stellar age (e.g., Bruzual A.
1983; Balogh et al. 1999; Kauffmann et al. 2003; Siudek et al. 2017; Haines et
al. 2017; Damjanov et al. 2022, 2023). The spectral break $D_{n}4000$ is
defined as the ratio of the integrated spectrum over the wavelength ranges
$4000$-$4100$ Å and $3850$-$4100$ Å from the narrower definition of Balogh et
al. (1999), which is less impacted by reddening compare to the former
definition of Bruzual A. (1983), although this should not be critical as
quiescent galaxies are usually not very dusty. The corresponding uncertainty
on $D_{n}4000$ is estimated by propagating the uncertainties of the spectrum
over both wavelength ranges.
One downside of using $D_{n}4000$ as a proxy for the stellar population age is
the existence of an age-metallicity degeneracy (Worthey, 1994). For VIPERS
data, Siudek et al. (2017) studied the impact of different metallicities on
the stellar age of quiescent galaxies and showed that it does not strongly
affect their conclusions. We therefore expect that this degeneracy will also
not affect our conclusions. When comparing samples of galaxies based on the
stellar age, we however use samples whose $D_{n}4000$ distribution is non-
contiguous to reduce this age-metallicity degeneracy (see Sect. 2.5.3).

###  2.4 Physical properties of galaxies

The $M_{*}$ and SFR used in this work were derived by Moutard et al. (2016a)
from SED fitting using LePHARE (Arnouts et al., 1999; Ilbert et al., 2006)
with the galaxy evolution explorer (GALEX) far-ultraviolet (FUV) and near-
ultraviolet (NUV), the CFHTLS $u$, $g$, $r$, $i$, $z$, the VISTA Deep
Extragalactic Observations survey Z, Y, J, H and K, and the Wide-field
InfraRed Camera Ks bands from the photometric catalog of Moutard et al.
(2016b). The fitting procedure was performed with an exponentially declining
star formation history with 0.1 Gyr $<\tau<$ 30 Gyr, the Bruzual & Charlot
(2003) stellar population library, two different metallicities ($Z_{\odot}$
and 0.4$Z_{\odot}$), three different extinction laws (Prevot et al., 1984;
Bouchet et al., 1985; Calzetti et al., 2000; Arnouts et al., 2013) with
$E(B-V)_{\textrm{max}}=0.5$, contributions from emission lines (Ilbert et al.,
2009) and a Chabrier (2003) initial mass function. More information about the
SED fitting process can be found in Ilbert et al. (2013) and Moutard et al.
(2016a).

###  2.5 Sample selection

####  2.5.1 Selection of a reliable sample

We first performed a selection on the redshift quality of VIPERS galaxies
through their associated $z_{flag}$ (see Scodeggio et al. 2018 for a detailed
explanation), keeping galaxies with $2\leq z_{flag}\leq 9.5$ (90 to 99%
confidence level). We then reduced the redshift range to $0.5\leq z\leq 0.9$,
as the density estimation we used is complete up to $z=0.9$ (Cucciati et al.,
2017).
We kept galaxies with accurate morphological measurements ($0.2<n<10$,
$R_{e}>0.5$ kpc and $b/a>0.1$, Krywult et al. 2017). Small values of $n$ are
unphysical and their corresponding normalization factor in the Sersic profile
is less accurate (Ciotti & Bertin, 1999). In addition, we imposed a signal-to-
noise ($S/N$) threshold on $R_{e}$ of 3. We also required $S/N(D_{n}4000)>3$,
as $D_{n}4000$ is used later as a secondary criterion for quiescent galaxies
selection. Two galaxies having unphysical $R_{e}$ ($\geq 40$ kpc) were
discarded, and galaxies with GALFIT convergence warning and outside the PSF
mask region were excluded. In addition, galaxies for which the $i$-band
measurement was higher than 22.5 mag were excluded.222All VIPERS primary
targets have $17.5<i<22.5$ in the T005 release of CFHTLS, but their magnitudes
may slightly differ in the T007 release that is used in this work The reliable
sample selected by the criteria described above contains 43 739 galaxies.

The sample of quiescent galaxies is primarily defined using the NUVrK diagram
(Arnouts et al., 2013) and the criterion established by Moutard et al. (2016a)

$\displaystyle(NUV-r)$ $\displaystyle>3.372-0.029t_{L}$ (1)
$\displaystyle(NUV-r)$ $\displaystyle>2.25(r-K_{s})+2.368-0.029t_{L},$

where $t_{L}$ is the look-back time of each galaxy. Out of the 43 767 galaxies
in the reliable sample, 6942 are found to be quiescent.

####  2.5.2 Mass completeness

To estimate the mass completeness limit in the VIPERS flux-limited sample
($i_{lim}=22.5$ mag), we applied the method of Pozzetti et al. (2010) based on
the mass-luminosity ratio ($M/L$) and on the stellar mass limit ($M_{lim}$).
The latter is defined as the stellar mass a galaxy would have if its $i$-band
measurement would be equal to the magnitude limit of the survey. Assuming a
constant mass-to-luminosity ratio, (i.e., $M_{*}/L(i)=M_{lim}/L(i_{lim})$),
$M_{lim}$ is given by

$\textrm{log(}M_{lim})=\textrm{log(}M_{*})+0.4(i-i_{lim}).$ (2)

We binned the sample per redshift quartile ($0.50\leq z<0.60$, $0.60\leq
z<0.68$, $0.68\leq z<0.78$, and $0.78\leq z\leq 0.90$) and selected the 20%
faintest galaxies in the $i$-band in each redshift bin. We rescaled their
$M_{*}$ to $M_{lim}$ using Eq. 2 and computed the $M_{*}$ completeness limit
as the 90th percentile of the $M_{lim}$ distribution (Davidzon et al., 2016).
A second-order polynomial fit was performed to obtain the completeness limit
over the entire redshift range. The distribution of log($M_{*}/M_{\odot}$)
with respect to $z$ and the mass completeness limit for quiescent galaxies are
shown in Fig. 1. The mass-complete quiescent sample contains 5124 quiescent
galaxies (74% of the reliable quiescent sample).
Our $M_{*}$ completeness limit at redshifts $z=0.60,0.72,0.84$ is
$\textrm{log(}M_{lim}/M_{\odot}\textrm{)}=10.33$, $10.62$, and $10.84$,
comparable to the estimation of Davidzon et al. (2016) with a difference of
0.06, 0.02 and 0.01 dex, respectively. These small differences can be
attributed to a different estimation of $M_{*}$ (based on Hyperz with
different photometric bands for Davidzon et al. 2016), to the different NUVrK
criterion used to select the quiescent galaxies, and to the selection criteria
applied to obtain the reliable sample of galaxies.

Figure 1: Distribution of log($M_{*}/M_{\odot}$) with respect to $z$ where
galaxies are color coded based on their i-band magnitude. The black filled
circles represent the completeness limit in each redshift bin and the dashed
black line shows the completeness limit based on a 2${}^{\textrm{nd}}$ order
polynomial fit.

####  2.5.3 Final sample of quiescent galaxies

In addition to the selection based on the NUVrK diagram, as explained in Sect.
2.5.1, the final mass-complete sample of quiescent galaxies was further
constrained with $D_{n}4000$. Following Damjanov et al. (2023), the sample of
quiescent galaxies was restricted to $1.5<D_{n}4000<3$ (4786 galaxies). We
also defined the recently quenched population as galaxies for which
$1.5<D_{n}4000<1.6$ (hereafter newcomers, 474 galaxies). A total of 338
galaxies, quiescent following the NUVrK selection but star-forming following
the $D_{n}4000$ one, were discarded. To perform a more robust comparison
between the properties of newcomers and older galaxies, we also constructed a
sample of old galaxies defined to have high $D_{n}4000$ and as much galaxies
as the newcomer sample, leading to a sample of old quiescent galaxies with
$D_{n}4000>1.95$. Comparing two non-contiguous samples with respect to
$D_{n}4000$ will allow to weaken the dependence of $D_{n}4000$ on metallicity,
the $D_{n}4000$ difference corresponding to an age difference rather than a
metallicity difference, and this will strengthen the conclusions of such
comparison. Figure 2 shows the $D_{n}4000$ distribution of the quiescent
population selected with the NUVrK diagram before and after the $D_{n}4000$
constraint, and the newcomer and old quiescent populations.

Figure 2: $D_{n}4000$ distribution for the quiescent galaxies selected with
the NUVrK diagram (green dashed), further constrained with $D_{n}4000\geq 1.5$
(yellow filled), newcomers (blue dashed), and old quiescent galaxies (red
dashed).

In Fig. 3, we show the star-forming, quiescent and newcomer galaxies on the
NUVrK diagram with the thresholds from Moutard et al. (2016a) at $z=0.7$. We
also present the same three samples on the UVJ diagram (Williams et al.,
2009), one of the most popular criterion used to disentangle the star-forming
from the quiescent population, and note a good correlation between both
selections, even if the separation is, as expected, not perfectly equivalent.
We test the effect of different selections on the MSR in Sect. 4.1.

Figure 3: NUVrK (left) and UVJ (right) diagrams for the star-forming,
quiescent, and newcomer galaxies. The continuous black line represents the
boundary between star-forming and quiescent galaxies (at $z\sim 0.7$ for
NUVrK). The green valley for the NUVrK diagram is enclosed by the black dashed
lines.

###  2.6 Density estimation

To measure the environmental impact on the quiescent galaxies, we used the
density contrast $\delta$ estimated for VIPERS galaxies by Cucciati et al.
(2017), and defined as

$\delta=\frac{\rho(r)-\left<\rho[r(z)]\right>}{\left<\rho[r(z)]\right>},$ (3)

where $\rho(r)$ is the local density at the comoving position $r$ and
$\left<\rho[r(z)]\right>$ is the mean local density at redshift $z$.
The local density $\rho(r)$ of a galaxy was computed as the sum over all
tracers (i.e., galaxies used to estimate the density) inside the smoothing
filter divided by the selection function. The smoothing filter was chosen to
be a cylindrical top-hat filter centered on the galaxy with a 1000 km s-1
half-length and a radius equal to the distance to the 5${}^{\textrm{th}}$
neighbor ($D_{p,5}$). Using a cylindrical filter allows to reduce the effect
of the peculiar velocities of galaxies and a varying radius allows to estimate
the density on small-scales. Galaxy tracers are part of a volume-limited
sample characterized by $M_{B}\leq-20.4-z$, ensuring completeness up to
$z=0.9$ and a constant comoving number density with respect to the redshift.
When estimating the local density, the selection function that includes all
the different intrinsic selections of the VIPERS spectroscopic survey was not
considered, but this was mitigated by adding to the volume-limited sample of
tracers, all galaxies for which a photometric redshift was available. Local
densities of galaxies for which part of the filter was out of the boundaries
of the survey area are divided by the fraction of the cylinder found inside
the survey. To compute $\left<\rho[r(z)]\right>$, the number density $n(z)$
was integrated over the cylinder height and divided by the survey area. We
refer to Section 3 and Appendix. A of Cucciati et al. (2017) for more details
about the density estimation, to Cucciati et al. (2014) for a discussion about
the inclusion of the selection function and to Kovač et al. (2010a) for the
estimation of $\left<\rho[r(z)]\right>$. In the following, we refer to
$\delta$ simply as the density instead of density contrast. We note that this
density contrast has already been used to study the quiescent and red nugget
populations in VIPERS (Gargiulo et al., 2019; Siudek et al., 2022, 2023;
Lisiecki et al., 2023).

To study the impact of the environment, we selected a subsample of quiescent
galaxies for which the filter covered at least 60% of the field area. While
boundary corrections were applied, we preferred to keep galaxies for which
these corrections were low enough to ensure a good estimation of the density.
For quiescent and newcomer galaxies, the samples are reduced to 3998 and 399
galaxies, respectively.
The thresholds used to separate LD and HD environments were defined as the
first and third quartiles of the density distribution (Cucciati et al., 2017).
For the sample of quiescent galaxies used in this work, these thresholds are
equal to log($1+\delta)=0.22$ and log($1+\delta)=0.72$ for the LD and HD
environments, respectively, similar to Cucciati et al. (2017) (0.23 and 0.73,
respectively). We show the histogram of the density for newcomer and quiescent
galaxies with the density limits in Fig. 4. The newcomer and quiescent
galaxies have a mean log($1+\delta)$ of 0.39 and 0.47, and a Kolmogorov-
Smirnov (KS) test rules out that these two distributions come from the same
parent population. Above log($1+\delta)=1.2$, the number of newcomers
decreases abruptly, which is in agreement with the fact that these recently
quenched star-forming galaxies should be less present in high-density
environment where passive galaxies are preferentially found, following the
morphology-density relation (Goto et al., 2003). We reproduced the same
analysis with the sample of old quiescent galaxies and found the same results:
both populations do not have the same parent distribution and more older
galaxies are found in the HD environment. The mean log($1+\delta)$ increases
to 0.53, indicating that the older a quiescent galaxy is, the more likely it
is to belong to a HD environment.

Figure 4: Density distribution for quiescent (red) and newcomer (hash blue) galaxies. The black dashed lines indicate the LD and HD limits and the $p$-value from the KS test is indicated in top left. Top: Histogram for newcomers and quiescent galaxies ($D_{n}4000>1.6$). Bottom: Histogram for newcomers and old quiescent galaxies ($D_{n}4000>1.95$). Table 1: Number of galaxies in each sample Sample | Number of galaxies
---|---
Initial samples (Sect. 2.5.1)
VIPERS PDR-2 | 91 507
Reliable | 43 739
Quiescent (NUVrK) | 6942
Mass-complete samples (Sects. 2.5.2, 2.5.3)
Quiescent ($1.5\leq D_{n}4000\leq 3$) | 4786
Newcomers ($1.5\leq D_{n}4000\leq 1.6$) | 474
Old quiescent ($1.95\leq D_{n}4000\leq 3$) | 474
With reliable density estimation (Sect. 2.6)
Quiescent | 3998
Newcomers | 399

##  3 Analysis

###  3.1 MSR of the quiescent population

We analyze the MSR of quiescent galaxies in VIPERS, which is the spec-only
sample that large at this redshift range. We divided the sample into $M_{*}$
quartiles ($\sim$ 1197 galaxies per bin) and estimated the median $M_{*}$ and
$R_{e}$ in each bin. The uncertainties on $R_{e}$ are computed as the median
absolute deviation divided by the square root of the number of galaxies in
each bin. The general shape of the MSR is represented by a smoothly broken
power law (e.g., Mowla et al. 2019a) or a combination of two power law
functions (e.g., Shen et al. 2003; Fernández Lorenzo et al. 2013; Lange et al.
2015; Furlong et al. 2017; Nedkova et al. 2021), which for quiescent galaxies
at $M_{*}>10^{10}M_{\odot}$ can be reduced to a single power law,

Figure 5: MSR for quiescent galaxies from this work (black circles) and the
literature (see Tab. LABEL:tab:MS_literature) at $0.3\leq z\leq 1$ (blue to
red dashed lines, sorted by redshift). The linear fit for the VIPERS quiescent
sample is shown by the continuous black line.

$\textrm{log(}R_{e}\textrm{)}=\alpha\times\textrm{log}\left(\frac{M_{*}}{10^{11}M_{\odot}}\right)+\textrm{log(}A\textrm{)},$
(4)

where $\alpha$ is the slope and $\textrm{log}(A)$ is the intercept. We
performed the fit using an orthogonal distance regression technique from the
scipy python package, taking into account the uncertainties on $R_{e}$. As
noted by Saracco et al. (2017), an orthogonal distance or a linear least
squares regression can lead to parameters that can be different by $\sim
2\sigma$. We checked that the parameters for this MSR, and all MSRs that are
derived in this work, were consistent within 1$\sigma$ when using both
regression techniques. For the sample of quiescent galaxies, the fit gives a
slope $\alpha=0.62\pm 0.04$ and an intercept $\textrm{log(A}\textrm{)}=0.52\pm
0.01$. The MSR for VIPERS along with several MSRs from the literature at
$0.3\leq z\leq 1$ (see Tab. LABEL:tab:MS_literature for a more extensive list)
are shown in Fig. 5, where we observe a good agreement with our work despite
the different methodology used to select quiescent galaxies for instance.
While the slopes of the different relations are roughly similar, except for
the MSRs of Ichikawa et al. (2012) and Favole et al. (2018), we clearly
observe the decrease in the intercept with redshift indicating that quiescent
galaxies are smaller at higher redshift.

Figure 6: MSRs for quiescent galaxies in different redshift bins (left) where
the points represent the median values in each quartile and the solid lines
represent the fits to the data bin. The uncertainty on the stellar mass,
computed as the MAD divided by the square root of the number of galaxies, is
of the order of $\sim 0.01$. Dependence of $\alpha$ and log(A) with redshift
(right) for VIPERS (red triangles) and from the literature (blue circles). The
fit for the intercept with redshift is shown as a red dot-dash (VIPERS) and
blue dash line (all data points).

To check the evolution of the slope and the intercept with redshift, we
divided the VIPERS sample into redshift quartiles and fitted the MSR using Eq.
4 in each redshift bin (the slopes and intercepts are given in Tab.
LABEL:tab:MS_literature). The MSRs for the four redshift ranges are shown in
Fig. 6 (left) where we observe that the intercept decreases with redsfhit
between the first and fourth redshift bin ($\geq$3$\sigma$), while the slope
appears to slightly increase. The redshift dependence of the slope and
intercept for VIPERS are also shown on Fig. 6 (right, red triangle), together
with the slope and intercept values from the literature (Tab.
LABEL:tab:MS_literature). For a better comparison with the present study, a
recalibration of the relations, affecting only the value of log(A), was
performed, and already applied on Fig. 6 (bottom right). First, we corrected
for the different $M_{*}$ normalization used in Eq. 4 which is equal to
$10^{11}$ $M_{\odot}$ in this work. Secondly, we accounted for the fact that
$R_{e}$ can be either defined as the semi-major axis size of the galaxy (e.g.,
van der Wel et al. 2014; Belli et al. 2015; Faisst et al. 2017; Mowla et al.
2019a; Yang et al. 2021; Hamadouche et al. 2022) or its circularized radius
(e.g., Guo et al. 2009; Krogager et al. 2014; Damjanov et al. 2022, 2023; this
work), which differs by a factor of $\sim$1.4 (Dutton et al., 2011).
Therefore, the new intercept is given by
$\alpha$log($10^{11}/N_{M}$)+log($A$)$-$log($N_{R}$), where $N_{M}$ is the
mass normalization used in the original calibration and $N_{R}$ is equal to
1.4 if the original calibration uses the semi-major axis size and 1 if using
the circularized radius. The uncertainty on the new intercept is estimated by
keeping the relative uncertainty identical.

On Fig. 6 (right), the slopes of VIPERS between the two first and two last
redshift ranges seem to increase with redshift. However, when slopes from the
literature are added, we observe that most of them are scattered between 0 and
1 (on average $0.56\pm 0.20$) without a clear trend, as shown by Newman et al.
(2012), while the intercept is decreasing with redshift. This comparison
suffers from different drawbacks such as different quiescent galaxies
selection, color gradient (van der Wel et al., 2014), stellar mass estimation
(e.g., Cigale, EAZY, BAGPIPES), or radius estimation from a single/double
Sersic profile. Correcting for these effects is not possible based on the fit
of the MSR only. However, and despite several differences between different
studies, we found the same trend for the evolution of the intercept with
redshift as other works such as van der Wel et al. (2014) or Mowla et al.
(2019a) where gradient color corrections were taken into account. Remarkably,
such a trend is robust against all the different selection effects.
The evolution of the size at $M_{*}=10^{11}$ $M_{\odot}$ with redshift for the
VIPERS sample is given by $R_{e}(z)=(8.20\pm 0.34)\times(1+z)^{-1.70\pm
0.08}$, in agreement with the evolution found in other works such as van der
Wel et al. (2014) and Damjanov et al. (2019) with an exponent of -1.48 and
-1.6, respectively, and slightly higher than the fit from Mowla et al. (2019a)
with -1.25. We also fitted the evolution of log(A) with redshift using the
data from the literature (including data from this work). For log(A) values
without uncertainties, because they were not written or the MSR parameters
were derived by eye, we set an arbitrary relative uncertainty of 50%. Using
data from the literature, the evolution is given by $R_{e}(z)=(4.76\pm
0.38)\times(1+z)^{-0.81\pm 0.12}$.
The mass-normalized radius ($R_{e}$ at $M_{*}=10^{11}$ $M_{\odot}$) of the
population of quiescent galaxies increases by a factor of 1.3, from 3.01 to
3.91 kpc over 1.6 Gyr ($0.5\leq z\leq 0.9$), with a median size of 3.4 kpc at
$z\sim 0.7$. These values are in agreement with other studies at the same
redshift (e.g., Hamadouche et al. 2022).

###  3.2 The newcomer population

As the redshift decreases, the passive population is constantly enriched with
star-forming galaxies that have experienced a quenching process. Using
$D_{n}4000$ together with the criterion from Damjanov et al. (2023, see also
Sect. 2.5.3) allow us to study the properties of these newcomers at different
cosmic times. Because star-forming galaxies are larger than the quiescent ones
at fixed stellar mass, we would expect newcomers to be larger than the
quiescent population. This effect is important to consider as the arrival of
large quenched galaxies would enhance the mean size of the quiescent
population without any size growth mechanisms needed, and could explain, at
least partially, the apparent observed size evolution over cosmic time.

In the following, we compared the population of newcomers with the population
of old quiescent galaxies defined in Sect. 2.5.3. The distributions of several
properties shown in Fig. 7 indicate that newcomers have a smaller Sersic index
($\overline{n_{e}}$ of 3.2 and 3.5), a smaller $M_{*}$
($\overline{\textrm{log(}M_{*})}$ of 10.8 and 10.9), and a larger star-
formation activity ($\overline{sSFR}$ of -11.9 and -13.3), in agreement with
being star-forming galaxies that have recently quenched. The log($R_{e}$)
distribution is shifted toward lower size for newcomers, while the mean size
of star-forming galaxies is higher than the quiescent ones. Therefore, the
quenching process of these star-forming galaxies appears to go along with a
size diminution, such as disk fading for instance. A KS test indicates that
both populations, either based on their $n$, $M_{*}$, $R_{e}$ and sSFR are
drawn from different samples.

Figure 7: Distributions of $n$, $M_{*}$, sSFR, and $R_{e}$ for newcomer (hash
blue) and old quiescent (red) galaxies.

If progenitor bias is responsible for the average size evolution of the
quiescent population, the average size of newcomers should be larger compared
to that of old quiescent galaxies at fixed mass. We constructed mass-match
(MM) samples (see Sect. 3.3) of the newcomer and old quiescent populations and
show their size distributions in Fig. 3. The size distribution of newcomers is
similar to that of the old quiescent galaxies and this is also confirmed by
the KS test indicating that these distributions may have the same origin. It
is therefore not clear if the progenitor bias could be the dominant process of
size evolution, contrary to what is observed in Carollo et al. (2013);
Gargiulo et al. (2017, 2019) and Damjanov et al. (2019) as it would require
the mean size of the newly quenched galaxies to be larger in order to explain
the size increase of the whole quiescent population. We also checked the size
distributions in different redshift bins ($0.50\leq z\leq 0.62$, $0.61\leq
z\leq 0.68$, $0.68\leq z\leq 0.76$ and $0.76\leq z\leq 0.90$) and found the
same trend: the size distribution is similar with $p=0.05,0.5,0.9$ and 0.4 in
each redshift bin.

Figure 8: $R_{e}$ distribution for old quiescent (red) and newcomer (hash
blue) galaxies.

###  3.3 Impact of the environment

We made use of the density estimations computed by Cucciati et al. (2014,
2017) and presented in Sect. 2.6 to study the environmental impact on the mean
properties of the quiescent population. We recall that the sample of quiescent
galaxies with accurate density estimations is reduced due to the removal of
those having more than 40% of their filter outside the surveyed area.
Additionally, the samples used in the following analysis were further reduced
as the HD and LD samples were defined as galaxies below and above the first
and third quartile of the density distribution, respectively (see Fig. 4).

We show the $\textrm{log(}M_{*})$ and $\textrm{log(}R_{e})$ distributions for
the sample of quiescent galaxies in the HD and LD environments in Fig. 9.
Galaxies in the HD environment are found to be more massive and larger
($\overline{\textrm{log(}M_{*})}=10.9$ and
$\overline{\textrm{log(}R_{e})}=0.5$) while low-mass and small galaxies
dominate the LD environment ($\overline{\textrm{log(}M_{*})}=10.8$ and
$\overline{\textrm{log(}R_{e})}=0.4$). Above $\textrm{log(}M_{*})\sim 10.9$
and $\textrm{log(R}_{e})\sim 0.4$, more than 50% of the galaxies in each bin
are found in HD environment and this fraction increases to 75% at
$\textrm{log(}M_{*})\sim 11.4$ and $\textrm{log(R}_{e})\sim 1.4$.
Quantitatively, these differences in $M_{*}$ and $R_{e}$ for both environments
are seen from the $p$-value of the KS test indicating that the
$\textrm{log(}M_{*})$ and $\textrm{log(}R_{e})$ distributions in HD and LD
environments are different. The difference in $M_{*}$ and $R_{e}$ between HD
and LD environments is further observed from a two-dimensional two-sample KS
test (Peacock, 1983) giving $p=5.1\times 10^{-11}$.
Galaxies with larger mass and size in clusters than in fields have been
observed in Raichoor et al. (2011) and Saracco et al. (2017) at $z\sim 1.3$.
We do not observe a sharp cut in the $\textrm{log(}M_{*})$ and
$\textrm{log(}R_{e})$ distributions for low-mass and smaller galaxies (large
and massive) galaxies in HD (LD) environment, indicating that those exist but
are more rare. The formation of massive galaxies seem to be favored in the
highest-density environment, but to decipher the true impact of environment,
we have to ensure that the observed difference, if any, is exclusively due to
the environment.

The evolution of quiescent galaxies can be impacted by in situ processes
depending on the mass of the galaxies or by environmental processes. To ensure
that any changes observed between the LD and HD environments would be solely
due to the environment, we created two new samples that we refer to as MM HD
and LD samples. By definition, these MM samples have the same stellar mass
distribution (Fig. 9 (top), the $M_{*}$ distribution of the MM samples is the
intersection between the LD and HD histograms) and allow us to study the
average size of the galaxies in both environments independently of their
$M_{*}$. To create these MM samples, we divided the HD and LD samples into 20
equal-width $M_{*}$ bins and populated them so that the same $M_{*}$ bin in HD
or LD environment has the same number of galaxies. Because the LD and HD
samples do not have the same $M_{*}$ distribution, it follows that only a
fraction of LD galaxies will end up in the LD MM sample in the low-mass regime
and the same for HD galaxies in the high-mass regime (see Fig. 9 top). To take
into account this random sampling we created 500 MM samples, both for the HD
and LD environments. The physical properties were derived as the mean over the
500 MM samples and the uncertainty was estimated as the quadratic sum of the
uncertainty due to the scatter in the size distribution and the uncertainty
due to the random sampling.

We show in Fig. 10 the average distributions of $R_{e}$, $n$, sSFR, and
$D_{n}4000$ in HD and LD environments over the 500 random samplings with their
associated $p$-value. The $p$-value associated with the distribution of
$R_{e}$, $n$, and $D_{n}4000$ of galaxies in LD and HD environments show that
we cannot reject the hypothesis that they come from the same distribution.
However, the $p$-value of the sSFR distribution weakly suggests that this
property differs in the LD and HD samples, with galaxies in LD environment
having a higher sSFR while remaining quiescent since the peak of the
distribution is lower than -11 (Salim et al., 2018; Figueira et al., 2022;
Pearson et al., 2023). The highest sSFR observed in LD could arise from the
predominance of newcomers having a higher sSFR (see Figs. 4, 7) and not
specifically to processes related to the environment. We created LD and HD MM
samples for quiescent galaxies with $D_{n}4000>1.6$ and $D_{n}4000>1.95$, as
in Fig. 4, and recomputed the $p$-value for the sSFR and $D_{n}4000$
distributions. The $p$-values are equal to 0.06 and to 0.75 suggesting that
the highest sSFR and lower $D_{n}4000$ is not a direct consequence of the
environment, but due to the predominance of newcomers in the LD environment.

The MSRs for the MM HD and LD samples are shown in Fig. 11, and the parameters
of the fits are given in Tab. LABEL:tab:MS_literature. At $M_{*}\leq 10^{11}$
$M_{\odot}$, the sizes are very similar in the HD and LD environments within
$1\sigma$ and we observe a larger difference of size at $M_{*}\geq 10^{11}$
$M_{\odot}$ although they agree within $2\sigma$. Therefore, the impact of
environment-dependent mechanisms increasing the size of ETGs (such as mergers)
does not seem to be efficient enough at high density to cause a significant
size difference between both environments.
On Figure 12 we show the MSRs in four redshift bins (as in Fig. 6) in the HD
and LD environments, as well as the evolution of the slope and the intercept.
We observe in both environments the same trend as shown in Fig. 6 (right): the
constant slope and the intercept decrease with redshift. In addition, this
trend is found to be independent of the environment.

Figure 9: Distributions of log($M_{*}$) for the HD (red), LD (dashed orange),
and MM (hashed black) samples, and distribution of log($R_{e}$) for the HD
(red) and LD (dashed orange) samples.

Figure 10: Distributions of log($R_{e}$), $n$, log(sSFR), and $D_{n}4000$ for
the HD (red) and LD (orange hash) MM samples. The average $p$-value of the KS
two-sample test between the HD and LD galaxies for the 500 random samplings is
shown at the top of each plot.

Figure 11: MSR for HD and LD quiescent galaxies in the MM samples. Red filled
and orange circles represent the median $M_{*}$, and the associated linear
fits are shown as a red line and orange dashed line.

Figure 12: MSR for quiescent galaxies in different redshift bins for the HD
(top left) and LD (bottom left) environments, and $\alpha$ (top right) and
log(A) (bottom right) as a function of redshift for the HD (red) and LD
(orange) environments. The fitted evolutionary trends are shown as red dashed
and orange dotted lines. The data showing the evolution of $\alpha$ and log(A)
between LD and HD are shown with a slight offset to make the errorbars
visible.

###  3.4 The $D_{n}4000$-$M_{*}$ relation

The $D_{n}4000$ spectral index has been shown to increase with stellar mass
and to be offset with redshift: high-mass galaxies are older than the low-mass
ones and galaxies at fixed stellar mass are older at low redshift (Kauffmann
et al., 2003; Brinchmann et al., 2004; Haines et al., 2017; Siudek et al.,
2017; Wu et al., 2018). In VIPERS, this relation has been briefly studied by
Haines et al. (2017) and more in-depth by Siudek et al. (2017) for a slightly
lower number of quiescent galaxies using stacked spectra in the redshift range
$0.4\leq z\leq 1.0$. They found a positive slope independent of redshift and
the $D_{n}4000$ increase with $M_{*}$ is explained by the aging of the stellar
population with a non-negligible contamination from metallicity. However, the
observed shift of the relation with redshift does not seem to be fully
consistent with a simple passive evolution. By estimating the formation time,
$z_{form}$, as the time of the latest burst of star formation, Siudek et al.
(2017) found that massive galaxies formed around $z_{form}=1.7$ while the low-
mass ones formed at $z_{form}=1.0$. The fact that $z_{form}$ increases with
$M_{*}$ is a signature of downsizing.
In this work, we found the same trends with $M_{*}$ (Fig. 13 left) with
slightly higher $D_{n}4000$ values, despite the different selection criteria
used to select the quiescent population. Contrary to Siudek et al. (2017), we
find a weak increase in the slope with decreasing redshift, ranging from
$0.086\pm 0.006$ to $0.13\pm 0.02$ and equal to $0.074\pm 0.006$ for the
entire redshift range. This evolution of the slope remains in agreement with
the SDSS slope of 0.15 (Haines et al., 2017) or $0.141\pm 0.002$ (Siudek et
al., 2017). This evolution could be partially due to a progenitor bias with
newly quenched galaxies entering the passive population at low $M_{*}$ and low
$D_{n}4000$, steepening the slope as the redshift decreases.

To see how the environment impacts the $D_{n}4000-M_{*}$ relation, we used the
MM samples that were defined in Sect. 3.3 and computed the mean $D_{n}4000$ in
each bin of mass over the 500 MM samples. In Fig. 13 (right), we show the
$D_{n}4000-M_{*}$ relation for both environments. In the HD and LD
environments, $D_{n}4000$ increases with stellar mass, as for the whole
quiescent population. We do not observe a significant difference for the age
of galaxies at fixed $M_{*}$ between both environments. If the average size
evolution was mainly due to mergers, we would have expected the age of the
galaxies in HD to be higher than in LD while if the size evolution was mainly
due to the progenitor bias, the age offset would have been smaller due to the
addition of newly quenched star-forming galaxies. This would be in agreement
with Gargiulo et al. (2019) who found that the size evolution is mainly
governed by progenitor bias rather than environmentally-dependent processes
such as mergers at log($M_{*}/M_{\odot}\geq 11$). As in Sects. 3.3 and 2.6, we
constructed the $D_{n}4000-M_{*}$ relation in LD and HD environments with the
samples of quiescent ($D_{n}4000>1.6$) and old quiescent galaxies
($D_{n}4000>1.95$) to check the impact of newcomers. In this case, no offset
is observed and the largest age difference at low mass in Fig. 13 between the
LD and HD environments likely originates from the galaxies that recently
quenched to join the quiescent population. This is in agreement with the fact
that newcomers are more present in the LD environment, which lower the
$D_{n}4000$.

Figure 13: Relation between $D_{n}4000$ and log($M_{*}/M_{\odot}$) for the
quiescent population in several redshift ranges (left), and for the HD (red)
and LD (orange) environments (right).

##  4 Discussion

###  4.1 How the quiescent selection criterion impacts the MSR

How the quiescent population is selected is crucial as we want to
simultaneously obtain the largest sample of quiescent galaxies with the lowest
contamination by blue star-forming, dusty star-forming galaxies, and active
galactic nuclei (AGNs). Several methods are available in the literature to
perform such separation. While a morphological classification between
ellipticals and spirals can be done at low redshift, classifications at higher
redshift are often based on the observed bimodal distribution of physical
parameters (sSFR, colors, Sersic index, $D_{n}4000$). As expected, applying
different selection methods on the same sample leads to different samples of
quiescent galaxies. In addition, the quiescent population resulting from one
selection is also dependent on the procedure used and assumptions made to
estimate the required physical parameters, such as using different SED fitting
routines, different dust attenuation laws, or different SFR tracers.

The bimodality of the $D_{n}4000$ distribution has been used to disentangle
the quiescent and star-forming populations with old and young stellar
populations, respectively (e.g., Damjanov et al. 2019, 2022, 2023; Hamadouche
et al. 2022, this work). The evolution of $D_{n}4000$ in VIPERS has been
investigated by Haines et al. (2017), who found that the cut from Kauffmann et
al. (2003) at $D_{n}4000=1.55$, was in good agreement with the observed
bimodal distribution. The morphology-color relation can also be used to
disentangle the two populations as elliptical and spiral galaxies are also
well defined from their Sersic index (Trujillo et al., 2001; McLure et al.,
2013; De Looze et al., 2014). Krywult et al. (2017) found the mean $n$ for
disk-like and spheroid-like galaxies in VIPERS to be between 0.81-1.11 and
2.42-3.69, respectively. Star formation tracers such as [O ii] or the sSFR can
also be used as a way to separate both populations (e.g., Franzetti et al.
2007; Mignoli et al. 2009; García et al. 2014; Zanella et al. 2016; Salim et
al. 2018; Pearson et al. 2023).

The $U-V$ color bimodal distribution associated with a constant color cut has
been used to select quiescent galaxies (e.g., Bell et al. 2004), but the lack
of redshift evolution in this cut makes this selection too restrictive,
excluding less luminous and less massive quiescent galaxies. This $U-V$
bimodal distribution with a redshift-dependent color cut has been applied to
VIPERS in Fritz et al. (2014).
Criteria based on optical colors only (e.g., $U-V$, $U-B$, UVB diagram) are
impacted by dust absorption, leading to higher contamination of the quiescent
sample from dusty star-forming galaxies. To account for this effect,
diagnostics including infrared rest-frame bands were introduced to allow for a
more accurate selection, such as the UVJ (e.g., Williams et al. 2009; van der
Wel et al. 2014; Mowla et al. 2019a; Hamadouche et al. 2022), NUVrJ (e.g.,
Ilbert et al. 2010) or NUVrK (e.g., Arnouts et al. 2013; Fritz et al. 2014;
Davidzon et al. 2016; Moutard et al. 2016a) diagrams. Other color selections,
that were perhaps less employed, include the BRI (Kuchner et al., 2017), urz
(Kawinwanichakij et al., 2021), the $U-B$ (Peng et al., 2010) or NUVr
(Huertas-Company et al., 2013b) diagram. The UBJ diagram for VIPERS galaxies
shows a bimodal distribution but was not used directly for selection of
quiescent/star-forming galaxies (Krywult et al., 2017). VIPERS galaxies were
also classified by Siudek et al. (2018) using a Fisher Expectation-
Maximization unsupervised machine learning algorithm into 12 classes sharing
similar physical and spectral properties. While this kind of technique is
difficult to apply, in particular to relatively small samples of galaxies, we
decided to add this selection as clustering methods will be more and more
applied for future large surveys. It is therefore interesting to see the
robustness of such selections.

In the following, we compared the level of agreement between different star-
forming/quiescent galaxies selections and examined the impact of these
different selections on the MSR. To this end, we used the NUVrK boundary
between quiescent and blue galaxies given by Eq. 1 (Moutard et al., 2016a),
the $D_{n}4000$ criterion from (Damjanov et al., 2023), the UVJ criterion from
Hamadouche et al. (2022), the redshift dependent $U-V$ color cut from Fritz et
al. (2014), the $n$ limit from Krywult et al. (2017), the NUVrJ selection from
Ilbert et al. (2010), and the clustering method from Siudek et al. (2018).
Similarly to Fritz et al. (2014), we defined the completeness as the fraction
of quiescent galaxies according to the main selection used as a reference,
which remains quiescent following another selection, and the contamination as
the fraction of blue galaxies according to the main selection, which become
quiescent following another selection. We performed the selection in two
redshift bins ($0.5\leq z<0.75$ and $0.75\leq z\leq 0.9$) and the results are
shown in Tab. 3. No selection criterion provides completeness of 100% together
with no contamination. Therefore no selections are equivalent, making
comparisons with literature a bit more complicated. When we use the NUVrK
diagram to select quiescent galaxies, most of the other selections have good
completeness, except for $U-V$ and $n$, which appear to be much more
restrictive. The $D_{n}4000$ appears less restrictive, with most of the NUVrK
passive population being selected with $\sim$40% of blue galaxies that would
be added to the sample. This contamination is important for studies of the
MSR, as it directly impacts the slope of the passive population, as shown
below. We note the very good completeness of the clustering method while
having star-forming contamination equivalent to the other criteria. We also
provide the completeness and the contamination for other selection criteria if
they are used as the main reference criterion.

Table 2: Comparison of quiescent galaxies selections

| Redshift | NUVrK | NUVrJ | $D_{n}4000$ | UVJ | $U-V$ | $n$ | Class
---|---|---|---|---|---|---|---|---
NUVrK | $0.5\leq z<0.75$ |  | 100.0 | 15.9 | 93.6 | 36.4 | 93.2 | 21.8 | 56.4 | 15.0 | 75.2 | 26.1 | 98.3 | 14.0
$0.75\leq z\leq 0.9$ |  | 100.0 | 22.5 | 92.8 | 40.7 | 91.4 | 20.6 | 68.3 | 18.2 | 74.0 | 29.6 | 98.5 | 25.1
NUVrJ | $0.5\leq z<0.75$ | 78.9 | 0.0 |  | 90.4 | 27.7 | 89.9 | 11.1 | 53.8 | 9.6 | 92.9 | 43.7 | 87.9 | 7.2
$0.75\leq z\leq 0.9$ | 78.5 | 0.0 |  | 88.7 | 29.7 | 85.0 | 8.4 | 62.0 | 11.0 | 91.8 | 49.7 | 91.0 | 11.5
$D_{n}4000$ | $0.5\leq z<0.75$ | 60.2 | 5.4 | 73.6 | 10.7 |  | 74.0 | 13.0 | 48.1 | 6.5 | 87.4 | 39.1 | 72.1 | 10.8
$0.75\leq z\leq 0.9$ | 65.2 | 8.7 | 79.3 | 17.4 |  | 73.0 | 15.3 | 57.3 | 10.9 | 86.3 | 51.3 | 79.9 | 20.8
UVJ | $0.5\leq z<0.75$ | 71.5 | 4.6 | 87.7 | 8.7 | 88.7 | 27.1 |  | 53.8 | 7.8 | 91.6 | 43.3 | 79.1 | 14.2
$0.75\leq z\leq 0.9$ | 78.5 | 8.1 | 93.0 | 18.0 | 89.4 | 36.4 |  | 67.2 | 11.1 | 90.9 | 54.5 | 86.2 | 27.6
$U-V$ | $0.5\leq z<0.75$ | 70.2 | 21.9 | 83.4 | 30.1 | 91.6 | 40.6 | 84.9 | 30.7 |  | 89.1 | 55.8 | 84.7 | 30.9
$0.75\leq z\leq 0.9$ | 75.2 | 23.4 | 87.7 | 34.9 | 90.8 | 44.1 | 85.9 | 27.7 |  | 88.8 | 62.7 | 91.7 | 38.1
$n$ | $0.5\leq z<0.75$ | 49.6 | 5.6 | 62.5 | 10.1 | 71.6 | 21.8 | 63.5 | 12.5 | 36.9 | 10.3 |  | 59.4 | 13.1
$0.75\leq z\leq 0.9$ | 55.9 | 9.8 | 69.4 | 16.7 | 72.4 | 31.0 | 62.7 | 16.5 | 44.8 | 16.9 |  | 68.9 | 22.8
Class | $0.5\leq z<0.75$ | 82.5 | 1.5 | 92.4 | 11.5 | 91.6 | 29.1 | 85.3 | 19.7 | 54.8 | 9.2 | 92.2 | 48.7 |
$0.75\leq z\leq 0.9$ | 79.4 | 2.1 | 92.0 | 12.4 | 88.5 | 28.2 | 80.2 | 17.5 | 61.3 | 7.5 | 90.8 | 54.0 |

333Lines indicate the main selection method, while columns show the method we
compared against. Each column is separated in two: the completeness and the
contamination (in %) for two redshift bins.

To check how the slope of the MSR changes with the quiescent selection method,
we used the different selection cuts shown in Tab. 3. Compared to the
selection used in this work, the other criteria lead to MSR with milder slopes
ranging from 0.44$\pm$0.04 to 0.59$\pm$0.02 (Fig. 14, left) and higher
intercepts such that the impact of the difference selection mainly affects the
low-$M_{*}$ regime. Contamination by the blue population could explain the
different slopes as star-forming galaxies are larger with lower stellar mass.
In Fig. 14 (right), we checked the specific star formation rate (sSFR) of the
passive sample selected with the different methods. Below a sSFR of
$\lesssim-12$ yr-1, all the distributions are similar, but a change occurs
above this threshold where the sSFR drops for all the selections but the
$D_{n}4000$ and $n$. Taking a threshold between quiescent and star-forming
galaxies of log(sSFR/yr${}^{-1})=-11$ (Salim et al., 2018), 46, 34, 25 and 24%
of quiescent galaxies from $D_{n}4000$, Sersic index, UV and UVJ are found to
be active while being lesser than 17% for all the remaining selections. In
particular, the NUVrK+$D_{n}4000$ selection leads to only 3% of active
galaxies in the final sample. Above this contamination of 24%, the slope of
the MSR is found to be milder and distinct (at 1$\sigma$ level) from the slope
derived in this work (Sect. 3.1). These different selections partially explain
the different slopes estimated in the literature (shown as gray dashed lines
in Fig. 14).

Figure 14: Comparison of the MSR depending on different selection methods.
Left: MSR for the different selection criteria discussed in the text with
their associated slope and uncertainty. The dashed gray lines represent the
MSRs from the literature shown in Fig. 5. Right: sSFR distribution for the
different selection criteria with the fraction of blue galaxies
(log($\mathrm{sSFR/yr}^{-1})\geq-11$) for each of them shown on the top left
corner.

###  4.2 How different density limits and quiescent selection criteria impacts
the size variation in LD and HD environment

In this work, we used the density contrast (Eq. 3) as a proxy for the
environment and defined the HD and LD samples using the density distribution.
However, the definition of the environment, and consequently the HD and LD
samples, may differ from one study to another. In general HD and LD
environments are defined as voids and fields, and groups and clusters,
respectively. In Cucciati et al. (2017), a comparison is made between the LD
and HD environments and the voids, groups, and clusters. The $D_{p,5}$ in LD
is similar to that in voids while it is larger than the typical size of groups
and clusters, although the highest density tail of the HD environment is
populated by galaxies in rich groups. The median number density of the field
sample in ATLAS${}^{\textrm{3D}}$ and of the Coma cluster is
log($\Sigma_{p,3}\textrm{)}=-0.5$ and log $\Sigma_{p,3}=2$ (Cappellari, 2013)
corresponding to $D_{p,5}=2.89$ and 0.16 Mpc, respectively. The threshold for
the HD environment in VIPERS ($D_{p,5}=2.85$ Mpc) is therefore similar to the
$D_{p,5}$ estimated with ATLAS${}^{\textrm{3D}}$. Therefore the HD environment
is less dense compared to works using clusters and groups but cannot be
strictly compared to field since it comprises more than half of the rich
groups in VIPERS (see Fig. 2 in Cucciati et al. 2017).

In Fig. 11, we show that no significant size difference is observed between
the LD and HD environments. It may be that the HD environment traced by VIPERS
is not dense enough to highlight an environmental impact on the size. To check
if the definition of HD and LD environments impacts the observed size
difference, we choose more extreme thresholds to define both density regimes.
By reducing the portion of the density distribution considered as HD and LD
environments (see Fig. 4), we are increasing the probability of finding a
difference in the mean size of ETGs. Nonetheless, increasing the density
difference between the LD and HD environments comes at the cost of decreasing
the statistic of both samples.
Instead of defining LD (HD) environment as the first (fourth) quartile
($q=25$%) of the density distribution, we defined them as the least dense
(denser) 20, 15, 10, and 5% part of the density distribution and recomputed
the MSR for the new MM samples. We show in Fig. 15 the size difference,
$\Delta\textrm{log(}R_{e}\textrm{)}=R_{e}$(HD)-$R_{e}$(LD), in each stellar
mass bin for different definitions of LD and HD samples represented by their
$q$ value. The first plot for $q=25\%$ shows the same result than Fig 11 in a
different way. For $q=20\%$, $15\%$, and $5\%$, the mean size in HD and LD
environments in each mass bin agrees within $1-2\sigma$. The second stellar
mass bin shows a peculiar behavior at $q=10$% since the size difference
increases but agrees within $3\sigma$. While this difference remains not
statistically significant, we do not have explanations for the higher
difference in this stellar mass bin.

Figure 15: Size difference between the LD and HD environments (red points) in
four mass bins. Each plot is done for different $q$ values representing the
thresholds used to define the LD and HD samples from the density distribution.

In the previous section, we observed that the selection criterion used to
define the quiescent population has a mild impact on the slope of the MSR due,
at least partially, to the contamination by star-forming galaxies that follow
a different MSR. We checked if this selection could change the conclusions
about the environmental impact. We reproduced the analysis performed above but
with different selection criteria instead of different $q$ values (Fig. 16)
and keeping $q=25\%$. We observe that the mean size in the LD and HD
environments agrees within $1-2\sigma$ ($3\sigma$ for the fourth mass bin
using the UVJ selection). Because no statistical significant size difference
is observed between the HD and LD environments, we conclude that the partial
contamination by star-forming galaxies that results from different selection
criteria is not sufficient to change our conclusions about the environmental
impact on the MSR.

Figure 16: Size difference between the LD and HD environments (red points) in
four mass bins. Each plot is done for different selection criteria:
NUVrK+$D_{n}4000$ (this work), NUVrJ, n, UV, UVJ, and $D_{n}4000$.

###  4.3 Growth of galaxies from $z=0.9$ to $z=0.5$

The mean size of quiescent galaxies evolves with redshift, being more compact
at higher $z$ (see Fig. 6) compared to the local Universe. The present
consensus favors the scenario where dry minor mergers are mostly responsible
for the size evolution at $z<1$. While major mergers increase the size
proportionally to the mass, minor mergers are more efficient in terms of size
enhancement. Following the virial theorem (Binney & Tremaine, 2008), the
merger size depends on the mass ratio, $\eta$, of both merging galaxies (e.g.,
Naab & Ostriker 2009; Bezanson et al. 2009). For minor mergers
($0.10\leq\eta\leq 0.25$), the radius increases by a factor $(1+\eta)^{2}$
and, as a result, the evolutionary path of a galaxy after a minor merger event
has a slope $\gamma\sim 2$ in the mass-size plane. Following virial arguments,
Newman et al. (2012) express $\gamma$, also called the growth efficiency, as a
function of $\alpha$ (the slope of the MSR) and $\eta$:

$\gamma=2-\frac{\textrm{log}(1+\eta^{2-\alpha})}{\textrm{log}(1+\eta)}.$ (5)

For $\alpha=0.62$ (Fig. 5), and a minor merger scenario ($\eta=1/10$),
$\gamma$ is equal to 1.6, in good agreement with Newman et al. (2012). In
other works, $\gamma$ was found to vary for minor mergers with values ranging
from 1.3 (Nipoti et al., 2009), 1.14 (Sweet et al., 2017), 1.6 (Newman et al.,
2012), $\sim 2$ (Naab & Ostriker, 2009; Hamadouche et al., 2022), 2.24 (Oogi
et al., 2016) to $\gtrsim 2.7$ (Bezanson et al., 2009), and between 1 and 2.5
(Belli et al., 2014).

To check how the mass and size evolve as the redshift decreases, we divided
the sample into two bins $z_{1}$ and $z_{2}$. For a consistent comparison, we
applied a cut to the sample of galaxies at both redshift ranges at
log($M_{*}/M_{\odot})=10.9$, which is the completeness limit at $z=0.9$. The
quiescent population at $z_{2}$ will not be the direct progenitors of the
quiescent population at $z_{1}$ due to the newly quenched galaxies that joined
the population between $z_{2}$ and $z_{1}$ (Carollo et al., 2013). The
fraction of newcomers entering the quiescent population depends on the choice
of $z_{1}$ and $z_{2}$. To avoid a contamination by newcomers, we choose
$z_{1}$ and $z_{2}$ so that the comoving number density of quiescent galaxies
remains constant. In this way, we ensure that we are following the same
population from $z_{2}$ to $z_{1}$ (Marchesini et al., 2014). The sample was
cut at $z=0.65$ (whole sample) and $z=0.70$ (LD and HD samples) and we
estimated the comoving number density $\phi$ in the two redshift bins. To
correct for the selections of VIPERS, each galaxy was weighted by its target
sampling rate and spectroscopic success rate (TSR and SSR, see Garilli et al.
2014), and the $V_{max}$ method is used:

$\displaystyle\phi=\sum_{i}\frac{w_{i}}{V_{max}}=\sum_{i}\frac{(\mathrm{TSR}_{i}\times\mathrm{SSR}_{i})^{-1}}{V_{max}^{i}},$
(6) $\displaystyle
V_{max}^{i}=\left[V(z_{max}^{i})-V(z_{min}^{i})\right]\times\frac{\Omega}{4\pi}.$
(7)

Here $V_{max}^{i}$ is the maximum volume in which the $i^{th}$ galaxy can be
observed as part of the survey, estimated between $z_{min}^{i}$ and
$z_{max}^{i}$ that were computed based on the absolute luminosities obtained
from the SED fitting, and $\Omega$ is the solid angle of the VIPERS surveyed
field ($\sim 24$ deg2). We found a comoving density of $2.94\times 10^{-5}$,
$6.95\times 10^{-6}$, and $4.24\times 10^{-6}$ for the whole sample, the HD
and the LD samples, respectively.

Figure 17: MSR for the whole (left), HD (center), and LD (right) samples of
passive galaxies in the two redshift bins (lower in blue and higher in red).

We present in Fig. 17 the mass-size plane for the whole population, the HD and
LD environments. The median size of the population increases from 4.42 to 4.82
kpc (whole sample), from 4.62 to 5.22 kpc (HD), and from 4.08 to 4.44 kpc (LD)
while the median stellar mass changes by less than 0.02 dex. In the minor
merger scenario, the size and mass of galaxies that merge are related by the
relation (Naab et al., 2009)

$\frac{R_{f}}{R_{1}}\approx(1+\eta)^{2}=\left(1+\frac{M_{2,*}}{M_{1,*}}\right)^{2},$
(8)

where $R_{1}$ is the size of the galaxy, $R_{f}$ the size of the merged
galaxy, $M_{1,*}$ and $M_{2,*}$ the mass of the galaxies that are merging. The
change in stellar mass associated to the observed change in size from $0.7\leq
z\leq 0.9$ to $0.5\leq z\leq 0.7$ is very minor (lesser than 0.03 dex) and
would be difficult to detect. This is may be due to the low elapsed time of
$\sim 2$ Gyr between both redshift bins. For instance, Hamadouche et al.
(2022) found that the average size evolution from $z=1.1$ to $z=0.7$ is in
agreement with a series of 3 minor mergers within 2 Gyr, leading to a
difference in stellar mass of 0.13 dex. Given the very low evolution of
stellar mass in VIPERS, it is difficult to confirm if $\Delta R\propto\Delta
M_{*}^{2}$ as it should be for minor mergers. However, the change in size
depends on the environment, with an increase of 13% in the HD environment and
an increase of 9% in the LD environment. This fact in agreement with minor
mergers as the merging rate should be lower in LD environments, leading to a
smaller size evolution compared to denser environments. This is also in
agreement with Yoon et al. (2017) who found that the merger history of the
most massive galaxies ($M_{*}\geq 10^{11}$) depends on the environment and
Cooper et al. (2012) who found that the structural evolution of quiescent
galaxies at $0.4\leq z\leq 1.2$ happens in dense environments.

For the whole, the HD and LD samples, the mean size is increasing by a factor
of 1.10, 1.13, and 1.09, corresponding to $\eta$ values ranging from 0.045 to
0.062. These values are lower than the usual range $0.10\leq\eta\leq 0.25$,
indicating that not all the quiescent galaxies have experienced a minor merger
event from $z=0.9$ to $z=0.5$. Considering $\eta=0.25$ and 0.10, 17 to 45% of
the population in the LD and 23 to 62% in the HD environment should experience
such merging process to increase the mean size by 9 and 13% within 2 Gyr. It
corresponds to an average merger rate of 0.16 and 0.21 Gyr-1 in the LD and HD
environments, respectively.

How do these merger rates compared with other works from the literature? Using
VANDELS and LEGA-C, Hamadouche et al. (2022) found that the mean size
evolution from $z=1.3$ and $z=0.6$ is in agreement with a series of 3 minor
mergers with $\eta=0.1$, that is around one minor merger per Gyr. Using the
minor merger ($0.10\leq\eta\leq 0.25$) rate from Lotz et al. (2011), Damjanov
et al. (2023) found that minor mergers could explain the mean size evolution
from $z=0.6$ to $z=0.2$ in the HectoMAP survey. Other works also found that
minor mergers could explain the mean size evolution at $z\leq 1.2$ (i.e.,
Cooper et al. 2012; Damjanov et al. 2019, 2022). From the minor merger rate
per galaxy from Lotz et al. (2011) (their tab. 4), the number of minor mergers
at $0.5\leq z\leq 0.9$ ranges between 0.58 to 0.74 depending on the method
used to estimate this rate. A comparable minor merger rate of $\sim$0.5 Gyr-1
is found by Yoon et al. (2017) at $z\sim 0.7$ in the lowest dense environment
for log($M_{*}/M_{\odot})\geq 11.2$, leading to one minor merger for the
redshift range of this work. The work of Oogi & Habe (2013) explains the
evolution of the size from $z=2$ to $z=0$ with a sequential minor merger rate
every 0.2 Gyr with however a lower mass ratio ($1/20\leq\eta\leq 1/10$). These
values support the number of minor merger required to explain the observe size
growth in VIPERS. However we note that other works found much lower values for
minor merger rate. Conselice et al. (2022) found that 0.14 minor merger occurs
over $0.5\leq z\leq 0.9$, which is too low to explain the mean size evolution
in VIPERS, and the same conclusion is reached by Man et al. (2016) who found
that additional processes, in addition to mergers, are needed to explain the
strong size evolution from $z=2.5$ downwards and López-Sanjuan et al. (2011)
in which the upper-limit on the number of minor mergers from $z=0.9$ and
$z=0.5$ is equal to 0.13, this last work being however focusing on luminous
galaxies. This discrepancy in the merger rate seems to originate, at least
partially, from the dataset used as the merger rate in Lotz et al. (2011),
Oogi & Habe (2013) and Yoon et al. (2017) are based on simulations while the
ones in Man et al. (2016), López-Sanjuan et al. (2011), and Conselice et al.
(2022) are based on observations.

Based on previous works and on the observed size evolution at a roughly
constant stellar mass, the major merger scenario seems to be discarded at
$z\leq 1$. Bernardi et al. (2011) proposed the curvature of the MSR above
$2\times 10^{11}$ $M_{\odot}$ to be due to major dry mergers. The last bin of
Fig. 5 is slightly higher than the linear relation, and the dispersion of
galaxies above and below this $M_{*}$ could hide such curvature. Instead of a
binning per quartile, we divide the sample into 10, 15, and 20 bins with equal
numbers of galaxies, to see if any curvature occurs at $M_{*}\leq 2\times
10^{11}$ $M_{\odot}$. For each binning, no curvature is observed, suggesting
that major dry mergers are not responsible for the size evolution of the
quiescent population at $z\leq 1$.

Using 2000 massive (log($M_{*}$/$M_{\odot})\geq 11$) galaxies from VIPERS,
Gargiulo et al. (2017) studied the evolution of low and high stellar mass
density galaxies at redshift $0.5\leq z\leq 1.0$. They found that: 1) the
comoving number density of dense galaxies is constant while increasing by a
factor of four for less dense objects, 2) less dense galaxies are younger than
the dense ones, and 3) the decreasing comoving number density of massive star-
forming galaxies is compensated by the increasing comoving number density of
quiescent galaxies over the same period of time. They concluded that the main
channel by which the quiescent population is built up is the quenching of
star-forming galaxies while a build-up through mergers is ruled out. With a
sample of 900 massive passive galaxies from VIPERS Gargiulo et al. (2019)
confirm this result but notice that the higher number of less dense galaxies
in the HD environment is in agreement with satellite accretion, but only for
$\leq 1\%$ of low-density massive passive galaxies.
Some differences between the sample selection of this work and their can be
noted. Gargiulo et al. (2017, 2019) used the redshift-independent NUVrK colors
selection and the physical parameters catalog from Davies et al. (2016) while
we used the redshift-dependent NUVrK selection from Moutard et al. (2016a) and
the associated physical parameters catalog based on more photometric bands. In
Gargiulo et al. (2019) the highest density bin is set at log($1+\delta)=0.84$,
which is slightly higher than in this work (log($1+\delta)=0.73$) so their HD
environment is slightly denser with this limit than our.
In the present work we study the size evolution in two bins with an equal
comoving number density of galaxies to remove the progenitor bias, in order to
look at the residual size evolution that would be caused by other processes.
Because we found the size evolution to be environment-dependent, this points
toward a scenario where mergers are involved. The associated $\eta$ for the
merger are 0.045 and 0.062 for the LD and HD environments and $\eta=0.045$ for
the whole sample of massive galaxies. The similar value for the LD environment
and the whole population indicates that the merger rate does not increase with
increasing density but rather shows an increase only in the HD environment.
This is in line with Gargiulo et al. (2019) (see their Fig. 8) where the
number of low-density passive galaxies is flat in the first three density bins
and increases in the last density bin (the HD environment), indicating that
the evolution is mostly independent of the environment except at high density
where satellite accretion may play a role.
From Fig. 6 and Fig. 12, the mean size of the quiescent population from the
last to the first redshift bin increases by 30%. With an increase by minor
mergers of 9 and 13% in the LD and HD environments, the mean size increase due
to minor merger accounts for 30 and 40% in the LD and HD environments while
the remaining size increase may be due to progenitor bias. Because the size
increase for the whole population is similar to that of the LD environment,
the minor merger contribution is identical. This result is different from
Gargiulo et al. (2019) where progenitor bias totally accounts for the size
evolution in the first three density bins and minor mergers plays a role in
the HD environment. Nevertheless we retrieved two general results from
Gargiulo et al. (2019): 1) the evolution in the first three density bins is
independent of environment and 2) minor merger is not the dominant mechanism
by which the galaxies evolve in size - the progenitor bias may be more
important - and plays a more significant role in the HD environment compared
to the first three density bins.

##  5 Conclusions

In this paper, we used the VIPERS PDR-2 catalog, a spectroscopic survey of
$\sim$90 000 galaxies, to study the MSR of the quiescent population and the
impact of the environment on their evolution. The effective circularized
radius was computed from $i$-band images using GALFIT through a Sersic
profile. The stellar mass and rest-frame photometry were estimated through SED
fitting with LEPHARE based on the CFHTLS photometric catalog complemented by
GALEX. The $D_{n}4000$ spectral break was measured directly from the VIPERS
spectra. The environment was traced by the density contrast estimated using a
cylinder of 1000 km s-1 half-length and a radius given by the fifth nearest
neighbor, where the LD and HD environments were defined as the first and
fourth quartile of the density distribution. We selected the quiescent
population using the NUVrK diagram and the $D_{n}4000$ spectral break. The
final sample contains 4786 quiescent galaxies and 3998 quiescent galaxies with
good density measurements. Our main results are the following:

  * •

The slope and intercept of the MSR, $\alpha=0.62\pm 0.04$ and
$\textrm{log}(A)=0.52\pm 0.01$, are in agreement with the slopes and
intercepts from the literature at a similar redshift. The intercept decreases
with increasing redshift, following $R_{e}(z)=(8.20\pm
0.34)\times(1+z)^{-1.70\pm 0.08}$ and $R_{e}(z)=(4.76\pm
0.38)\times(1+z)^{-0.81\pm 0.12}$ when using additional values from the
literature.

  * •

Newcomers, defined as quiescent galaxies with $1.5\leq D_{n}{4000}\leq 1.6$,
are preferentially found in LD environment. In average, newcomers have lower
$n$, $M_{*}$, $R_{e}$, and higher sSFR when compared to the oldest quiescent
galaxies ($D_{n}{4000}\geq 1.95$).

  * •

We do not find a significant difference ($\leq 3\sigma$) in size between the
HD and LD environments when using MM samples to suppress the impact of in situ
processes depending on the stellar mass. The size between both environments
remains identical (i.e., within $3\sigma$) even when changing the definition
of LD and HD environments, that is to say when choosing a smaller percentile
of the density distribution.

  * •

A positive correlation is observed between $D_{n}4000$ and the $M_{*}$ in the
HD and LD environments, similar to what was already observed for the whole
population. The ages of quiescent galaxies in HD and LD environments are
similar within $2\sigma$ at low mass and $1\sigma$ at high mass. The higher
offset at low mass is consistent with newcomers being preferentially found in
the LD environment.

  * •

The slope of the MSR slightly increases when using a different quiescent
galaxy selection ($D_{n}4000$, NUVrJ, n, UVJ, and UV) due to a higher fraction
of star-forming galaxies, but remains similar within $2\sigma$ and in
agreement with the literature.

  * •

By dividing the sample in two redshift bins with equal comoving number
density, we observed that the increase in size is larger in the HD than in the
LD environment. Using the model of Naab & Ostriker (2009), we found that 31
and 43% of the quiescent population in the LD and HD environments experienced
a minor merger ($0.10\leq\eta\leq 0.25$) within $0.5\leq z\leq 0.9$ at $M\geq
10^{10.9}$ $M_{\odot}$. Using the offset of the MSR between $0.5\leq z\leq
0.9$, we estimated that minor mergers are responsible for 30 to 40% of the
total size increase of the quiescent population.

###### Acknowledgements.

We thank the anonymous referee for his comments that help to improve and
clarify the results presented in this work. AP, JK, and MF acknowledge support
from the Polish National Science Centre via the grants UMO-2018/30/E/ST9/00082
and UMO-2022/47/D/ST9/00419. MF and MS have been supported by the Polish
National Agency for Academic Exchange (Bekker grants
BPN/BEK/2023/1/00036/DEC/01 and BPN/BEK/2021/1/00298/DEC/1). MS acknowledges
support from the European Union’s Horizon 2020 Research and Innovation
programme under the Maria Sklodowska-Curie grant agreement (No. 754510).

## References

  * Afanasiev et al. (2023) Afanasiev, A. V., Mei, S., Fu, H., et al. 2023, A&A, 670, A95
  * Ahn et al. (2014) Ahn, C. P., Alexandroff, R., Allende Prieto, C., et al. 2014, ApJS, 211, 17
  * Allen et al. (2015) Allen, R. J., Kacprzak, G. G., Spitler, L. R., et al. 2015, ApJ, 806, 3
  * Arnouts et al. (1999) Arnouts, S., Cristiani, S., Moscardini, L., et al. 1999, MNRAS, 310, 540
  * Arnouts et al. (2013) Arnouts, S., Le Floc’h, E., Chevallard, J., et al. 2013, A&A, 558, A67
  * Bait et al. (2017) Bait, O., Barway, S., & Wadadekar, Y. 2017, MNRAS, 471, 2687
  * Balogh et al. (1999) Balogh, M. L., Morris, S. L., Yee, H. K. C., Carlberg, R. G., & Ellingson, E. 1999, ApJ, 527, 54
  * Barone et al. (2022) Barone, T. M., D’Eugenio, F., Scott, N., et al. 2022, MNRAS, 512, 3828
  * Bassett et al. (2013) Bassett, R., Papovich, C., Lotz, J. M., et al. 2013, ApJ, 770, 58
  * Bell et al. (2004) Bell, E. F., Wolf, C., Meisenheimer, K., et al. 2004, ApJ, 608, 752
  * Belli et al. (2014) Belli, S., Newman, A. B., & Ellis, R. S. 2014, ApJ, 783, 117
  * Belli et al. (2015) Belli, S., Newman, A. B., & Ellis, R. S. 2015, ApJ, 799, 206
  * Bernardi et al. (2011) Bernardi, M., Roche, N., Shankar, F., & Sheth, R. K. 2011, MNRAS, 412, L6
  * Bertin & Arnouts (1996) Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393
  * Bezanson et al. (2009) Bezanson, R., van Dokkum, P. G., Tal, T., et al. 2009, ApJ, 697, 1290
  * Bialas et al. (2015) Bialas, D., Lisker, T., Olczak, C., Spurzem, R., & Kotulla, R. 2015, A&A, 576, A103
  * Binney & Tremaine (2008) Binney, J. & Tremaine, S. 2008, Galactic Dynamics: Second Edition
  * Bouchet et al. (1985) Bouchet, P., Lequeux, J., Maurice, E., Prevot, L., & Prevot-Burnichon, M. L. 1985, A&A, 149, 330
  * Bournaud et al. (2007) Bournaud, F., Jog, C. J., & Combes, F. 2007, A&A, 476, 1179
  * Brinchmann et al. (2004) Brinchmann, J., Charlot, S., White, S. D. M., et al. 2004, MNRAS, 351, 1151
  * Bruzual & Charlot (2003) Bruzual, G. & Charlot, S. 2003, MNRAS, 344, 1000
  * Bruzual A. (1983) Bruzual A., G. 1983, ApJ, 273, 105
  * Calzetti et al. (2000) Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682
  * Capak et al. (2007) Capak, P., Abraham, R. G., Ellis, R. S., et al. 2007, ApJS, 172, 284
  * Cappellari (2013) Cappellari, M. 2013, ApJ, 778, L2
  * Carollo et al. (2013) Carollo, C. M., Bschorr, T. J., Renzini, A., et al. 2013, ApJ, 773, 112
  * Cavaliere et al. (1992) Cavaliere, A., Colafrancesco, S., & Menci, N. 1992, ApJ, 392, 41
  * Cebrián & Trujillo (2014) Cebrián, M. & Trujillo, I. 2014, MNRAS, 444, 682
  * Chabrier (2003) Chabrier, G. 2003, PASP, 115, 763
  * Chan et al. (2016) Chan, J. C. C., Beifiori, A., Mendel, J. T., et al. 2016, MNRAS, 458, 3181
  * Chan et al. (2018) Chan, J. C. C., Beifiori, A., Saglia, R. P., et al. 2018, ApJ, 856, 8
  * Chen et al. (2022) Chen, Z., Sefako, R., Yang, Y., et al. 2022, Research in Astronomy and Astrophysics, 22, 075017
  * Choi et al. (2010) Choi, Y.-Y., Han, D.-H., & Kim, S.-S. S. 2010, Journal of Korean Astronomical Society, 43, 191
  * Cimatti et al. (2008) Cimatti, A., Cassata, P., Pozzetti, L., et al. 2008, A&A, 482, 21
  * Cimatti et al. (2012) Cimatti, A., Nipoti, C., & Cassata, P. 2012, MNRAS, 422, L62
  * Ciotti & Bertin (1999) Ciotti, L. & Bertin, G. 1999, A&A, 352, 447
  * Coil et al. (2008) Coil, A. L., Newman, J. A., Croton, D., et al. 2008, ApJ, 672, 153
  * Colless et al. (2001) Colless, M., Dalton, G., Maddox, S., et al. 2001, MNRAS, 328, 1039
  * Colless et al. (2003) Colless, M., Peterson, B. A., Jackson, C., et al. 2003, arXiv e-prints, astro:ph/0306581
  * Conselice et al. (2022) Conselice, C. J., Mundy, C. J., Ferreira, L., & Duncan, K. 2022, ApJ, 940, 168
  * Cooper et al. (2012) Cooper, M. C., Griffith, R. L., Newman, J. A., et al. 2012, MNRAS, 419, 3018
  * Cooper et al. (2007) Cooper, M. C., Newman, J. A., Coil, A. L., et al. 2007, MNRAS, 376, 1445
  * Cooper et al. (2006) Cooper, M. C., Newman, J. A., Croton, D. J., et al. 2006, MNRAS, 370, 198
  * Cox et al. (2006) Cox, T. J., Dutta, S. N., Di Matteo, T., et al. 2006, ApJ, 650, 791
  * Cucciati et al. (2017) Cucciati, O., Davidzon, I., Bolzonella, M., et al. 2017, A&A, 602, A15
  * Cucciati et al. (2014) Cucciati, O., Granett, B. R., Branchini, E., et al. 2014, A&A, 565, A67
  * Daddi et al. (2005) Daddi, E., Renzini, A., Pirzkal, N., et al. 2005, ApJ, 626, 680
  * Damjanov et al. (2011) Damjanov, I., Abraham, R. G., Glazebrook, K., et al. 2011, ApJ, 739, L44
  * Damjanov et al. (2009) Damjanov, I., McCarthy, P. J., Abraham, R. G., et al. 2009, ApJ, 695, 101
  * Damjanov et al. (2023) Damjanov, I., Sohn, J., Geller, M. J., Utsumi, Y., & Dell’Antonio, I. 2023, ApJ, 943, 149
  * Damjanov et al. (2022) Damjanov, I., Sohn, J., Utsumi, Y., Geller, M. J., & Dell’Antonio, I. 2022, ApJ, 929, 61
  * Damjanov et al. (2019) Damjanov, I., Zahid, H. J., Geller, M. J., et al. 2019, ApJ, 872, 91
  * Darg et al. (2010) Darg, D. W., Kaviraj, S., Lintott, C. J., et al. 2010, MNRAS, 401, 1552
  * Davidzon et al. (2016) Davidzon, I., Cucciati, O., Bolzonella, M., et al. 2016, A&A, 586, A23
  * Davies et al. (2016) Davies, L. J. M., Driver, S. P., Robotham, A. S. G., et al. 2016, MNRAS, 461, 458
  * Davies et al. (2018) Davies, L. J. M., Robotham, A. S. G., Driver, S. P., et al. 2018, MNRAS, 480, 768
  * Davis et al. (2019) Davis, B. L., Graham, A. W., & Cameron, E. 2019, ApJ, 873, 85
  * De Looze et al. (2014) De Looze, I., Fritz, J., Baes, M., et al. 2014, A&A, 571, A69
  * De Lucia & Blaizot (2007) De Lucia, G. & Blaizot, J. 2007, MNRAS, 375, 2
  * De Lucia et al. (2014) De Lucia, G., Tornatore, L., Frenk, C. S., et al. 2014, MNRAS, 445, 970
  * Delaye et al. (2014) Delaye, L., Huertas-Company, M., Mei, S., et al. 2014, MNRAS, 441, 203
  * Díaz-García et al. (2019a) Díaz-García, L. A., Cenarro, A. J., López-Sanjuan, C., et al. 2019a, A&A, 631, A156
  * Díaz-García et al. (2019b) Díaz-García, L. A., Cenarro, A. J., López-Sanjuan, C., et al. 2019b, A&A, 631, A158
  * Dressler (1980) Dressler, A. 1980, ApJ, 236, 351
  * Driver et al. (2016) Driver, S. P., Wright, A. H., Andrews, S. K., et al. 2016, MNRAS, 455, 3911
  * Dutton et al. (2011) Dutton, A. A., van den Bosch, F. C., Faber, S. M., et al. 2011, MNRAS, 410, 1660
  * Eisenstein et al. (2023) Eisenstein, D. J., Willott, C., Alberts, S., et al. 2023, arXiv e-prints, arXiv:2306.02465
  * Euclid Collaboration et al. (2022) Euclid Collaboration, Scaramella, R., Amiaux, J., et al. 2022, A&A, 662, A112
  * Faisst et al. (2017) Faisst, A. L., Carollo, C. M., Capak, P. L., et al. 2017, ApJ, 839, 71
  * Fakhouri & Ma (2009) Fakhouri, O. & Ma, C.-P. 2009, MNRAS, 394, 1825
  * Fan et al. (2010) Fan, L., Lapi, A., Bressan, A., et al. 2010, ApJ, 718, 1460
  * Fan et al. (2008) Fan, L., Lapi, A., De Zotti, G., & Danese, L. 2008, ApJ, 689, L101
  * Favole et al. (2018) Favole, G., Montero-Dorta, A. D., Prada, F., Rodríguez-Torres, S. A., & Schlegel, D. J. 2018, MNRAS, 480, 1415
  * Ferland et al. (2013) Ferland, G. J., Porter, R. L., van Hoof, P. A. M., et al. 2013, Rev. Mexicana Astron. Astrofis., 49, 137
  * Fernández Lorenzo et al. (2013) Fernández Lorenzo, M., Sulentic, J., Verdes-Montenegro, L., & Argudo-Fernández, M. 2013, MNRAS, 434, 325
  * Ferreras et al. (2014) Ferreras, I., Trujillo, I., Mármol-Queraltó, E., et al. 2014, MNRAS, 444, 906
  * Figueira et al. (2022) Figueira, M., Pollo, A., Małek, K., et al. 2022, A&A, 667, A29
  * Franx et al. (2008) Franx, M., van Dokkum, P. G., Förster Schreiber, N. M., et al. 2008, ApJ, 688, 770
  * Franzetti et al. (2007) Franzetti, P., Scodeggio, M., Garilli, B., et al. 2007, A&A, 465, 711
  * Fritz et al. (2014) Fritz, A., Scodeggio, M., Ilbert, O., et al. 2014, A&A, 563, A92
  * Furlong et al. (2017) Furlong, M., Bower, R. G., Crain, R. A., et al. 2017, MNRAS, 465, 722
  * García et al. (2014) García, P., Bronfman, L., Nyman, L.-Å., Dame, T. M., & Luna, A. 2014, ApJS, 212, 2
  * Gargiulo et al. (2017) Gargiulo, A., Bolzonella, M., Scodeggio, M., et al. 2017, A&A, 606, A113
  * Gargiulo et al. (2019) Gargiulo, A., Cucciati, O., Garilli, B., et al. 2019, A&A, 631, A15
  * Gargiulo et al. (2016) Gargiulo, A., Saracco, P., Tamburri, S., Lonoce, I., & Ciocca, F. 2016, A&A, 592, A132
  * Garilli et al. (2010) Garilli, B., Fumana, M., Franzetti, P., et al. 2010, PASP, 122, 827
  * Garilli et al. (2014) Garilli, B., Guzzo, L., Scodeggio, M., et al. 2014, A&A, 562, A23
  * Garilli et al. (2008) Garilli, B., Le Fèvre, O., Guzzo, L., et al. 2008, A&A, 486, 683
  * Girardi et al. (2000) Girardi, L., Bressan, A., Bertelli, G., & Chiosi, C. 2000, A&AS, 141, 371
  * Goranova et al. (2009) Goranova, Y., Hudelot, P., Magnard, & al. 2009, , http://terapix.iap.fr/cplt/table_syn_T0006.html
  * Goto et al. (2003) Goto, T., Okamura, S., Sekiguchi, M., et al. 2003, PASJ, 55, 757
  * Guo et al. (2009) Guo, Y., McIntosh, D. H., Mo, H. J., et al. 2009, MNRAS, 398, 1129
  * Guzzo & VIPERS Team (2013) Guzzo, L. & VIPERS Team. 2013, The Messenger, 151, 41
  * Haines et al. (2017) Haines, C. P., Iovino, A., Krywult, J., et al. 2017, A&A, 605, A4
  * Hamadouche et al. (2022) Hamadouche, M. L., Carnall, A. C., McLure, R. J., et al. 2022, MNRAS, 512, 1262
  * Hon et al. (2022) Hon, D. S. H., Graham, A. W., Davis, B. L., & Marconi, A. 2022, MNRAS, 514, 3410
  * Hon et al. (2023) Hon, D. S. H., Graham, A. W., & Sahu, N. 2023, MNRAS, 519, 4651
  * Huang et al. (2018) Huang, S., Leauthaud, A., Greene, J., et al. 2018, MNRAS, 480, 521
  * Hubble (1936) Hubble, E. P. 1936, Realm of the Nebulae
  * Huertas-Company et al. (2013a) Huertas-Company, M., Mei, S., Shankar, F., et al. 2013a, MNRAS, 428, 1715
  * Huertas-Company et al. (2013b) Huertas-Company, M., Shankar, F., Mei, S., et al. 2013b, ApJ, 779, 29
  * Ichikawa et al. (2012) Ichikawa, T., Kajisawa, M., & Akhlaghi, M. 2012, MNRAS, 422, 1014
  * Ilbert et al. (2006) Ilbert, O., Arnouts, S., McCracken, H. J., et al. 2006, A&A, 457, 841
  * Ilbert et al. (2009) Ilbert, O., Capak, P., Salvato, M., et al. 2009, ApJ, 690, 1236
  * Ilbert et al. (2013) Ilbert, O., McCracken, H. J., Le Fèvre, O., et al. 2013, A&A, 556, A55
  * Ilbert et al. (2010) Ilbert, O., Salvato, M., Le Floc’h, E., et al. 2010, ApJ, 709, 644
  * Jian et al. (2012) Jian, H.-Y., Lin, L., & Chiueh, T. 2012, ApJ, 754, 26
  * Jiang et al. (2018) Jiang, D., Liu, F. S., Zheng, X., et al. 2018, ApJ, 854, 70
  * Joshi et al. (2020) Joshi, G. D., Pillepich, A., Nelson, D., et al. 2020, MNRAS, 496, 2673
  * Kauffmann et al. (2003) Kauffmann, G., Heckman, T. M., White, S. D. M., et al. 2003, MNRAS, 341, 33
  * Kawinwanichakij et al. (2021) Kawinwanichakij, L., Silverman, J. D., Ding, X., et al. 2021, ApJ, 921, 38
  * Kelkar et al. (2015) Kelkar, K., Aragón-Salamanca, A., Gray, M. E., et al. 2015, MNRAS, 450, 1246
  * Khochfar & Silk (2006) Khochfar, S. & Silk, J. 2006, ApJ, 648, L21
  * Kovač et al. (2010a) Kovač, K., Lilly, S. J., Cucciati, O., et al. 2010a, ApJ, 708, 505
  * Kovač et al. (2010b) Kovač, K., Lilly, S. J., Knobel, C., et al. 2010b, ApJ, 718, 86
  * Krogager et al. (2014) Krogager, J. K., Zirm, A. W., Toft, S., Man, A., & Brammer, G. 2014, ApJ, 797, 17
  * Krywult et al. (2017) Krywult, J., Tasca, L. A. M., Pollo, A., et al. 2017, A&A, 598, A120
  * Kuchner et al. (2017) Kuchner, U., Ziegler, B., Verdugo, M., Bamford, S., & Häußler, B. 2017, A&A, 604, A54
  * Lange et al. (2015) Lange, R., Driver, S. P., Robotham, A. S. G., et al. 2015, MNRAS, 447, 2603
  * Lange et al. (2016) Lange, R., Moffett, A. J., Driver, S. P., et al. 2016, MNRAS, 462, 1470
  * Lani et al. (2013) Lani, C., Almaini, O., Hartley, W. G., et al. 2013, MNRAS, 435, 207
  * Le Fèvre et al. (2003) Le Fèvre, O., Saisse, M., Mancini, D., et al. 2003, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 4841, Proc. SPIE, ed. M. Iye & A. F. M. Moorwood, 1670–1681
  * Le Fèvre et al. (2005) Le Fèvre, O., Vettolani, G., Garilli, B., et al. 2005, A&A, 439, 845
  * Lin et al. (2010) Lin, L., Cooper, M. C., Jian, H.-Y., et al. 2010, ApJ, 718, 1158
  * Lin et al. (2008) Lin, L., Patton, D. R., Koo, D. C., et al. 2008, ApJ, 681, 232
  * Lisiecki et al. (2023) Lisiecki, K., Małek, K., Siudek, M., et al. 2023, A&A, 669, A95
  * Łokas (2020) Łokas, E. L. 2020, A&A, 638, A133
  * López-Sanjuan et al. (2009) López-Sanjuan, C., Balcells, M., Pérez-González, P. G., et al. 2009, A&A, 501, 505
  * López-Sanjuan et al. (2011) López-Sanjuan, C., Le Fèvre, O., de Ravel, L., et al. 2011, A&A, 530, A20
  * López-Sanjuan et al. (2012) López-Sanjuan, C., Le Fèvre, O., Ilbert, O., et al. 2012, A&A, 548, A7
  * Lotz et al. (2011) Lotz, J. M., Jonsson, P., Cox, T. J., et al. 2011, ApJ, 742, 103
  * Maltby et al. (2010) Maltby, D. T., Aragón-Salamanca, A., Gray, M. E., et al. 2010, MNRAS, 402, 282
  * Man et al. (2016) Man, A. W. S., Zirm, A. W., & Toft, S. 2016, ApJ, 830, 89
  * Marchesini et al. (2014) Marchesini, D., Muzzin, A., Stefanon, M., et al. 2014, ApJ, 794, 65
  * Matharu et al. (2019) Matharu, J., Muzzin, A., Brammer, G. B., et al. 2019, MNRAS, 484, 595
  * Matteuzzi et al. (2022) Matteuzzi, M., Marinacci, F., Nipoti, C., & Andreon, S. 2022, MNRAS, 513, 3893
  * McIntosh et al. (2008) McIntosh, D. H., Guo, Y., Hertzberg, J., et al. 2008, MNRAS, 388, 1537
  * McLure et al. (2013) McLure, R. J., Pearce, H. J., Dunlop, J. S., et al. 2013, MNRAS, 428, 1088
  * Mei et al. (2015) Mei, S., Scarlata, C., Pentericci, L., et al. 2015, ApJ, 804, 117
  * Mignoli et al. (2009) Mignoli, M., Zamorani, G., Scodeggio, M., et al. 2009, A&A, 493, 39
  * Miller et al. (2023) Miller, T. B., van Dokkum, P., & Mowla, L. 2023, ApJ, 945, 155
  * Miller et al. (2019) Miller, T. B., van Dokkum, P., Mowla, L., & van der Wel, A. 2019, ApJ, 872, L14
  * Moffat (1969) Moffat, A. F. J. 1969, A&A, 3, 455
  * Mosleh et al. (2020) Mosleh, M., Hosseinnejad, S., Hosseini-ShahiSavandi, S. Z., & Tacchella, S. 2020, ApJ, 905, 170
  * Moutard et al. (2016a) Moutard, T., Arnouts, S., Ilbert, O., et al. 2016a, A&A, 590, A103
  * Moutard et al. (2016b) Moutard, T., Arnouts, S., Ilbert, O., et al. 2016b, A&A, 590, A102
  * Moutard et al. (2018) Moutard, T., Sawicki, M., Arnouts, S., et al. 2018, MNRAS, 479, 2147
  * Mowla et al. (2019a) Mowla, L., van der Wel, A., van Dokkum, P., & Miller, T. B. 2019a, ApJ, 872, L13
  * Mowla et al. (2019b) Mowla, L. A., van Dokkum, P., Brammer, G. B., et al. 2019b, ApJ, 880, 57
  * Naab et al. (2009) Naab, T., Johansson, P. H., & Ostriker, J. P. 2009, ApJ, 699, L178
  * Naab et al. (2006) Naab, T., Khochfar, S., & Burkert, A. 2006, ApJ, 636, L81
  * Naab & Ostriker (2009) Naab, T. & Ostriker, J. P. 2009, ApJ, 690, 1452
  * Nadolny et al. (2021) Nadolny, J., Bongiovanni, Á., Cepa, J., et al. 2021, A&A, 647, A89
  * Nedkova et al. (2021) Nedkova, K. V., Häußler, B., Marchesini, D., et al. 2021, MNRAS, 506, 928
  * Newman et al. (2014) Newman, A. B., Ellis, R. S., Andreon, S., et al. 2014, ApJ, 788, 51
  * Newman et al. (2012) Newman, A. B., Ellis, R. S., Bundy, K., & Treu, T. 2012, ApJ, 746, 162
  * Nipoti et al. (2009) Nipoti, C., Treu, T., Auger, M. W., & Bolton, A. S. 2009, ApJ, 706, L86
  * Noordeh et al. (2021) Noordeh, E., Canning, R. E. A., Willis, J. P., et al. 2021, MNRAS, 507, 5272
  * Oke (1974) Oke, J. B. 1974, ApJS, 27, 21
  * Oogi & Habe (2013) Oogi, T. & Habe, A. 2013, MNRAS, 428, 641
  * Oogi et al. (2016) Oogi, T., Habe, A., & Ishiyama, T. 2016, MNRAS, 456, 300
  * Oser et al. (2010) Oser, L., Ostriker, J. P., Naab, T., Johansson, P. H., & Burkert, A. 2010, ApJ, 725, 2312
  * Papovich et al. (2012) Papovich, C., Bassett, R., Lotz, J. M., et al. 2012, ApJ, 750, 93
  * Parker et al. (2005) Parker, Q. A., Phillipps, S., Pierce, M. J., et al. 2005, MNRAS, 362, 689
  * Paulino-Afonso et al. (2019) Paulino-Afonso, A., Sobral, D., Darvish, B., et al. 2019, A&A, 630, A57
  * Peacock (1983) Peacock, J. A. 1983, MNRAS, 202, 615
  * Pearson et al. (2023) Pearson, W. J., Pistis, F., Figueira, M., et al. 2023, A&A, 679, A35
  * Peng et al. (2002) Peng, C. Y., Ho, L. C., Impey, C. D., & Rix, H.-W. 2002, AJ, 124, 266
  * Peng et al. (2010) Peng, Y.-j., Lilly, S. J., Kovač, K., et al. 2010, ApJ, 721, 193
  * Pietrinferni et al. (2004) Pietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2004, ApJ, 612, 168
  * Poggianti et al. (2013) Poggianti, B. M., Calvi, R., Bindoni, D., et al. 2013, ApJ, 762, 77
  * Poggianti et al. (2008) Poggianti, B. M., Desai, V., Finn, R., et al. 2008, ApJ, 684, 888
  * Poglitsch et al. (2010) Poglitsch, A., Waelkens, C., Geis, N., et al. 2010, A&A, 518, L2
  * Pozzetti et al. (2010) Pozzetti, L., Bolzonella, M., Zucca, E., et al. 2010, A&A, 523, A13
  * Prevot et al. (1984) Prevot, M. L., Lequeux, J., Maurice, E., Prevot, L., & Rocca-Volmerange, B. 1984, A&A, 132, 389
  * Ragone-Figueroa & Granato (2011) Ragone-Figueroa, C. & Granato, G. L. 2011, MNRAS, 414, 3690
  * Raichoor et al. (2011) Raichoor, A., Mei, S., Nakata, F., et al. 2011, ApJ, 732, 12
  * Raichoor et al. (2012) Raichoor, A., Mei, S., Stanford, S. A., et al. 2012, ApJ, 745, 130
  * Rettura et al. (2009) Rettura, A., Rosati, P., & Nonino, M. 2009, in American Institute of Physics Conference Series, Vol. 1111, Probing Stellar Populations Out to the Distant Universe: Cefalu 2008, Proceedings of the International Conference, ed. G. Giobbi, A. Tornambe, G. Raimondo, M. Limongi, L. A. Antonelli, N. Menci, & E. Brocato, 183–186
  * Sahu et al. (2019) Sahu, N., Graham, A. W., & Davis, B. L. 2019, ApJ, 876, 155
  * Salim et al. (2018) Salim, S., Boquien, M., & Lee, J. C. 2018, ApJ, 859, 11
  * Saracco et al. (2014) Saracco, P., Casati, A., Gargiulo, A., et al. 2014, A&A, 567, A94
  * Saracco et al. (2017) Saracco, P., Gargiulo, A., Ciocca, F., & Marchesini, D. 2017, A&A, 597, A122
  * Saracco et al. (2009) Saracco, P., Longhetti, M., & Andreon, S. 2009, MNRAS, 392, 718
  * Saracco et al. (2010) Saracco, P., Longhetti, M., & Gargiulo, A. 2010, MNRAS, 408, L21
  * Saracco et al. (2011) Saracco, P., Longhetti, M., & Gargiulo, A. 2011, MNRAS, 412, 2707
  * Savorgnan & Graham (2016) Savorgnan, G. A. D. & Graham, A. W. 2016, ApJS, 222, 10
  * Scodeggio et al. (2018) Scodeggio, M., Guzzo, L., Garilli, B., et al. 2018, A&A, 609, A84
  * Sérsic (1963) Sérsic, J. L. 1963, Boletin de la Asociacion Argentina de Astronomia La Plata Argentina, 6, 41
  * Shankar et al. (2013) Shankar, F., Marulli, F., Bernardi, M., et al. 2013, MNRAS, 428, 109
  * Shen et al. (2003) Shen, S., Mo, H. J., White, S. D. M., et al. 2003, MNRAS, 343, 978
  * Siudek et al. (2023) Siudek, M., Lisiecki, K., Krywult, J., et al. 2023, MNRAS, 523, 4294
  * Siudek et al. (2022) Siudek, M., Małek, K., Pollo, A., et al. 2022, A&A, 666, A131
  * Siudek et al. (2018) Siudek, M., Małek, K., Pollo, A., et al. 2018, A&A, 617, A70
  * Siudek et al. (2017) Siudek, M., Małek, K., Scodeggio, M., et al. 2017, A&A, 597, A107
  * Springel et al. (2005) Springel, V., White, S. D. M., Jenkins, A., et al. 2005, Nature, 435, 629
  * Strazzullo et al. (2013) Strazzullo, V., Gobat, R., Daddi, E., et al. 2013, ApJ, 772, 118
  * Suess et al. (2019) Suess, K. A., Kriek, M., Price, S. H., & Barro, G. 2019, ApJ, 877, 103
  * Sweet et al. (2017) Sweet, S. M., Sharp, R., Glazebrook, K., et al. 2017, MNRAS, 464, 2910
  * Toft et al. (2012) Toft, S., Gallazzi, A., Zirm, A., et al. 2012, ApJ, 754, 3
  * Tran et al. (2008) Tran, K.-V. H., Moustakas, J., Gonzalez, A. H., et al. 2008, ApJ, 683, L17
  * Trujillo et al. (2001) Trujillo, I., Aguerri, J. A. L., Gutiérrez, C. M., & Cepa, J. 2001, AJ, 122, 38
  * Trujillo et al. (2011) Trujillo, I., Ferreras, I., & de La Rosa, I. G. 2011, MNRAS, 415, 3903
  * Trujillo et al. (2006a) Trujillo, I., Feulner, G., Goranova, Y., et al. 2006a, MNRAS, 373, L36
  * Trujillo et al. (2006b) Trujillo, I., Förster Schreiber, N. M., Rudnick, G., et al. 2006b, ApJ, 650, 18
  * van der Wel et al. (2014) van der Wel, A., Franx, M., van Dokkum, P. G., et al. 2014, ApJ, 788, 28
  * van der Wel et al. (2008) van der Wel, A., Holden, B. P., Zirm, A. W., et al. 2008, ApJ, 688, 48
  * van Dokkum (2005) van Dokkum, P. G. 2005, AJ, 130, 2647
  * van Dokkum et al. (2008) van Dokkum, P. G., Franx, M., Kriek, M., et al. 2008, ApJ, 677, L5
  * Wang et al. (2020) Wang, E., Wang, H., Mo, H., van den Bosch, F. C., & Yang, X. 2020, ApJ, 889, 37
  * Ward et al. (2024) Ward, E., de la Vega, A., Mobasher, B., et al. 2024, ApJ, 962, 176
  * Watkins et al. (2022) Watkins, A. E., Salo, H., Laurikainen, E., et al. 2022, A&A, 660, A69
  * Weinmann et al. (2009) Weinmann, S. M., Kauffmann, G., van den Bosch, F. C., et al. 2009, MNRAS, 394, 1213
  * Whitaker et al. (2012) Whitaker, K. E., van Dokkum, P. G., Brammer, G., & Franx, M. 2012, ApJ, 754, L29
  * Williams et al. (2009) Williams, R. J., Quadri, R. F., Franx, M., van Dokkum, P., & Labbé, I. 2009, ApJ, 691, 1879
  * Williams et al. (2010) Williams, R. J., Quadri, R. F., Franx, M., et al. 2010, ApJ, 713, 738
  * Worthey (1994) Worthey, G. 1994, ApJS, 95, 107
  * Wu et al. (2018) Wu, P.-F., van der Wel, A., Gallazzi, A., et al. 2018, ApJ, 855, 85
  * Yang et al. (2021) Yang, L., Roberts-Borsani, G., Treu, T., et al. 2021, MNRAS, 501, 1028
  * Yoon et al. (2017) Yoon, Y., Im, M., & Kim, J.-W. 2017, ApJ, 834, 73
  * York et al. (2000) York, D. G., Adelman, J., Anderson, Jr., J. E., et al. 2000, AJ, 120, 1579
  * Zanella et al. (2016) Zanella, A., Scarlata, C., Corsini, E. M., et al. 2016, ApJ, 824, 68
  * Zanisi et al. (2021) Zanisi, L., Shankar, F., Bernardi, M., Mei, S., & Huertas-Company, M. 2021, MNRAS, 505, L84
  * Zirm et al. (2007) Zirm, A. W., van der Wel, A., Franx, M., et al. 2007, ApJ, 656, 66

##  Appendix A MSR parameters from the literature

Table 3: MSR parameters of ETGs and properties of the sample used in this work and from the literature. (1) reference, (2) slope, (3) intercept, (4) redshift range, (5) photometric/spectroscopic redshift, (6) number of galaxies ($\sim$ indicates that the number of galaxies was estimated/counted from plots and $<$ indicates that only an upper limit could be found), (7) criteria for quiescent galaxies selection, (8) mass range (in log($M_{*}/M_{\odot}$)). The MSR parameters, if estimated by eye, have no uncertainties unless the $\pm 1\sigma$ lines were plotted, in which case the uncertainty on log(A) was also estimated by eye. Reference | $\alpha$ | log(A) | Redshift range |  $z$ type | $N_{\textrm{gal}}$ | Selection | Mass range
---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
This work | $0.62\pm 0.04$ | $0.52\pm 0.01$ | $0.5\leq z\leq 0.9$ | Spec | 4786 |  NUVrK+$D_{n}4000$ |  9.3 $-$ 11.6
| $0.64\pm 0.01$ | $0.59\pm 0.01$ | $0.50\leq z<0.58$ | Spec | 1197 |  NUVrK+$D_{n}4000$ |  10.1 $-$ 11.8
| $0.64\pm 0.04$ | $0.57\pm 0.01$ | $0.58\leq z<0.65$ | Spec | 1196 |  NUVrK+$D_{n}4000$ |  10.3 $-$ 11.8
| $0.73\pm 0.02$ | $0.52\pm 0.01$ | $0.65\leq z<0.74$ | Spec | 1198 |  NUVrK+$D_{n}4000$ |  10.5 $-$ 11.7
| $0.75\pm 0.03$ | $0.47\pm 0.01$ | $0.74\leq z\leq 0.90$ | Spec | 1195 |  NUVrK+$D_{n}4000$ |  10.7 $-$ 11.7
HD-MM | $0.66\pm 0.07$ | $0.54\pm 0.02$ | $0.5\leq z\leq 0.9$ | Spec | 826 |  NUVrK+$D_{n}4000$ |  10.1 $-$ 11.7
| $0.63\pm 0.06$ | $0.61\pm 0.02$ | $0.50\leq z<0.58$ | Spec | 183 |  NUVrK+$D_{n}4000$ |  10.1 $-$ 11.4
| $0.65\pm 0.02$ | $0.58\pm 0.01$ | $0.58\leq z<0.65$ | Spec | 182 |  NUVrK+$D_{n}4000$ |  10.4 $-$ 11.4
| $0.72\pm 0.09$ | $0.52\pm 0.02$ | $0.65\leq z<0.74$ | Spec | 206 |  NUVrK+$D_{n}4000$ |  10.5 $-$ 11.5
| $0.84\pm 0.22$ | $0.50\pm 0.03$ | $0.74\leq z\leq 0.90$ | Spec | 207 |  NUVrK+$D_{n}4000$ |  10.7 $-$ 11.6
LD-MM | $0.62\pm 0.05$ | $0.51\pm 0.01$ | $0.5\leq z\leq 0.9$ | Spec | 826 |  NUVrK+$D_{n}4000$ |  10.1 $-$ 11.7
| $0.62\pm 0.05$ | $0.58\pm 0.02$ | $0.50\leq z<0.58$ | Spec | 183 |  NUVrK+$D_{n}4000$ |  10.1 $-$ 11.4
| $0.78\pm 0.05$ | $0.57\pm 0.02$ | $0.58\leq z<0.65$ | Spec | 182 |  NUVrK+$D_{n}4000$ |  10.4 $-$ 11.4
| $0.76\pm 0.05$ | $0.48\pm 0.02$ | $0.65\leq z<0.74$ | Spec | 206 |  NUVrK+$D_{n}4000$ |  10.5 $-$ 11.5
| $0.81\pm 0.05$ | $0.47\pm 0.02$ | $0.74\leq z<0.90$ | Spec | 207 |  NUVrK+$D_{n}4000$ |  10.7 $-$ 11.5
Allen et al. (2015)111 The slope is fixed and taken from van der Wel et al. (2014). The relations are for cluster and field galaxies, respectively.  | $0.76\pm 0.04$ | $0.41\pm 0.16$ | $2.0\leq z\leq 2.2$ | Phot | 7 | UVJ |  9.8 $-$ 11.5
Allen et al. (2015) | $0.76\pm 0.04$ | $0.34\pm 0.09$ | $2.0\leq z\leq 2.2$ | Phot | 30 | UVJ |  9.5 $-$ 11.2
Barone et al. (2022)222 ETGs defined as galaxies with $\textrm{SFR}<\textrm{SFR}_{MS}-2\sigma_{RMS}$ with the MS from Whitaker et al. (2012). The MSRs are estimated by eye.  | $0.54$ | $0.67\pm 0.02$ | $0.014\leq z\leq 0.1$ | Spec | 524 | MS |  10 $-$ 11.5
Barone et al. (2022) | $0.66$ | $-1.36\pm 0.02$ | $0.6\leq z<0.68$ | Spec | 219 | MS |  10.5 $-$ 11.5
Barone et al. (2022) | $0.78$ | $-3.16\pm 0.05$ | $0.68\leq z\leq 0.76$ | Spec | 273 | MS |  10.5 $-$ 11.5
Belli et al. (2015)333 The MSR is estimated by eye.  | $0.76$ | $0.31$ | $1.0\leq z\leq 1.6$ | Spec | 51 | sSFR |  10.7 $-$ 11.5
Chan et al. (2016)444 MSR for the cluster XMMUJ2235-2557. MSRs using $r_{\textrm{mass}}$ are also available (see their Tab. 2).  | $0.138\pm 0.192$ | $0.40\pm 2.55$ | $z=1.39$ | Spec | 12 | sSFR |  10 $-$ 11.5
Chan et al. (2016) | $0.447\pm 0.268$ | $0.37\pm 7.29$ | $z=1.39$ | Spec | 12 | sSFR |  10.5 $-$ 11.5
Chan et al. (2016) | $0.359\pm 0.135$ | $0.44\pm 2.41$ | $z=1.39$ | Phot/Spec | 36 | sSFR |  10 $-$ 11.5
Chan et al. (2016) | $0.576\pm 0.173$ | $0.40\pm 6.58$ | $z=1.39$ | Phot/Spec | 36 | sSFR |  10.5 $-$ 11.5
Chen et al. (2022)555 Quiescent galaxies are defined such as $\textrm{log(SFR)}<0.64\times\textrm{log(}M_{*}\textrm{)}-7.22$ and further reduced using the $M_{*}-z$ plane to match the number of post-starburst galaxies.The MSR is estimated by eye.  | $0.69$ | $0.66$ | $0.012\leq z\leq 0.324$ | Spec | 4437 | MS/Mz relation |  10 $-$ 12
Cimatti et al. (2012)666 The sample is taken from different works (see their Tab. 1). The intercept is estimated by eye.  | $0.52\pm 0.05$ | $0.69$ | $0.0\leq z<0.6$ | Phot/Spec |  $\sim$360 | Color/Spectra/sSFR/Morph |  10.5 $-$ 11.8
Cimatti et al. (2012) | $0.47\pm 0.04$ | $0.4$ | $0.6\leq z<0.9$ | Phot/Spec |  $\sim$360 | Color/Spectra/sSFR/Morph |  10.5 $-$ 11.8
Cimatti et al. (2012) | $0.50\pm 0.04$ | $0.27$ | $0.9\leq z\leq 3.0$ | Phot/Spec |  $\sim$360 | Color/Spectra/sSFR/Morph |  10.5 $-$ 11.6
Damjanov et al. (2011)777 Work based on different spectroscopic surveys where the quiescent galaxies selection are either spectroscopically selected objects with old stellar population, morphology or color. The intercept is estimated by eye.  | $0.47\pm 0.06$ | $0.42$ | $0.2\leq z<0.8$ | Spec | 212 | Spectro/Morph/Color |  10 $-$ 12
Damjanov et al. (2011) | $0.51\pm 0.06$ | $0.41$ | $0.8\leq z<1.4$ | Spec | 199 | Spectro/Morph/Color |  10 $-$ 12.1
Damjanov et al. (2011) | $0.52\pm 0.12$ | $0.21$ | $1.4\leq z<2.0$ | Spec | 44 | Spectro/Morph/Color |  10 $-$ 11.8
Damjanov et al. (2011) | $0.51\pm 0.36$ | $-0.06$ | $2.0\leq z\leq 2.7$ | Spec | 10 | Spectro/Morph/Color |  10 $-$ 11.2
Damjanov et al. (2019) | $0.79\pm 0.05$ | $0.65\pm 0.02$ | $0.16\leq z<0.26$ | Spec | 492 | $D_{n}4000$ |  10.2 $-$ 11.6
Damjanov et al. (2019) | $0.90\pm 0.04$ | $0.58\pm 0.02$ | $0.26\leq z<0.36$ | Spec | 1527 | $D_{n}4000$ |  10.2 $-$ 12.2
Damjanov et al. (2019) | $0.87\pm 0.03$ | $0.51\pm 0.01$ | $0.36\leq z<0.48$ | Spec | 840 | $D_{n}4000$ |  10.6 $-$ 11.9
Damjanov et al. (2019) | $0.70\pm 0.09$ | $0.49\pm 0.03$ | $0.48\leq z\leq 0.65$ | Spec | 487 | $D_{n}4000$ |  11 $-$ 12.1
Damjanov et al. (2022) | $0.510\pm 0.012$ | $0.76\pm 0.01$ | $0.05\leq z\leq 0.07$ | Spec | 31001 | $D_{n}4000$ |  10 $-$ 11.7
Damjanov et al. (2022) | $0.643\pm 0.024$ | $0.61\pm 0.01$ | $0.1\leq z\leq 0.6$ | Spec | 2906 | $D_{n}4000$ |  9.2 $-$ 12.3
Damjanov et al. (2023)888 In addition, MSRs at fixed $D_{n}4000$ are given (see their Tab. 2) as well as MSRs for newcomers and the aging population (see their Tab. 3).  | $0.67\pm 0.01$ | $0.57\pm 0.01$ | $0.2\leq z\leq 0.5$ | Spec | 23113 | $D_{n}4000$ |  10 $-$ 12
Damjanov et al. (2023) | $0.661\pm 0.009$ | $0.799\pm 0.003$ | $0.2\leq z<0.3$ | Spec | 9205 | $D_{n}4000$ |  10.4 $-$ 11.8
Damjanov et al. (2023) | $0.749\pm 0.011$ | $0.762\pm 0.020$ | $0.3\leq z<0.4$ | Spec | 7710 | $D_{n}4000$ |  10.6 $-$ 11.9
Damjanov et al. (2023) | $0.788\pm 0.014$ | $0.720\pm 0.003$ | $0.4\leq z<0.5$ | Spec | 6198 | $D_{n}4000$ |  10.6 $-$ 11.9
Damjanov et al. (2023) | $0.882\pm 0.029$ | $0.614\pm 0.010$ | $0.5\leq z\leq 0.6$ | Spec | 2949 | $D_{n}4000$ |  10.9 $-$ 12
Delaye et al. (2014)999 MSRs with free slope for cluster and field galaxies, respectively. MSRs with fixed slope ($\alpha=0.57$) and for each cluster are available (see their Tabs. 7 and 8). | $0.52\pm 0.08$ | $0.52\pm 0.03$ | $0.7\leq z<0.9$ | Phot/Spec | 130 | Morph |  10.5 $-$ 11.6
Delaye et al. (2014) | $0.48\pm 0.08$ | $0.48\pm 0.03$ | $0.9\leq z<1.1$ | Phot/Spec | 96 | Morph |  10.5 $-$ 11.6
Delaye et al. (2014) | $0.34\pm 0.10$ | $0.44\pm 0.04$ | $1.1\leq z\leq 1.6$ | Phot/Spec | 94 | Morph |  10.5 $-$ 11.6
Delaye et al. (2014) | $0.47\pm 0.07$ | $0.47\pm 0.02$ | $0.7\leq z<0.9$ | Phot/Spec | 123 | Morph |  10.5 $-$ 11.6
Delaye et al. (2014) | $0.57\pm 0.07$ | $0.47\pm 0.02$ | $0.9\leq z<1.1$ | Phot/Spec | 135 | Morph |  10.5 $-$ 11.6
Delaye et al. (2014) | $0.5\pm 0.1$ | $0.30\pm 0.02$ | $1.1\leq z\leq 1.6$ | Phot/Spec | 125 | Morph |  10.5 $-$ 11.6
Díaz-García et al. (2019b)101010 MCDE: Rest-frame stellar mass color diagram corrected for extinction (see Díaz-García et al. 2019a). MSRs for galaxies whose properties were derived using the BC03 simple stellar populations models. MSRs using EMILES (Girardi et al. 2000 Padova00 and Pietrinferni et al. 2004 BaSTI) are available (see their Tab. 3).  | $0.71\pm 0.02$ | $0.73\pm 0.04$ | $0.1\leq z<0.3$ | Phot |  $\sim$50 | MCDE |  10.5 $-$ 11.6
Díaz-García et al. (2019b) | $0.71\pm 0.02$ | $0.65\pm 0.04$ | $0.3\leq z<0.5$ | Phot |  $\sim$150 | MCDE |  10.5 $-$ 11.5
Díaz-García et al. (2019b) | $0.71\pm 0.02$ | $0.57\pm 0.05$ | $0.5\leq z<0.7$ | Phot |  $\sim$180 | MCDE |  10.5 $-$ 11.5
Díaz-García et al. (2019b) | $0.71\pm 0.02$ | $0.49\pm 0.05$ | $0.7\leq z\leq 0.9$ | Phot | 263 | MCDE |  10.5 $-$ 11.6
Faisst et al. (2017)111111 The low-mass sample contains 9000 star-forming and quiescent galaxies, and the high-mass samples contains 403 star-forming and quiescent galaxies. The intercept is estimated by eye.  | $0.55\pm 0.05$ | $0.5$ | $0.5\leq z<1.0$ | Phot |  $\sim$800 | NUVrJ |  10 $-$ 12
Faisst et al. (2017) | $0.62\pm 0.09$ | $0.3$ | $1.0\leq z<1.5$ | Phot |  $\sim$800 | NUVrJ |  10 $-$ 11.8
Faisst et al. (2017) | $0.59\pm 0.15$ | $0.18$ | $1.5\leq z\leq 2.0$ | Phot |  $\sim$750 | NUVrJ |  10 $-$ 11.9
Favole et al. (2018)121212 The number of red galaxies per redshift range is not indicated.  | $0.238\pm 0.044$ | $0.67\pm 0.18$ | $0.2\leq z<0.3$ | Spec | ¡75441 | De Veaucouleurs profile |  11.1 $-$ 12
Favole et al. (2018) | $0.219\pm 0.022$ | $0.70\pm 0.11$ | $0.3\leq z<0.43$ | Spec | ¡75441 | De Veaucouleurs profile |  11.1 $-$ 12
Favole et al. (2018) | $0.202\pm 0.021$ | $0.73\pm 0.12$ | $0.43\leq z<0.55$ | Spec | ¡153304 | De Veaucouleurs profile |  11 $-$ 12.1
Favole et al. (2018) | $0.172\pm 0.015$ | $0.75\pm 0.12$ | $0.55\leq z\leq 0.6$ | Spec | ¡153304 | De Veaucouleurs profile |  11.1 $-$ 12.2
Fernández Lorenzo et al. (2013)131313 The Shen et al. (2003) slope is used for the two first MSRs, where the Sersic’s size and Sextractor’s size are used for the two other MSRs. For the last MSR, there are 824 ETGs (Sersic index) but no number are given for the morphological separation.  | $0.56$ | $0.62$ | $0.01\leq z\leq 0.05$ | Spec | 15 |  Morph/$n$ |  9.9 $-$ 11.4
Fernández Lorenzo et al. (2013) | $0.56$ | $0.58$ | $0.01\leq z\leq 0.05$ | Spec | 67 | Morph |  9.4 $-$ 11.4
Fernández Lorenzo et al. (2013) | $0.54$ | $0.54\pm 0.01$ | $0.01\leq z\leq 0.05$ | Spec | 23 |  Morph/$n$ |  10.1 $-$ 11.3
Fernández Lorenzo et al. (2013) | $0.60$ | $0.66\pm 0.01$ | $0.01\leq z\leq 0.05$ | Spec |  $\sim$500 |  Morph/$n$ |  9.3 $-$ 11.6
Gargiulo et al. (2017) | $0.59\pm 0.07$ | $0.60\pm 0.01$ | $0.5\leq z<0.7$ | Spec | 782 | NUVrK |  11 $-$ 11.5
Gargiulo et al. (2017) | $0.70\pm 0.08$ | $0.53\pm 0.02$ | $0.7\leq z<0.9$ | Spec | 868 | NUVrK |  11 $-$ 11.5
Gargiulo et al. (2017) | $0.52\pm 0.10$ | $0.53\pm 0.02$ | $0.9\leq z\leq 1.0$ | Spec | 372 | NUVrK |  11 $-$ 11.5
Guo et al. (2009)141414 CEN: Central galaxies. The second MSR excludes the bright galaxies ($M_{r}-5\textrm{log(}h\textrm{)}<-22$). The intercept is estimated by eye.  | $0.91\pm 0.03$ | $0.08$ | $0.0\leq z\leq 0.08$ | Spec | 911 |  CEN/$n$ |  9.9 $-$ 11.7
Guo et al. (2009) | $0.70\pm 0.05$ | $0.63$ | $0.0\leq z\leq 0.08$ | Spec |  $\sim$450 |  CEN/$n$ |  9.9 $-$ 11.7
Hamadouche et al. (2022) | $0.56\pm 0.04$ | $0.47\pm 0.02$ | $0.6\leq z\leq 0.8$ | Spec | 377 | UVJ |  10.3 $-$ 11.5
Hamadouche et al. (2022) | $0.72\pm 0.06$ | $0.28\pm 0.03$ | $1.0\leq z\leq 1.3$ | Spec | 137 | UVJ |  10.3 $-$ 11.6
Hon et al. (2023)151515 MSR for bulge/spheroid (including LTGs) from different datasets (Savorgnan & Graham 2016; Davis et al. 2019; Sahu et al. 2019; Hon et al. 2022).  | $0.88$ | $0.53$ |  $D\leq 110$ Mpc |  | 202 | Bulge/Spheroid |  9.5 $-$ 12
Huertas-Company et al. (2013b)161616 The first three MSRs are for field galaxies and the three last for group galaxies. More MSRs with different ETGs selections are available (see their Tab. 1).  | $0.59\pm 0.09$ | $0.59\pm 0.10$ | $0.2\leq z<0.5$ | Phot/Spec | 59 | NUVr |  10.5 $-$ 11.4
Huertas-Company et al. (2013b) | $0.50\pm 0.11$ | $0.34\pm 0.08$ | $0.5\leq z<0.8$ | Phot/Spec | 123 | NUVr |  10.5 $-$ 11.7
Huertas-Company et al. (2013b) | $0.59\pm 0.05$ | $0.28\pm 0.02$ | $0.8\leq z\leq 1.0$ | Phot/Spec | 210 | NUVr |  10.5 $-$ 11.8
Huertas-Company et al. (2013b) | $0.52\pm 0.03$ | $0.47\pm 0.03$ | $0.2\leq z<0.5$ | Phot/Spec | 128 | NUVr |  10.5 $-$ 11.9
Huertas-Company et al. (2013b) | $0.56\pm 0.04$ | $0.41\pm 0.03$ | $0.5\leq z<0.8$ | Phot/Spec | 110 | NUVr |  10.5 $-$ 11.7
Huertas-Company et al. (2013b) | $0.49\pm 0.04$ | $0.41\pm 0.03$ | $0.8\leq z\leq 1.0$ | Phot/Spec | 155 | NUVr |  10.5 $-$ 11.9
Ichikawa et al. (2012)171717 MSRs for resolved and resolved+unresvolved galaxies. MSRs using $R_{90}$ are also available (see their Tab. 1).  | $0.126\pm 0.009$ | $0.54\pm 0.01$ | $0.25\leq z\leq 3.0$ | Phot/Spec | 408 | UVJ |  8 $-$ 11.5
Ichikawa et al. (2012) | $0.129\pm 0.02$ | $0.54\pm 0.03$ | $0.25\leq z\leq 0.5$ | Phot/Spec | 28 | UVJ |  8 $-$ 11.5
Ichikawa et al. (2012) | $0.133\pm 0.018$ | $0.55\pm 0.02$ | $0.5\leq z\leq 0.75$ | Phot/Spec | 70 | UVJ |  8.2 $-$ 11.5
Ichikawa et al. (2012) | $0.118\pm 0.017$ | $0.56\pm 0.01$ | $0.75\leq z\leq 1.0$ | Phot/Spec | 134 | UVJ |  9 $-$ 11.5
Ichikawa et al. (2012) | $0.153\pm 0.024$ | $0.55\pm 0.01$ | $1.0\leq z\leq 1.25$ | Phot/Spec | 83 | UVJ |  9.5 $-$ 11.5
Ichikawa et al. (2012) | $0.125\pm 0.037$ | $0.57\pm 0.02$ | $1.25\leq z\leq 1.5$ | Phot/Spec | 32 | UVJ |  9.5 $-$ 11.5
Ichikawa et al. (2012) | $0.166\pm 0.074$ | $0.52\pm 0.03$ | $1.5\leq z\leq 2.0$ | Phot/Spec | 28 | UVJ |  10.3 $-$ 11.5
Ichikawa et al. (2012) | $0.250\pm 0.083$ | $0.48\pm 0.02$ | $2.0\leq z\leq 2.5$ | Phot/Spec | 27 | UVJ |  10.3 $-$ 11.5
Ichikawa et al. (2012) | $0.48\pm 0.07$ | $0.48\pm 0.02$ | $2.5\leq z\leq 3.0$ | Phot/Spec | 6 | UVJ |  10.5 $-$ 11.2
Ichikawa et al. (2012) | $0.132\pm 0.008$ | $0.54\pm 0.01$ | $0.25\leq z\leq 3.0$ | Phot/Spec | 445 | UVJ |  8 $-$ 11.5
Ichikawa et al. (2012) | $0.165\pm 0.023$ | $0.55\pm 0.03$ | $0.25\leq z\leq 0.50$ | Phot/Spec | 31 | UVJ |  8 $-$ 11.5
Ichikawa et al. (2012) | $0.137\pm 0.017$ | $0.55\pm 0.02$ | $0.50\leq z\leq 0.75$ | Phot/Spec | 73 | UVJ |  8.2 $-$ 11.5
Ichikawa et al. (2012) | $0.119\pm 0.015$ | $0.56\pm 0.01$ | $0.75\leq z\leq 1.0$ | Phot/Spec | 141 | UVJ |  9 $-$ 11.5
Ichikawa et al. (2012) | $0.150\pm 0.022$ | $0.55\pm 0.01$ | $1.0\leq z\leq 1.25$ | Phot/Spec | 88 | UVJ |  9.5 $-$ 11.5
Ichikawa et al. (2012) | $0.152\pm 0.045$ | $0.56\pm 0.02$ | $1.25\leq z\leq 1.5$ | Phot/Spec | 35 | UVJ |  9.5 $-$ 11.5
Ichikawa et al. (2012) | $0.077\pm 0.069$ | $0.48\pm 0.02$ | $1.5\leq z\leq 2.0$ | Phot/Spec | 36 | UVJ |  10.3 $-$ 11.5
Ichikawa et al. (2012) | $0.281\pm 0.068$ | $0.48\pm 0.02$ | $2.0\leq z\leq 2.5$ | Phot/Spec | 32 | UVJ |  10.3 $-$ 11.5
Ichikawa et al. (2012) | $0.251\pm 0.133$ | $0.43\pm 0.04$ | $2.5\leq z\leq 3.0$ | Phot/Spec | 9 | UVJ |  10.3 $-$ 11.2
Kawinwanichakij et al. (2021) | $0.34\pm 0.01$ | $0.55$ | $0.2\leq z<0.4$ | Phot | 40259 | urz |  8.5 $-$ 11.8
Kawinwanichakij et al. (2021) | $0.36\pm 0.01$ | $0.53$ | $0.4\leq z<0.6$ | Phot | 82714 | urz |  8.5 $-$ 12
Kawinwanichakij et al. (2021) | $0.41\pm 0.01$ | $0.47$ | $0.6\leq z<0.8$ | Phot | 61486 | urz |  8.5 $-$ 12
Kawinwanichakij et al. (2021) | $0.44\pm 0.01$ | $0.42$ | $0.8\leq z\leq 1.0$ | Phot | 57059 | urz |  8.8 $-$ 12.1
Krogager et al. (2014) | $0.82\pm 0.22$ | $0.30\pm 0.08$ | $1.85\leq z\leq 2.3$ | Phot/Spec | 34 | UVJ |  10.6 $-$ 11.7
Krogager et al. (2014) | $0.53\pm 0.29$ | $0.29\pm 0.07$ | $1.85\leq z\leq 2.3$ | Spec | 14 | UVJ |  10.8 $-$ 11.7
Kuchner et al. (2017)181818 MSR for the cluster MACS J1206.2-0847. The parameters are estimated by eye. There are 543 star-forming and quiescent galaxies in the sample.  | $0.43$ | $0.55$ | $z=0.44$ | Spec |  $\sim$293 | BRI |  9.2 $-$ 11.3
Lani et al. (2013) | $0.31$ | $0.45$ | $0.5\leq z<1.0$ | Phot |  $\sim$2900 | UVJ/sSFR |  9.8 $-$ 12.2
Lani et al. (2013) | $0.44$ | $0.3$ | $1.0\leq z\leq 2.0$ | Phot |  $\sim$2200 | UVJ/sSFR |  10.4 $-$ 11.9
Lange et al. (2015)191919 There are 2010 elliptical galaxies but the sample is cut at $2\times 10^{10}$ $M_{\odot}$ and we take the $g$-band as it is closer to the $i$-band at $z\sim 0.7$ (see their Appendix B). MSRs for ETGs based on different ETGs selection are shown in their Tab. 3.  | $0.63\pm 0.03$ | $0.580\pm 0.003$ | $0.01\leq z\leq 0.1$ | Spec | 1300 | Morph |  10.3 $-$ 11.3
Lange et al. (2016)202020 The different MSRs correspond to different range of stellar mass (see their Tab. 1 and their conclusions).  | $0.329\pm 0.010$ | $0.51\pm 0.01$ | $0.002\leq z\leq 0.06$ | Spec | 806 | Morph |  8 $-$ 11.2
Lange et al. (2016) | $0.643\pm 0.032$ | $0.64\pm 0.09$ | $0.002\leq z\leq 0.06$ | Spec |  $\sim$400 | Morph |  10 $-$ 11.2
Lange et al. (2016) | $0.786\pm 0.048$ | $0.64\pm 56.99$ | $0.002\leq z\leq 0.06$ | Spec |  $\sim$400 | Morph |  10.3 $-$ 11.2
Maltby et al. (2010)212121 The MSR parameters are estimated based on their Table. 3. The relations are for cluster and field galaxies, respectively. The MSR for core ellipticals agrees with cluster elliptical within uncertainties and is not shown here.  | $0.26\pm 0.07$ | $0.47\pm 0.06$ | $0.122\leq z\leq 0.205$ | Phot | 167 | Hubble type |  9 $-$ 11.5
Maltby et al. (2010) | $0.30\pm 0.04$ | $0.55\pm 0.04$ | $0.05\leq z\leq 0.3$ | Phot | 89 | Hubble type |  9 $-$ 11.5
McLure et al. (2013)222222 The formation time is derived using SED fitting.  | $0.56$ | $0.23$ | $1.3\leq z\leq 1.5$ | Spec | 41 | sSFR |  10.8 $-$ 11.7
McLure et al. (2013) | $0.56$ | $0.24$ | $1.3\leq z\leq 1.5$ | Spec | 37 | $n$ |  10.8 $-$ 11.7