# Post-starburst galaxies in the centers of intermediate redshift clusters

Ariel Werle INAF- Osservatorio Astronomico di Padova, Vicolo Osservatorio 5,
35122 Padova, Italy  Bianca Poggianti INAF- Osservatorio Astronomico di
Padova, Vicolo Osservatorio 5, 35122 Padova, Italy  Alessia Moretti INAF-
Osservatorio Astronomico di Padova, Vicolo Osservatorio 5, 35122 Padova, Italy
Callum Bellhouse INAF- Osservatorio Astronomico di Padova, Vicolo Osservatorio
5, 35122 Padova, Italy  Benedetta Vulcani INAF- Osservatorio Astronomico di
Padova, Vicolo Osservatorio 5, 35122 Padova, Italy  Marco Gullieuszik INAF-
Osservatorio Astronomico di Padova, Vicolo Osservatorio 5, 35122 Padova, Italy
Mario Radovich INAF- Osservatorio Astronomico di Padova, Vicolo Osservatorio
5, 35122 Padova, Italy  Jacopo Fritz Instituto de Radioastronomía y
Astrofísica, Universidad Nacional Autónoma de México, Morelia, Michoacán,
58089 México
Alessandro Ignesti INAF- Osservatorio Astronomico di Padova, Vicolo
Osservatorio 5, 35122 Padova, Italy  Johan Richard Univ Lyon, ENS de Lyon,
CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, 69230 Saint-Genis-
Laval,France
Geneviève Soucail Institut de Recherche en Astrophysique et Planétologie
(IRAP), Université de Toulouse, CNRS, UPS, CNES,14 Av. Edouard Belin, 31400
Toulouse, France
Gustavo Bruzual Instituto de Radioastronomía y Astrofísica, Universidad
Nacional Autónoma de México, Morelia, Michoacán, 58089 México
Stephane Charlot Sorbonne Universités, UPMC-CNRS, UMR7095, Institut
d’Astrophysique de Paris, F-75014, Paris, France
Matilde Mingozzi Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA  Cecilia Bacchini INAF- Osservatorio Astronomico di
Padova, Vicolo Osservatorio 5, 35122 Padova, Italy  Neven Tomicic INAF-
Osservatorio Astronomico di Padova, Vicolo Osservatorio 5, 35122 Padova, Italy
Rory Smith Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-
ro, Yuseong-gu, Daejeon 34055, Republic of Korea  Andrea Kulier INAF-
Osservatorio Astronomico di Padova, Vicolo Osservatorio 5, 35122 Padova, Italy
Giorgia Peluso INAF- Osservatorio Astronomico di Padova, Vicolo Osservatorio
5, 35122 Padova, Italy  Dipartimento di Fisica e Astronomia “G. Galilei”,
Università di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy  Andrea
Franchetto INAF- Osservatorio Astronomico di Padova, Vicolo Osservatorio 5,
35122 Padova, Italy  Dipartimento di Fisica e Astronomia “G. Galilei”,
Università di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy

###### Abstract

We present results from MUSE spatially-resolved spectroscopy of 21 post-
starburst galaxies in the centers of 8 clusters from $z\sim 0.3$ to $z\sim
0.4$. We measure spatially resolved star-formation histories (SFHs), the time
since quenching ($t_{Q}$) and the fraction of stellar mass assembled in the
past 1.5 Gyr ($\mu_{1.5}$). The SFHs display a clear enhancement of star-
formation prior to quenching for 16 out of 21 objects, with at least 10% (and
up to $>50$%) of the stellar mass being assembled in the past 1.5 Gyr and
$t_{Q}$ ranging from less than 100 Myrs to $\sim 800$ Myrs. By mapping $t_{Q}$
and $\mu_{1.5}$, we analyze the quenching patterns of the galaxies. Most
galaxies in our sample have quenched their star-formation from the outside-in
or show a side-to-side/irregular pattern, both consistent with quenching by
ram-pressure stripping. Only three objects show an inside-out quenching
pattern, all of which are at the high-mass end of our sample. At least two of
them currently host an active galactic nucleus. In two post-starbursts, we
identify tails of ionized gas indicating that these objects had their gas
stripped by ram pressure very recently. Post-starburst features are also found
in the stripped regions of galaxies undergoing ram-pressure stripping in the
same clusters, confirming the link between these classes of objects. Our
results point to ram-pressure stripping as the main driver of fast quenching
in these environments, with active galactic nuclei playing a role at high
stellar masses.

galaxies: clusters: general — galaxies: general — galaxies: evolution

##  1 Introduction

Post-starburst (also known as k+a or E+A) galaxies are a population of
galaxies undergoing a rapid transition from star-forming to quiescent. These
objects were first identified as a distinct population in clusters at
intermediate redshift (Dressler & Gunn, 1983; Couch & Sharples, 1987) but have
since been recognized in a variety of environments and redshifts (e.g
Poggianti et al., 2004). Post-starbursts are usually identified by their
strong Balmer absorption lines and lack of emission lines associated with
star-formation (e.g Poggianti et al., 1999; Dressler et al., 1999; Goto,
2007), although recently other selection methods have been developed (e.g Wild
et al. 2007, 2014; Belli et al. 2019; see French 2021 for a description of
various selection criteria). These characteristic spectral features indicate
significant levels of star-formation in the recent past ($\sim 1-1.5$ Gyr) but
no ongoing star-formation, indicating fast quenching sometime in the recent
past.

There is strong evidence that post-starbursts were more common at higher
redshift in all environments. In fact D’Eugenio et al. (2020) has recently
shown that the stacked spectra of 9 massive quiescent field galaxies at $z\sim
3$ has clear post-starburst features. Wild et al. (2009) finds that the number
density of post-starbursts decreases by a factor of 200 from $z\sim 0.7$ to
$z\sim 0.07$ and that they account for $38^{+4}_{-11}\%$ of the growth of the
red sequence at $0.5<z<1.0$. Post-starbursts represent less then $1\%$ of the
field galaxy population at $z\sim 0.5$ and more then $5\%$ at $z\sim 2$ (Wild
et al., 2016). Using a different approach, Belli et al. (2019) found that
$34\%$ of quiescent galaxies are post-starbursts at $z\sim 2.5$, while at
$z\sim 1$ they are only $4\%$. Fritz et al. (2014) found that the fraction of
bright post-starbursts in cluster decreases from 18% at redshifts
$0.37<z<0.56$ to 4.6% at $0.04<z<0.07$. The mass function of post-starburst
galaxies also evolves with redshift in all environments, shifting towards
lower masses at lower redshift according to a downsizing trend (Poggianti et
al., 2004; Wild et al., 2016).

Post-starburst galaxies are also known to favor denser environments, being
more common in clusters (Poggianti et al., 2009; Dressler et al., 2013;
Paccagnella et al., 2017, 2019; Wilkinson et al., 2021). The main process
responsible for fast quenching in these environments seems to be ram-pressure
stripping. For example, Poggianti et al. (2009) finds a correlation between
the fraction of post-starbursts and the cluster velocity dispersion. This
correlation establishes a link between the rapid quenching of star-formation
and the properties of the intra-cluster medium (ICM), as ram pressure
stripping becomes more efficient in more massive clusters. A perhaps more
direct evidence of this connection is found by Poggianti et al. (2004), where
the authors identify a spatial correlation between post-starbursts and
substructures of the hot ICM detected using X-Ray data from XMM-Newton. When
studying cluster galaxies in the GASP (GAs Stripping Phenomena in galaxies
Poggianti et al., 2017) survey, Vulcani et al. (2020) finds that the star-
formation histories and location within the cluster of rapidly quenched
galaxies is consistent with quenching by ram-pressure stripping. Furthermore,
Gullieuszik et al. (2017) and Poggianti et al. (2019) showed that regions of
jellyfish galaxies (i.e galaxies with long tails of gas stripped by ram-
pressure) that were already stripped of gas have spectral features typical of
post-starburst galaxies, further suggesting that galaxies undergoing ram
pressure stripping could be the progenitors of post-starbursts.

In the field and group environments, post-starbursts are usually associated
with other processes, most commonly galaxy interactions and mergers.
Simulations show that gas-rich major mergers can lead to centrally
concentrated starbursts, followed by a post-starburst phase and significant
morphological transformation (Wild et al., 2009; Bekki et al., 2005; Snyder et
al., 2011; Pawlik et al., 2019; Zheng et al., 2020). These features are
consistent with several observational studies of field/group post-starbursts
(Blake et al., 2004; Pawlik et al., 2018; Chen et al., 2019; D’Eugenio et al.,
2020). Using spatially resolved spectroscopy from the MaNGA (Mapping Nearby
Galaxies at Apache Point Observatory Bundy et al., 2015) survey, Rowlands et
al. (2018) found that more asymmetric galaxies have a larger fraction of post-
starburst spaxels, which also favors the merger hypothesis. Most post-
starbursts in the field have a spheroidal morphology expected of merger
remnants (Blake et al., 2004; Pawlik et al., 2018), while cluster post-
starbursts have more prominent disks that indicates quenching through a
process that does not significantly disturbs the structure of the stellar
disk, such as ram-pressure stripping (Dressler et al., 1999; Tran et al.,
2003).

Post-starbursts are also known to be connected with feedback from active
galactic nuclei (AGN, Yan et al., 2006; Sanmartim et al., 2013; Pawlik et al.,
2018). However, it is unclear if AGN are efficient enough to be the main
driver of quenching (e.g Kaviraj et al., 2007; Baron et al., 2018) or only
prevent any residual star-formation from taking place after a main quenching
event is triggered by a different process (e.g Yesuf et al., 2014).

In the local universe, “rejuvenation events” in early-type galaxies (Werle et
al., 2020; de Sá-Freitas et al., 2021) triggered by minor mergers can also
lead to a post-starburst phase (Pawlik et al., 2018; Dressler et al., 2013).
In particular, Pawlik et al. (2018) finds that this process is the origin of
$\sim 40$% of massive post-starbursts at $z<0.05$. However, Chauke et al.
(2019) finds rejuvenated galaxies at $z\sim 0.8$ to have weaker Balmer lines
than typical post-starbursts.

Other processes can also lead to the quenching of star-formation, but act on
longer timescales that are inconsistent with the spectral features of post-
starbursts. The heating or removal of gas in the circumgalactic medium (CGM,
see Tumlinson et al., 2017) via ram-pressure or tidal interactions can prevent
the accretion of new gas onto galaxy disks, a processes referred to as
“starvation” (Larson et al., 1980). This leads to the cessation of star-
formation once the remaining gas in the disk is consumed. Since the gas-
depletion times in normal star-forming galaxies are longer than 1 Gyr
(Saintonge et al., 2011; de los Reyes & Kennicutt, 2019), this effect would
lead to a very slow quenching process that cannot produce a post-starburst
spectra. We note, however, that the gas-depletion times for starburst galaxies
are shorter than 1 Gyr (see Kennicutt & De Los Reyes, 2021), indicating that
the starvation of a starburst galaxy could in principle lead to a post-
starburst. The cumulative effect of weak tidal interactions (“harassement”,
Moore et al., 1996) also acts on long time scales and cannot lead to a post-
starburst phase.

The extent to which each of these processes contributes to the quenching of
star-formation in galaxies residing in different environments remains as an
open topic. In this work, we take advantage of MUSE (Multi Unit Spectroscopic
Explorer) data collected by the GTO program to study a sample of post-
starburst galaxies using rest-frame optical spatially resolved spectroscopy of
the central regions of intermediate redshift clusters ($0.308<z<0.451$). This
allows us to study how fast-quenching happens in different regions of galaxies
in dense environments, as has been previously done for field and group
galaxies (e.g Rowlands et al., 2018; Chen et al., 2019; D’Eugenio et al.,
2020).

The paper is organized as follows: Section 2 describes the data-set and the
sample selection. Our spectral synthesis method is described in section 3 and
results from the synthesis are presented in 4. In section 5 we present some
special cases of post-starbursts with distinct features in their emission line
maps. Further clues on ram-pressure stripping are presented in 6 and
conclusions are laid out in 7.

We assume a standard $\Lambda$CDM cosmology with $\Omega_{\rm M}=0.3$,
$\Omega_{\Lambda}=0.7$ and $h=0.7$. We adopt the solar metallicity value of
$Z_{\odot}=0.017$ and a Chabrier (2003) initial mass function. The chosen
epoch for right ascension and declination (RA and Dec) is J2000.

##  2 Data and Sample

###  2.1 The data set

This work is based on MUSE data cubes from the MUSE Lensing Cluster GTO
program, which provides deep observations of the central regions of clusters.
These fields were originally targeted due to the abundance of gravitationally
lensed background sources. The pixel size in the redshift range of our work is
of $\sim 1$ kpc, while the seeing is of of $1^{\prime\prime}$ ($\sim 4-5$
kpc). The cluster sample is extracted from a multitude of surveys, including
the MAssive Clusters Survey (MACS, Ebeling et al., 2001), the Frontier Fields
program (FFs, Lotz et al., 2017), the Grism Lens-Amplified Survey from Space
(GLASS, Treu et al., 2015) and the Cluster Lensing And Supernova survey with
Hubble (CLASH, Postman et al., 2012). The complete data set is extensively
described by Richard et al. (2021).

Here we use data from the clusters Abell 2744, Abell 370, MACS J1206.2-0847,
MACS J0257.6-2209, RX J1347.5-1145, SMACS J2031.8-4036, SMACS J2131.1-4019 and
Abell S1063. Basic information about these clusters is given in table 1, where
we include the central redshift, position, and the velocity dispersion of
galaxies in the cluster ($\sigma$). Redshifts, positions and $\sigma$ were
extracted from Richard et al. (2021), except for AS1063 for which these data
come from Sartoris et al. (2020) (position and redshift) and Gómez et al.
(2012) ($\sigma$). The cluster sample is quite massive as it was selected to
study gravitational lensing. This characteristic also makes the sample ideal
for finding post-starburst galaxies, as the frequency of post-starburst
galaxies is known to increase with cluster mass (Poggianti et al., 2009;
Dressler et al., 2013; Paccagnella et al., 2019).

Table 1: Basic information about the clusters studied in this work. Cluster | Redshift | RA | Dec | $\sigma\mathrm{[km/s]}$
---|---|---|---|---
Abell 2744 | 0.308 | 00:14:20.702 | -30:24:00.63 | 1357
Abell 370 | 0.375 | 02:39:53.122 | -01:34:56.14 | 1789
MACS J1206.2-0847 | 0.438 | 12:06:12.149 | -08:48:03.37 | 1842
MACS J0257.6-2209 | 0.322 | 02:57:41.070 | -22:09:17.70 | 1633
RX J1347.5-1145 | 0.451 | 13:47:30.617 | -11:45:09.51 | 1097
SMACS J2031.8-4036 | 0.331 | 20:31:53.256 | -40:37:30.79 | 1531
SMACS J2131.1-4019 | 0.442 | 21:31:04.831 | -40:19:20.92 | 1378
Abell S1063 | 0.3458 | 22:48:43.99 | -44:31:50.98 | 1660

For the clusters MACS J0257.6-2209, RX J1347.5-1145 and SMACS J2131.1-4019,
observations were carried out using the MUSE adaptive optics system. In these
cases the region around $\sim 5900$Å in the observed-frame cannot be used for
science due to the NaD notch filter (Stuik et al., 2006).

In addition to the MUSE cubes, we also use images from the Hubble Space
Telescope (HST) in the F814W filter, but these are shown only for illustrative
purposes in sections 2.2 and 5.1. These data are taken from the HST archive,
for MACS fields, the images are re-reduced as presented in Richard et al.
(2021).

###  2.2 Post-starburst galaxy sample

As described by Moretti et al. (2021), each datacube was visually inspected to
find post-starbursts, as well as the stripped galaxies presented in that
paper. Post-starburst galaxies are identified as those generally lacking
emission lines but still presenting strong Balmer absorption features anywhere
in the stellar disk. After visual inspection, the rest-frame $H\delta$ and
$H\beta$ equivalent widths ($H\delta_{A}$ and $H\beta_{A}$, respectively) were
quantified to confirm the galaxies as post-starburst. We calculate
$H\delta_{A}$ and $H\beta_{A}$ using the rest frame spectral regions of
4076-4088Å and 4806-4826Å for the blue continuum, 4091-4112Å and 4826-4896Å
for the lines, and 4117-4136Å and 4896-4918Å for the red continuum.

In Table 2 we list some basic information about the 21 post-starbursts in our
sample, namely the IDs, cluster names, redshifts, coordinates, $H\delta_{A}$
and $H\beta_{A}$ of the integrated spectra and stellar masses determined using
our spectral synthesis procedure (see section 3). The IDs represent an
abbreviation of the cluster name followed by an integer, for Abell S1063 we
also include the acronyms NE (north east) and SW (south west) to indicate two
different MUSE pointings.

Table 2: Basic information about our sample of post-starburst galaxies. Equivalent widths marked with * were obtained from synthetic spectra. ID | Cluster | Redshift | RA | Dec | $H\delta_{A}\,\mathrm{[\AA]}$ | $H\beta_{A}\,\mathrm{[\AA]}$ | $\log\,M_{\star}/M_{\odot}$
---|---|---|---|---|---|---|---
A2744-01 | Abell 2744 | 0.291 | 00:14:19.754 | -30:23:57.83 | 6.8 | 8.9 | 8.9
A2744-02 | Abell 2744 | 0.320 | 00:14:20.175 | -30:23:56.77 | 4.0 | 8.5 | 9.9
A2744-05 | Abell 2744 | 0.307 | 00:14:18.806 | -30:23:13.48 | 6.2 | 9.7 | 9.5
A2744-07 | Abell 2744 | 0.299 | 00:14:20.474 | -30:23:15.10 | 4.2 | 8.5 | 10.2
A2744-08 | Abell 2744 | 0.305 | 00:14:18.975 | -30:24:00.287 | 4.8 | 8.0 | 9.3
A370-04 | Abell 370 | 0.361 | 02:39:51.370 | -1.33.59.091 | 7.5* | 10.4 | 9.5
A370-05 | Abell 370 | 0.390 | 02:39:53.544 | -01:34:31:751 | 5.3 | 10.1 | 10.0
MACS1206-06 | MACS J1206.2-0847 | 0.422 | 12:06:13.17 | -08:47:45.05 | 5.6 | 9.5 | 10.7
MACS1206-09 | MACS J1206.2-0847 | 0.427 | 12:06:11.36 | -08:48:22.0 | 4.9 | 11.1 | 10.4
MACS1206-11 | MACS J1206.2-0847 | 0.427 | 12:06:14.856 | -08:48:15.6 | 5.2 | 9.2 | 10.5
MACS0257-01 | MACS J0257.6-2209 | 0.335 | 02:57:42.581 | -22:09:20.61 | 6.6 | 10.4 | 9.2
MACS0257-03 | MACS J0257.6-2209 | 0.325 | 02:57:40.15 | -22:08:54.4 | 6.3 | 8.7 | 9.5
MACS0257-04 | MACS J0257.6-2209 | 0.323 | 02:57:40.7 | -22:09:21.6 | 5.4 | 7.3 | 9.6
MACS0257-05 | MACS J0257.6-2209 | 0.332 | 02:57:39.9 | -22:09:14.2 | 4.2* | 7.8 | 9.9
RXJ1347-02 | RX J1347.5-1145 | 0.431 | 13:47:31.36 | -11:45:50.7 | 8.5* | 11.1 | 9.9
SMACS2031-02 | SMACS J2031.8-4036 | 0.329 | 20:31:51.1 | -40:37:21.6 | 5.0 | 8.5 | 10.1
SMACS2131-05 | SMACS J2131.1-4019 | 0.459 | 21:31:03.0 | -40:19:06.2 | 4.9* | 8.0 | 9.9
SMACS2131-06 | SMACS J2131.1-4019 | 0.445 | 21:31:03.0 | -40:19:00.8 | 4.7* | 8.5 | 9.5
AS1063NE-01 | Abell S1063 | 0.332 | 22:48:44.22 | -44:31:41.0 | 5.1 | 7.6 | 10.7
AS1063NE-02 | Abell S1063 | 0.339 | 22:48:43.11 | -44:31:22.98 | 7.4 | 10.3 | 9.8
AS1063SW-01 | Abell S1063 | 0.326 | 22:48:40.11 | -44:32:04.6 | 7.4 | 10.9 | 9.6

All visually inspected galaxies were confirmed as post-starbursts by
comparison with typical criteria from the literature. For most of our sample
(14 galaxies), the integrated spectra are above the threshold of
$H\delta_{A}=5$Å, which is commonly used to select post-starbursts (e.g Goto,
2007; Alatalo et al., 2016), others have slightly lower $H\delta_{A}$, but are
also post-starbursts (k+a) according to the criteria of Poggianti et al.
(1999) ($3<H\delta_{A}<5$Å). Note that for MACS0257-05, RXJ1347-02,
SMACS2131-06, part of the spectral window required for calculating
$H\delta_{A}$ is unavailable as it is affected by the NaD notch filter. In the
case of A370-04, the 5577Å sky line overlaps with the $H\delta$ region which
brings down the $H\delta_{A}$ value and makes it unreliable. Nevertheless, for
these objects we report in the table the $H\delta_{A}$ values measured from
the integrated model spectra obtained by SINOPSIS (see section 3); these are
marked with * on the table. Although $H\delta_{A}$ is the most commonly used
index to select post-starbursts, other Balmer lines can also be used. In the
cases where $H\delta$ is missing, we confirm the post-starburst nature of the
objects by their $H\beta_{A}$ index ($H\beta_{A}>2.5$Å), as done by Vulcani et
al. (2020) for local cluster galaxies.

The galaxies are distributed in 8 clusters and span a redshift range from
0.291 for A2744-01 to 0.459 for SMACS2131-05. The ages of the universe in
these limiting redshifts are 10.1 Gyr and 8.8 Gyr, respectively. Our sample
spans a wide range of stellar masses, from $10^{8.9}M_{\odot}$ for A2744-01 to
$10^{10.7}M_{\odot}$ for MACS1206-06. We note that our sample typically
includes galaxies of low mass, mostly less massive than, e.g, the Milky Way.
The low mass indicates that these galaxies could be very quickly stripped by
ram-pressure in timescales shorter than the cluster crossing times, e.g before
or soon after the pericenter passage.

Figure 1: Maps of the $[\rm{O}\,\textsc{iii}]\lambda 5007/{\mathrm{H}\beta}$
line ratio for two AGN candidates: A2744-07 (top) and MACS1206-06 (bottom).
Only spaxels with $S/N>3$ in both $[\rm{O}\,\textsc{iii}]\lambda 5007$ and
${\mathrm{H}\beta}$ are included. HST F814W images are shown in gray scale in
the background. On the top left we show the spectrum of a specific spaxel
(marked with a dark x in the figure) around the ${\mathrm{H}\beta}$ and
$[\rm{O}\,\textsc{iii}]\lambda 5007$ lines (4776-5092Å). The observed spectrum
is plotted in black and the model obtained for the stellar continuum (see sec
3) is shown in green, both spectra are convolved with a 5 pixel box filter for
clarity. Figure 2: $[\text{N}\,\textsc{ii}]\lambda 6584/{\mathrm{H}\alpha}$ vs
$[\rm{O}\,\textsc{iii}]\lambda 5007/{\mathrm{H}\beta}$ BPT diagram. Blue
points are spaxels from A2744-07 with $S/N>3$ in all lines in the diagram. The
purple horizontal line is the median $\log\,[\rm{O}\,\textsc{iii}]\lambda
5007/{\mathrm{H}\beta}$ for spaxels in MACS1206-06 with $S/N>3$ in
$[\rm{O}\,\textsc{iii}]\lambda 5007$ and ${\mathrm{H}\beta}$, the purple band
indicates the region between the 10 and 90% percentiles of
$[\rm{O}\,\textsc{iii}]\lambda 5007/{\mathrm{H}\beta}$ for the same spaxels.
For reference, we plot the demarcation lines of Stasińska et al. (2006, dotted
line), Kewley et al. (2001, dot-dashed line) and the transposition of the
Kewley et al. (2006) line proposed by Cid Fernandes et al. (2010, dashed
line), separating LINERs and Seyferts.

We have included in our sample two objects that show emission lines in the
central regions of their stellar disk, these are MACS1206-06 and A2744-07. We
include these objects because we interpret this emission as due to AGN. In
Fig. 1, we show maps of the $[\rm{O}\,\textsc{iii}]\lambda
5007/{\mathrm{H}\beta}$ line ratio for these galaxies, including spaxels with
signal-to-noise ratio ($S/N$) larger than 3 in both emission lines. The
emission lines used here and throughout the paper were measured using the
highelf code as described in Moretti et al. (2021). In the case of A2744-07 we
are also able to measure the ${\mathrm{H}\alpha}$ and
$[\text{N}\,\textsc{ii}]\lambda 6584/{\mathrm{H}\alpha}$ lines, allowing the
full characterization of the central spaxels in a BPT diagram (Baldwin et al.,
1981). Unfortunately, these lines are redshifted out of the MUSE spectral
range for MACS1206-06. In Fig. 2 we analyze the central spaxels of these two
objects in the $[\text{N}\,\textsc{ii}]\lambda 6584/{\mathrm{H}\alpha}$ vs
$[\rm{O}\,\textsc{iii}]\lambda 5007/{\mathrm{H}\beta}$ BPT diagram. For
A2744-07 (blue points) we include spaxels with $S/N>3$ in all four lines.
Since for MACS1206-06 we have only information on
$[\rm{O}\,\textsc{iii}]\lambda 5007$ and $H\beta$, we can only constrain the
y-axis of the diagram. In this case, we plot a horizontal line (purple line)
indicating the median $[\rm{O}\,\textsc{iii}]\lambda 5007/{\mathrm{H}\beta}$
and a band indicating the region between the 10 and 90% percentiles of
$[\rm{O}\,\textsc{iii}]\lambda 5007/{\mathrm{H}\beta}$ in this galaxy, again
considering only spaxels with $S/N>3$ in the two lines.

All spaxels in A2744-07 that satisfy the $S/N$ criteria lie above the Kewley
et al. (2001) line (dot-dashed line in Fig. 2), and can thus be considered as
ionized by AGN. The BPT classification for MACS1206-06 is ambiguous: not only
are we unable to constrain the x-axis, but the y-axis values fall in a region
where star-formation regions and LINERs (which can be AGN) coexist. However,
since an X-ray point source is detected within the galaxy in the Chandra
catalog (Ehlert et al., 2015; Wang et al., 2016) and there is no evidence for
current star-formation from the spectral synthesis, we conclude that an AGN is
the most likely ionization source.

For A2744-01 and SMACS2131-06 we also identify emission lines, but outside of
the stellar disk. This will be discussed in section 5.1.

##  3 Spectral Synthesis

In this section we will go into details regarding the spectral synthesis
method and the determination of physical parameters for our sample of 21 post-
starburst galaxies. The spectral synthesis code is described in section 3.1,
details on the synthesis procedure are presented in section 3.2, and in
section 3.3 we present the definition of parameters calculated from the star-
formation histories.

###  3.1 Spectral synthesis code: SINOPSIS

This work is heavily based on results from the spectral synthesis code
SINOPSIS (SImulatiNg OPtical Spectra wIth Stellar populations models Fritz et
al., 2007, 2011, 2014, 2017). SINOPSIS performs a non-parametric decomposition
of galaxy spectra into a combination of stellar population models. This non-
parametric approach allows the code to capture even very complex star-
formation histories (Leja et al. 2019; Conroy 2013, but see also Cid Fernandes
2007).

There are a few design choices that set SINOPSIS apart from other widely used
non-parametric synthesis codes. First, unlike codes such as STARLIGHT (Cid
Fernandes et al., 2005) and pPXF (Penalized PiXel-Fitting Cappellari, 2017),
SINOPSIS does not perform full spectral fitting. Instead, the fitting
procedure is performed in a selection of continuum band fluxes and spectral
indexes (equivalent widths and $D_{n}4000$), which focuses the fitting efforts
in parts of the spectrum that are more information-rich while also making the
code less susceptible to problems regarding sky lines and other observational
issues. Another distinct design choice in SINOPSIS is the inclusion of
emission features in the fitting of stellar population parameters. The
emission lines produced by each stellar population element up to the age of 20
Myrs are modeled using cloudy (Ferland et al., 2017), allowing us to get
better constraints for young components. Finally, SINOPSIS allows for a full
treatment of dust attenuation (Charlot & Fall, 2000). Each stellar population
component can be fitted with an independent value of dust optical depth,
although we do not take advantage of this feature in this work since our
galaxies do not have young stars and this effect is not prominent.

In particular, including emission lines in the fit is very useful for modeling
post-starburst galaxies. Since these galaxies do not have emission lines, this
provides clear information to the code about the lack of current star-
formation and prevents solutions that might include small fractions of young
stellar populations that are poorly constrained from the optical stellar
continuum (see Werle et al., 2019). The fitting of emission lines coupled with
the versatility of a non-parametric method make SINOPSIS the most suitable
tool for the current work.

###  3.2 Synthesis ingredients and fitting procedure

Our spectral synthesis method is based on stellar population spectra from the
latest update of the Bruzual & Charlot (2003) models (Charlot & Bruzual, in
prep). In the optical region, these models rely on the MILES (Sánchez-Blázquez
et al., 2006) and IndoUS (Valdes et al., 2004) libraries of stellar spectra,
which are combined according to the PARSEC isochrones from Chen et al. (2015)
and Bressan et al. (2012). The spectral resolution of the models in the
optical ($\sim 2.50\mathrm{\AA}$ FWHM) is very similar to the one of MUSE
spectra ($\sim 2.55\mathrm{\AA}$ FWHM). In this work, we use models generated
with a Chabrier (2003) initial mass function. A more detailed description of
these models is provided in Werle et al. (2019).

To generate the final set of model spectra used in our fitting procedure, we
combined the simple stellar population models from Charlot & Bruzual into 16
age bins from 0 to 10 Gyrs111The limiting ages of the bins are (in years):
$0$, $1.99\times 10^{6}$, $3.98\times 10^{6}$, $6.91\times 10^{6}$,
$1.99\times 10^{7}$, $5.71\times 10^{7}$, $2.028\times 10^{8}$, $5.093\times
10^{8}$, $8.072\times 10^{8}$, $1.014\times 10^{9}$, $1.435\times 10^{9}$,
$2.0\times 10^{9}$, $3.0\times 10^{9}$, $4.5\times 10^{9}$, $6.25\times
10^{9}$, $8.0\times 10^{9}$ and $10\times 10^{9}$. and generated composite
stellar populations assuming a constant SFR within the bins.

We use three values of metallicity: 0.004, 0.017 (solar) and 0.04. The fitting
is done separately for sets of models of different metallicities and the one
with the lowest $\chi^{2}$ is chosen, i.e there is no chemical evolution in
the derived SFHs.

The effects of dust can be modeled using independent values of extinction with
a Cardelli et al. (1989) extinction law. However, since usually higher
extinction values affect only stars younger than 20 Myrs and these are not
identified in our galaxies due to the lack of emission lines, we use one
single value of extinction.

In the fits used in this work, we include the equivalent widths of $H\alpha$,
$H\beta$, $H\delta$ and calcium H and K lines, as well as the flux in 32
continuum bands. We note that the features used for each specific galaxy vary
according to redshift.

For each of our datacubes, we run SINOPSIS on all spaxels in a contiguous area
around the center of the target galaxy where a stellar continuum can be
detected, throughout this paper we refer to these as “valid spaxels”. The
total number of valid spaxels in all 21 galaxies in our sample is 2230,
ranging from 36 for MACS0257-05 to 318 for MACS1206-06 with an average of 106
per galaxy. The redshifts for each spaxel, which are required for running
SINOPSIS, were determined using pPXF (Cappellari, 2017) on Voronoi binned
regions with $S/N>5$ (as thoroughly described in Moretti et al. (2021)). For
A2744-05, AS1063SW-01 and SMACS2131-06, foreground objects were manually
masked out.

To obtain the total stellar masses, we sum up the masses obtained with
SINOPSIS for all valid spaxels and multiply it by a scale factor so the total
mass corresponds to the entire region where the galaxy emission in the MUSE
g-band image is 3$\sigma$ above the background level.

Figure 3: Three examples of SINOPSIS fits for post-starburst galaxies in our
sample. Panels show integrated observed (gray) and model (green) spectra for
(top to bottom) A370-04, A370-05 and A2744-02. Spectra are convolved with a
5-pixel box filter to improve visualization. We include a zoom-in to the
spectral region around the $H\beta$ line ($4861\pm 75$Å).

Fig. 3 shows examples of SINOPSIS fits for individual spaxels in three post-
starburst galaxies in our sample. The examples (A370-04, A370-05 and A2744-02)
were chosen to illustrate different levels of post-starburst features.

###  3.3 Star-formation history feature extraction

To interpret the 2230 derived SFHs (one for each valid spaxel), we chose to
reduce their dimensionality by extracting two relevant features: (i) The time
since quenching ($t_{Q}$), and (ii) the fraction of stellar mass formed in the
past 1.5 Gyr ($\mu_{1.5}$).

We define the time since quenching $t_{Q}$ as the time elapsed since the
moment when the galaxy reaches 98% of the total mass ever assembled, i.e
counting also stars that have already died. This parameter is calculated from
a cumulative SFH obtained by converting the SFR of each age bin to mass
fractions, summing the mass fractions cumulatively from the oldest to the
youngest and linearly interpolating between points. We then find the age where
the mass fraction is 98%. We choose not to use the 100% mass fraction to avoid
the influence of possible tiny insignificant fluctuations in the SFR. The
value of 98% is close enough to 100% to give a robust definition of quenching
without being affected by these fluctuations.

From the same cumulative SFHs we calculate the fraction of stellar mass
assembled in the past 1.5 Gyr ($\mu_{1.5}$). The same quantity was explored
also by Pawlik et al. (2018) and Wild et al. (2020). Although 1 Gyr would be
closer to the lifetime of A-type stars that characterize the spectra of post-
starburst galaxies, there can be a SFR enhancement starting slightly before
that time. Thus, we chose the 1.5 Gyr limit as it includes the whole timescale
over which the SFR may have been enhanced. Nevertheless, the mass fractions
calculated using 1 or 1.5 Gyr are very similar and this choice does not affect
our results. Note that here and throughout the paper we are not using a strict
terminology when saying “in the past 1.5 Gyr” or “time since quenching” as we
are referring to lookback times that have as reference the age of the universe
in the galaxy redshift, and not at $z=0$ as would be implied by taking these
sentences literally.

##  4 Star-formation histories

We now focus on the star-formation histories derived by SINOPSIS. In section
4.1 we show the integrated SFHs of all galaxies, we then look at the
distributions and maps of $t_{Q}$ and $\mu_{1.5}$ (sections 4.2 and 4.3,
respectively) and present our interpretation of the general trends in section
4.4.

###  4.1 Integrated star-formation histories

Figure 4: Median SFHs for galaxies in our sample, with shaded bans indicating
the interquartile regions. Points are plotted at the central lookbacktime of
each age bin. Dashed vertical lines indicate the reference lookback time of
1.5 Gyr.

The definition of post-starburst is purely empirical and can accommodate a
variety of SFHs. The lack of emission lines implies that
$\mathrm{SFR(t<\;20Myr)}=0$, and the strong Balmer absorption lines indicate
the presence of A-type stars whose lifetime is $\sim 1$ Gyr. This constrains
the galaxies to SFHs that were rapidly quenched in $t<1$ Gyr but does not
indicate if the SFR was actually enhanced before quenching (i.e if there was a
burst) or if the SFR suddenly dropped some time in the past 1 Gyr without any
prior enhancement. To examine this, we have calculated the median of the
spaxel-by-spaxel SFHs for each galaxy, as shown in Fig. 4. Median SFHs are
plotted in blue with shaded regions indicating the interquartile regions
(between the 25 and 75% percentiles), a dashed line indicates a lookback time
of 1.5 Gyr. Note that we choose to represent the SFHs as SFR vs. $\log\,t$ to
highlight the bursts, but we should keep in mind that older bins are much
wider and thus low SFRs at old ages can still correspond to a very large
fraction of mass formed.

For most galaxies (16 out of 21) it is possible to identify a clear and
isolated burst of star-formation prior to quenching, and in some cases this
burst is the main feature in the SFH. In other cases the SFHs are more complex
and it is hard to identify a single burst. In the case of A2744-02, A2744-07
and SMACS2031-02 (panels b, d and p) there seems to be an enhancement in SFR
close to the 1.5 Gyr mark followed by a smaller enhancement in more recent
times. For A2744-08 (panel e) there is a strong drop in the SFR at around 1.5
Gyr ago after which SFR is sustained at an almost constant level until
quenched. In the case of MACS0257-05 (panel n) there seems to be a burst 1.5
Gyr ago but the feature is unclear as the SFR was rising prior to that event.

Notwithstanding these peculiarities, all of these SFHs can be described as
rapidly quenched, as all of them display a sharp decrease in the SFR at $t<$1
Gyr. Although in some cases (e.g. A2744-07, A2744-08, MACS0257-04 and
SMACS2131-05; panels d, e, m and q) some residual star-formation is sustained
after the main quenching event. This residual star-formation is associated
with very small mass fractions that do not count towards our definition of
quenched. That being said, it is important to have this effect in mind when
analyzing the results for these galaxies.

In most cases, the interquartile regions traced by the shaded bands in Fig. 4
do not deviate from the median shape of the SFH, indicating that the SFH is
somewhat similar across the spaxels of a single galaxy. Indeed, galaxies in
our sample are generally post-starburst in all spaxels. Only 3.5% of the
spaxels for which $H\delta_{A}$ can be measured (91% of the spaxels in our
sample) have $H\delta_{A}<3\mathrm{\AA}$, the typical threshold to define a
spectrum as quiescent.

###  4.2 Distributions of $t_{Q}$ and $\mu_{1.5}$

In Fig. 5, we show box plots tracing the distributions of $t_{Q}$ (top panel)
and $\mu_{1.5}$ (bottom panel). Boxes indicate the interquartile regions with
horizontal lines within the boxes showing the median value. Dark lines outside
the boxes extend from the 15th to the 85th percentile.

The median values of $t_{Q}$ vary from 65 Myr for A2744-01 to 621 Myr for
SMACS2131-05, with some spaxels reaching times older than 800 Myr. The spaxel-
by-spaxel mean value for the entire sample is 327 Myr with a standard
deviation of 250 Myr.

Figure 5: Box plots tracing the distributions of time since quenching
($t_{Q}$, top) and the fraction of the mass assembled in the past 1.5 Gyrs
($\mu_{1.5}$, bottom). Boxes in shades of green indicate the regions between
the 25th and 75th percentiles (interquartile regions), horizontal lines within
the boxes indicate the median and whiskers (dark lines outside the boxes)
indicate the extent between the 15th and 85th percentiles. The color scale is
only to improve readability and does not indicate any physical quantity.

As for $\mu_{1.5}$, median values go from 7.7% for SMACS2131-05 to 52.3% for
MACS0257-03, with some spaxel-by-spaxel values reaching more then 60%. Keeping
in mind that 1.5 Gyr corresponds only to $15-17$% of the time over which these
galaxies could form stars (from the Big Bang to the age of the universe at the
redshift of observation) and considering that generally the SFR declines with
time in normal galaxies, it is noteworthy that the majority of our galaxies
have median $\mu_{1.5}$ values greater than 15%. The average $\mu_{1.5}$ over
all spaxels is 26.10% with standard deviation of 14.15%. We note that the
median values obtained for $\mu_{1.5}$ are generally in the same range as
previous works based on integrated spectra (e.g. Pawlik et al., 2018; Wild et
al., 2020), which is noteworthy considering the different population synthesis
methods and post-starburst selection criteria.

###  4.3 Quenching directions

We now proceed to a spatially resolved analysis of the SINOPSIS results. In
Fig. 6 we show maps of $t_{Q}$ for the 12 biggest (in apparent size) galaxies
in our sample, for which the datacubes have more then 70 valid spaxels (see
definition in section 3.2). Darker colors indicate older $t_{Q}$, and the
limits of the colorbars are set to the 20% and 80% percentiles of $t_{Q}$ in
each galaxy. The variation of $t_{Q}$ within each galaxy ($\Delta t_{Q}$) is
annotated in each panel, this parameter is an estimate of how quickly the
quenching happened. To ensure a robust estimation and prevent eventual outlier
spaxels from biasing our results, we define $\Delta t_{Q}$ as the difference
between the 90th and 10th percentiles of $t_{Q}$, instead of the difference
between the maximum and minimum values.

Figure 6: Maps of quenching time ($t_{Q}$) for all cubes with more then 70
valid spaxels and no foreground objects. Darker colors indicate spaxels
quenched at older lookback times. Minimum and maximum values of the colorbars
are set to the 20% and 80% percentiles of each $t_{Q}$ map. $\Delta t_{Q}$
values are annotated in each panel. Figure 7: Maps of the fraction of mass
assembled in the past 1.5 Gyrs ($\mu_{1.5}$) for all cubes with more then 70
valid spaxels and no foreground objects. Minimum and maximum values of the
colorbars are set to the 20% and 80% percentiles of each map.

The maps in Fig. 6 indicate a diversity of quenching patterns. For 4 out of 12
galaxies the quenching clearly happened first in the outskirts, this is the
case for A2744-02, MACS0257-04, SMACS2031-02 and AS1063NE-01 (panels a, h, j
and k). This outside-in pattern is reminiscent of the truncated gas disks
observed in galaxies undergoing ram-pressure stripping (e.g Gullieuszik et
al., 2017; Poggianti et al., 2019). We note that D’Eugenio et al. (2020) also
finds centrally concentrated starbursts in post-starbursts in environments
that are not prone to ram-pressure, where this stellar population gradient is
attributed to mergers. However, as we will shown in Fig. 13, the stellar
kinematics maps of our galaxies are very regular and inconsistent with the
merger hypothesis.

For A370-04, A370-05, MACS1206-11, RXJ1347-02 and AS1063NE-02 (panels c, d, g,
i and l) the $t_{Q}$ distribution is less clear, following a side-to-side or
irregular pattern that is also consistent with ram-pressure stripping. The low
dynamic range of $t_{Q}$ in these galaxies (except for MACS1206-11 in panel g)
points to a very fast quenching process, uniform over the whole galaxy.

For 3 galaxies (A2744-07, MACS1206-06 and MACS1206-09, panels b, e and f), the
$t_{Q}$ maps indicate an inside-out quenching, which is consistent with the
stellar population gradients of the general population of star-forming
galaxies (older in the center). In the cases of A2744-07 and MACS1206-06, we
find indication of AGN emission in the central region of the stellar disks
(see section 2.2).

For MACS1206-09, despite the general inside-out pattern we do see that the
outer parts of the disk quenched slightly earlier, pointing to a combination
of inside-out and outside-in. This pattern could be interpreted as the
combination of inside-out quenching due to AGN and outside-in quenching due to
ram-pressure, as found by George et al. (2019). We note that this pattern
should not be interpreted as peculiar, as there is evidence in the literature
for an enhanced AGN fraction among galaxies undergoing ram-pressure stripping
(e.g Poggianti et al., 2017; Ricarte et al., 2020; Peluso et al., 2021),
although this is still debated (see Roman-Oliveira et al., 2019; Boselli et
al., 2021) Despite this duality, we choose to define this galaxy as quenched
from the inside out as this is the most conspicuous pattern.

The maps of $\mu_{1.5}$ for the same 12 galaxies are shown in Fig. 7. To
improve visualization we saturate the color scales in the 20th and 80th
percentiles of $\mu_{1.5}$ in each galaxy. In most cases, the $\mu_{1.5}$ maps
follow trends that are similar to what we see for $t_{Q}$. For the galaxies
that show an outside-in pattern in the $t_{Q}$ maps (A2744-02, MACS0257-04,
SMACS2031-02 and AS1063NE-01), the same trend is clearly reproduced for 3/4.
In the case of SMACS2031-02 (panel j), the $\mu_{1.5}$ morphology is slightly
more complex, as the central region of this galaxy has low mass fractions.
This can be understood the central regions of the galaxy were more gas-poor
prior to the quenching event and thus not assembling large mass fractions
during the burst. On the other hand, MACS1206-11 shows a clear outside-in
pattern in the $\mu_{1.5}$ map, while the $t_{Q}$ map is less clear, showing
something between a side-to-side and an outside-in pattern. In this case, we
understand that it is safer to classify the galaxy as quenched from the
outside-in, since $\mu_{1.5}$ is a more robust parameter and the $\Delta
t_{Q}$ of this galaxy is larger then the typical value associated with side-
to-side/irregular quenching patterns.

###  4.4 Putting the pieces together

So far, we have presented results in a case-by-case basis, which is necessary
due to the diversity of quenching histories in our sample. However, within
this diversity lies a general trend. In Fig. 8, we plot log stellar mass
against $\Delta t_{Q}$ coloring galaxies according to the direction of their
quenching maps. Besides the galaxies already shown in Fig. 6 and Fig. 7, we
also include classifications for other 5 galaxies that are not among the
biggest (fewer then 70 valid spaxels) but still display clear patterns: these
are A2744-01 MACS0257-01, MACS0257-03, MACS0257-05, and SMACS2131-05. We still
omit galaxies where part of the stellar disk is obscured by a foreground
object, which can affect the observed quenching patterns and render them
unclear.

Figure 8: Log stellar mass ($\log\,M/M_{\odot}$) versus the variation of
$t_{Q}$ within each galaxy ($\Delta t_{Q}$). Colors indicate the quenching
direction measured from the $\mu_{1.5}$ and $t_{Q}$ maps. Galaxies without a
clear enhancement of SFR prior to quenching are shown as open circles.

Fig. 8 shows that (i) all of the side-to-side/irregular quenching patterns are
in low-mass galaxies ($\log M/M_{\sun}<10.5$) and (ii) all of the inside-out
patterns are more massive galaxies. For the low-mass end, we observe generally
lower $\Delta t_{Q}$ (fast quenching) with either a side-to-side pattern or an
irregular/unclear morphology in the $t_{Q}$ and $\mu_{1.5}$ maps. Our
interpretation, based on the classical Gunn & Gott (1972) model, is that the
anchoring force that binds the gas to the stellar disk is generally lower,
making it easier for ram-pressure to quickly remove the gas. In more massive
galaxies we expect AGN to be more common (Kauffmann et al., 2003; Lopes et
al., 2017; Sánchez et al., 2018), and stellar population gradients to be more
strongly affected the evolution of the galaxy before entering the cluster.
Indeed, for high-mass galaxies we observe some inside-out patterns left by
their previous evolution in a low density environment and/or AGN-induced
quenching. Note that this does not mean that the effects of ram-pressure
should be completely discarded for these galaxies, just that their stellar
population gradients are more strongly shaped by other processes. In fact, as
stated before, for MACS1206-09 the maps point to a combination of secular
growth and ram-pressure, as both the inner regions and the outskirts have
older $t_{Q}$ and lower $\mu_{1.5}$.

The stellar mass range is unconstrained for galaxies displaying outside-in
quenching patterns. These seem to be objects that, while affected by ram-
pressure, are able to better retain their gas, leading to a longer global
timescale for stripping of the gas (longer $\Delta t_{Q}$). Since the stellar
mass surface density is lower in the outskirts, these regions are stripped
first and the starburst is centrally concentrated, ultimately leading to the
outside-in gradients that we observe.

Galaxies lacking a clear enhancement of SFR prior to quenching (as seen in
their integrated SFHs, Fig. 4) are shown as open circles in Fig. 8. These
objects have typically large $\Delta t_{Q}$ ($>300$ Myrs) regardless of the
quenching direction. These longer timescales can be interpreted as indication
that the lack of a burst is not related to how much gas was initially
available for star-formation, but to other factors (e.g more circular orbits
within the cluster, feedback, etc) that lead to the slow (when compared to
other post-starbursts) conversion of this gas into stars.

In addition to what was previously discussed, Fig. 8 also shows that there is
a certain relation between $\log\,M/M_{\odot}$ and $\Delta t_{Q}$. In
particular, it is interesting to see this relation for galaxies displaying an
outside-in quenching pattern: although these are observed in a wide range of
masses, the quenching seems to happen faster at lower masses. We note that,
although our sample is large enough so we can identify a variety of objects,
it is too small to allow us to reliably study statistical trends, and larger
samples will be required to confirm this interpretation.

##  5 Special cases

Some objects in our sample have particularly interesting features revealed by
the analysis of their emission line maps. In this section, we deviate from the
main thread of the paper to concentrate on those cases. In section 5.1 we
showcase two objects with tails of ionized gas, and in section 5.2 we take a
closer look at the emission line properties of A2744-07.

###  5.1 Tails of ionized gas

We have identified two post-starbursts that, although lacking any emission
lines in their stellar disks, display long tails of ionized gas, these are
A2744-01 and SMACS2131-06. We note that for A2744-01 these tails have already
been identified by Owers et al. (2012) and Moretti et al. (2021). This
intriguing feature is shown in Fig. 9, where we plot HST F814W images of these
two objects with $[\rm{O}\,\textsc{ii}]\lambda 3727$ flux in red. These tails
can be interpreted as the smoking gun of ram-pressure stripping, setting these
objects as missing links between post-starbursts and jellyfish galaxies.

Figure 9: HST F814W images (gray) of A2744-01 (top) and SMACS2131-06 (bottom)
with $[\rm{O}\,\textsc{ii}]\lambda 3727$ flux (in $\mathrm{erg/s/cm^{2}}$)
measured from the MUSE data cubes shown in red. The position of the galaxies
is marked by dashed circles of arbitrary radius centered in the HST
coordinates of each galaxy. Figure 10: Maps of $\mu_{1.5}$ (yellow to blue
color map) and $[\rm{O}\,\textsc{ii}]\lambda 3727$ flux (red color map) for
the galaxy A2744-01.

The case of A2744-01 is particularly interesting. In Fig. 10, we plot the map
of $\mu_{1.5}$ for this galaxy (yellow to blue color map) and the flux map in
of the $[\rm{O}\,\textsc{ii}]\lambda 3727$ line (red color map). The
$\mu_{1.5}$ map has a side-to-side gradient that is aligned with the tail of
ionized gas in such a way that spaxels closer to the tail have larger
fractions of young stellar populations (more prominent bursts). Unfortunately,
we are unable to do the same analysis for SMACS2131-06, as in the MUSE data
cube it is strongly blended with a foreground object in the south, which
prevents us from reliably probing the stellar population gradient.

Other properties of A2744-01 are also worth mentioning. Of all galaxies in our
sample, it is the one with the lowest mass ($\log M_{\star}/M_{\odot}=8.9$),
lowest median $t_{Q}$ (64 Myr, see Fig. 5) and a very low $\Delta t_{Q}$ of 51
Myr. It also has very strong features with a blue spectrum (see top panel of
Fig. 3), integrated $H\delta_{A}$ of 6.78$\mathrm{\AA}$ and a very clear
recent burst in the star-formation history (see first panel in Fig. 4). Its
median $\mu_{1.5}$ is 14.78%.

###  5.2 The case of A2744-07

Another object with peculiar emission line features is A2744-07. In Fig. 11 we
show the $[\rm{O}\,\textsc{ii}]\lambda 3727$ flux (top) and velocity (bottom)
for this object.

Figure 11: MUSE $[\rm{O}\,\textsc{ii}]\lambda 3727$ map for all spaxels where
the line is detected with $S/N>3$ (top panel) and
$[\rm{O}\,\textsc{ii}]\lambda 3727$ velocity field (bottom panel) for the
galaxy A2744-07. HST F814W image is shown in gray scale in the background.

Besides the AGN in the central region (see section 2.2), two strips of gas can
be seen in the map, one to the North-East, extending $\sim$ 20 kpc along and
beyond the stellar disk, and one to the East, extending $\sim$ 12 kpc
perpendicular to the stellar disk. In addition to
$[\rm{O}\,\textsc{ii}]\lambda 3727$, these features are also visible in
$H\alpha$, but not in $[\rm{O}\,\textsc{iii}]\lambda 5007$, which points to a
soft ionization source, although the strips seem to be spatially correlated
with the central AGN. Both gas strips are blueshifted with respect to the
central region (bottom panel of Fig. 11), in the case of the northern strip
the velocities reach up to $\sim-500\,\mathrm{km/s}$.

We are unable to determine if these features are caused by the AGN, by ram-
pressure or (most likely) a complex combination of the two. Given that ram-
pressure stripping is known to trigger (or maybe be helped by) an AGN (e.g
Poggianti et al., 2017; Ricarte et al., 2020), we should expect some
transition objects such as A2744-07 to display features of both AGN and ram-
pressure.

##  6 Further clues on ram-pressure stripping

Our results so far indicate that ram-pressure stripping is the main driver of
fast quenching in the centers of clusters at intermediate redshift. This
hypothesis is strengthened by several results in the literature that also
point to ram-pressure as the most common path to the post-starburst phase in
dense environments (Poggianti et al., 2004, 2009; Vulcani et al., 2020). In
this work, the main evidence for this comes from the direction of the
quenching traced by $t_{Q}$ and $\mu_{1.5}$, as these maps show that most
galaxies are quenched from the outside-in or display a side-to-side/irregular
stellar population gradient. Both features are consistent with the stripping
of gas via ram-pressure. Inside-out quenching patterns expected from AGN-
driven quenching are observed only in 3 galaxies, all of which are in the
high-mass end of the distribution for our sample.

Figure 12: $[\rm{O}\,\textsc{ii}]\lambda 3727$ flux map of two jellyfish
galaxies from Moretti et al. (2021), A370-06 in the top and A370-08 in the
bottom, with dashed ellipses showing the extension of the stellar disk. A dark
”x” marks the position of a spaxel that has recently been stripped of gas, the
model (green) and observed (black) spectra of these spaxels in a 75Å window
centered on the $H\beta$ line are plotted on the right-hand side. The HST
F814W image is shown in gray scale in the background. Figure 13: Stellar
velocity ($v^{\star}$) maps derived with pPXF for the same 12 galaxies shown
in Figures 6 and 7.

Complementary evidence comes from two special cases (shown in Fig. 9) for
which we find tails of ionized gas indicating that the gas was very recently
stripped. This connection between post-starburst and jellyfish galaxies can
also be explored from the other way around, i.e identifying post-starburst
features in galaxies undergoing ram-pressure stripping, as done by Gullieuszik
et al. (2017) and Poggianti et al. (2019) for jellyfish galaxies in the local
universe. Thus, it is natural to attempt the same analysis for stripped
galaxies in the same clusters from which we selected our sample of post-
starbursts. In Fig. 12 we show maps of $[\rm{O}\,\textsc{ii}]\lambda 3727$
flux from two jellyfish galaxies from the Moretti et al. (2021) sample,
A370-06 on the top panel and A370-08 on the bottom panel. Dashed ellipses in
each panel indicate the extent of the stellar disk. For each of these galaxies
we choose a spaxel that has already been stripped of gas (marked with a dark
”x”) and plot the corresponding spectra around the $H\beta$ line. The spectra
in these stripped regions show strong $H\beta$ absorption lines, and the same
happens for other Balmer lines, indicating that these objects are likely to be
the progenitors of post-starburst galaxies.

A crucial piece of information for confirming ram-pressure stripping is the
stellar velocity field of a galaxy (e.g Vulcani et al., 2020). Disturbed
stellar kinematics can be associated with gravitational interactions or
mergers, while ram-pressure affects only the gas and leaves the stellar
kinematics unperturbed. Unfortunately, at this redshift, due to the spatial
resolution and signal to noise ratio it is not possible to establish if an
irregular velocity map corresponds to actually disturbed stellar kinematics or
just noise. Therefore, irregular kinematic maps should be interpreted as
ambiguous. However, it is possible to confirm when the kinematics is globally
regular.

Stellar velocity fields derived with pPXF for the same 12 galaxies of Figures
6 and 7 are shown in Fig. 13. The stellar kinematics is usually very regular.
Exceptions are A370-04, AS1063NE-02 and RXJ1347-02, all of which are faint and
have small apparent size, for which the velocity maps are not reliable. Thus,
the kinematical maps for these galaxies are very uncertain. We interpret these
regular kinematical maps as complementary evidence that ram-pressure is the
main driver of fast quenching in our sample.

Figure 14: Box plots tracing the absolute value of $v/\sigma$ for (from left
to right) the General population of cluster galaxies, Jellyfish galaxies from
the same clusters, post-starbursts not including the ones with inside-out
quenching, and post-starbursts with inside-out quenching. Boxes between the
interquartile regions, horizontal lines within the boxes indicate the median,
whiskers extend out to 1.5 times the interquartile regions.

Another relevant piece of the puzzle is the galaxy environment. To probe this,
we calculate the absolute value of the peculiar velocity of each galaxy
relative to the cluster redshift, normalized by the cluster velocity
dispersion ($|v/\sigma|$). The value of $|v/\sigma|$ gives us an indication to
the infall stage of each galaxy. Objects with higher $|v/\sigma|$ are more
likely to be rapidly infalling and experiencing ram-pressure stripping, while
objects with lower $|v/\sigma|$ are generally more likely to be relaxed.

Box plots tracing the distributions of $|v/\sigma|$ for different galaxy
classes are shown in Fig. 14. We divide the post-starburst population (marked
as PSB in the Figure) in two sub-classes: the ones with outside-in or side-by-
side/irregular quenching patterns and the ones with inside-out quenching
patterns. Note that in the case of inside-out quenched post-starbursts the box
plot is produced with only 3 galaxies, the $|v/\sigma|$ values for these
galaxies correspond to the median and to the extremes of the whiskers in the
box plot.

The box plots in Fig. 14 show that post-starbursts with outside-in or side-to-
side/irregular quenching patterns have a $|v/\sigma|$ distribution similar to
the one of jellyfish galaxies. While post-starbursts with inside-out quenching
patterns are closer to the general population of cluster galaxies. This serves
as further evidence that the post-starbursts with outside-in or side-to-
side/irregular quenching patterns had their gas removed by ram-pressure
stripping, while inside-out quenching patterns may be related also to other
processes such as AGN feedback.

##  7 Conclusions

In this work, we have presented results from the analysis of MUSE integral
field spectroscopy of 21 post-starburst galaxies in the centers of 8 clusters
at $z\sim 0.3-0.4$.

We used the SINOPSIS spectral synthesis code to retrieve spatially-resolved
star-formation histories of all 21 objects, finding a clear enhancement in SFR
prior to quenching in 16 cases. From these, we calculate the time since
quenching ($t_{Q}$) and the fraction of stellar mass assembled in the past 1.5
Gyr ($\mu_{1}.5$).

We find that most galaxies in our sample have quenched their star-formation
from the outside-in (7 objects) or show a side-to-side/irregular pattern (8
objects). Only 3 objects show an inside-out quenching pattern, all of which
are at the high-mass end of our sample. For 2 of them the quenching can be
associated with an AGN. For 3 objects the quenching direction is unclear. The
variation in quenching times within each galaxy ($\Delta t_{Q}$) correlates
(although weakly) with galaxy mass, in the sense that less massive galaxies
are more rapidly quenched.

For two objects in our sample, we identify tails of ionized gas showing that
these galaxies are caught in a transition from jellyfish to post-starburst. In
the case of A2744-01, we are able to identify a stellar population gradient in
the direction of the tail: spaxels closer to the tail have assembled higher
fractions of stellar mass in the recent past.

We have shown that the stellar kinematics of galaxies in our sample is
generally regular. Also, post-starbursts displaying an outside-in or a side-
to-side/irregular quenching pattern have a distribution of absolute velocities
within the cluster similar to the one of galaxies currently undergoing ram-
pressure stripping. On the other hand, the three galaxies for which we
identify an inside-out quenching pattern, the velocities within the cluster
are closer to the ones of the general population of cluster galaxies.

As a whole, our results point to ram-pressure stripping as the main driver of
fast quenching in dense environments at intermediate redshift, with active
galactic nuclei being relevant only for galaxies of high stellar mass
($\log\,M/M_{\sun}>10.5$).

## Acknowledgments

AW thanks Catarina Aydar and Daniel Ruschel Dutra for important discussions
about this work, and Abilio Mateus for providing a first contact with post-
starburst galaxies. We thank the anonymous referee for suggestions that have
improved the paper. This project has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation program (grant agreement No. 833824, GASP project). B. V. and M. G.
also acknowledge the Italian PRIN-Miur 2017 (PI A. Cimatti). We acknowledge
funding from the INAF main-stream funding programme (PI B. Vulcani). J.F.
acknowledges financial support from the UNAM- DGAPA-PAPIIT IN111620 grant,
México. GB acknowledges financial support from the National Autonomous
University of México (UNAM) through grant DGAPA/PAPIIT BG100622.

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