11institutetext: Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique
de Paris, 98bis Bd Arago, 75014, Paris, France 22institutetext: Instituto de
Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das
Estrelas, PT4150-762 Porto, Portugal 33institutetext: Departamento de Física e
Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre
687, PT4169-007 Porto, Portugal 44institutetext: Institute for Astronomy,
University of Hawaii, 2680 Woodlawn Dr, Honolulu, HI 96822, USA
55institutetext: Centre for Extragalactic Astronomy, Durham University, South
Road, Durham DH1 3LE, UK 66institutetext: Institute for Computational
Cosmology, Durham University, South Road, Durham DH1 3LE, UK 77institutetext:
Astrophysics Research Centre, University of KwaZulu-Natal, Westville Campus,
Durban 4041, South Africa 88institutetext: School of Mathematics, Statistics &
Computer Science, University of KwaZulu-Natal, Westville Campus, Durban 4041,
South Africa 99institutetext: Academia Sinica Institute of Astronomy and
Astrophysics (ASIAA), No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan

# Ram pressure stripping in the $z\sim 0.5$ galaxy cluster MS 0451.6-0305

F. Durret 11 L. Degott 11 C. Lobo 2233 H. Ebeling 44 M. Jauzac 55667788 S.-I.
Tam Based on observations made with the NASA/ESA Hubble Space Telescope,
obtained from the Space Telescope Science Institute Data Archive, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5-26555. These observations are associated with
programmes GO-09722, -09836, -10493, and -111591. This paper has made use of
the NASA Extragalactic Database and of the GAZPAR tool to apply the LePhare
software. 99

###### Abstract

Context. The pressure exerted by the ambient hot X-ray gas on cluster galaxies
can lead to the presence of ram pressure stripped (RPS) galaxies,
characterized by asymmetric shapes, and, in some cases, tails of blue stars
and/or X-ray gas, with increased star formation.

Aims. With the aim of increasing the known sample of RPS galaxies at redshift
$z\sim 0.5$, notably higher than most RPS samples presently known, we extended
our searches for such galaxies to the cluster MS 0451.6-0305.

Methods. Our study is based on Hubble Space Telescope (HST) imaging in the
F814W band (corresponding to a restframe wavelength of 529 nm), covering a
region of about $6\times 6$ Mpc2, an eight magnitude ground-based catalogue
with photometric redshifts, and a spectroscopic redshift catalogue. We defined
as cluster members a spectroscopic redshift sample of 359 galaxies within $\pm
4\sigma_{v}$ of the mean cluster velocity, and a photometric redshift sample
covering the [$0.48,0.61$] range. We searched for RPS galaxies in the HST
images and tested the error on their classification with a Zooniverse
collaboration. We also computed the phase space diagram of RPS candidates in
the spectroscopic sample. Finally, we ran the LePhare stellar population
synthesis code through the GAZPAR interface to analyze and compare the
properties of RPS and non-RPS galaxies.

Results. We find 56 and 273 RPS candidates in the spectroscopic and
photometric redshift samples, respectively. They are distributed throughout
the cluster and tend to avoid high density regions. The phase space diagram
gives the percentages of virialized, backsplash, and infall galaxies. RPS
galaxy candidates typically show rather high star formation rates, young ages,
and relatively low masses. We compare all our results to those previously
obtained for the massive merging cluster MACS J0717+3745, at a similar
redshift.

Conclusions. This study increases by at least 56 objects if we only consider
galaxies with spectroscopic redshifts, and probably much more if galaxies with
photometric redshifts are taken into account. This study increases the number
of RPS candidates at redshift $z>0.5$, and confirms that they host, on
average, younger stellar populations and strongly form stars when compared
with non-RPS counterparts. The fact that RPS candidates with spectroscopic and
with photometric redshifts have comparable properties shows that large samples
of such objects could be gathered based on multi-band photometry only, a
promising result in view of the very large imaging surveys planned in the
coming years (DES, Euclid, LSST, etc.).

###### Key Words.:

Clusters – Galaxies – RPS galaxies

##  1 Introduction

Among the most important mechanisms affecting galaxies in clusters are ram
pressure stripping (Gunn & Gott, 1972), hereafter RPS, which affects the gas
contained in galaxies, and tidal effects (e.g. Toomre & Toomre, 1972) which
affect both gas and stars and can lead to harrassment (Moore et al., 1996)
when high-speed encounters predominate (as is the case in massive clusters). A
complete summary of all the physical processes affecting galaxy evolution and
taking place in clusters can be found, for example, in the introduction of the
paper by Poggianti et al. (2017).

Ram Pressure Stripped galaxies, which are the topic of the present paper, can
be signalled by asymmetric shapes, sharp edges, blue knots, and/or tails, and
they often show enhanced star formation. Not only are they interesting objects
by themselves, allowing us to study galaxy evolution in dense environments,
but they also provide important indications for the properties of the clusters
in which they are embedded. However, even though we can learn much from these
objects, they are still difficult to identify.

While detailed hydrodynamical simulations have only recently started to be
developed for RPS galaxies (Yun et al., 2019), observational evidence for gas
stripping at various wavelengths has been accumulating for a number of years.
First evidence came from the HI deficiency detected in cluster galaxies
(Haynes et al., 1984), particularly in the well-known examples of Virgo
(Cayatte et al., 1990) and Coma (Bravo-Alfaro et al., 2001). Although the star
formation in a galaxy deprived of some of its gas is expected to eventually
drop, the observation of ionized gas at optical wavelengths, a good tracer of
star formation, shows that in some cluster galaxies, likely caught at an
earlier phase of action of this mechanism, the star formation rate (SFR) can
increase for a limited amount of time. This is attributed to the compression
effect of ram pressure, which can also be at the origin of spectacular tails
of stripped, ionized gas reaching tens of kpc in length, and often containing
blue knots revealing intense star formation. Many observations of such ionized
tails are now available (Owen et al., 2006; Cortese et al., 2007; Sun et al.,
2007; Yoshida et al., 2008; Smith et al., 2010; Yagi et al., 2010; Fossati et
al., 2012; Boselli et al., 2016, among others) and galaxies with such tails of
star-forming material, likely produced by RPS, were named ”jellyfish galaxies”
following Bekki (2009). A systematic search for jellyfish galaxies by
Poggianti et al. (2016) in the WINGS and OMEGAWINGS surveys showed that
disturbed morphologies suggestive of stripping phenomena are ubiquitous in
clusters and could also be present in groups and low mass halos. RPS can also
have more modest effects on galaxies, leading to features such as asymmetric
shapes or sharp edges on one side of the galaxy, that can indicate in which
direction the galaxy is moving relatively to the intracluster medium (see e.g.
McPartland et al., 2016).

Hereafter, we use the generic term of RPS galaxies, since not all RPS galaxies
look like jellyfish, and also because the term jellyfish refers to very
specific signatures. To illustrate this, we refer the reader to a conspicuous
example of a ram pressure stripped galaxy with an H$\alpha$ (and X-ray) tail
that was found by Laudari et al. (2022) to show little star formation
activity. This is not an isolated case (see references in Laudari et al.,
2022) but these authors use this argument to suggest that this particular
object, and others alike, cannot be classified as a jellyfish. This finding
also exposes the complexity of this phenomenon that, although fascinating,
involves a lengthy discussion that is beyond the scope of this paper. Vulcani
et al. (2021) and Laudari et al. (2022) further stressed the difficulty of
selecting “clean” samples of RPS galaxies, a problem that we briefly discuss
in Sections 2.1 and 5.

VLT/MUSE has been very successfully used to observe RPS galaxies, first by
Fumagalli et al. (2014), who detected a double tail reaching 80 kpc,
previously seen in X-rays, in ESO 137-001 (z=0.01625). A complementary study
with APEX (Jáchym et al., 2014) uncovered an exceptionally long molecular tail
in this galaxy, and follow-up observations with ALMA (Jáchym et al., 2019)
allowed the first detection of the molecular gas at the heads of several
fireballs located in the complex tail structure of this spectacular galaxy.
This confirmed the importance of multi-wavelength observations to fully
understand these objects. Radio observations of 20 Coma galaxies were then
obtained by Chen et al. (2020), showing that radio continuum emission could
also be detected in ionized gas tails.

A dedicated, programme using VLT/MUSE was pursued with the GASP(GAs Stripping
Phenomena in galaxies with MUSE) survey of nearby RPS galaxies (Poggianti et
al., 2017), leading to a large number of very interesting results presented in
more than 30 papers. VLT/MUSE data on GASP were also complemented with data at
other wavelengths such as ALMA, VLA, UVIT, and Chandra (Poggianti et al.,
2019), the latter paper proposing that heating due to interaction with the
intracluster medium is responsible for the X-ray tail.

The molecular gas in RPS galaxies was analyzed in JW100 (Moretti et al.,
2020b) and four other comparable objects (Moretti et al., 2020a). They
interpreted this large molecular gas content as newly born from stripped HI
gas or recently condensed from stripped diﬀuse molecular gas. Ramatsoku et al.
(2020) observed two RPS galaxies of the GASP survey in HI and H$\alpha$ and
found them to be similar, based on their H I content, stellar mass, and star
formation rate, an unexpected finding in view of their different environments.
Deb et al. (2020) observed in HI one of the most spectacular GASP galaxies,
JO204, and detected an extended 90 kpc long ram-pressure stripped tail of
neutral gas, stretching beyond the 30 kpc long ionized gas tail and pointing
away from the cluster centre. The comparison of the distributions and
kinematics of the neutral and ionized gas in the tail indicates a highly
turbulent medium.

In four RPS galaxies, Moretti et al. (2020b) found within the disk an H2
molecular gas mass a factor between 4 and $\sim 100$ times higher than the
neutral gas mass, and interpreted these results as due to the fact that ram
pressure in disks of galaxies during the RPS phase causes a very efficient
conversion of HI into H2.

Recently, still another result of the GASP survey, Vulcani et al. (2021)
separated galaxies into several categories, depending on the different
processes they were undergoing in low-density environments: galaxy–galaxy
interactions, mergers, ram pressure stripping, cosmic web stripping, cosmic
web enhancement, gas accretion, and starvation.

Besides the GASP survey, a few other authors studied large samples of RPS
galaxies at various wavelengths. Roberts et al. (2021) observed galaxies with
LOFAR in a large sample of $\sim 500$ galaxy groups and clusters, and showed
that galaxies also undergo RPS in groups, with differences between groups and
clusters. They underline in particular that: the frequency of RPS galaxies is
highest in clusters and lowest in low-mass groups; there is weaker ram
pressure stripping in groups relative to clusters; many jellyfish galaxies in
groups are consistent with having already passed pericentre, which does not
seem to be the case for jellyfish galaxies in clusters; and unlike jellyfish
galaxies in clusters, jellyfish galaxies in groups do not have systematically
enhanced SFR.

The study of RPS galaxies at intermediate redshift ($z=0.3-0.5$) started quite
recently. Based on the slitless spectroscopy taken as part of the Grism Lens-
Amplified Survey from Space (GLASS), Vulcani et al. (2016) presented an
extended analysis of the spatial distribution of star formation in 76 galaxies
in 10 clusters at $0.3<z<0.7$, together with 85 foreground and background
galaxies in the same redshift range as a field sample. They find a large
diversity of H$\alpha$ morphologies, suggesting a diversity of physical
processes: some galaxies are regular (30%), some are asymmetric or jellyfish
(28%), and their shape can be attributed to RPS, which is much less prominent
in the field (2%). In a following paper based on the same data, Vulcani et al.
(2017) correlate the properties of the H$\alpha$ emitters to several tracers
of the cluster environment and conclude that local effects, uncorrelated to
the clustercentric radius, play a more important role than the global
environment in shaping galaxy properties.

VLT/MUSE also led to new results on RPS galaxies in intermediate redshift
clusters. Boselli et al. (2019) observed with VLT/MUSE a cluster at z = 0.73
containing two massive star-forming galaxies with extended tails of diffuse
ionized gas reaching a projected length of $\sim$100 kpc and not associated
with any stellar component. Moretti et al. (2022) found 13 RPS galaxies in the
clusters A2744 (z=0.306) and A370 (z=0.373) and detected not only H$\alpha$
but [OII]$\lambda\lambda 3726,3729$. They found that the resolved
[OII]/H$\alpha$ line ratio in the stripped tails is exceptionally high
compared to that in the disks of these galaxies, suggesting lower gas
densities and/or an interaction with the hot surrounding ICM. With the IFU
device of the Keck telescope, Kalita & Ebeling (2019) observed the A1758N_JFG1
jellyfish galaxy at z=0.28 and detected [OII]3727 emission as far as 40 kpc
from the cluster centre.

Though dedicated IFU studies are extremely rich and relevant for understanding
the details of the evolution of galaxies subject to RPS and of the direct
consequences for their star formation and metallicity histories, larger
samples are still lacking, in particular at intermediate redshifts. These can
be used to tentatively infer some statistical trends and serve as a starting
point for follow-up studies.

With this in mind, a search for RPS candidates has been undertaken in the HST
images of 40 DAFT/FADA and CLASH surveys by Durret et al. (2021) in the
redshift range $0.2<z<0.9$. They studied in particular the case of MACS
J0717.5+3745 (hereafter MACS0717), a very interesting X-ray luminous and
complex merging cluster located at z=0.5458. For this system, not only HST
data were available for the cluster and its extended filament, but also a
spectroscopic redshift catalogue with several hundreds of objects, and ground-
based magnitudes in six optical and two infrared photometric bands in a large
region around the cluster.

Merging clusters should actually be sweet spots for searches of RPS galaxies,
as suggested by different authors (e.g. Owers et al., 2012; McPartland et al.,
2016; Kalita & Ebeling, 2019; Ebeling & Kalita, 2019; Moretti et al., 2022),
so additional candidates in the sample of Durret et al. (2021) are worth
further exploration.

With the aim of increasing the sample of RPS galaxies at z $\sim 0.5$ and
comparing the two systems, we present here observations of another cluster, MS
0451.6-0305 (hereafter MS0451, also named MACS J0454.1-0300), located at
redshift $z=0.5377$, very similar to that of MACS0717. For this cluster, we
have data comparable to those for MACS0717, namely large spatial coverage up
to clustercentric radius larger than $r_{100}$ (though we have fewer redshifts
for MS0451). MS0451 was identified as a post-merger system (Tam et al., 2020),
and is a member of the DAFT/FADA sample (massive clusters with HST data in the
$0.4<z<0.9$ redshift range). Its galaxy density map shows no strong elongation
or particular features, but it was noted that the peak of the density map
(where the contours reach a maximum) does not coincide with the position of
the cluster given by NED, the displacement being about 0.011 deg,
corresponding to 0.25 Mpc at the cluster distance. The weak lensing analysis
detects two peaks (Martinet et al., 2016), following the general elongation of
the galaxy density map of Durret et al. (2016). We present in this paper a
search for RPS candidates, selected as cluster members on the basis of
spectroscopic and photometric redshifts.

We assume here H${}_{0}=70$ km s-1 Mpc-1, $\Omega_{\Lambda}=0.7$ and
$\Omega_{\rm m}=0.3$. At this redshift, the scale is 6.34 kpc/arcsec.
Magnitudes are given in the AB system. The cluster centre is taken from NED:
RA(J2000)=73.54635 deg, DEC(J2000)=$-3.01494$ deg.

##  2 The data

Our study is based on a large HST/ACS mosaic in the F814W filter covering a
region of about 6 × 6 Mpc2 at the cluster redshift, collected for the
programmes GO$-09836$, $-10493$, and $-11591$. We also examined F555W imaging
from a single ACS pointing obtained for GO-09722 but found the covered area
too small to be significant for the purpose of this work. We reduced the
imaging data with the pyHST software
package111https://github.com/davidharvey1986/pyHST. For the details of data
reduction process, we refer the reader to Tam et al. (2020).

###  2.1 RPS characterization: systematic concerns

Since the most easily recognizable RPS features involve triggered star
formation, either at the ICM/ISM interface or in the debris trail (see Cortese
et al. (2007) or Kalita & Ebeling (2019) for textbook examples), images in a
band bluer than the 4000 Å break at the cluster redshift are best suited to
identify and characterize RPS galaxies. At the redshift of our target, such an
endeavour would thus require wide-area imaging in F555W or an even bluer
HST/ACS filter, which are unfortunately not available for MS0451. We
nonetheless attempt to identify RPS features in the F814W filter, relying less
on “jellyfish” tentacles but basing our selection on broader morphological
features such as global asymmetry, sharp edges and/or notable unilateral
distortion of disks or spiral arms. Although we have excluded galaxies with a
nearby galaxy neighbour (see next section), the resulting sample of RPS
candidates will invariably be contaminated by minor mergers in addition to
irregular galaxies and dusty spirals. We estimate by eye inspection that at
the very most 15 galaxies in our sample of 56 spectroscopic RPS candidates
could be minor mergers (namely #4, #6, #7, #11, #15, #16, #18, #24, #30, #32,
#36, #44, #45, #46, #49). We have checked that these 15 galaxies are not
located in a specific zone of Fig. 11 (13 out of 15 are in the virialized
zone) and of Fig. 16 (they cover the whole mass and SFR ranges). On the other
hand, we may have missed RPS galaxies with features emitting more in the blue,
due to the red filter we used. We keep these caveats in mind in our analysis.
Acknowledging the importance (and lack) of imaging in a bluer filter, we did
not attempt to assign a velocity vector (relative to the ICM) to each
candidate.

We can note that McPartland et al. (2016) and Roman-Oliveira et al. (2021)
suggested and tested various automatic classification algorithms, but since
these techniques are still under development we preferred not to use them.

###  2.2 Sample 1 (spectroscopic redshifts)

We put together the spectroscopic redshift catalogue of Tam et al. (2020) and
the redshifts taken from NED in the area covered by the HST mosaic, keeping in
priority the values from Tam et al. (2020) when they were also present in NED.
For the 129 galaxies with redshifts in the cluster range and appearing both in
NED and in Tam et al. (2020), the redshifts agree very well: the mean value of
the difference between the redshifts is $4.1\times 10^{-5}$ with a dispersion
of $3.3\times 10^{-5}$. In order not to miss high velocity galaxies, we chose
to consider as cluster members all the galaxies with velocities within $\pm
4\sigma_{v}$ of the mean cluster velocity (see section 3.1.2). This
corresponds to the redshift interval $0.5086<z<0.5678$. Within this range, we
finally obtained a spectroscopic redshift catalogue of 359 galaxies.

Two of us (FD and LD) looked at the HST images of all these galaxies and gave
them a J classification (respectively JF and JL for FD and LD), following
Poggianti et al. (2016). This classification grades galaxies from J=1 to J=5,
with the value of J increasing as the likeliness of being affected by RPS
increases. We chose as final classification the mean of the two values, which
usually did not differ much, Jmean. We eliminated objects with J${}_{mean}<1$
(i.e., considered as non-RPS by one of us and classified as J=1 by the other)
and thus obtained the list of 56 RPS candidates presented in Table 1. We note
that in this process we also eliminated galaxies that could be undergoing a
gravitational interaction with a neighbouring galaxy (since their shape would
then not be due to ram pressure stripping) or that had a shape similar to that
of a gravitational arc.

In order to measure the F814W magnitudes, we computed the zero points ${\rm
ZP_{AB}}$ by applying the HST
formula:222http://www.stsci.edu/hst/instrumentation/acs/data-
analysis/zeropoints

${\rm-2.5*log10(PHOTFLAM)-5*log10(PHOTPLAM)-2.408},$

where the PHOTFLAM and PHOTPLAM values were found in the image headers (they
were identical for all the images, each having an exposure time of 2036 s). We
then ran SExtractor (Bertin & Arnouts, 1996) on the mosaic and retrieved the
MAG_AUTO magnitudes. The values given in Table 1 are not corrected for
Galactic extinction.

Table 1: Sample 1 RPS candidates in MS0451 (galaxies with spectroscopic redshifts). The columns are: running number, J2000 right ascension and declination (in degrees), spectroscopic redshift, flag for the origin of the redshift (1 for Tam et al. (2020) and 2 for NED), J classifications JL and JF according to two of us (LD and FD), mean J classification, F814W magnitude and its error, distance to cluster centre in units of r200, $\Delta v/\sigma_{v}$ (difference between the galaxy and the cluster velocities divided by the cluster velocity dispersion). Number | RA | DEC | z | flag | JL | JF | Jmean | F814W | error | r/r200 | $\Delta v/\sigma_{v}$
---|---|---|---|---|---|---|---|---|---|---|---
1 | 73.3313 | -3.0023 | 0.5390 | 2 | 5 | 4 | 4.5 | 20.792 | 0.004 | 2.381 | 0.176
2 | 73.4129 | -2.9304 | 0.5342 | 1 | 3 | 3 | 3.0 | 22.407 | 0.011 | 1.746 | -0.474
3 | 73.4182 | -3.0043 | 0.5350 | 2 | 4 | 3 | 3.5 | 23.149 | 0.014 | 1.425 | -0.365
4 | 73.4277 | -3.0033 | 0.5343 | 1 | 2 | 2 | 2.0 | 22.828 | 0.009 | 1.318 | -0.460
5 | 73.4304 | -3.0367 | 0.5336 | 1 | 1 | 2 | 1.5 | 20.731 | 0.003 | 1.302 | -0.556
6 | 73.4361 | -3.0897 | 0.5460 | 2 | 3 | 3 | 3.0 | 21.384 | 0.004 | 1.479 | 1.118
7 | 73.4557 | -2.9902 | 0.5488 | 1 | 1 | 1 | 1.0 | 21.932 | 0.005 | 1.035 | 1.492
8 | 73.4600 | -3.1263 | 0.5481 | 2 | 5 | 5 | 5.0 | 22.164 | 0.005 | 1.563 | 1.399
9 | 73.4731 | -2.9390 | 0.5405 | 1 | 3 | 3 | 3.0 | 21.092 | 0.003 | 1.168 | 0.379
10 | 73.4742 | -3.1007 | 0.5416 | 2 | 5 | 5 | 5.0 | 21.903 | 0.008 | 1.236 | 0.527
11 | 73.4748 | -2.9576 | 0.5320 | 2 | 2 | 3 | 2.5 | 22.796 | 0.012 | 1.014 | -0.773
12 | 73.4777 | -3.0037 | 0.5300 | 2 | 2 | 2 | 2.0 | 22.751 | 0.009 | 0.764 | -1.046
13 | 73.4911 | -3.1496 | 0.5440 | 2 | 2 | 2 | 2.0 | 23.062 | 0.012 | 1.615 | 0.850
14 | 73.4931 | -2.9430 | 0.5450 | 2 | 1 | 1 | 1.0 | 21.622 | 0.004 | 0.991 | 0.984
15 | 73.4933 | -2.9684 | 0.5278 | 1 | 2 | 3 | 2.5 | 22.715 | 0.007 | 0.781 | -1.347
16 | 73.4947 | -2.9820 | 0.5381 | 1 | 2 | 2 | 2.0 | 21.656 | 0.005 | 0.672 | 0.055
17 | 73.4946 | -2.9827 | 0.5390 | 2 | 2 | 1 | 1.5 | 21.756 | 0.006 | 0.676 | 0.176
18 | 73.4979 | -2.9677 | 0.5512 | 1 | 1 | 1 | 1.0 | 21.183 | 0.005 | 0.748 | 1.812
19 | 73.4991 | -3.0529 | 0.5348 | 1 | 3 | 4 | 3.5 | 21.618 | 0.005 | 0.669 | -0.393
20 | 73.5044 | -3.0522 | 0.5405 | 1 | 2 | 2 | 2.0 | 21.326 | 0.003 | 0.620 | 0.379
21 | 73.5062 | -2.9934 | 0.5313 | 1 | 3 | 3 | 3.0 | 22.833 | 0.011 | 0.502 | -0.869
22 | 73.5069 | -2.9466 | 0.5404 | 1 | 1 | 2 | 1.5 | 22.230 | 0.007 | 0.875 | 0.365
23 | 73.5078 | -2.9789 | 0.5288 | 1 | 1 | 1 | 1.0 | 22.634 | 0.007 | 0.583 | -1.210
24 | 73.5138 | -2.9891 | 0.5310 | 2 | 1 | 1 | 1.0 | 22.581 | 0.007 | 0.457 | -0.909
25 | 73.5217 | -2.9974 | 0.5388 | 2 | 3 | 3 | 3.0 | 21.429 | 0.003 | 0.334 | 0.149
26 | 73.5288 | -2.9073 | 0.5357 | 2 | 1 | 2 | 1.5 | 23.393 | 0.010 | 1.209 | -0.270
27 | 73.5311 | -2.9636 | 0.5330 | 2 | 5 | 5 | 5.0 | 22.011 | 0.006 | 0.593 | -0.637
28 | 73.5431 | -3.1726 | 0.5463 | 2 | 2 | 3 | 2.5 | 21.986 | 0.005 | 1.751 | 1.158
29 | 73.5507 | -3.1334 | 0.5487 | 2 | 1 | 2 | 1.5 | 22.319 | 0.008 | 1.316 | 1.479
30 | 73.5525 | -3.0554 | 0.5524 | 2 | 2 | 3 | 2.5 | 20.309 | 0.003 | 0.457 | 1.972
31 | 73.5553 | -3.0057 | 0.5571 | 2 | 1 | 1 | 1.0 | 24.271 | 0.022 | 0.146 | 2.595
32 | 73.5560 | -3.0301 | 0.5478 | 2 | 3 | 3 | 3.0 | 21.979 | 0.006 | 0.201 | 1.359
33 | 73.5593 | -3.0662 | 0.5310 | 2 | 1 | 1 | 1.0 | 23.007 | 0.012 | 0.590 | -0.909
34 | 73.5594 | -3.0255 | 0.5404 | 1 | 1 | 1 | 1.0 | 21.011 | 0.002 | 0.188 | 0.365
35 | 73.5625 | -3.0062 | 0.5240 | 2 | 5 | 5 | 5.0 | 19.979 | 0.001 | 0.206 | -1.868
36 | 73.5631 | -3.0599 | 0.5350 | 2 | 1 | 1 | 1.0 | 22.169 | 0.004 | 0.524 | -0.365
37 | 73.5640 | -3.1474 | 0.5420 | 2 | 2 | 2 | 2.0 | 22.072 | 0.007 | 1.484 | 0.581
38 | 73.5716 | -3.0991 | 0.5441 | 2 | 5 | 5 | 5.0 | 20.767 | 0.004 | 0.978 | 0.863
39 | 73.5743 | -3.1364 | 0.5471 | 2 | 2 | 2 | 2.0 | 20.083 | 0.002 | 1.382 | 1.265
40 | 73.5823 | -3.0678 | 0.5446 | 2 | 3 | 3 | 3.0 | 21.826 | 0.004 | 0.712 | 0.930
41 | 73.5830 | -3.0264 | 0.5472 | 2 | 2 | 2 | 2.0 | 22.498 | 0.007 | 0.429 | 1.278
42 | 73.5885 | -3.0571 | 0.5420 | 2 | 2 | 2 | 2.0 | 22.773 | 0.008 | 0.663 | 0.581
43 | 73.5968 | -3.0625 | 0.5410 | 2 | 1 | 1 | 1.0 | 22.977 | 0.010 | 0.772 | 0.446
44 | 73.5974 | -3.0635 | 0.5420 | 2 | 1 | 1 | 1.0 | 21.059 | 0.003 | 0.784 | 0.581
45 | 73.5996 | -3.1177 | 0.5350 | 2 | 1 | 1 | 1.0 | 23.277 | 0.011 | 1.282 | -0.365
46 | 73.6035 | -3.1313 | 0.5340 | 2 | 1 | 2 | 1.5 | 21.775 | 0.005 | 1.437 | -0.501
47 | 73.6274 | -3.1215 | 0.5391 | 2 | 1 | 2 | 1.5 | 21.614 | 0.004 | 1.484 | 0.190
48 | 73.6317 | -3.1075 | 0.5490 | 2 | 3 | 3 | 3.0 | 20.989 | 0.003 | 1.397 | 1.519
49 | 73.6349 | -3.0398 | 0.5503 | 1 | 1 | 1 | 1.0 | 22.086 | 0.006 | 1.019 | 1.692
50 | 73.6433 | -3.1345 | 0.5400 | 2 | 1 | 1 | 1.0 | 22.317 | 0.008 | 1.708 | 0.311
51 | 73.6461 | -3.1212 | 0.5367 | 2 | 1 | 1 | 1.0 | 22.783 | 0.007 | 1.616 | -0.135
52 | 73.6481 | -3.1027 | 0.5379 | 2 | 1 | 1 | 1.0 | 21.462 | 0.004 | 1.489 | 0.027
53 | 73.6542 | -3.1415 | 0.5400 | 2 | 2 | 2 | 2.0 | 21.138 | 0.003 | 1.845 | 0.311
54 | 73.6650 | -3.1494 | 0.5390 | 2 | 3 | 3 | 3.0 | 21.427 | 0.004 | 1.990 | 0.176
55 | 73.6744 | -3.1331 | 0.5450 | 2 | 1 | 2 | 1.5 | 22.957 | 0.007 | 1.930 | 0.984
56 | 73.6819 | -3.0045 | 0.5470 | 2 | 2 | 2 | 2.0 | 22.868 | 0.009 | 1.507 | 1.252
Figure 1: Spectroscopic redshift histograms for galaxies in the
[0.5086,0.5678] redshift interval, normalized to the same area. The grey
histogram shows non-RPS galaxies and the blue one the 56 RPS candidates
(Sample 1). Figure 2: Histogram of the mean J classification Jmean for Sample
1. The colours correspond to the following figures for sub-samples 1a (green),
1b (cyan), 1c (blue), and 1d (red). Figure 3: Magnitude histograms of the
galaxies in the [0.5086,0.5678] redshift interval in the F814W filter,
normalized to the same area. The grey histogram shows non-RPS galaxies and the
blue one the 56 RPS candidates (Sample 1).

The 56 RPS candidates with spectroscopic redshifts in the cluster range
(hereafter Sample 1) are listed in Table 1 and the corresponding individual
images are displayed in the Appendix. They are in the magnitude range
$19.98\leq F814W\leq 24.27$.

The histograms of the redshifts, mean J values and F814W magnitudes are shown
in Figs. 1, 2 and 3 respectively, for the 359 galaxies with spectroscopic
redshifts in the cluster range, among which the 56 RPS candidates. We can see
from Fig. 1 that the redshift distributions of the overall cluster population
and of the RPS candidates are quite similar. The median redshifts of the two
samples are 0.5394 and 0.5400 respectively, and a Kolmogorov-Smirnov (KS) test
does not reject the hypothesis that these two samples are drawn from the same
parent population (with a probability of 12%).

Fig. 2 shows the distribution of J values. Based on this figure, the bins we
consider hereafter are as follows: Jmean=1 and 1.5 (24 galaxies, Sample 1a),
Jmean=2 and 2.5 (15 galaxies, Sample 1b), Jmean=3 and 3.5 (11 galaxies, Sample
1c), and Jmean=4 to 5 (6 galaxies, Sample 1d). The results in these four bins
will be discussed in the following sections. We adopt the following colour
code for the sub-samples: 1a in green, 1b in cyan, 1c in blue, and 1d in red.

The median F814W magnitudes of the two spectroscopic samples (the 359 galaxies
in the cluster redshift range and the 56 RPS galaxies) are 21.517 and 21.986
respectively, suggesting that RPS galaxies tend to be fainter than the overall
sample. A KS test does not reject the hypothesis that these two samples are
drawn from the same parent population at a probability of 24%.

###  2.3 Test on the J classification

Figure 4: Zooniverse J classification as a function of our mean classification
for the 56 RPS candidates of Sample 1. The grey points show the initial
classification and the red ones that obtained after harmonizing the
classifications. The point sizes increase with the standard deviation on the
measurement of J.

In order to test the reliability of our J classification, we used the
Zooniverse software333https://www.zooniverse.org/ and asked volunteers (mostly
graduate students in astronomy with or without knowledge on galaxies) to
classify part or all of the 56 RPS candidates of Sample 1. As a training, we
first gave them two examples of each class (only one for class 4). In total,
23 people participated, but 10 of them classified fewer than 10 galaxies, so
their results were not taken into account, and some galaxies were classified
by the same person several times.

Each galaxy taken into account here was classified between 11 and 18 times.
For the 56 galaxies of Sample 1, Table 4 gives the Zooniverse results: the
number of times the galaxy was classified, the minimum and maximum values of
J, the mean value of J on all the measurements and the corresponding
dispersion. This dispersion varies between 0.61 and 1.98.

Another bias could be due to the fact that some of the volunteers tend to
grade too optimistically or pessimistically compared to others, and a weighing
of the J values should then be applied. To quantify this rigorously, we would
need each person to have classified all 56 galaxies, and this was not the
case. However, we have tried to harmonize the J grades given by each
classifier. The set of grades given by each volunteer have a mean value
$mean_{ref}$ and a standard deviation $\sigma_{ref}$. For this harmonization,
we used the following relation:

$J_{i,harmonized}=(\sigma_{ref}/\sigma)*(J_{i}-mean)+mean_{ref},$

where classifier $i$ gave a series of grades $J_{i}$, that have a mean value,
$mean$, and a standard deviation, $\sigma$. It then becomes possible to
compare the different classifications.

Figure 4 shows that galaxies rated with a small standard deviation tend to be
correlated with low marks, and that the harmonization increases their values.
High grade galaxies have larger standard deviations. One can conclude that
volunteers have, most of the time, given lower grades compared to us, and were
reluctant to give high grades (especially J=4 or 5).

We can see from Fig. 4 that the difference between the classification obtained
with the Zooniverse and ours is between 1 and 2, except for J=5 where it
becomes smaller. This confirms our general feeling that, even with some
training, classifiers often hesitate between two consecutive values of J.

Interestingly, we find no correlation between the dispersion in the J
measurements from the Zooniverse and the galaxy magnitude, so the
classification does not appear more secure for bright objects than for faint
ones.

As pointed by the referee, when many people classify the same galaxy and the
mean value is considered, chances of getting a J=5 mean value are very low
(all classifiers must give a value of 5), and these chances decrease with the
increasing number of classifiers. In contrast, to get an average value of
three, for example, many more combinations of classifications can be given.
This bias is difficult to quantify and to correct but should be kept in mind.

This classification method could contribute to boosting the development of
machine learning algorithms with satisfactory performances by increasing the
size of the learning sample, thus providing a still-lacking precise tool of
shape identification to classify RPS galaxies. However, we must remember how
difficult it is to select RPS galaxies in an unambiguous way.

###  2.4 Sample 2 (photometric redshifts)

We have an 8-band magnitude catalogue (in the U, B, V, Rc, Ic, Z, J, and K
bands) covering a larger zone than the HST mosaic and containing 14731
photometric redshifts (see Tam et al. (2020)) that we consider here to make a
tentative study of a large sample of RPS galaxy candidates in this cluster. If
we consider that the typical error on photometric redshifts is $0.05(1+z)$,
the redshift interval for galaxies to be possible cluster members is
approximately $0.48<z<0.61$. This corresponds to about $\pm 8.7\sigma_{v}$, a
large value that is due to the large error on photometric redshifts. There are
2180 galaxies in this photometric redshift interval, out of which 1326 are
inside the HST mosaic.

We first checked the general agreement between the classifications made by two
of us (FD and LD) for Sample 1 by calculating the mean (standard deviation) of
JF and JL. We find respective values of 2.125 (1.27) and 2.286 (1.19), showing
a good agreement between the two classifiers. Therefore, only one of us (LD)
looked at the HST images of the 1326 galaxies with photometric redshifts in
the $0.48<z<0.61$ redshift interval and gave them a J classification,
resulting in 217 RPS candidates. The catalogue of 217 RPS candidates based on
their photometric redshift will be available in electronic form at the CDS via
anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. This catalogue contains the
following columns: number, RA, DEC, photometric redshift, J classification,
F814W magnitude and its error. We added to this sample the 56 galaxies of
Sample 1, which all have a photometric redshift in the $0.48<z<0.61$ interval,
and thus created a sample with 273 RPS candidates, that we refer to as Sample
2 hereafter.

Obviously, some of these galaxies do not belong to the cluster. To have an
idea on the errors caused by a selection based on photometric redshifts, we
can analyze several facts. First, we note that all galaxies of Sample 1 pass
the photometric redshift selection and are thus included in Sample 2. Second,
we have a full spectroscopic redshift catalogue of 620 galaxies, out of which
359 and 261 have spectroscopic redshifts respectively in and out of the
cluster [0.5086,0.5678] spectroscopic range. Out of the 261 galaxies that are
out of the cluster spectroscopic range, 27 have a photometric redshift in the
[0.48,0.61] photometric redshift cluster range, or 10%. If we now consider the
273 RPS candidates of Sample 2, which are all cluster members based on their
photometric redshift, there are 8 galaxies with spectroscopic redshifts
outside the cluster spectroscopic range.

Finally, even though the morphological properties of these RPS candidates -
that led to their selection - are interpreted as due to their interaction with
the dense intracluster medium, some contaminants belonging to
foreground/background structures are still likely to be present. This is
discussed in Sect. 5.

Figure 5: Photometric redshift histograms normalized to the same area: the
1326 galaxies in the [0.48,0.61] redshift interval are shown in grey and the
273 RPS candidates of Sample 2 in magenta. Figure 6: Histogram of the J
classification for the 273 RPS candidates of Sample 2. Figure 7: Magnitude
histograms for the 1326 galaxies in the [0.48,0.61] redshift interval in grey
and for the 273 RPS candidates of Sample 2 in magenta, normalized to the same
area.

The histograms of the redshifts, J values and F814W magnitudes are shown in
Figs. 5, 6 and 7 for the 1326 galaxies in the [0.48,0.61] photometric redshift
interval and for the 273 RPS candidates of Sample 2.

The median photometric redshifts of the two samples are 0.5394 and 0.5441 for
all galaxies and RPS candidates of Sample 2 respectively. A KS test does not
reject the hypothesis that these two samples are drawn from the same parent
population at a probability of 12%. The median F814W magnitudes of the two
samples are 22.44 and 22.53 for all galaxies and RPS candidates of Sample 2
respectively. A KS test does not reject the hypothesis that these two samples
are drawn from the same parent population at a probability of 6.4%.

One can note that there are more faint galaxies in Sample 2 than in Sample 1,
since it is obviously easier to obtain photometric redshifts than
spectroscopic redshifts.

##  3 Spatial and phase space distributions

###  3.1 Sample 1

####  3.1.1 Spatial distribution

Figure 8: Figure 4 from Tam et al. (2020) showing the large scale-structure in
a total region of $30\times 30$ arcmin2 around MS0451. The positions of RPS
candidates of Samples 1a, 1b, 1c, and 1d are respectively shown as green,
cyan, blue and red circles. The RPS candidates of Sample 2 with grades J=1 to
3 are shown as magenta crosses, and those with J=4 and 5 with magenta squares.
The white cross indicates the position of the cluster centre. North is up and
east is left. Figure 9: Figure 9 from Tam et al. (2020) showing the low
density large scale structure in a total region of $30\times 30$ arcmin2
around MS0451 with the substructures (red circles) and three filaments (in
green) superimposed. The orange circles are unlikely to be cluster
substructures, and are possibly the projection of large-scale structures at
other redshifts along the line of sight. The positions of RPS candidates of
Samples 1a, 1b, 1c and 1d are respectively shown as small green, cyan, blue
and red circles. The RPS candidates of Sample 2 with grades J=1 to 3 are shown
as magenta crosses, and those with J=4 and 5 with magenta squares. The white
cross indicates the position of the cluster centre. The two yellow dashed
circles have radii of $0.6\times r_{200}$ and $1.4\times r_{200}$,
corresponding to the peaks seen in Fig. 10. North is up and east is left.

Tam et al. (2020) combined strong and weak lensing constraints to reconstruct
the density field of MS0451 in a $6\times 6$ Mpc2 area. For the cluster
centre, they adopted the best-fit strong lensing mass model from Jauzac et al.
(2021). For the large-scale structures, they measured the weak lensing shear
signal of background galaxies from the HST images and reconstructed the
projected (2D) mass distribution by using LENSTOOL (Jullo et al., 2007; Jullo
& Kneib, 2009) and the method presented in Jauzac et al. (2015). The total
mass distribution reconstructed from their joint strong and weak lensing
analysis is shown in Tam et al. (2020) Figure 4, and the low density large
scale structure with strong lensing potentials subtracted appears in their
Figure 9. In the reconstructed large scale environment, there were 14 weak
lensing peaks with S/N¿3 detected. Tam et al. (2020) further investigated the
validity of these overdense regions by considering the redshift information.
They found that only 6 of these 14 weak lensing peaks were at the cluster
redshift. These were then considered as substructures, constituting a part of
the extended cluster (they are noted as red circles in Fig. 9, while the
others were considered as projections of structures at other redshifts along
the line of sight (the orange circles in Fig. 9). Based on the distribution of
these six cluster substructures, Tam et al. (2020) proposed that three
filaments (in green in Fig. 9) are connected to the cluster core.

The large scale structure drawn by Tam et al. (2020) is shown in Fig. 8 with
our four spectroscopic samples of RPS candidates (Samples 1a, 1b, 1c, and 1d)
drawn in different colours, according to their Jmean class (likeliness to be a
RPS galaxy), as well as the photometric sample (Sample 2) in magenta, with
different symbols for J$\leq 3$ and for J$>3$ (we address the photometric
sample in 3.2). We can see that overall the spectroscopic RPS candidates are
spread over the entire mosaic, and only a few of them are located in the dense
central cluster region. This contrasts with the distribution of all
spectroscopic cluster members that show the typical higher concentration
toward the cluster core (RPS candidates being more sparsely distributed). The
RPS candidates show a somewhat higher concentration along the southeast to
northwest cluster elongation axis, but in view of the small numbers involved
it is difficult to make a statistical analysis of the significance of this
observation. If one now looks at the low density large scale structure drawn
by Tam et al. (2020) displayed in Fig. 9, we can see that RPS candidates tend
to avoid the substructures highlighted as red circles, and they show no trend
of being spatially linked to the three filaments. This is discussed further in
Sect. 5.

Figure 10: Histogram of the distances of the 56 spectroscopic RPS candidates
to the cluster centre in units of $r_{200}$. Samples 1a and 1b are shown in
light pink, 1c is blue and 1d is red.

The histogram of the distances of the 56 RPS Sample 1 candidates to the
cluster centre in units of $r_{200}$ is displayed in Fig. 10, with
$r_{200}=2110$ kpc (Durret et al., 2021). We can see that there are only five
RPS candidates at small clustercentric distances ($r<0.4\times r_{200}$).
There are two peaks in the distribution around 0.6$\times r_{200}$ and
1.4$\times r_{200}$. There is no obvious feature at a clustercentric radius of
0.6$\times r_{200}$. On the other hand, substructures shown as red circles in
Figs. 8 and 9 fall close to a clustercentric radius of 1.4$\times r_{200}$,
shown in Fig. 9 by the outer dashed yellow circle. One may note that this is
also the case for orange circles, though Tam et al. (2020) consider that they
are probably not structures belonging to the cluster. An excess of RPS
candidates at this clustercentric radius may therefore be linked to an excess
of cluster galaxies in that region (that we are unable to probe with our
data).

We note that Fig. 10 is quite similar to the analogous figure for MACS0717
(Fig. 6 left, in Durret et al. (2021), where an absence of RPS candidates in
the cluster core was also noted. We further discuss this in our final remarks.

####  3.1.2 Phase space distribution

Figure 11: Projected phase space diagrams (see text) for MS0451 (left) and MACS0717 (right). For MS0451, the 359 galaxies with spectroscopic redshifts in the cluster range are in grey, and RPS candidates of samples 1a, 1b, 1c and 1d are respectively shown as small green, large green, blue, and red points. For MACS0717, all galaxies in the cluster range are in black and RPS candidates are in red. The vertical and oblique dashed lines are those of figure 9 of Mahajan et al. (2011) as explained in the text.  Table 2: Percentages of RPS candidates in the virialized (limit ar $r=r_{100}$), infall and backsplash regions of MS0451 and MACS0717. Region |  |  MS0451 |  |  |  |  MACS0717 |  |
---|---|---|---|---|---|---|---|---
| RPS |  | non-RPS |  | RPS |  | non-RPS |
virialized | 37/56 | 66% | 282/359 | 79% | 40/81 | 49% | 347/557 | 62%
infall | 6/56 | 11% | 32/359 | 9% | 25/81 | 31% | 136/557 | 24%
backsplash | 13/56 | 23% | 45/359 | 12% | 16/81 | 20% | 74/557 | 13%

In order to get more insight on the dynamical properties of the RPS
candidates, we drew projected phase space diagrams for MS0451 and for
MACS0717, as a comparison, and since both clusters lie at z$\sim$0.5.

We chose MACS0717 as a comparison cluster because it is a well-studied very
massive cluster (Ebeling et al., 2007) at a redshift (z=0.54) similar to that
of MS0451, with deep and extended HST observations, since it is part of the
Hubble Frontier Fields survey (Lotz et al., 2017). It is a very strong
gravitational lens, and a lensing analysis coupled with X-ray data has
revealed a complex merging system involving four cluster-scale components (Ma
et al., 2009; Zitrin et al., 2009; Limousin et al., 2012, 2016). A long
filament extending southeast of the cluster core has been detected in the 3D
distribution of galaxies (Ma et al., 2008), of red-sequence galaxies (Durret
et al., 2016), and through weak lensing (Jauzac et al., 2012; Medezinski et
al., 2013; Martinet et al., 2016; Jauzac et al., 2018). Based on HST data of
comparable depth as those presented here (but for MACS0717 we had images in
the two filters F555W and F814W), a search for RPS galaxies in MACS0717 has
been presented by Durret et al. (2021), one of the two galaxy classifiers
being the same in both studies (FD).

To draw the phase diagrams of these two clusters, we computed the values of
$\Delta v/\sigma_{v}$, where $\Delta v$ is the difference between each galaxy
velocity and the mean cluster velocity, and drew these values as a function of
the projected distance to the cluster centre in units of $r_{100}$,
$r/r_{100}$. For MS0451, we have previously estimated $r_{200}=2110$ kpc
(Durret et al., 2021), and from this value we estimate $r_{100}=(1.34\pm
0.04)\times r_{200}=2827$ kpc (G. Mamon, private communication). Based on a
weak lensing analysis, Tam et al. (2020) give a mass M${}_{200}=1.65\times
10^{15}$ M⊙ for MS0451. The cluster velocity dispersion can then be computed
using equation (1) from Munari et al. (2013):

$\sigma_{v}=1090\times[h(z)\times M_{200}]^{(1/3)},$

where $h(z)=H(z)/100$, $M_{200}$ is expressed in units of $10^{15}$ M⊙, and
$\sigma_{v}$ is the unidimensional velocity dispersion in units of km/s, and
we obtain $\sigma_{v}=1205$ km s-1, as in Durret et al. (2021). The result is
shown in Fig. 11, together with a similar figure for MACS0717, for which the
corresponding values are given by Durret et al. (2021).

The plots in Fig. 11 can be compared to results by Mahajan et al. (2011), who
define classes based on the radial phase-space distribution of particles. For
them, particles that are outside the virial radius ($r_{100}$), and travelling
at velocities lower than the critical velocity, are falling into the cluster
for the first time (infalling), while particles outside the virial radius with
higher velocities must have crossed the cluster at least once (backsplash).
The critical velocity is the radial velocity that separates infalling galaxies
entering the cluster for the first time from galaxies entering or crossing the
cluster for the second time (or more). It is shown as an oblique red line in
Fig. 9 of Mahajan et al. (2011) and is defined by their equation (2).

In their Fig. 9, Mahajan et al. (2011) separate virialized, infall, and
backsplash galaxies with cuts taken from Sanchis et al. (2004) in units of
$r_{100}$. In a similar way, we draw the limits between the virialized and
non-virialized regions as lines in Fig. 11 for the two clusters. The oblique
lines separating infall and backsplash galaxies were drawn as in Mahajan et
al. (2011) Figure 9.

For MS0451, applying the Sanchis et al. (2004) cuts to our data, the numbers
and percentages of RPS candidates are given in Table 2: 66% are located in the
virialized region ($r/r_{200}\leq 1$), and 34% have $r/r_{200}>1$: 11% of the
total sample in the infall region and 23% in the backsplash region. The
corresponding numbers for non-RPS galaxies are: 79% in the virialized region,
and for the remaining 91 galaxies, 9% of the total sample in the infall region
and 12% in the backsplash region.

For MACS0717, 49% of the RPS candidates are in the virialized region, 31% in
the infall region and 20% in the backplash region. Fpr non-RPS galaxies, 62%
are in the virialized region, 24% and 13% in the infall and backsplash
regions. These percentages will be discussed in Section 5.

###  3.2 Sample 2

The spatial distribution of RPS candidates in Sample 2 is shown in Figs. 8 and
9. They are found over the entire cluster field of view but those with J$\leq
3$ in particular do not tend to avoid the dense zones as much as RPS
candidates of Sample 1, possibly because some of these objects are not cluster
members, and are just seen in projection on the cluster. These are also the
candidates with less obvious RPS features.

Alternatively, and since these are generally less luminous, thus less massive
galaxies when compared to Sample 1 (as confirmed in Section 4), this could
highlight a real difference in the spatial distribution of different mass RPS
candidates.

##  4 Stellar populations of RPS candidates

###  4.1 Method

We used LePhare (Ilbert et al., 2006), through the GAZPAR
interface444https://gazpar.lam.fr/home, to fit the spectral energy
distributions (SEDs) of the four samples. Sample 1 includes the 56 RPS
candidates with spectroscopic redshifts. Sample 2 includes the 273 RPS
candidates with photometric redshifts in the cluster range. Sample 3 includes
282 non-RPS galaxies with spectroscopic redshifts in the same range as Sample
1. Sample 4 includes 1027 non-RPS galaxies with photometric redshifts in the
same range as Sample 2. The fits were made with the Bruzual & Charlot (2003)
models assuming a Chabrier (2003) initial mass function. Based on an input
catalogue with positions, eight magnitudes and corresponding errors, and
redshifts, LePhare fits the galaxy SEDs and infers from the best fit template
for each galaxy the stellar mass, mean stellar population age, star formation
rate (SFR), and specific star formation rate (sSFR). The input parameter space
was carefully selected so as to cover the expected characteristics of late-
type galaxies with probable star forming activity as well as the SEDs of the
typically abundant early-type galaxies in clusters.

Out of the 56 spectroscopically confirmed RPS candidates, the best fit
template spectrum includes all the main emission lines in the optical
([OII]3727, [OIII]4959, 5007, H$\beta$ and H$\alpha$) for 33 of them, and an
H$\alpha$ (and weak H$\beta$) line for 20 of them (see examples of fits in
Fig. 7 of Durret et al. (2021)). Only three of the best fit template spectra
include no emission line. This implies that the majority of our RPS candidates
are forming stars.

The histograms of the stellar masses, ages, SFRs and sSFRs are respectively
shown in Figs. 12, 13, 14, and 15 for Samples 1, 2, 3, and 4, and will be
discussed in detail along the next sub-sections.

###  4.2 Stellar masses

Figure 12: Histograms of the stellar masses (in units of solar masses)
normalized to the same area. Top: Samples 1 and 3 (spectroscopic redshifts),
with RPS candidates in blue and non-RPS galaxies in red. Bottom: Samples 2 and
4 (photometric redshifts), with RPS candidates in green and non-RPS galaxies
in light pink.

Figure 12 shows that RPS candidates (Samples 1 and 2) appear to have lower
mass galaxies than non-RPS galaxies (Samples 3 and 4). The median masses for
Samples 1 and 2 are respectively $10^{9.57}$ and $10^{9.15}$ M⊙, while they
are $10^{10.28}$ and $10^{9.73}$ M⊙ for Samples 3 and 4. Differences between
mass distributions of RPS and non-RPS candidates are confirmed statistically
by a KS test, the results of which are given in Table 5 (as for all other
quantities).

If we now compare the masses of Sample 1 and Sample 2 galaxies, a KS test also
confirms that these two distributions differ. The fact that galaxies of Sample
1 are predominantly more massive than those of Sample 2 is not surprising
since galaxies observed spectroscopically are intrinsically brighter, and thus
likely to be more massive. As expected, our photometric redshift samples allow
us to probe the low mass regime, missed in the bright spectroscopic samples.

In order to understand if completeness issues are affecting these comparisons,
we apply a cut in mass, limiting the samples to $10^{9}\leq$M$\leq 10^{10.5}$
M⊙ (frontier values suggested by Fig. 12 \- top). The median masses for
Samples 1 and 2 are then respectively $10^{9.57}$ and $10^{9.63}$ M⊙, while
they are $10^{9.97}$ and $10^{9.79}$ M⊙ for Samples 3 and 4. KS tests confirm
that all these samples are likely drawn from different populations, so the
above inferences should hold, and RPS galaxies appear to have, in general,
lower masses than non-RPS galaxies. Although uncertainties in the mass
determination are large, the trend we find agrees with what is observed in the
local Universe across groups and clusters, as probed at z¡0.04 in the SDSS-
UNIONS survey by Roberts et al. (2022): RPS candidates commonly seem to be
low-mass galaxies.

At similar redshifts, the mass distribution of the 81 spectroscopic RPS
candidates in MACS0717 (Fig. 8 in Durret et al. (2021)) was found to be in the
$10^{9}\leq$M$\leq 10^{11}$ M⊙ range, while in MS0451, they are lower mass
galaxies, with 16% of Sample 1 galaxies having masses below $10^{9}$ M⊙. HST
imaging of MS0451 is deeper than for MACS0717. This difference in depth could
explain the difference in RPS mass ranges observed between MS0451 and
MACS0717.

Moretti et al. (2022) observed RPS galaxies in the merging clusters A2744 and
A370, at $z\sim 0.3-0.4$ with VLT/MUSE and found masses in the
$10^{8}\leq$M$\leq 10^{10.6}$ M⊙ range, but comparing our Sample 1 values with
theirs is hazardous due to a different selection procedure of RPS galaxies
(indeed, their project specifically identified RPS galaxies with tails),
different observational limits (e.g. in magnitude and cluster radial
coverage), and different SED fitting codes to derive stellar masses. We thus
refrain from drawing any conclusion.

###  4.3 Stellar ages

Figure 13: Same as Fig. 12, but for stellar ages (in years).

To estimate the accuracy of the stellar ages estimated by Le Phare, we
considered for the galaxies of Samples 1 and 3 the quantity
$(age_{max}-age_{min})/2$, where $age_{max}$ and $age_{min}$ are the upper and
lower limits on the age given by Le Phare. We find that this quantity is much
smaller for RPS than for non-RPS galaxies. For RPS galaxies, it is smaller
than $2.5\times 10^{8}$ yrs for 30% of the sample and smaller than $5\times
10^{8}$ yrs for 79% of the sample. On the other hand, for non-RPS galaxies the
error on the stellar age is smaller than $5\times 10^{8}$ yrs for only 8% of
the sample. The percentages of non-RPS galaxies with age errors smaller than
$10^{9}$ yrs, $1.5\times 10^{9}$ yrs, and $2\times 10^{9}$ yrs, are
respectively 48%, 70%, and 87%.

The mean stellar age distributions (Fig. 13) show that RPS candidates (Samples
1 and 2) are predominantly younger than non-RPS galaxies (Samples 3 and 4). KS
tests show that the differences between the distributions are statistically
significant, so we can infer that RPS candidates typically have less evolved
stellar populations than non-RPS galaxies. The median ages for Samples 1 and 3
are $5.4\times 10^{8}$ and $5.5\times 10^{9}$ yrs respectively, while the
corresponding values for Samples 2 and 4 are $5.1\times 10^{8}$ and $2.3\times
10^{9}$ yrs.

However, the difference in age distribution between RPS candidates and non-RPS
galaxies could simply be driven by the different mass distributions of these
galaxies (discussed in the previous sub-section). We thus redid our analysis
after limiting the samples to $10^{9}\leq$M$\leq 10^{10.5}$ M⊙ (as before). We
then find that the median ages for Samples 1 and 3 are $5.1\times 10^{8}$ and
$3.0\times 10^{9}$ yrs respectively, while the corresponding values for
Samples 2 and 4 are $8.1\times 10^{8}$ and $2.3\times 10^{9}$ yrs. As found
without applying a mass cut, KS tests still imply that RPS candidates are
typically younger than non-RPS candidates.

If we compare the age distribution of Sample 1 to that of RPS candidates in
MACS0717, we find that RPS candidates tend to be younger in MS0451: 86% of the
galaxies in Sample 1 have mean ages younger than $10^{9}$ yrs, while this
percentage is only 29% in MACS0717. A cut in mass ($10^{9}\leq$M$\leq
10^{10.5}$ M⊙) respectively changes these percentages to 64% and 27%.

###  4.4 Star formation rates

Figure 14: Same as Fig. 12 for star formation rates (in units of M⊙ yr-1). A
few non-RPS galaxies with even lower SFR are not shown to avoid shrinking too
much the histograms.

The SFR distributions of RPS and non-RPS galaxies look different (Fig. 14), as
there is a low SFR tail in non-RPS galaxies (both Samples 3 and 4) that is
almost absent when considering RPS candidates (Samples 1 and 2).

This is also hinted by the median values of the distributions, which are
$10^{0.679}$ and $10^{-1.004}$ M⊙ yr-1 for Samples 1 and 3 respectively, and
$10^{-0.75}$ and $10^{-1.26}$ M⊙ yr-1 for Samples 2 and 4. Indeed, KS tests
confirm that SFR distributions of Samples 1 and 3 on the one hand, and of
Samples 2 and 4 on the other hand, differ. Therefore, the global trend for
higher SFR in RPS candidates compared to non-RPS galaxies is statistically
significant.

As before, we check the effect of a mass cut ($10^{9}\leq$M$\leq 10^{10.5}$
M⊙) on the SFR distributions. We then find median values of $10^{-0.05}$ and
$10^{-0.965}$ M⊙ yr-1 for Samples 1 and 3 respectively, and $10^{0.718}$ and
$10^{-1.33}$ M⊙ yr-1 for Samples 2 and 4. KS tests again confirm that these
samples are not drawn from the same population.

The SFRs measured for RPS galaxies in MACS0717 show values between $10^{-1.0}$
and $10^{1.8}$ M⊙ yr-1, with a median of $10^{0.625}$ M⊙ yr-1, comparable to
that of MS0451. However, if one compares SFR histograms of Fig. 14 for Sample
1 of MS0451 and Fig. 9 (left) in Durret et al. (2021) for MACS0717, one can
note that MS0451 has 22 galaxies (out of 56) with a SFR larger than the higher
value observed in MACS0717 (SFR=$10^{1.75}$ M⊙ yr-1).

If we apply a mass cut ($10^{9}\leq$M$\leq 10^{10.5}$ M⊙) to MACS0717, we find
a median SFR of $10^{0.73}$ M⊙ yr-1, much higher than the corresponding value
of $10^{-0.708}$ M⊙ yr-1 estimated for Sample 1 with the same cut. However, in
view of the broader distribution of masses in MS0451, a comparison of the
sSFRs of the two clusters is probably more relevant (see below).

In the Moretti et al. (2022) study of the galaxy populations of clusters A2744
and A370, dynamically similar to ours but at lower redshifts, they measure SFR
values up to 73 M⊙ yr-1 (i.e. $\sim 10^{1.86}$ M⊙ yr-1) for their RPS
candidates. Figure 14 reveals that 18 RPS candidates of Sample 1 (i.e. 32%)
and 19 RPS candidates of Sample 2 (7%) exceed this value - an effect that,
uncertainties apart, can be simply due to the redshift difference and to the
likely larger gas reservoirs of galaxies at z $\sim 0.5$.

It would be very interesting to do a spatially resolved assessment of the star
formation within the galaxies but, unfortunately, the lack of spatially
resolved data (spectroscopy and/or magnitudes) prevents us from estimating the
SFR in galaxy disks and tails separately, as done e.g. in Gullieuszik et al.
(2020) based on VLT/MUSE data.

###  4.5 Specific star formation rates

Figure 15: Same as Fig. 12 for specific star formation rates (in units of
yr-1). The vertical dashed line signals the commonly used limit between
quiescent and star-forming galaxies.

Specific star formation rates should be more informative than plain SFR since
they are normalized to galaxy stellar masses. Figure 15 shows that RPS
candidates appear to typically have larger sSFR than non-RPS galaxies. Also,
only 5% and 7% of galaxies in Samples 1 and 2 have log(sSFR)$<-11$, the usual
limit that separates non star forming galaxies from star forming ones. On the
other hand, 63% and 51% of galaxies in Samples 3 and 4 have log(sSFR)$<-11$
(these likely make up the quiescent galaxy population of the cluster).
Noticeably, Sample 1 shows a somewhat bimodal sSFR distribution, with a non-
negligible fraction of high sSFR galaxy members, which are commonly absent in
lower-z clusters especially in their cores (e.g. Oemler, 1974; Dressler, 1980;
Goto et al., 2003; Kauffmann et al., 2004; Blanton et al., 2005).

The differences between the typical sSFRs of RPS and non-RPS galaxies is
confirmed by the median values of the distributions, $10^{-9.57}$ and
$10^{-11.55}$ yr-1 for Samples 1 and 3 respectively, and $10^{-9.57}$ and
$10^{-11.12}$ yr-1 for Samples 2 and 4, respectively, and the differences
between the samples are confirmed by KS tests.

When we apply a mass cut as before ($10^{9}\leq$M$\leq 10^{10.5}$ M⊙), we find
median values of sSFR of $10^{-9.32}$ and $10^{-11.10}$ yr-1 for Samples 1 and
3 respectively, and $10^{-8.92}$ and $10^{-11.33}$ yr-1 for Samples 2 and 4
respectively, and the differences between the samples are here again confirmed
by KS tests. Therefore, the higher typical sSFRs of RPS candidates compared to
non-RPS galaxies seem to be statistically significant.

In MACS0717, the median sSFR of RPS candidates is $10^{-9.36}$ yr-1, and 10%
of these galaxies have log(sSFR)$<-11$, results which are perfectly similar to
those derived for Sample 1 of MS0451. If we apply a mass cut
($10^{9}\leq$M$\leq 10^{10.5}$ M⊙), the median sSFR of MACS0717 becomes
$10^{-9.13}$ yr-1, probably not significantly different from the value of
$10^{-9.79}$ for MS0451, within uncertainties. The sSFR histograms of MS0451
and MACS0717 also look similar.

To summarize these results, RPS candidates and non-RPS galaxies do not seem to
be drawn from the same parent population, as confirmed by KS tests. As already
mentioned by Durret et al. (2021) and references therein, RPS candidates tend
to have smaller masses, younger mean stellar ages, and larger SFRs and sSFRs
than non-RPS galaxies. This agrees with the general picture of these galaxies
having star formation triggered by their interaction with the hot intracluster
gas, and our findings for MS0451 are consistent with this hypothesis.

###  4.6 Star formation rate to mass relation

Figure 16: SFR as a function of stellar mass for samples 1 (blue), 2 (green),
3 (red), and 4 (light pink). The black line indicates the relation by Vulcani
et al. (2016) and its approximate dispersion of $\pm 0.28$ (light black
lines).

A plot of the SFR as a function of stellar mass is shown in Fig. 16 for our
four samples, together with the main sequence (MS) of star forming galaxies
established by Vulcani et al. (2016) for a sample of 76 galaxies belonging to
10 clusters in the $0.3<z<0.7$ redshift range, and spanning a similar stellar
mass range as ours, $10^{8.25}\la$ M$\leavevmode\nobreak\ \la 10^{11}$ M⊙. We
note that the striped pattern that appears in Fig. 16 is due to the limited
number (12) of templates used by LePhare (Ilbert et al., 2006), namely in what
concerns star formation histories and ages. This is especially the case for
typical SEDs of low or non star forming galaxies, for which there are only two
templates (that, moreover, do not consider dust attenuation). The ensemble of
templates should, however, cover all the parameter space conveniently while
avoiding degeneracies among too similar models (that might hamper convergence
and would not provide better results for our data, given the usual
uncertainties associated with estimating SFRs from template fitting).

The percentages of galaxies - separated by samples and having M$\leq
10^{10.5}$ M⊙ \- located above, within, and below the Vulcani MS are provided
in Table 3. We have added the corresponding percentages for the RPS candidates
found in MACS0717 (these should be directly comparable to Sample 1 of MS0451).
These numbers are meant to guide the eye but one should however consider that
they can only indicate possible trends, given the usual uncertainties
associated with the estimates of both stellar mass and star formation rates.
With this in mind, we can still infer that, globally, RPS candidates seem to
be forming stars more actively than their non-RPS counterparts (49% and 43% of
Samples 1 and 2 lie within or above the star forming main sequence, against
just 37% and 29% for Samples 3 and 4). This trend was more strongly marked for
MACS0717, where only 21% of the RPS candidates lie below the MS. The other
difference between the two clusters seems to be the inversion of RPS
candidates within and above the MS: MACS0717 has both regions equally
populated whereas, if we take Sample 1 of MS0451, only 4% of the 49%
previously mentioned are found between the thin black lines in Fig. 16 that
delimit the region populated by galaxies with normal star formation rates for
their stellar masses.

Table 3: Percentages of galaxies located above (top line) and within (bottom line) the Vulcani et al. (2016) main sequence (MS) for our four samples and for the RPS candidates of MACS0717, all the samples being cut at $10^{9}\leq$M$\leq 10^{10.5}$ M⊙.  | Sample 1 | Sample 2 | Sample 3 | Sample 4 | MACS0717
---|---|---|---|---|---
above MS | 50% | 47% | 13% | 18% | 38%
in MS | 5% | 32% | 20% | 20% | 41%

If we check the literature, we find that Cooper et al. (2022) derived the
star-forming main sequence for 163 galaxies in four EDisCS clusters in the
redshift range $0.4<z<0.7$, out till the respective infall regions. Their
points (see their Fig. 8), essentially in the mass range
$[10^{8.5},10^{11.5}]$ M⊙, are almost all below the Vulcani relation,
confirming that a significant number of our RPS candidates typically have
large SFRs for their stellar masses. In that same figure, we can see that the
SFR values estimated by Finn et al. (2005) for galaxies belonging to three
EDISCS clusters at $z\sim 0.75$ are above the Vulcani relation, particularly
at low mass, so as mentioned by Finn et al. (2005) there is probably a
redshift dependence, though there are other factors (such as mass) influencing
the SFR.

If we now compare with low redshift observations targetting specifically RPS
galaxies as well, our findings seem to agree with those of various authors.
For example, Poggianti et al. (2016) detected 344 RPS candidates in 71
clusters (OMEGAWINGS+WINGS surveys comprising galaxies with stellar masses
above $10^{8}$ M⊙) and showed that they had increased SFRs (see their Fig. 8).
Vulcani et al. (2018) found a similar result when comparing 42 RPS cluster
galaxies to a control sample of 32 galaxies (field and undisturbed galaxies)
from the GASP survey, all with stellar masses above $10^{9}$ M⊙. Roberts et
al. (2022) observed a large sample of isolated field galaxies at low redshift
and found that 77% of their RPS galaxies (stellar masses above $10^{8.8}$ M⊙)
lie above the star-forming main sequence drawn in their Figure 8. The general
assessment thus seems to be that environment, particular RPS, is indeed
triggering episodes of enhanced SFR at various redshifts.

Apart from these global trends, a closer inspection of Fig. 16 appears to
indicate that there is a transition of behaviour at M$\sim 10^{9.4}$ M⊙ in
MS0451: more massive RPS candidates lie notably above the MS (having boosted
SFRs), whereas lower mass RPS candidates actually populate preferably the
lower part of the plane (appearing to have lost the capacity to form stars).
This insight is confirmed by the median values of SFR: $10^{-0.94}$ and
$10^{1.87}$ M⊙ yr-1 for M$\leq 10^{9.4}$ M⊙ and M$>10^{9.4}$ M⊙ in Sample 1,
$10^{-1.05}$ and $10^{0.97}$ in Sample 2, respectively. This dichotomy,
especially marked in Sample 1, was already apparent in Fig. 14 and could be an
artefact of the SED fitting tool, a completeness issue, or a real trend. In
the last case, a tentative interpretation is that normal star forming galaxies
with available gas reservoirs and large masses have boosted SFRs when subject
to RPS (thus moving upward from the main sequence). In the lower mass regime,
the increased SF episode leaves its marks on the galaxy (allowing its
selection as having been affected by RPS), but either its gas is totally
consumed in that episode or, due to the weaker gravitational potentials of
these galaxies, what is left of it is rapidly swept away. Either way,
subsequent SF is prevented.

This different behaviour for the different mass regimes of RPS candidates was
not detected in low-z clusters (e.g. Poggianti et al., 2016) nor in the field
(Roberts et al., 2022) and will definitely need to be confirmed - or not -
with a deeper and more complete set of spectroscopic data. If true, it might
be linked to the specific dynamical conditions of this post-merging cluster.
We note that the directly comparable study of MACS0717 was performed on a
somewhat shallower dataset (see section 4.2), which did not allow us to probe
down to the same lower mass regime. This would have been especially
interesting since MACS0717 is also a dynamically complex cluster - a merging
system.

On a final note, we have looked at the distribution of the different J class
galaxies in the SFR-mass plane: a simple separation between J$>3$ and J$\leq
3$ does not show any particular trend. The former, showing stronger RPS
characteristics, are not distinguishable from the others in what regards their
SFR-mass properties. We have also checked the positions of the 6 infall and 10
backsplash RPS candidates of Sample 1 in Fig. 16: here, again, the different
categories of galaxies are spread throughout the graph, without revealing any
particular trend. These tentative analyses are, however, based on small
numbers in each category, which renders any inference difficult.

##  5 Discussion and conclusions

We present in this paper a search for RPS candidates in the post-merging
cluster MS0451 located at redshift $z=0.5377$. This study is based on HST
images covering a very large region reaching almost $2\times r_{200}$ (i.e. a
spatial coverage reaching the cluster infall region), complemented with a
large spectroscopic redshift catalogue and a magnitude catalogue in eight
bands that allowed us to derive photometric redshifts. We compare our results
to those obtained by Durret et al. (2021) in MACS0717, a massive merging
cluster at similar redshift with comparable data, analyzed in the same way.
Though spatially resolved spectroscopic data would obviously give much more
information, it is very challenging to acquire and analyze integral field
datacubes for so many galaxies spread out till large clustercentric distances.
For example, Moretti et al. (2022) study two clusters at $z\sim 0.3-0.4$ with
MUSE up to $(0.1-0.15)\times r_{200}$.

For MS0451, we find a percentage of RPS candidates with redshifts secured by
spectroscopy of 56/359=15.6%, which is close to the value of 81/557=14.5%
found for MACS0717 by Durret et al. (2021). Tam et al. (2020) found that
MS0451 is in a post-merger state, so it is not a relaxed cluster. However,
MS0451 is less perturbed and extended than MACS0717. The fact that the
percentages of RPS candidates in these two clusters are comparable could
suggest that, at least for these two particular systems, the percentage of RPS
galaxies is not correlated to the merging activity of the cluster, but there
are some differences in their star formation properties - we shall come back
to this issue below. We can note that these percentages of RPS galaxies are
within the range found by Roberts et al. (2022) in a sample of more than 50
low redshift clusters, based on data from the UNIONS survey.

We show in Figs. 8 and 9 the overall and low density large scale distributions
derived by Tam et al. (2020), with the positions of our 56 spectroscopic RPS
candidates (Sample 1) superimposed. We clearly see that there are few RPS
candidates in the central dense cluster region, and that they completely avoid
the Substructures numbered 1 to 14 in the Tam et al. (2020) paper. They do not
particularly follow the filaments, since few of them are very close to the
three filaments. For the 273 RPS galaxies of Sample 2 (photometric redshift
sample) also shown in Figs. 8 and 9, the spatial distributions of those with J
classes of 4 and 5 also tend to avoid the dense regions, while this is not the
case for galaxies with J$<3$. However, we must keep in mind that there must be
some contaminants in Sample 2, that is to say foreground or background
objects. If these are RPS galaxies, they will lead to an overestimation of the
number of RPS cluster members in Sample 2. On the other hand, if their
distorted morphologies are due to other processes that are especially relevant
in low density regions, as unveiled by the pioneering work of Vulcani et al.
(2021), only possible with IFU data, then this will introduce a bias in our
results issued with Sample 2. The difficulty of selecting clean samples of RPS
galaxies was also discussed by Laudari et al. (2022).

If we look at the distribution of RPS candidates as a function of distance to
the cluster centre (in units of $r_{200}$), the comparison of Fig. 10 with
Fig. 4 obtained for MACS0717 by Durret et al. (2021) shows that there are
comparable, low numbers of RPS candidates near the cluster centres in MS0451
and MACS0717: RPS candidates tend to avoid the central, denser regions
($r<0.4\times r_{200}$) in both clusters. This was also the case in 97 RPS
candidates in a sample of 39 clusters analyzed by Durret et al. (2021) – see
their Figure 6. Hydrodynamical simulations have indeed found that RPS galaxies
tend to avoid cluster centres (Yun et al., 2019). This is different from what
was observed at low redshift, where RPS galaxies were, on the contrary, in
majority detected close to the central regions, for example by Jaffé et al.
(2018) or Gullieuszik et al. (2020) \- although these authors focus on
galaxies with ionized gas tails, a very specific and extreme population of
objects undergoing RPS. We acknowledge the fact that our redder selection band
may miss such spectacular galaxies.

From the projected phase space diagrams of MS0451 and MACS0717 described in
Section 3.1.2, we can see that the distributions of galaxies between the
virialized, infall, and backsplash regions differ between RPS and non-RPS
galaxies, as well as from one cluster to the other. As seen in Table 2, in
MS0451 66% of the RPS candidates are virialized (with the definition
$r<r_{100}$) while 79% of the non-RPS galaxies are virialized. For both types
of galaxies, there are more objects in the backsplash than in the infall
region, and the difference is larger for RPS candidates. On the other hand, in
MACS0717 only about half of all galaxies are virialized (49% and 62% for RPS
and non-RPS galaxies), and the rest are distributed with 31% in the infall
region and 20% in the backsplash region for RPS galaxies, and 24% in the
infall region and 13% in the backsplash region for non-RPS galaxies. These
differences could be linked to the different dynamical histories of the two
clusters. Though Roberts et al. (2022) define virialized objects in a
different way, they mention that they see no evidence for stripping on first
infall in their sample. This result seems to disagree with Jaffé et al.
(2018), who concluded from their study that many of the jellyfish galaxies
seen in clusters likely formed via fast ($\sim 1-2$ Gyr) outside-in ram-
pressure stripping during their first infall into the cluster following highly
radial orbits. This does not seem to be the case for MS0451, where the
percentage of RPS candidates in the infall region is small, but is more likely
to be true for MACS0717, where the percentage of RPS candidates in the infall
region is higher.

As discussed above, the plot of the SFR as a function of stellar mass (Fig.
16) shows that about half of our RPS candidates are star-forming objects,
lying within or above the Vulcani et al. (2016) sequence, in contrast with
non-RPS counterparts (of which the majority are located in the quiescent
region of the plane). This result is comparable to that of Durret et al.
(2021) for MACS0717, where an even stronger trend was found. Among the two
clusters, MS0451 star-forming RPS galaxies show increased levels of SF
activity, lying mostly above the MS. We can only conjecture that this is due
to the different dynamical states of the clusters. The enhanced median values
of SFRs and sSFRs of our RPS candidates agree with those already found by
previous authors such as Durret et al. (2021), Roberts et al. (2022) and
references therein.

Both clusters, MACS0717 and MS0451, located at z$\sim 0.5$, host a non
negligible population of RPS candidates showing important levels of star
formation activity. It would be very interesting to see if dynamically
”quieter/older” clusters, located at a similar redshift such as the four
clusters observed by Cooper et al. (2022), show similar results. It has indeed
been suggested (e.g. Owers et al., 2012; McPartland et al., 2016; Vulcani et
al., 2017; Ebeling & Kalita, 2019; Moretti et al., 2022) that extreme ICM
conditions in merging clusters tend to boost RPS events (that, in turn, seem
to correlate with increased SFR as we have shown).

However, and in spite of this global trend, our MS0451 data and analysis
points to a different behaviour for the low mass RPS candidates in this
cluster: the ones we sample - in a notably incomplete way - below stellar
masses of about $10^{9.4}$ M⊙ have suppressed SF instead. This is a tentative
result that apparently does not align with what has been found at lower
redshifts and in different environments (non merging clusters and field), and
strongly needs confirmation with better data and a finer analysis.

Finally: it is interesting to note that RPS candidates selected from the
photometric redshift sample have properties that are comparable to those of
our 56 spectroscopically confirmed RPS candidates, though they reach lower
masses. This means that large samples of ram pressure stripped galaxies in
clusters can potentially be obtained only based on photometric redshifts. With
the advent of very large imaging surveys (DES, Euclid, LSST, etc.), this is a
very promising method to acquire large samples of such objects at relatively
low cost, and therefore to be able to study their physical properties in a
statistical way. Of course, it will not be possible to look individually at
tens or hundreds of thousands of galaxies. However, machine learning should
allow the automatic detection of asymmetries and particular features in
galaxies in a near future, and by combining several constraints on the
features expected from RPS galaxies, it should then become possible to extract
large samples of RPS candidates, and thus to understand better the underlying
physical processes that drive them. Simpler methods such as applying the
scattering transform, as proposed by Cheng & Ménard (2021) are also very
promising (B. Ménard, private communication).

###### Acknowledgements.

We are grateful to the referee for many constructive comments that helped us
to improve the paper. We thank Andrea Biviano for enlightening discussions on
phase space diagrams and for making some of his statistical programmes
available to us. F.Durret acknowledges continuous support from CNES since
2002. M. Jauzac is supported by the United Kingdom Research and Innovation
(UKRI) Future Leaders Fellowship ‘Using Cosmic Beasts to uncover the Nature of
Dark Matter’ (grant number MR/S017216/1). H.Ebeling is grateful for financial
support for programme GO-09722, provided by NASA through a grant from the
Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.
C. Lobo acknowledges support by Fundação para a Ciência e a Tecnologia (FCT)
through the research grants UIDB/04434/2020 and UIDP/04434/2020. C. Lobo
further acknowledges support from the project ”Identifying the Earliest
Supermassive Black Holes with ALMA (IdEaS with ALMA)” (PTDC/FIS-
AST/29245/2017). S.-I. Tam acknowledges support from the Ministry of Science
and Technology of Taiwan (MOST grants 109-2112-M-001-018-MY3) and from the
Academia Sinica Investigator Award (grant AS-IA-107-M01). This work is partly
based on tools and data products produced by GAZPAR operated by CeSAM-LAM and
IAP and we further acknowledge the dedicated support of O. Ilbert. This
research has made use of the SVO Filter Profile Service (http://svo2.cab.inta-
csic.es/theory/fps/) supported from the Spanish MINECO through grant
AYA2017-84089. This research has also made use of the NASA/IPAC Extragalactic
Database (NED), which is funded by the National Aeronautics and Space
Administration and operated by the California Institute of Technology. We
further acknowledge M. Taylor for developing TOPCAT, making our life so much
easier.

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##  Appendix A Results of the Zooniverse test

Table 4: Zooniverse classification of the 56 Sample 1 RPS candidates in MS0451. The columns are: running number, J classifications JL and JF according to two of us (LD and FD), mean J classification, number of times the galaxy was classified in Zooniverse, minimum J value in Zooniverse classifications, maximum J value in Zooniverse classifications, mean J value resulting from the Zooniverse classifications, dispersion on this J value, reason(s) to classify as an RPS candidate. Number | JL | JF | Jmean | ${\rm n_{class}}$ | Jmin | Jmax | Jzoo | $\sigma_{J_{zoo}}$ | comment
---|---|---|---|---|---|---|---|---|---
1 | 5 | 4 | 4.5 | 14 | 1 | 5 | 3.1 | 1.4 | edge, tails
2 | 3 | 3 | 3.0 | 13 | 0 | 3 | 1.4 | 0.9 | sharp edge, tails
3 | 4 | 3 | 3.5 | 12 | 1 | 3 | 2.1 | 0.9 | sharp edge
4 | 2 | 2 | 2.0 | 11 | 1 | 4 | 2.7 | 1.1 | edges
5 | 1 | 2 | 1.5 | 13 | 0 | 5 | 1.8 | 1.6 | moderately sharp edge
6 | 3 | 3 | 3.0 | 17 | 0 | 3 | 1.5 | 0.8 | edge
7 | 1 | 1 | 1.0 | 15 | 0 | 4 | 1.7 | 1.3 | small tail
8 | 5 | 5 | 5.0 | 17 | 1 | 5 | 4.1 | 1.3 | edge+long tail
9 | 3 | 3 | 3.0 | 12 | 0 | 5 | 1.8 | 1.5 | sharp edge
10 | 5 | 5 | 5.0 | 12 | 1 | 5 | 3.3 | 1.4 | edge+tail
11 | 2 | 3 | 2.5 | 13 | 1 | 5 | 3.0 | 1.5 | blobs and tail
12 | 2 | 2 | 2.0 | 12 | 0 | 3 | 1.2 | 1.1 | tails
13 | 2 | 2 | 2.0 | 10 | 0 | 3 | 1.1 | 0.7 | bright knots
14 | 1 | 1 | 1.0 | 16 | 0 | 3 | 2.2 | 0.9 | tail
15 | 2 | 3 | 2.5 | 15 | 0 | 5 | 2.7 | 1.1 | tail
16 | 2 | 2 | 2.0 | 15 | 0 | 5 | 2.3 | 1.4 | edges, very disturbed
17 | 2 | 1 | 1.5 | 15 | 0 | 4 | 1.3 | 1.2 | edges, tails
18 | 1 | 1 | 1.0 | 16 | 0 | 5 | 2.5 | 1.4 | edges, tail
19 | 3 | 4 | 3.5 | 14 | 0 | 5 | 2.8 | 1.6 | edge, tail
20 | 2 | 2 | 2.0 | 13 | 0 | 3 | 1.8 | 1.1 | sharp edge
21 | 3 | 3 | 3.0 | 14 | 0 | 3 | 1.9 | 1.2 | edge, tail
22 | 1 | 2 | 1.5 | 13 | 0 | 4 | 2.4 | 1.3 | tail
23 | 1 | 1 | 1.0 | 14 | 0 | 2 | 0.7 | 0.6 | moderately sharp edge
24 | 1 | 1 | 1.0 | 11 | 0 | 3 | 1.4 | 0.8 | moderately sharp edges
25 | 3 | 3 | 3.0 | 14 | 0 | 2 | 1.1 | 0.8 | edges
26 | 1 | 2 | 1.5 | 14 | 0 | 3 | 1.4 | 1.1 | tail
27 | 5 | 5 | 5.0 | 12 | 2 | 5 | 3.8 | 0.8 | edges+tail
28 | 2 | 3 | 2.5 | 14 | 0 | 3 | 1.6 | 0.7 | tails
29 | 1 | 2 | 1.5 | 14 | 0 | 4 | 1.4 | 1.1 | moderately sharp edge
30 | 2 | 3 | 2.5 | 16 | 0 | 5 | 3.4 | 1.5 | edges
31 | 1 | 1 | 1.0 | 12 | 0 | 3 | 1.2 | 0.7 | asymmetric+edge
32 | 3 | 3 | 3.0 | 13 | 0 | 4 | 2.0 | 1.2 | edge, blobs
33 | 1 | 1 | 1.0 | 13 | 0 | 3 | 0.8 | 0.8 | diffuse, bent
34 | 1 | 1 | 1.0 | 14 | 0 | 2 | 0.6 | 0.7 | weak tail
35 | 5 | 5 | 5.0 | 12 | 2 | 5 | 4.2 | 1.0 | sharp edges
36 | 1 | 1 | 1.0 | 12 | 0 | 5 | 1.9 | 1.4 | tails
37 | 2 | 2 | 2.0 | 13 | 0 | 5 | 2.0 | 1.6 | edges +blobs
38 | 5 | 5 | 5.0 | 13 | 1 | 5 | 3.1 | 1.4 | sharp edges+blobs
39 | 2 | 2 | 2.0 | 18 | 0 | 5 | 2.6 | 1.2 | edge
40 | 3 | 3 | 3.0 | 11 | 1 | 4 | 3.0 | 1.1 | tail
41 | 2 | 2 | 2.0 | 16 | 0 | 3 | 1.6 | 1.0 | weak tail
42 | 2 | 2 | 2.0 | 13 | 1 | 3 | 2.0 | 0.8 | tail
43 | 1 | 1 | 1.0 | 14 | 1 | 4 | 2.4 | 1.0 | edge
44 | 1 | 1 | 1.0 | 14 | 0 | 5 | 2.3 | 2.0 | edges
45 | 1 | 1 | 1.0 | 16 | 0 | 4 | 2.4 | 1.2 | edge, tail
46 | 1 | 2 | 1.5 | 15 | 0 | 4 | 1.8 | 1.3 | edge
47 | 1 | 2 | 1.5 | 16 | 1 | 5 | 3.0 | 1.4 | edge, possible tail
48 | 3 | 3 | 3.0 | 14 | 1 | 5 | 3.0 | 1.2 | edge
49 | 1 | 1 | 1.0 | 12 | 0 | 4 | 1.9 | 1.4 | possible tail
50 | 1 | 1 | 1.0 | 15 | 1 | 4 | 2.1 | 1.0 | edge, possible tail
51 | 1 | 1 | 1.0 | 14 | 1 | 3 | 2.0 | 0.7 | possible tail
52 | 1 | 1 | 1.0 | 13 | 0 | 2 | 0.9 | 0.9 | possible tail
53 | 2 | 2 | 2.0 | 13 | 0 | 5 | 2.2 | 1.5 | tails
54 | 3 | 3 | 3.0 | 15 | 2 | 4 | 3.0 | 0.8 | sharp edge, tail
55 | 1 | 2 | 1.5 | 12 | 1 | 4 | 2.2 | 1.1 | weak tail
56 | 2 | 2 | 2.0 | 13 | 1 | 4 | 2.5 | 1.1 | tail
Figure 17: Grades given by the Zooniverse classifiers for each of the 56
galaxies of Sample 1.

A summary of the results of the J classification with Zooniverse is shown in
Fig. 17 and Table 4. The corresponding results are discussed in Section 2.3.

##  Appendix B Results of KS tests

Table 5: Percentages at which a KS test does not reject the hypothesis that the two samples are drawn from the same parent population. The second and third columns give the values for the whole sample, the fourth column gives the corresponding values after applying a mass cut at $10^{9}\leq$M$\leq 10^{10.5}$ M⊙. Quantity | samples | percentages | percentages
---|---|---|---
Masses | S1-S3 | 31.6% | 28.5%
| S2-S4 | 27.1% | 16.1%
Ages | S1-S3 | 73.6% | 84.9%
| S2-S4 | 47.7% | 47.8%
SFR | S1-S3 | 43.9% | 43.7%
| S2-S4 | 31.2% | 43.1%
sSFR | S1-S3 | 57.6% | 46.3%
| S2-S4 | 46.5% | 47.5%

The results of the KS tests applied in Section 4 are given in Table 5.

##  Appendix C Images of RPS galaxies in MS0451

The images of the 56 RPS galaxy candidates with spectroscopic redshifts in
MS0451 are shown below. For each galaxy, we indicate the classifications
estimated by two of us in parentheses (as in Table 1).

Figure 18: From top to bottom and left to right, we show galaxies #1 (J-class
5-4), #2 (3-3), #3 (4-3), #4 (2-2), #5 (1-2), #6 (3-3), #7 (1-1), #8 (5-5), #9
(3-3), #10 (5-5), #11 (2-3), and #12 (2-2) in the F814W filter.

Figure 19: From top to bottom and left to right, we show galaxies #13 (2-2),
#14 (1-1), #15 (2-3), #16 (2-2), #17 (2-1), #18 (1-1), #19 (3-4), #20 (2-2),
#21 (3-3), #22 (1-2), #23 (1-1), and #24 (1-1), in the F814W filter.

Figure 20: From top to bottom and left to right we show galaxies #25 (3-3),
#26 (1-2), #27 (5-5), #28 (2-3), #29 (1-2), #30 (2-3), #31 (1-1), #32 (3-3),
#33 (1-1), #34 (1-1), #35 (5-5), and #36 (1-1), in the F814W filter.

Figure 21: From top to bottom and left to right we show galaxies #37 (2-2),
#38 (5-5), #39 (2-2), #40 (3-3), #41 (2-2), #42 (2-2), #43 (1-1), #44 (1-1),
#45 (1-1), #46 (1-2), #47 (1-2), and #48 (3-3), in the F814W filter.

Figure 22: From top to bottom and left to right we show galaxies #49 (1-1),
#50 (1-1), #51 (1-1), #52 (1-1), #53 (2-2), #54 (3-3), #55 (1-2), and #56
(2-2), in the F814W filter.