11institutetext: INAF — Osservatorio Astronomico di Trieste, via Tiepolo 11,
I-34131, Trieste, Italy 22institutetext: Astronomy Unit, Department of
Physics, University of Trieste, via Tiepolo 11, I-34131 Trieste, Italy
33institutetext: IFPU - Institute for Fundamental Physics of the Universe, Via
Beirut 2, 34014 Trieste, Italy 44institutetext: Faculty of Physics, Ludwig-
Maximilians-Universität, Scheinerstr. 1, 81679 Munich, Germany
55institutetext: Max Planck Institute for Extraterrestrial Physics,
Giessenbachstr. 1, 85748 Garching, Germany 66institutetext: Excellence Cluster
Universe, Boltzmannstr. 2, 85748 Garching, Germany 77institutetext: INFN -
National Institute for Nuclear Physics, Via Valerio 2, I-34127 Trieste, Italy
88institutetext: Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden
St, Cambridge MA, 02138, USA 99institutetext: Department of Physics,
University of Cincinnati, Cincinnati, OH 45221, USA 1010institutetext:
Institute of Cosmology and Gravitation, University of Portsmouth, Burnaby
Road, Portsmouth PO1 3FX, UK 1111institutetext: Department of Physics and
Astronomy, University of Missouri, Kansas City, MO 64110, USA
1212institutetext: Department of Astronomy, University of Florida,
Gainesville, FL 32611 1313institutetext: Department of Physics and Astronomy
and PITT PACC, University of Pittsburgh, Pittsburgh, PA 15260, USA
1414institutetext: Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA
02139 1515institutetext: School of Physics, University of Melbourne,
Parkville, VIC 3010, Australia 1616institutetext: Department of Physics,
University of Michigan, 450 Church Street, Ann Arbor, MI, 48109
1717institutetext: Kavli Institute for Particle Astrophysics & Cosmology, P.O.
Box 2450, Stanford University, Stanford, CA 94305, USA

# Galaxy populations in the most distant SPT-SZ clusters
II. Galaxy structural properties in massive clusters at $1.4\lesssim z\lesssim
1.7$

V. Strazzullo<EMAIL_ADDRESS>populations in the most
distant SPT-SZ clusters II. Galaxy structural properties in massive clusters
at $1.4\lesssim z\lesssim 1.7$Galaxy populations in the most distant SPT-SZ
clusters II. Galaxy structural properties in massive clusters at $1.4\lesssim
z\lesssim 1.7$Galaxy populations in the most distant SPT-SZ clusters II.
Galaxy structural properties in massive clusters at $1.4\lesssim z\lesssim
1.7$Galaxy populations in the most distant SPT-SZ clusters II. Galaxy
structural properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ M. Pannella,,,
Galaxy populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ J. J. Mohr,,
Galaxy populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ A. Saro,,,
Galaxy populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ M. L. N. Ashby
Galaxy populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$
M. B. Bayliss Galaxy populations in the most distant SPT-SZ clusters II.
Galaxy structural properties in massive clusters at $1.4\lesssim z\lesssim
1.7$Galaxy populations in the most distant SPT-SZ clusters II. Galaxy
structural properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ R. E.
A. Canning Galaxy populations in the most distant SPT-SZ clusters II. Galaxy
structural properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ B. Floyd Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ A. H. Gonzalez
Galaxy populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ G. Khullar
Galaxy populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ K. J. Kim Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$
M. McDonald Galaxy populations in the most distant SPT-SZ clusters II. Galaxy
structural properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ C. L. Reichardt
Galaxy populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ K. Sharon Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$Galaxy
populations in the most distant SPT-SZ clusters II. Galaxy structural
properties in massive clusters at $1.4\lesssim z\lesssim 1.7$ T.
Somboonpanyakul Galaxy populations in the most distant SPT-SZ clusters II.
Galaxy structural properties in massive clusters at $1.4\lesssim z\lesssim
1.7$Galaxy populations in the most distant SPT-SZ clusters II. Galaxy
structural properties in massive clusters at $1.4\lesssim z\lesssim 1.7$

We investigate structural properties of massive galaxy populations in the
central regions ($<0.7r_{500}$) of five very massive (M${}_{200}>4\times
10^{14}$ M⊙), high-redshift ($1.4\lesssim z\lesssim 1.7$) galaxy clusters from
the 2500 deg2 South Pole Telescope Sunyaev Zel’dovich effect (SPT-SZ) survey.
We probe the connection between galaxy structure and broad stellar population
properties at stellar masses of log(M/M⊙)$>$10.85. We find that quiescent and
star-forming cluster galaxy populations are largely dominated by bulge- and
disk-dominated sources, respectively, with relative contributions being fully
consistent with those of field counterparts. At the same time, the enhanced
quiescent galaxy fraction observed in these clusters with respect to the
coeval field is reflected in a significant morphology-density relation, with
bulge-dominated galaxies already clearly dominating the massive galaxy
population in these clusters at $z\sim 1.5$. At face value, these observations
show no significant environmental signatures in the correlation between broad
structural and stellar population properties. In particular, the Sersic index
and axis ratio distribution of massive, quiescent sources are consistent with
field counterparts, in spite of the enhanced quiescent galaxy fraction in
clusters. This consistency suggests a tight connection between quenching and
structural evolution towards a bulge-dominated morphology, at least in the
probed cluster regions and galaxy stellar mass range, irrespective of
environment-related processes affecting star formation in cluster galaxies. We
also probe the stellar mass - size relation of cluster galaxies, and find that
star-forming and quiescent sources populate the mass-size plane in a manner
largely similar to their field counterparts, with no evidence of a significant
size difference for any probed sub-population. In particular, both quiescent
and bulge-dominated cluster galaxies have average sizes at fixed stellar mass
consistent with their counterparts in the field.

##  1 Introduction

Quiescent, early-type galaxies dominating the massive galaxy population are
considered to be a defining signature of cluster environments up to $z\sim 1$,
marking the extremes in the long-known relations between environment and
galaxy properties both in terms of galaxy morphology (morphology-density
relation, e.g. Dressler 1980; Goto et al. 2003; van der Wel et al. 2008;
Cappellari et al. 2011) and of star formation (colour-density and star
formation rate–density relations, e.g. Carlberg et al. 2001; Gómez et al.
2003; Balogh et al. 2004; Kauffmann et al. 2004; Baldry et al. 2006; Peng et
al. 2010; Boselli et al. 2016). Fossil record results up to $z\sim 1$ (e.g.
Gobat et al. 2008; Mei et al. 2009; Mancone et al. 2010; Jørgensen et al.
2017; Webb et al. 2020; Khullar et al. 2022) and the direct observation of
proto-clusters at $z>2$ (e.g. Wang et al. 2016; Oteo et al. 2018; Miller et
al. 2018) point towards these sources being formed in massive star formation
events at high redshift, followed by efficient suppression of star formation
leading to the emergence of the red sequence by $z\sim 2$ (e.g. Kodama et al.
2007; Zirm et al. 2008; Strazzullo et al. 2016; Willis et al. 2020; Trudeau et
al. 2022).

A tight correlation between suppressed star formation and an early-type
morphology has long been observed in the nearby Universe (e.g. Humason 1936;
Morgan & Mayall 1957; de Vaucouleurs 1961; Fioc & Rocca-Volmerange 1999;
Strateva et al. 2001). The evolution of this correlation at higher redshifts
is necessarily intertwined with the nature and timescales of the most relevant
processes in galaxy evolution, and it has thus been extensively investigated.
Many studies have found that galaxy morphology and stellar population
properties are already tightly coupled at high redshift up to at least $z\sim
2$, with quiescent sources typically being characterised by a centrally
denser, more bulge-dominated structure (e.g. Wuyts et al. 2011; Bell et al.
2012; Lee et al. 2013; Lang et al. 2014; Kawinwanichakij et al. 2017; Kim et
al. 2018; Mowla et al. 2019; Matharu et al. 2019; Osborne et al. 2020; Suess
et al. 2021; Lustig et al. 2021) – though this conclusion is not necessarily
uniform across the literature (e.g. Stockton et al. 2008; van der Wel et al.
2011; McLure et al. 2013; Hill et al. 2019; Stockmann et al. 2020). Probing
the environmental dependence of this correlation constrains the physical link
between suppression of star formation and structural evolution in different
environments.

Constraining such a link is especially relevant at $1.5\lesssim z\lesssim 2$,
which is often considered as the epoch when massive galaxies in the central
regions of cluster progenitor environments transition from highly star-forming
$z\gtrsim 2$ proto-clusters, to established $z\lesssim 1$ clusters where star
formation is already efficiently suppressed. Indeed, a wealth of literature
over the last decade has discussed this critical phase, revealing significant
star formation activity even in massive galaxies in clusters at $z>1.3$, and
sometimes even in cluster core regions (e.g. Tran et al. 2010, 2015; Hayashi
et al. 2010; Brodwin et al. 2013; Santos et al. 2015; Alberts et al. 2016;
Nantais et al. 2017; Alberts et al. 2021). At the same time, other studies
have highlighted that environmental quenching is already active at this
redshift with massive, quiescent galaxies already characterising
(proto-)cluster cores even up to $z\sim 2$ (e.g. Papovich et al. 2010;
Strazzullo et al. 2010, 2018, 2019; Spitler et al. 2012; Tanaka et al. 2013;
Andreon et al. 2014; Cooke et al. 2016; Lemaux et al. 2019; Zavala et al.
2019; Willis et al. 2020, and rare examples even beyond, e.g. McConachie et
al. 2022), although with a likely significant cluster-to-cluster variation.

In this context, the evolution of the morphology-density relation together
with the star formation rate–density relation has been an important subject of
study. Indeed, the environmental dependence of structural properties of
galaxies at high redshift, and particularly in cluster environments, may
provide fundamental insight into the environment-related processes affecting
the evolution of galaxies in the critical proto-cluster to cluster transition
phase.

Several investigations have shown that, at least for massive galaxies, the
morphology-density relation is already in place by $z\sim 1$, possibly with
some evolution with cosmic time at lower masses and depending on the sample
selection (e.g. Postman et al. 2005; Capak et al. 2007; van der Wel et al.
2007; Holden et al. 2007; Mei et al. 2012; Paulino-Afonso et al. 2019). We
focus here on the comparison between galaxies in the ‘average field’ (i.e. a
representative galaxy population averaging environments across large volumes)
and in the most extreme, massive cluster environments at $1.5\lesssim
z\lesssim 2$. Very massive clusters in this transition epoch are possibly
affected by the strongest star formation suppression. Therefore, an
environmental dependence of structural properties (e.g. galaxy size, surface
brightness profile, and radial gradients in stellar population properties), in
particular for quiescent galaxies, would reflect different evolutionary paths
in cluster versus field environments, especially in connection with their
quenching. More specifically, at this redshift one might expect that a
putative widespread quenching event across the (massive) cluster galaxy
population might leave a signature on the galaxy structure, and notably an
excess of quiescent galaxies with structural properties differing from those
of reference field analogues.

Studies investigating such aspects in clusters at this redshift have
highlighted the presence of a morphology-density relation, at least in some
systems up to $z\sim 2$, with an excess of early-type galaxies with respect to
field environments, albeit with a potentially significant cluster-to-cluster
variation possibly also partly depending on cluster properties and the local
galaxy density (e.g. Newman et al. 2014; Sazonova et al. 2020; Mei et al.
2022). A variety of findings have been presented on the environmental
dependence of quiescent galaxy sizes, as well as of morphology proxies such as
the Sersic (1968) index, axis ratio, and concentration. Lower Sersic indices
and axis ratios in cluster versus field environments, at least in some range
of stellar mass and/or cluster-centric distance (e.g. Papovich et al. 2012;
Bassett et al. 2013; Chan et al. 2021), are suggestive of a signature of
environmental quenching mechanisms affecting the galaxy structure in a
different way with respect to dominant quenching processes in the field.
Conversely, other studies suggested a higher fraction of bulge-dominated
quiescent galaxies in cluster versus field environments (e.g. Newman et al.
2014; Noordeh et al. 2021), or yet a negligible environmental dependence of
quiescent galaxy structural properties (e.g. Saracco et al. 2017;
Kawinwanichakij et al. 2017) in line with results in the same stellar mass
range at lower redshift (e.g. Wijesinghe et al. 2012; Carollo et al. 2016;
Paulino-Afonso et al. 2019) highlighting the tight connection between the
morphology-density relation and the high quiescent fraction in dense
environments.

Similarly, a potential environmental dependence of galaxy sizes has been
widely investigated in the last decade and is still debated, with different
studies finding quiescent cluster galaxies to be larger (e.g. Papovich et al.
2012; Lani et al. 2013; Strazzullo et al. 2013; Delaye et al. 2014; Chan et
al. 2018; Andreon 2018; Noordeh et al. 2021; Afanasiev et al. 2022, and
references therein), similarly sized (e.g. Newman et al. 2014; Saracco et al.
2017), or smaller (Raichoor et al. 2012; Matharu et al. 2019) than field
analogues. Each of these different results suggests a different evolutionary
path – and thus more specifically different environment-related mechanisms
affecting such a path – for the quiescent population (e.g. see discussion in
Andreon 2018; Matharu et al. 2019, and references therein). Such potentially
conflicting results – at least at face value – are likely at least partly
driven by the considerable measurement uncertainties, often small sample
sizes, a different galaxy sample selection, and intrinsic differences in the
analysis approach.

In this work, we investigate structural properties of galaxies in a sample of
five very massive galaxy clusters at $1.4\lesssim z\lesssim 1.7$ selected
through the detection of the Sunyaev Zel’dovich effect (SZE, Sunyaev &
Zeldovich 1972) signature, as detailed in Sect. 2.1. As discussed more
specifically in Sect. 2, this sample is particularly well suited for cluster
galaxy evolution studies at this redshift, because of two important aspects:
1) the cluster selection does not rely on galaxy population properties, and
thus does not bias the investigation of cluster galaxies; and 2) the high
cluster masses imply a likely significant impact of environmental effects, as
well as large numbers of cluster members, improving the statistics of galaxy
studies. We have already investigated galaxy populations in these clusters
with respect to environmental quenching and broad stellar population
properties in Strazzullo et al. (2019, hereafter S19), suggesting that the
suppression of star formation is already efficient in the cores of these
systems. In this work, we combine these results with the related investigation
of structural properties of the same populations of cluster galaxies, by
comparison with coeval field counterparts, to investigate environmental
signatures.

In the following we adopt a flat $\Lambda$CDM cosmological model with
$\Omega_{\textrm{M}}$=0.3 and $H_{0}$=70 km s-1 Mpc-1. Magnitudes are quoted
in the AB system and a Salpeter (1955) initial mass function is assumed
throughout.

##  2 Data and measurements

###  2.1 Cluster sample

The cluster sample studied in this work was selected from the Bleem et al.
(2015) catalogue of galaxy clusters identified through Sunyaev-Zel’dovich
effect in the 2500 deg2 South Pole Telescope (SPT, Carlstrom et al. 2011) SPT-
SZ survey. From the whole SPT-SZ sample of confirmed clusters associated with
SZE detections with a signal-to-noise ratio S/N$>$5 as presented in Bleem et
al. (2015), we selected all systems with photometric or spectroscopic redshift
$z>1.4$ for a dedicated follow-up with the Hubble Space Telescope (HST) and
Spitzer Space Telescope (see Sect. 2.2). These are five clusters at
$1.4\lesssim z\lesssim 1.7$ with estimated virial masses M${}_{200}\sim
5\times 10^{14}$ M⊙ (see Table 1 and S19; cluster names are shortened to SPT-
CLJxxxx hereafter). Irrespective of selection, the clusters in this sample are
among the few known examples of the first, rarest massive clusters emerging at
this redshift (see Mullis et al. 2005; Rosati et al. 2009; Andreon et al.
2009, 2014; Stanford et al. 2012; Brodwin et al. 2012; Bayliss et al. 2014;
Newman et al. 2014; Tozzi et al. 2015; Finner et al. 2020; Dicker et al. 2020;
Di Mascolo et al. 2020).

Table 1: Cluster sample. Columns 1 to 5 list main cluster properties: name, coordinates, redshift, mass M500,c and scale radius r500, as indicated. Redshifts marked with a † are spectroscopic determinations from Bayliss et al. (2014), Khullar et al. (2019), Mantz et al. (2020); the remaining photometric redshifts are from S19. Columns 6 and 7 list, for each cluster, the limiting m140 magnitude and stellar mass completeness limit adopted in this work (from S19). Column 8 lists the quiescent galaxy fraction as estimated in S19 in the $r<0.7r_{500}$ region and for stellar masses above log(M/M⊙)$>$10.85 (left), and the quiescent fraction for the corresponding reference field sample (right).  cluster | coordinates | redshift | M500,c | r500 | m140${}_{\textrm{lim}}$ | log(M∗,compl/M⊙) |  $f_{q}$ vs $f_{q,field}$
---|---|---|---|---|---|---|---
|  |  | [1014M⊙] | [Mpc] | [mag] |  | [%]
SPT-CLJ0421-4845 | $04^{h}21^{m}16.9^{s},-48\degree 45^{\prime}40^{\prime\prime}$ | $1.38^{+0.02}_{-0.02}$ | $2.90^{+0.65}_{-0.72}$ | 0.60$\pm$0.04 | 23.5 | 10.54 |  $80^{+6}_{-12}$ $56^{+11}_{-12}$
SPT-CLJ0607-4448 | $06^{h}07^{m}35.6^{s},-44\degree 48^{\prime}12^{\prime\prime}$ | $1.401^{\dagger}$ | $3.28^{+0.76}_{-0.75}$ | 0.62$\pm$0.04 | 23.5 | 10.56 |  $64^{+11}_{-16}$ $59^{+10}_{-12}$
SPT-CLJ2040-4451 | $20^{h}40^{m}59.6^{s},-44\degree 51^{\prime}37^{\prime\prime}$ | $1.478^{\dagger}$ | $3.44^{+0.75}_{-0.80}$ | 0.61$\pm$0.04 | 23.5 | 10.60 |  $88^{+4}_{-9}$ $53^{+11}_{-12}$
SPT-CLJ0446-4606 | $04^{h}46^{m}55.8^{s},-46\degree 06^{\prime}04^{\prime\prime}$ | $1.52^{+0.13}_{-0.02}$ | $2.74^{+0.65}_{-0.69}$ | 0.56$\pm$0.04 | 23.4 | 10.65 |  $85^{+5}_{-16}$ $56^{+11}_{-12}$
SPT-CLJ0459-4947 | $04^{h}59^{m}42.5^{s}-49\degree 47^{\prime}14^{\prime\prime}$ | $1.71^{\dagger}$ | $2.85^{+0.64}_{-0.68}$ | 0.53$\pm$0.04 | 23.2 | 10.85 |  $83^{+6}_{-12}$ $49^{+8}_{-8}$

The spectroscopic follow-up of the high-redshift tail of the SPT-SZ sample,
carried out in large part after the selection of the sample studied here (see
S19), confirms that this sample includes five of the six most distant SZE
detections with $S/N>5$ in the SPT-SZ survey at $z\gtrsim 1.4$ (e.g. Khullar
et al. 2019; Strazzullo et al. 2019; Mantz et al. 2020). Indeed, as discussed
in S19, because of photometric redshift uncertainties one cluster with
photo-z$<$1.4 in the Bleem et al. (2015) catalogue used for our cluster sample
selection, turned out to be at $z>1.4$ from later spectroscopic follow-up. On
the other hand, based on such follow-up (Stalder et al. 2013; Khullar et al.
2019) the possibility that we are missing further $z>1.4$ clusters due to
photo-z uncertainties is rather small, and we thus consider the sample studied
here as representative of the SPT-SZ cluster population above $z\sim 1.4$.

As discussed in detail in Andersson et al. (2011), Bocquet et al. (2015, 2019)
and de Haan et al. (2016), the $S/N$ of a cluster SZE detection is a proxy of
cluster mass that is largely redshift independent and has a relatively low
scatter ($\sim$20%). As described in S19, even after accounting for
potentially significant contamination of the SZE measurement by mm-wave
emission from star-forming cluster galaxies, this sample is deemed to be
representative of the cluster population in the probed mass and redshift
range, independent of the properties of cluster galaxies. This cluster sample
is therefore especially advantageous for investigations of galaxy evolution in
early massive cluster environments.

S19 investigated broad galaxy population properties in this sample with
respect to environmental quenching, finding already established red-sequence
populations and typically enhanced quiescent galaxy fractions among massive
galaxies in the inner cluster region ($<r_{500}$111Overdensity radii $r_{500}$
and $r_{200}$ quoted in the following are the cluster-centric radii within
which the mean density is 500 and 200 times, respectively, the critical
density of the Universe at the cluster redshift. The cluster masses $M_{500}$
and $M_{200}$ refer to the mass enclosed within these radii.) with respect to
coeval field analogues (see Table 1 and S19). This supports an efficient
suppression of star formation in massive cluster environments already at this
redshift, at least in the probed cluster central regions ($r/r_{500}<0.7$) and
stellar mass range (log(M/M⊙)$>$10.85), with environmental quenching
efficiencies typically in the range $\sim$0.5-0.8 (or possibly higher, see S19
for full details).

###  2.2 HST and Spitzer observations, photometric measurements and derived
properties

All five clusters were observed with HST with the Advanced Camera for Surveys
(ACS) in the F814W band ($\sim$4800 s per cluster), and with the Wide Field
Camera 3 (WFC3) in the F140W band ($\sim$2400 s per cluster; all data from
GO-14252, PI: Strazzullo, with the exception of F140W band imaging of cluster
SPT-CLJ2040, for which we used $\sim$9200 s archival observations from the
“See Change” program GO-14327, PI: Perlmutter). Data reduction and first
analysis of these observations are described in S19. For the surface
brightness modelling discussed in Sect. 2.4, we exploit the 6 dithers
available in F140W band for each cluster field to produce mosaics with a pixel
scale of 0.03”.

Similarly, all five clusters were observed to homogeneous depth with the
Infrared Array Camera (IRAC) on board the Spitzer Space Telescope (PID 12030;
PI Strazzullo), with each cluster observed for 5500 s in both the 3.6 and
4.5$\mu$m bands, with the exception of SPT-CLJ2040 that, lying in a region of
higher background, was observed for 7500 s in each band to ensure similar
point-source sensitivity. We again refer the reader to S19 for full details on
data reduction and characteristics.

####  2.2.1 Galaxy samples in cluster fields: definition and properties of
candidate cluster members

The available spectroscopic coverage in these clusters is not sufficient for a
galaxy population study based on spectroscopically confirmed members. This
work thus relies (as for S19) on photometrically-selected candidate cluster
member samples. More specifically, this analysis is based on the same samples
of candidate cluster members used in S19. We refer the reader to Sects. 2 and
3 of S19 for a detailed description of the definition and characterisation of
these samples, and only briefly summarise here the most important aspects
relevant to this work.

Candidate cluster member samples are selected purely based on photometry in
the HST F814W and F140W and Spitzer 3.6 $\mu$m and 4.5 $\mu$m bands (in the
following, magnitudes in these bands are denoted by m814, m140, [3.6], [4.5],
respectively). We focus on the central cluster regions where homogeneous HST
imaging is available, limiting the analysis to cluster-centric
distances222Following S19, the adopted definition of cluster centre is the
position of the brightest red galaxy within 100 kpc (proper) of the projected
number density peak of candidate cluster members. The adopted cluster centre
thus corresponds to the most massive galaxy lying at the centre of the red
galaxy concentration associated with the cluster. See Sect. 3.4 in S19 for
full details. $r<0.7r_{500}$. We further focus on the m140-selected
galaxy333To remove stars from our samples, point-like sources were identified
based on the SExtractor’s MAG_AUTO (“total magnitude”) vs FLUX_RADIUS
sequence, down to a F140W band magnitude m140=22 mag. This is a purely
morphological criterion and thus unresolved non-stellar sources might be
misclassified, but as discussed in Sect. 2.1 of S19, the contamination from
non-stellar objects of our sample of 120 removed point-like sources across all
five clusters is at most at the few percent level.  population down to
m140$\sim$23.2-23.5 mag, depending on the cluster redshift, as reported in
Table 1. The F140W imaging used for source detection is much deeper than this
limit, with F140W-band source catalogues estimated to be $>$95% complete at
m140$<$24 mag for all clusters. The adopted m140 limits are driven by: 1) the
F814W imaging depth, in order to secure a S/N$>$5 on the colour measurements
used in the following also for red sources (see Sect. 3 in S19 for full
details); and 2) specifically relevant to this work, the S/N in the F140W band
imaging required to carry out the surface brightness analysis (see Sect. 2.4).

Within the m140-selected galaxy sample, candidate cluster members are colour-
selected mainly based on their [3.6]-[4.5] colour, with the addition of
optical/NIR colour constraints to remove low-redshift interlopers. The
obtained cluster candidate member sample is deemed to be highly complete
(Sect. 3.3 in S19) but affected by residual contamination from interlopers.
Although such contamination is estimated to be rather small ($\sim$10%) for
red galaxies in the cluster region of interest, it may increase up to even
$>$50% as a function of galaxy colour for the blue population (Fig. 1 in S19).
This residual foreground and background contamination is thus dealt with
statistically, by means of a suitable control field sample (full details in
Sect. 3.2 in S19). As a brief summary, we assign to each galaxy a weight,
which is based on the excess number density of colour-selected (as mentioned
above) galaxies in the cluster versus control field at the given galaxy
location in the m140 - (m814-m140) - (m140-[3.6]) magnitude-colour-colour
space. Such weight thus corresponds, for each galaxy, to the statistical
excess of the candidate member sample over the control field density at the
magnitude and colours of the given galaxy. We then use these weights in the
analysis to account for the interloper contamination of the candidate cluster
member sample.

Exactly as in S19, candidate cluster members are classified as star-forming or
quiescent with a photometric criterion similar to the routinely used UVJ
selection (Labbé et al. 2005; Williams et al. 2009). In the probed redshift
range $z\sim 1.4-1.7$, the F814W, F140W and 3.6 $\mu$m bands probe,
respectively, the rest-frame ranges $\sim$2900-3400$\AA$, $\sim$5000-6000$\AA$
and $\sim$13000-15000$\AA$. Indeed, these passbands were explicitly selected
to approximate the restframe UVJ colour diagram when designing the imaging
follow-up of these clusters. As explained in full detail in S19 (their Sect.
5.2 and Fig. 6) we thus use the m814–m140 vs m140–[3.6] colour diagram to
disentangle quiescent galaxies from star-forming (including dusty) sources
with the colour selection444The colour selection in the m814–m140 vs
m140–[3.6] diagram is different from cluster to cluster because, being based
on observed colours, it is redshift dependent. The actual selection adopted
for each cluster is shown in Fig. 1. shown in Fig. 1, which was determined
based on Bruzual & Charlot (2003) stellar population models and empirically
confirmed to be analogous to the standard UVJ classification by comparison
with UVJ-selected galaxies at the clusters’ redshifts from the GOODS-S field
(see Sect. 5.2 in S19). To limit the impact of the boundary region in the
colour diagram along the dividing line between quiescent and star-forming
populations, some results in the following are also quoted excluding from the
analysis a band of $\pm$0.1 mag around the dividing line.

Figure 1: Observed m814-m140 vs m140-[3.6] colour-colour diagram of candidate
cluster members at $r/r_{500}<0.7$ for all clusters, down to the m140 limit
indicated in each panel, coded by best-fit Sersic index as indicated in the
legend (dark red, green and blue symbols). Filled and empty symbols show,
respectively, galaxies above and below the stellar mass completeness limit for
the individual cluster (Table 1). Symbol size scales with the statistical
background-subtraction weight (Sect. 2.2.1; smaller symbols are overall more
likely to be interlopers). In each panel, the black line marks the adopted
separation between quiescent and star-forming galaxies, following S19. The
background colour scale traces the median Sersic index (see legend) across the
colour diagram (within a colour distance of 0.1 mag) of galaxies in the
reference field sample with photo-zs within $\pm$0.1 from the cluster’s
redshift, and same m140 magnitude limit (only colour bins with at least five
galaxies are shown).

Finally, for these galaxy samples we use the same empirical stellar mass
estimates as in S19. These are derived by scaling the 3.6 $\mu$m flux555In a
minority of cases where a reliable measurement of the 3.6 $\mu$m flux is not
available, stellar masses were estimated by scaling the F140W band flux with a
M/L ratio calibrated on the m814-m140 colour. The uncertainty on such
estimates deriving from the empirical calibration is $\sim$30-40%. These
F140W-flux based masses are only used for a very small fraction of sources in
the mass complete samples used in the following, and any small related
systematic with respect to the 3.6 $\mu$m-flux based masses does not
appreciably affect our results, as discussed in Sect. 2.3.1 of S19. to stellar
mass with a mass-to-light ratio (M/L) based on the m814–m140 colour, as
calibrated on stellar masses derived by parametric SED modelling for a
reference sample of galaxies at each cluster redshift from the GOODS-S field
(full details in Sect. 2.3.1 in S19). The estimated uncertainty on the
individual stellar mass estimates deriving from the scatter in this empirical
calibration is of order 20-30% - as stressed in S19 this relies on the
assumptions adopted to estimate stellar masses for the reference sample, and
thus this uncertainty does not correspond to the stellar mass uncertainty on
an absolute scale.

In contrast with stellar mass estimates adopted in S19 that were scaled to a
“total flux” as estimated by SExtractor (Bertin & Arnouts 1996) FLUX_AUTO,
mass estimates used in the following are scaled to total fluxes as measured by
T_PHOT in the attempt to more closely recover the whole source flux as also
done for the field sample (see Sect. 2.3). Differences on the total flux are
$\sim$10%, implying that stellar mass estimates used in the following are
larger than those in S19 by the same amount.

In this respect, we further note that for several aspects of the analyses
presented here we compare the cluster galaxy samples with reference field
samples in four fields from the CANDELS survey, as discussed in Sect. 2.3. We
stress that the stellar masses measured for the cluster galaxy sample as
discussed above are not derived in the same way as those for the field
reference sample (see Sect. 2.3). While this was also the case for our
analysis in S19, the S19 mass estimates were directly calibrated on galaxies
from the very same galaxy catalogue in GOODS-S that was also adopted as a
control field sample, where we could very closely match the photometry in the
relevant bands between cluster and field samples. Instead, in this work we use
independent stellar mass and photometric redshift catalogues for the four
adopted reference fields from Skelton et al. (2014), as detailed in Sect. 2.3.

The proper comparison of results for cluster galaxies and reference field
counterparts relies on the proper comparison of their stellar mass estimates.
As there is no overlap between the cluster and field sky areas, we cannot
directly compare mass estimates for individual sources. We thus attempt a
quantification of the impact of potential systematics in the mass estimates of
cluster versus field samples coming from their different measurement procedure
(i.e. Skelton et al. (2014) SED-fitting based masses versus empirical
estimates adopted for cluster galaxies) and possible systematic offsets in
photometric measurements driving stellar mass estimates. We evaluate the
impact of the former by computing empirical stellar mass estimates for the
Skelton et al. (2014) sources with the same procedure adopted for cluster
galaxies, separately for quiescent and star-forming sources and as a function
of redshift across the range of interest $1.3<z<1.8$. This evaluation suggests
stellar mass offsets of order $\lesssim$10% for galaxies at $z<1.6$, and of
order $\sim$10-15% at $z>1.6$. In the following, we correct by default the
stellar masses of cluster galaxies by the estimated systematics666The
corrections are estimated as a function of redshift, and for quiescent and
star-forming sources, separately. The applied corrections turn out to be as
follows: at $z<1.45$ (i.e. for SPT-CLJ0421 and SPT-CLJ0607), all mass
estimates are increased by 0.01 dex; at $1.45<z<1.6$ (i.e. for SPT-CLJ2040 and
SPT-CLJ0446) mass estimates are decreased by 0.04 and 0.06 dex for quiescent
and star-forming galaxies, respectively; at $z>1.6$ (i.e. for SPT-CLJ0459),
mass estimates are decreased by 0.04 dex and increased by 0.07 dex for
quiescent and star-forming galaxies, respectively.  to bring them on the same
scale of the reference field catalogue, and minimise the impact on the cluster
versus field galaxy comparison.

Concerning systematics in the photometry driving stellar mass estimates,
although galaxies in both cluster and field samples used in the following
analyses are all observed with sufficiently high S/N to limit concerns on the
uncertainty of photometric measurements, some differences may occur due to the
definition of the adopted total fluxes and/or their actual measurement (also
depending on specific characteristics of the images). In the S/N range of
interest, we consider such potential systematics very unlikely to exceed a
factor $\sim$10%, and given our adopted empirical estimation of stellar masses
discussed above we thus consider the impact of a 0.1 mag systematic on the 3.6
$\mu$m flux and/or on the m814-m140 colour, which result in systematics on the
estimated stellar mass of about 10% and $<$5%, respectively.

The sources of systematics on stellar mass estimates discussed above are
largely independent from each other, and we thus estimate that any residual
potential systematics affecting stellar masses in the cluster versus field
comparisons carried out in the following will stay below the $<$20% level
overall. We comment in the following on the impact of such potential
systematics on our results, as relevant.

For the analyses presented in the following, we consider cluster galaxy
samples complete down to a stellar mass limit defined as in S19. A mass
completeness limit is computed, for each cluster, as the stellar mass of an
unattenuated Bruzual & Charlot (2003) simple stellar population (SSP) of solar
metallicity, formed at $z_{f}\sim 8$, having at the cluster redshift a
F140W-band magnitude equal to the m140 limit adopted for the given cluster
(see Table 1). These mass completeness limits for the individual clusters
range between log(M/M⊙)=10.54-10.85 across the probed cluster redshift range
(see Table 1). The bulk of the analyses presented here refer to the combined
cluster galaxy sample across all five clusters, down to a mass completeness
limit of log(M/M⊙)=10.85.

###  2.3 Field reference

In this work we use a field reference sample from the CANDELS/3D-HST survey
fields in GOODS-S, AEGIS, COSMOS, and UDS (Grogin et al. 2011; Koekemoer et
al. 2011; Brammer et al. 2012)777The GOODS-N field is not included because of
the lack of F814W band imaging. This allows us to keep the photometric
coverage for the field reference sample as close as possible to the one used
for the cluster galaxy sample.. We use specifically multiwavelength photometry
and derived photometric redshifts (photo-zs), stellar masses and restframe
colours from Skelton et al. (2014), together with parametric morphology
measurements from van der Wel et al. (2014), analogous to those performed in
the cluster fields as described in Sect. 2.4. Following van der Wel et al.
(2014), stellar masses are corrected based on the ratio of the flux in the
photometric catalogue used for stellar mass estimation to the total flux as
measured by GALFIT in the van der Wel et al. (2014) morphological analysis.
For the galaxy sample relevant to this work (that is, within the photo-z and
stellar mass range of interest, and within morphological analysis flag
constraints as described below) this results in a median correction of stellar
masses by $\sim$6%, with $<$1% of galaxies having correction factors larger
than 2.

In the following analyses we focus on (various sub-samples of) galaxies with
photo-zs in the 1.3-1.8 range and stellar mass above the relevant mass
completeness limit for the corresponding cluster galaxy samples, with uniform
quality photometry (i.e. use$\\_$phot$>$0 as defined in Skelton et al. 2014).
With this selection, we start from $\sim$900 galaxies in the combined GOODS-S,
AEGIS, COSMOS and UDS sample from the Skelton et al. (2014) catalogues. We
then remove sources flagged as bad fits (with bad fits identified by
morphology flag $f\geq 2$ as defined in van der Wel et al. 2012) in the van
der Wel et al. (2014) morphology measurements, which leaves $\sim$770
galaxies. We further remove from this sample $\sim$1% of sources with
estimated uncertainties on Sersic index or effective radius larger than 20%.
The resulting sample with available morphological measurements thus contains
84% of the photo-z and stellar-mass selected sample at
log(M/M${}_{\odot}>10.85$). Finally, this sample still contains potentially
suspicious morphological measurements (morphology flag $f=1$, see definition
details in van der Wel et al. 2012, 2014), which if removed reduce the field
reference sample with morphological measurements to $\sim$570 galaxies, or 63%
of the photo-z and mass selected sample. Apart from lowering as discussed the
statistics of the control field sample, we verify that removing these
suspicious measurements does not affect the results presented in the following
(very few, marginal exceptions are mentioned where relevant). Results and
figures in the following are thus presented by default for the clean sample
(excluding suspicious measurements).

We classify galaxies from the field reference sample as quiescent vs star-
forming based on restframe UVJ colours from Skelton et al. (2014). We use in
particular the Williams et al. (2009) UVJ classification criterion. To limit
the impact of the boundary region between the quiescent and star-forming
populations in the UVJ colour plane, some results are also quoted excluding
from the analysis a band of $\pm$0.1 mag around the dividing line.

Finally, for the analyses below we need in some cases the F140W band magnitude
of the reference field galaxies. The depth of the CANDELS F140W-band imaging
is shallower than the depth of the F140W data on the cluster fields ($\sim$800
s vs $\gtrsim$2400 s per pointing), however in the magnitude range relevant to
this work (m140$\leq$23.5) the S/N of sources is still sufficiently high
($>$10 at the faintest end) for all our purposes. However, as the CANDELS
fields are only partially covered with F140W imaging (Brammer et al. 2012),
for some sources there is no F140W band magnitude available. In such cases
($\sim$40% of the used field galaxy sample at $1.3<z<1.8$ and log(M/M⊙)¿10.85
or m140$<$23.5), we substitute a m140 proxy based on the (deeper) F160W band
magnitude. We calibrate this proxy on sources in the magnitude and redshift
range of interest from the F140W-imaged part of the survey, for quiescent and
star-forming galaxies separately, which yields a m140-m160 colour term of
$\sim$0.21 mag independent of magnitude for quiescent sources, and between
$\sim$0.2 mag and $\sim$0.1 mag across the magnitude range of interest for
star-forming galaxies. By comparison with sources in the F140W-imaged part of
the survey we estimate that, in the magnitude (or mass) and redshift range
relevant to this work, our estimated m140 magnitudes have negligible
systematic offsets with respect to actually measured ones (within 0.02 mag at
most), and a scatter of at most 0.1 mag across the full magnitude range of
interest. Over such magnitude range, this scatter is dominated by scatter in
the colour term (rather than by F160W band magnitude uncertainty), and it is
indeed larger than the estimated uncertainty of the actually measured F140
magnitude for sources where it is available. We thus use actually measured
(rather than estimated from F160W) F140W band magnitudes where they are
available.

###  2.4 Morphological analysis of cluster galaxies

We use GALFIT (Peng et al. 2002, 2010) to fit PSF-convolved, single-component
Sersic profiles to the galaxy surface brightness distribution in the HST/WFC3
F140W band images, for all sources detected in the cluster fields down to
m140=24 mag. At the clusters’ redshift, the F140W band images approximately
probe the restframe V band.

GALFIT is run on the F140W images in counts units, with a non-zero background
(see e.g. Peng et al. 2002), and with pixel scale of 0.03”. An independent PSF
model for each of the five cluster fields is created from non-saturated,
high-S/N point-like sources selected from the F140W-band source catalogues
described in S19. We assess the impact of the adopted PSF model by comparing
results obtained with PSF models of the other clusters, or derived from other
surveys, or produced from our data but with different procedures. From these
comparisons we estimate at most a systematic offset of 5% and 1% for Sersic
indices and effective radii, respectively. This level of systematics has
negligible impact on the results presented in this work - including concerning
Sersic indices, which are only used for a rather broad morphological
classification, given the intrinsic scatter and uncertainties in the relation
between Sersic index and detailed structural properties. Indeed, in the
following we mostly consider three broad morphology classes with Sersic index
$n<1.5$ (disk-dominated galaxies), $n>2.5$ (bulge-dominated galaxies), and the
remaining intermediate sources with $1.5<n<2.5$.

The surface brightness profile of galaxies in the cluster fields is modelled
by means of an unsupervised fitting, to limit the introduction of
arbitrariness in the procedure. For each source in the F140W-band catalogue
satisfying the m140$<$24 magnitude limit, we model an image area centred on
the target and with size depending on the projected dimensions of the target
itself (10 times the size estimated from the SExtractor detection, in both x
and y directions). The background level is assumed to be constant over the
cutout area and is modelled as a free parameter. All objects falling in the
cutout area, and down to a limit of 3 magnitudes fainter than the given
target, are simultaneously modelled, as well as bright objects outside of the
selected region but close and bright enough that their light could produce
asymmetric background features. A proper treatment of neighbouring sources is
indeed necessary also to allow GALFIT to derive a robust background level, a
critical point even for single-Sersic profile fitting, especially for high
Sersic index sources having faint extended emission.

To quantify uncertainties on our estimates of morphological parameters, both
for individual sources and overall for the galaxy (sub-)populations of
interest in this work, we use simulations (injecting artificial sources in the
image, with known profile parameters spanning the range of interest) as well
as multiple fitting results deriving from objects falling in more than one
modelled cutout area. Over the magnitude range relevant to this work
(m140$<$23.5), we estimate that typical statistical uncertainties on the
measured Sersic index and effective radius are within $\sim$10% and 5%,
respectively, with systematics of $<$2% at most at all magnitudes of interest.

With this surface brightness modelling, we obtain measurements of structural
parameters (and in particular of the effective radius along the major axis of
the galaxy, the Sersic index, and the axis ratio) for 94% (97%) of the
magnitude (stellar mass, respectively) limited samples above the magnitude
(mass completeness) limit adopted for the individual clusters. For the overall
mass-complete sample above log(M/M⊙)¿10.85 used for the bulk of the analyses
presented here, structural measurements are available for 96 out of 99
galaxies. For consistency with the constraints applied for the measurements in
the reference field sample (van der Wel et al. 2014, see below and Sect. 2.3)
we also exclude from the analysis a further four sources with $n>8$
(specifically, $8<n<13$) above the log(M/M⊙)¿10.85 limit888A total of 17
sources with $n>8$, out of 321 with available structural measurements in the
combined magnitude-limited samples across all clusters, are excluded from the
analysis.. This has no relevant impact on the results presented here, which
would remain well within the quoted uncertainties if these four sources were
included.

In many analyses presented in the following, we rely on the comparison of
structural properties of cluster galaxies to those of field counterparts from
a control field. As described in Sect. 2.3, for this purpose we use
morphological measurements published in van der Wel et al. (2014). Although
the adopted parametric modelling in this work and in van der Wel et al. (2014)
is similar, a number of details in the adopted procedures, as well as in the
reduction and analysis of the imaging data, may potentially introduce biases
in the measurements used in the following, especially in the more sensitive
parameter estimates, namely Sersic indices and effective radii. As there is no
overlap between the cluster and control fields, in an attempt to quantify such
potential biases and assess their impact on our results, we reduce and analyse
a limited portion of the control field imaging data, and carry out the
morphological analysis with exactly the same procedures that we adopted for
the cluster fields. We then compare our results with the van der Wel et al.
(2014) measurements we use in the following, as detailed in Appendix A. Based
on that comparison, our estimated effective radii for the overall galaxy
population in the magnitude range considered here, as well as split by star-
forming and quiescent sources, might be at face value slightly biased towards
lower values with respect to van der Wel et al. (2014), by $<$5% for the
overall population in the probed magnitude range. As it could be expected,
such a bias might depend on the Sersic index of the source (at face value,
increasing from $\sim$3% up to $\sim$8% for low- to high-Sersic index
galaxies, see Appendix A). We specifically consider the impact of this
potential bias on our results on the environmental dependence of galaxy sizes
in Sect. 3.2.

Concerning Sersic indices, based on this comparison our estimates for the
whole population in the considered magnitude range might be biased by $\sim$4%
towards lower values with respect to van der Wel et al. (2014). Also here
there might be potential - but of marginal significance with the estimated
uncertainties - dependence of the bias on the Sersic index (anyway at the
$<$7% level for all sub-populations, see Appendix A). The impact of such bias
on the results presented in the following is always well within the estimated
statistical uncertainties, and it is in fact in most cases unnoticeable.
Therefore, we consider it negligible for the purposes of this work, and all
results presented in the following are shown for our estimated Sersic indices
with no corrections.

Based on the comparison discussed above, we estimate that any residual
systematics between cluster and field galaxy samples on both effective radii
and Sersic indices will not exceed the $\sim$5% level. We comment where
relevant in the following on the impact of potential systematics at such level
on the presented results.

In the following, galaxy sizes are intended as effective radii, and we adopt
specifically the semi-major axis of the ellipse containing half of the total
flux of the best-fitting Sersic model. The average restframe wavelength across
the probed redshift range, corresponding to the F140W band imaging where
cluster galaxy sizes are determined, is 5500 $\AA$. For the field galaxy
sample, we adopt sizes from van der Wel et al. (2014) measured in the F160W
band, for which the average restframe wavelength across the probed redshift
range is 6270 $\AA$. To account for the wavelength dependence of galaxy sizes,
all sizes discussed in the following for both cluster and field samples are
scaled to a restframe wavelength of 5500 $\AA$. For this purpose, we proceed
more specifically as follows: to scale the measured size to 5500 $\AA$
restframe, we adopt the relevant scalings of size as a function of wavelength
as given in van der Wel et al. (2014) for both quiescent and star-forming
galaxies. In general, we use the quiescent or star-forming scaling for
galaxies that are classified as quiescent or star-forming, respectively. For
galaxies within $\pm$0.1 mag from the colour separation between quiescent and
star-forming sources, we adopt the scaling for quiescent (star-forming)
galaxies based on their Sersic index being larger (smaller, respectively) than
2\. For a minority of sources ($\sim$10% and 20% of the log(M/M⊙)$>$10.85
field and cluster galaxy samples, respectively) we adopt instead the
alternative scaling with respect to that determined with these criteria, based
on their measured sizes. More specifically: we first determine the “reference
size” of each source, as the size corresponding to its stellar mass and
photo-z according to the van der Wel et al. (2014) mass-size relation for
quiescent and star-forming galaxies, scaled to the observed wavelength (F140W
for cluster galaxies, F160W for field galaxies). Then, for sources where the
quiescent galaxy scaling should be adopted based on the aforementioned
criteria, but whose sizes are larger than a factor 2x their supposed reference
size and closer to the star-forming mass-size relation, we use the scaling for
star-forming galaxies - and conversely for star-forming sources smaller than
2x their reference size. We stress that, as also described in van der Wel et
al. (2014), we apply these corrections with the aim of limiting the
introduction of systematic biases, but given the small redshift range of
interest and the chosen 5500 $\AA$ reference wavelength being close to the
observed wavelength, corrections are small. For the cluster galaxy sample, all
corrections for individual galaxies are within 3%, and average corrections
across the five clusters go from $\sim$0.2% to $\sim$1.5% depending on the
cluster redshift. For field galaxies in the relevant mass and redshift range,
corrections range from $\sim$1% to $\sim$10% with an average correction of 4%
and $>$90% of the galaxies having corrections $<$8%.

##  3 Structural properties of cluster galaxies

In the following we combine the S19 measurements summarised in Sect. 2.2.1
with the morphological analysis described in Sect. 2.4. We focus in particular
on the relation between broad structural and stellar population properties,
and environmental dependence of galaxy morphologies, in Sect. 3.1, and on the
stellar mass - size relation and environmental dependence of galaxy sizes in
Sect. 3.2.

In the analyses described in this Section we often mark or exclude as it is
customary the cluster brightest central galaxies (BCGs), because of their
intrinsically peculiar nature that may be reflected in their structural
properties. As detailed in S19, BCGs are identified in each cluster as the
brightest red galaxy999In fact, the BCG identification is not affected by the
specific choice of red colour selection (we formally considered
m814-m140$>$1.5), because the adopted BCG is the brightest candidate member -
irrespective of colour - in the considered $<$100 kpc region. The colour-
magnitude diagrams in the whole field probed in these clusters, shown in Fig.
1 of S19, indeed show no blue candidate members brighter than the brightest
red galaxies.  within a distance of 100 kpc (proper) from the projected number
density peak of candidate members (Fig. 4 in S19). The adopted BCG is thus the
brightest red - and most massive, with stellar masses in the range
2$\times$1011-1012 M⊙ \- galaxy at the centre of the red galaxy concentration
associated with the cluster (see S19 for more details). All BCGs in this
cluster sample are classified as quiescent galaxies. Their median Sersic index
is $\sim$5 (with individual estimates in the range $n\sim 3-6$). Estimated
sizes are shown in Fig. 4. We note that, as discussed in S19, the adopted BCG
is also the most massive galaxy of the whole candidate member sample in all
clusters except SPT-CLJ0459 (where six formally more massive (by factors 5% to
70%) sources are spread along the galaxy overdensity). Furthermore, in SPT-
CLJ0446 and SPT-CLJ0459 a similarly massive, bulge-dominated, quiescent galaxy
identified as a very likely cluster member is found within a distance of $<$7
kpc. In such cases of “double BCG” the BCG definition is arbitrary to this
extent, but this does not affect any of the results presented here.

We further note that, for what is relevant to the purposes of this analysis,
we cannot identify significant deviations between the cluster and field galaxy
stellar mass distributions in the probed mass range. Although there could be a
mild overabundance of the most massive galaxies in clusters with respect to
the field population (largely due to BCGs), its significance with the
uncertainties and sample statistics available in this work is marginal.

###  3.1 Morphological properties of cluster galaxy populations

Figure 1 shows the m814-m140 vs m140-[3.6] colour-colour diagram (as a proxy
of the restframe UVJ diagram, as discussed in Sect. 2.2.1) of candidate
cluster members. Colours of cluster members in this diagram, as well as the
separation between star-forming and quiescent galaxies, follow S19 (their
Figure 6, see Sect. 2.2.1). In Fig. 1, candidate members are coded according
to their best-fit Sersic index, dividing the overall population into low,
intermediate and high-Sersic index sources. The background colour shading
shows the median Sersic index of field counterparts across the diagram101010In
Fig. 1 we show field sources with van der Wel et al. (2014) morphology fit
quality flags $f=0$ (see Sect. 2.3). Including also sources with $f=1$ does
not affect the figure appreciably. Furthermore, a small fraction of the
overall reference field area is not covered by F814W imaging (and it is thus
not included in Fig. 1), corresponding to $\sim$10% of the total photo-z and
m140-selected sample relevant to this figure..

The distribution of galaxies in Figure 1 reflects the known correlation
between broad stellar population and structural properties, with quiescence
and active star formation preferentially occurring in high-Sersic index
(“bulge-dominated”) and disk-dominated structures, respectively. As shown in
Fig. 1, in general terms this correlation occurs similarly in both cluster and
field galaxy samples.

We quantify this correlation by investigating the morphology mix of different
galaxy sub-populations in the cluster and reference fields. For this purpose,
we combine all five clusters and only consider galaxies above the common mass
completeness limit of log(M/M⊙)=10.85. We then select a field comparison
sample at $1.3<z<1.8$ and with the same stellar mass limit. Figure 2 (left)
shows the fraction of galaxies with Sersic index $n\leq 1.5$, $1.5<n<2.5$ and
$n\geq 2.5$ among the full population of log(M/M⊙)$>$10.85 cluster galaxies,
as compared to the analogous fractions in the field reference sample.

Figure 2: Morphology mix of massive galaxies in the probed cluster regions and
in the reference field at $1.3<z<1.8$. Left panel shows the fraction of
log(M/M⊙) $>$ 10.85 cluster galaxies with Sersic indices $n\leq 1.5$,
$1.5<n<2.5$ and $n\geq 2.5$ (dark grey symbols), and the corresponding
fractions for the field reference sample (grey bars). For clarity, error bars
(binomial, Cameron 2011) are only shown for cluster samples. Right panel shows
the analogous fractions for the quiescent and star-forming populations, as
indicated. Solid (empty) symbols refer to cluster galaxy samples excluding
(including) sources within $\pm$0.1 mag around the quiescent vs star-forming
classification border. Solid (hatched) bars analogously refer to the
corresponding field reference samples.

Figure 2 (left) shows that the morphology mix of the massive galaxy population
in the probed cluster regions is skewed towards bulge-dominated systems with
respect to the field, showing that a morphology-density relation is already in
place in these environments.

On the other hand, the right-hand panel of Fig. 2 shows that the morphology
mix of the separate quiescent and star-forming populations in cluster versus
field environments is in fact fully consistent. Therefore, the morphology-
density relation in the left-hand panel is largely connected to the higher
quiescent fraction in the cluster galaxy population with respect to the field.

Fig. 2 (right) also quantifies more specifically the correlation between broad
structural and stellar population properties in the probed stellar mass range,
with $\sim$80% of quiescent galaxies being bulge-dominated ($n>2.5$) sources,
whereas $\sim$60% of star-forming galaxies are disk-dominated ($n<1.5$), in
both cluster and field environments. Likewise, the vast majority of bulge-
dominated galaxies is quiescent ($89^{+6}_{-3}$% and $77\pm 3$% in the cluster
and field samples, respectively111111With this analysis and in the probed
stellar mass range, we do not find an excess of star-forming early-type
galaxies in clusters with respect to the field at this redshift (as found in
e.g. Mei et al. 2022), with our estimated star-forming fraction for cluster
early-types being if anything somewhat lower than for field counterparts (we
note however the differences in stellar mass range, definitions and
methodologies between the two studies). ), while disk-dominated sources are
predominantly ($\sim$80-90%) star-forming.

Fractions for cluster galaxy samples in Fig. 2 are based on all candidate
members weighted as described in Sect. 2.2.1 to account for residual
background contamination. Such contamination amounts to $\lesssim$10% for all
quiescent samples (including Sersic index selected sub-samples), to typically
40-50% for star-forming samples, and to almost 20% for the overall full
population, going from 13% for n$>$2.5 sources to 35% for n$<$1.5. As also
shown in Fig. 2, the impact of excluding a region of $\pm$0.1 mag around the
star-forming vs quiescent classification border is typically marginal (and
largely within the estimated uncertainties) for both cluster and field
samples. The impact of matching the redshift distribution of the field sample
to that of the cluster galaxy sample (which is made of three spikes at $z\sim
1.4$, 1.5 and 1.7) is also marginal ($<$10% differences) and in any case
within the statistical uncertainties. The impact of residual systematics on
the Sersic index at the level described in Sect. 2.4, and of potential
residual systematics on stellar masses as discussed in Sect. 2.2.1, is largely
negligible and remains anyway well within the uncertainties shown in Fig. 2.

We note that with these observations our classification of quiescent vs star-
forming galaxies is necessarily broad in nature, and cannot identify recently
quenched, transition sources in any reliable nor statistically meaningful way.
Furthermore, focusing on the relatively central cluster regions implies that
our cluster galaxy samples are dominated by sources accreted onto the cluster
at earlier epochs. For these reasons, a potential environmental signature more
noticeable only on recently quenched galaxies might involve a minority
population in our samples, with no clear identification, and might thus go
undetected in our analysis. Furthermore, our analysis focusses on massive
galaxies, while more significant signatures might be visible at lower masses
(e.g. Chan et al. 2021), possibly in relation to a potential mass dependence
of environmental quenching mechanisms in clusters at this redshift, as
discussed in e.g. van der Burg et al. (2020); Baxter et al. (2022). However,
according to these studies the environmental quenching efficiency is higher
for more massive galaxies; therefore, the stellar mass regime probed here
should, in that respect, facilitate the detection of signatures related to
environmental quenching. We further note that the Sersic index classification
adopted here to separate bulge- vs disk-dominated galaxies has known
limitations and might also possibly affect the detection of specific
signatures. Nonetheless, these observations show no obvious environmental
signatures in the correlation between broad structural and stellar population
properties as probed here, suggesting a connection between environmental
quenching and structural evolution on timescales smaller than we can
disentangle with this analysis.

The average Sersic indices for quiescent versus star-forming cluster galaxies
above the log(M/M⊙)$>$10.85 stellar mass limit, all clusters combined and
accounting for background contamination, are n=3.8$\pm$0.2 and n=1.3$\pm$0.2,
respectively (uncertainties are determined by bootstrap, BCGs are excluded).
Corresponding values for the field reference sample above the same mass limit
are n=3.49$\pm$0.09 and 1.50$\pm$0.07 at $1.3<z<1.8$, with no significant
variation across this redshift range. We note though that including suspicious
sources (see Sect. 2.3) gives average Sersic indices of, respectively,
n=3.76$\pm$0.09 and 1.66$\pm$0.07. Although there might be small differences
in the average Sersic indices of quiescent and star-forming cluster galaxies
versus field counterparts, they are minor and cannot be considered significant
given the estimated measurement uncertainties.

Figure 3: Distribution of axis ratios of log(M/M⊙)$>$10.85 quiescent cluster
galaxies in the probed cluster regions across the whole cluster sample (red
shades) and in the reference field at $1.3<z<1.8$ (blue shades, as indicated).
For both cluster and field samples, darker (lighter) lines correspond to
excluding (including) sources within $\pm$0.1 mag around the quiescent vs
star-forming classification border. Error bars on the fractions over the whole
population (binomial, Cameron 2011) are slightly offset for clarity. For
comparison, the axis ratio distribution of star-forming field galaxies in the
same mass and redshift range (grey line, errors within line width), and for
$1<z<1.4$ cluster galaxies in the same stellar mass range from Chan et al.
(2021, hatched region, see text for details) are also shown.

Figure 4: Stellar mass - size relation of candidate cluster members and field
counterparts, split by Sersic index as indicated. All candidate members in the
m140-limited samples across the five clusters are shown, with symbol size
scaling with residual statistical background subtraction weights (Sect.
2.2.1). All sizes for both candidate members and field counterparts are scaled
to a common redshift $z=1.5$ for the purpose of this figure (see text).
Candidate cluster members are shown with darker symbols, colour-coded by
quiescent (red) vs star-forming (blue) classification (purple and black
symbols show, respectively, galaxies within $\pm$0.1 mag from the
classification border, and with no reliable classification). Large grey open
squares indicate cluster BCGs (right hand panel). Light blue and light red
squares in the background show counterparts from the control field sample at
$1.35<z<1.75$. The red and blue lines show the best-fit mass-size relations
for quiescent and star-forming galaxies from van der Wel et al. (2014, also
scaled to $z=1.5$). Vertical grey lines mark the minimum and maximum stellar
mass completeness limits across the five clusters.

As a further probe of potential environmental signatures on the morphology of
the quiescent galaxy population related to environmental quenching, we compare
in Figure 3 the axis ratio distribution of massive (log(M/M⊙)$>$10.85)
quiescent galaxies in the cluster and field ($1.3<z<1.8$) samples. As in Fig.
2, all candidate cluster members are shown, weighted as described in Sect.
2.2.1 to account for residual background contamination. Excluding sources
within $\pm$0.1 mag around the quiescent vs star-forming classification border
does not affect the result, as shown. Fig. 3 does not show any significant
difference between the axis ratio distributions of quiescent galaxies in the
cluster versus field samples (as also confirmed by K-S test, both including
and excluding sources around the classification border). As mentioned in Sect.
1, different studies found seemingly contrasting results on this aspect. In
particular at redshifts bracketing the range of clusters studied here, Newman
et al. (2014, at stellar masses log(M/M${}_{\odot})>10.8$, in the massive
cluster JKCS 041 at $z=1.8$) highlighted a lack of flattened, oblate quiescent
galaxies in cluster versus field samples, whereas Chan et al. (2021, 11
clusters at $1<z<1.4$ from the GOGREEN survey) found an excess (but most
remarkably at lower masses, $10.4<\textrm{log(M/M}_{\odot}<10.8$). We show in
Fig. 3 a rendition of the Chan et al. (2021)121212A similar comparison with
Newman et al. (2014) results is heavily affected by their small sample size
resulting in large statistical uncertainties that prevent the investigation of
subtle differences.  axis ratio distribution of massive, quiescent cluster
galaxies (hatched region, corresponding to the $1\sigma$ range around the
weighted average131313 Chan et al. (2021) present axis ratio distributions in
four stellar mass bins in the range log(M/M${}_{\odot})\sim 9.8-12$. Their two
highest-mass bins overlap with our sample. We show a weighted average of their
axis ratio distribution in their two most massive bins, weighting according to
the actual contribution of galaxies in these mass ranges in our sample.).
Although this rendition suggests that Chan et al. (2021) results are largely
consistent with our determination in this stellar mass range, our axis ratio
distribution might be somewhat less skewed towards very high axis ratios,
albeit the significance of this difference is marginal given the estimated
uncertainties. We note though that Chan et al. (2021) find that the most
noticeable environmental signatures on the axis ratio distribution of
quiescent galaxies is found at lower stellar masses than those probed here.

###  3.2 The stellar mass-size relation

As discussed in Sect. 2.4, we find a (small) bias between size measurements in
the cluster and control field samples. Given the direct impact of such bias on
results presented here, in the following we apply a correction to the measured
sizes of cluster galaxies to bring them on the same scale as the reference
field measurements. We specifically comment as needed on the impact of this
correction on the results.

Figure 4 shows the stellar mass - size relation of selected galaxy populations
in both the combined cluster and field samples. To combine all sources into
one figure limiting the impact of redshift-dependent effects, all galaxy sizes
are scaled to a common redshift of $z=1.5$ for the purpose of this figure,
using the redshift evolution141414For each galaxy, we scale sizes to $z=1.5$
based on the van der Wel et al. (2014, their Figure 6) relations for quiescent
or star-forming galaxies, adopting the star-forming or quiescent scaling based
on the same criteria described in Sect. 2.4 to scale sizes to 5500 $\AA$
restframe. of the mass-size relation for star-forming and quiescent galaxies
as determined in van der Wel et al. (2014). Cluster and field samples are
split based on Sersic index into disk-dominated ($n\leq 1.5$), intermediate
($1.5<n<2.5$) and bulge-dominated ($n\geq 2.5$) sources, and coded according
to their quiescent vs star-forming classification.

Figure 4 shows a substantial similarity in the mass-size relation of cluster
and field galaxies, and highlights again the clear correlation between broad
structural and stellar population properties discussed in Sect. 3.1. We note
in particular that star-forming and quiescent cluster galaxy populations
largely follow the respective van der Wel et al. (2014) mass-size relations
determined for field galaxies. Estimating a best-fit mass-size relation for
quiescent cluster galaxies from the data in Fig. 4, assuming a linear form in
log(size) vs log(mass) in the probed mass range log(M/M⊙)$>$10.85, would give
a best-fit relation within 5% of the adopted determination based on van der
Wel et al. (2014), and fully consistent within the estimated
uncertainties151515Although there might be evidence of possible deviations at
lower stellar masses, with sizes of quiescent cluster galaxies potentially
lying at face value preferentially above the best-fit relation, due to the
characteristics of the current observations (Sect. 2) and the possible related
biases on the results we do not explore this regime in this work. We leave any
related analysis to future investigations with data properly suited to
investigate lower-mass populations.. In the following we thus use the van der
Wel et al. (2014) relations as a reference, in quantifying size differences
between cluster galaxies and field counterparts.

The distribution of the selected subpopulations in the mass-size plane is
remarkably similar in the cluster and field environments, the most noticeable
difference occurring for intermediate Sersic index sources, for which larger,
typically star-forming galaxies are underrepresented in clusters with respect
to the field. Although this would be potentially very interesting in relation
to the investigation of the correlation and timescales of star formation
quenching and structural evolution in cluster versus field environments, we
note that at least part of this effect might be due to the combination of
uncertainties in the estimated Sersic indices and the higher quiescent
fraction in the cluster versus field samples. This combination results in a
larger number of star-forming (thus largely disk-dominated, and larger in
size) galaxies being scattered into the intermediate-$n$ sub-sample for the
field, whereas a larger number of quiescent (thus largely bulge-dominated, and
smaller in size) galaxies are scattered into the intermediate-$n$ sub-sample
for the clusters. Indeed, as noticeable in Fig. 4, the quiescent galaxy
fraction in the intermediate-$n$ sample is tendentially higher in clusters
than in the field, though with marginal significance with the given
uncertainties ($\sim$60$\pm$15% vs 40$\pm$10%). Although for the reason just
discussed we refrain from elaborating on this further, we note that this is
qualitatively similar (quantitative comparison is affected by the different
stellar mass range probed) to what observed in $z\sim 1$ clusters by Matharu
et al. (2019, see also references therein).

In Figure 5 we show the median size difference161616As stated throughout, size
measurements of cluster galaxies considered here are corrected by the
estimated systematic offset with respect to the adopted control field
measurements, as discussed in Sect. 2.4. For the sake of completeness, we show
for reference the corresponding measurements of the median size difference of
cluster versus field galaxies without this correction in Fig. 10. of cluster
and field galaxies more massive than log(M/M⊙)=10.85, adopting as a reference
the van der Wel et al. (2014) best-fit mass-size relations for star-forming
(left panel) and quiescent (right panel) galaxies. For each galaxy in the
combined cluster and in the control field samples, we estimate the log
difference of the measured size with respect to the expected size from the van
der Wel et al. (2014) relations171717The van der Wel et al. (2014) relations
are scaled to sizes at 5500 Å restframe, for consistency with the adopted
measurements (see Sect. 2.4).  for a galaxy of the given stellar mass and
redshift (for cluster galaxies, the cluster redshift is assumed).

Figure 5: Median log size difference of log(M/M⊙)¿10.85 cluster galaxies
(darker symbols with error bars, corrected for residual background
subtraction, see text) and of field counterparts at $1.3<z<1.8$ (shaded
rectangles showing the 16th-84th percentile range, see text) with respect to
the expected size from the van der Wel et al. (2014) star-forming (left panel)
and quiescent (right panel) relations. Median differences are shown for
different sub-samples based on Sersic index (symbols as in Fig. 4, or squares
for no Sersic index selection) and star-forming (blue colour shades) vs
quiescent (red colour shades) classification (grey symbols show samples
selected by Sersic index only, regardless of star-forming vs quiescent
classification; see text).

Given the intrinsic variety within, and overlap between, colour– and
morphology– selected galaxy populations, in order to probe the potential
effect of galaxy sample selection on the identification of environmental
signatures on galaxy sizes, we consider for both cluster and field samples
several galaxy sub-samples (always excluding BCGs). As shown in Fig. 5, we
divide the population according to Sersic index ($n<1.5$, $1.5<n<2.5$,
$n>2.5$) and star-forming vs quiescent classification (to limit differential
contamination issues between the quiescent and star-forming populations along
the border of the UVJ-like classification in cluster versus field samples,
Fig. 5 shows results excluding the $\pm$0.1 mag around the star-forming vs
quiescent classification border, but the impact of this removal remains well
within the $1\sigma$ uncertainties for all measurements shown, and has no
impact on the results). For each sub-sample, we compute for both cluster and
field populations the median log difference of the measured galaxy size with
respect to the expected size. To account for background contamination of the
cluster candidate member sample, for each sub-sample we estimate the expected
number of contaminants based on the statistical weights described in Sect.
2.2.1, and randomly remove the estimated number of interlopers according to
the size distribution of the corresponding field sub-sample. The uncertainties
shown in Fig. 5 for both cluster and field median size offsets with respect to
the van der Wel et al. (2014) mass-size relations are estimated from the
16${}^{\textrm{th}}$-84${}^{\textrm{th}}$ percentile range of the distribution
of median size offsets obtained by bootstrapping 10000 times for each sub-
sample. The quoted uncertainties thus reflect Poisson noise given the sample
size, and background contamination removal for cluster galaxy samples. We note
that, given the lack of evidence for a redshift dependence of the median size
offset of the control field sample (see Fig. 10) we do not match the redshift
distribution of field galaxies to that of the cluster galaxy sample, but use
instead the whole selected field sample in the $1.3<z<1.8$ range.

Figure 5 shows that for all considered sub-samples the median size offsets of
cluster and field galaxies with respect to the reference relations are
generally consistent181818A K-S test further confirms that the distributions
of size offsets of cluster and field galaxies with respect to the reference
relations are consistent. A two-sample K-S test is carried out for all sub-
populations shown in Fig. 5, with 10000 realisations for each sub-population
to statistically remove background contamination as discussed above. From
these tests, the cluster and field samples are consistent with being drawn
from the same distribution in 100% of the 10000 realisations for all sub-
populations except the $n<1.5$ (90%), star-forming (97%) and $1.5<n<2.5$ star-
forming (83% of the realisations) samples.  according to the statistical
uncertainties estimated as above. Cluster versus field galaxy size median
differences are within $\sim$10% (see Fig. 6) for all considered
subpopulations with the exception of intermediate Sersic index sources, where
cluster galaxies might be at face value smaller than field counterparts, but
average sizes are still consistent given the significant uncertainties.
Figures 4 (middle) and 5 show that this effect, if real, would largely be due
to the different composition of the cluster and field intermediate-$n$ samples
(see earlier discussion on Fig. 4), with a larger fraction of star-forming –
and thus typically larger – sources in the field sample increasing the average
size of intermediate-$n$ field galaxies with respect to cluster analogues.
However, as discussed above in relation to Fig. 4, this is at least partly due
to the higher quiescent fraction in the cluster versus field populations,
producing a differential contamination of the intermediate-$n$ samples. Also
in consideration of the significant statistical uncertainty that anyway
affects this estimated size difference, we thus do not comment further on this
potential difference in the following.

The general similarity of sizes of cluster and field galaxies in Fig. 5 is
reflected in Fig. 6 that quantifies more explicitly the median size difference
of cluster versus field galaxies, as derived from the results in Fig. 5. We
focus here on six most relevant sub-samples, concerning the bulk of star-
forming (disk-dominated galaxies, star-forming galaxies, and star-forming disk
galaxies) and quiescent populations (bulge-dominated galaxies, quiescent
galaxies, and quiescent bulge-dominated galaxies). Thin error bars show
statistical errors (as derived from bootstrap as discussed above for Fig. 5).
We estimate the possible impact of potential residual systematics on stellar
masses, effective radii and Sersic indices (as discussed in Sects. 2.2.1 and
2.4, respectively) by applying random combinations of such systematics up to
the estimated maximum level discussed in the relevant Sections, and evaluating
the impact on the estimated median size difference between cluster and field
galaxies, which is shown as the lighter thick error bar in Fig. 6. The darker
thick error bar shows the estimated overall uncertainties (adding in
quadrature the statistical and systematic error contributions).

From Fig. 6 we conclude that we see no evidence of a size difference between
massive cluster and field galaxies with these observations in the probed
redshift and cluster mass range, and in the probed cluster regions. On the
other hand, we note that potential differences of up to $\sim$15% remain
within our 1$\sigma$ uncertainties even for our better-constrained quiescent
samples (and up to 20-25% if including our estimate of potential unaccounted
systematics; for star-forming galaxies our measurements are even less
constraining, as shown in Fig. 6).

##  4 Summary and conclusions

We investigate structural properties of galaxy populations in the central
regions of five of the most massive known clusters at $1.4\lesssim z\lesssim
1.7$. This cluster sample is homogeneously selected from the wide-area SPT-SZ
Sunyaev Zel’dovich effect survey, and it is deemed to be representative of the
general population of very massive (M${}_{200}>4\cdot 10^{14}$ M⊙) clusters at
this cosmic time.

With a dedicated, homogeneous imaging follow-up from HST and Spitzer, we probe
the connection between broad structural and stellar population properties. We
find that a clear relation between the two is already in place at this epoch
in these cluster environments, which is in line with several studies in the
field up to a similar redshift (e.g. Wuyts et al. 2011; Bell et al. 2012;
Kawinwanichakij et al. 2017; Suess et al. 2021, see discussion in Sect. 1). In
the probed stellar mass range (log(M/M⊙)¿10.85), quiescent galaxies in both
cluster and field environments are largely ($\sim$80%) dominated by bulge-
dominated sources, while star-forming galaxies are typically ($\sim$60%) disk-
dominated.

Figure 6: Median log size difference between cluster and field galaxies as
derived from Fig. 5, for different population sub-samples (see text). Symbols
and colour coding follow Fig. 5. Error bars show statistical uncertainties
(including statistical background subtraction). Light shaded rectangles show
the maximum impact on the median difference from potential residual
uncorrected systematics. Dark shaded rectangles show the combined error
including both statistical and systematic uncertainties (see text).

Although the morphology mix of both the quiescent and the star-forming
populations is largely the same in clusters and in the field, the larger
quiescent galaxy fraction observed in these clusters (S19) is reflected in a
significant morphology-density relation, with bulge-dominated galaxies already
clearly dominating the massive galaxy population in these clusters at $z\sim
1.5$.

On the other hand, in the probed stellar mass range, we do not detect any
significant environmental dependence of the broad structural properties of
quiescent galaxies, which overall show a similar fraction of bulge- versus
disk-dominated sources, similar average Sersic indices, as well as a similar
axis ratio distribution in the probed cluster and field environments. As
discussed in Sect. 3, the analysis presented here is affected by intrinsic
limitations that might impact the detection of potential environmental
signatures. Indeed, the adopted photometric classification of quiescent versus
star-forming galaxies is rather broad in nature, and totally lacks the ability
of robustly identifying recently quenched galaxies transitioning towards the
quiescent population. Similarly, the classification of bulge- versus disk-
dominated systems based on the Sersic index is also inherently broad.
Furthermore, this work focusses on the cluster central regions, which are
dominated by sources that are accreted onto the cluster at earlier epochs.
These limitations may thus affect our ability to detect signatures that might
be mostly visible in more recently accreted, recently quenched populations.
Nonetheless, the results from this analysis show no significant environmental
signatures in the correlation between broad structural and stellar population
properties, thus suggesting that a tight connection between star formation
quenching and structural evolution towards a bulge-dominated morphology also
holds in central cluster regions at this redshift. Any differences in
timescales between these two processes in cluster versus field environments
are smaller than we can disentangle with this analysis and these observations.

We further probe the stellar mass - size relation of cluster galaxies, finding
that star-forming and quiescent cluster galaxy populations largely follow the
same relations as their field counterparts. When dividing the population
according to the estimated Sersic index, we find that cluster galaxies
populate the mass-size plane similarly to field counterparts. A possible
exception might be sources with intermediate Sersic index, for which cluster
galaxies might tend to be smaller on average due to a larger contribution of
quiescent - and thus smaller - sources; see discussion in Sect. 3.2. We
estimate the size difference at fixed stellar mass between analogously
selected cluster and field galaxies for different sub-populations. With our
measurements, we do not find any significant size difference for any of the
probed populations. On the other hand, in relation to the results from
previous studies (e.g. Andreon 2018; Matharu et al. 2019, see more references
and a discussion in Sect. 1), we note that potential differences of
$\lesssim$15% are within our estimated statistical uncertainties (1$\sigma$;
and up to 20-25% if including potential systematics, as discussed in Sect.
3.2), even for the best constrained sub-populations.

This work benefits from a large sample of candidate cluster members, which is
unusual for studies of cluster galaxies at this redshift, and it was made
possible in this case by the small yet sizeable sample of clusters and by
their high mass, implying high richness. These improved statistics result in a
better constrained cluster versus field comparison with respect to previous
studies at a similar redshift that rely on single and/or lower mass clusters.

Nonetheless, some of our results remain affected by limitations, as discussed
above, including – in particular – the relatively coarse characterisation of
both structural and stellar population properties, the limited field of view
of the observations probing only relatively central cluster regions, and
residual uncertainties related to cluster membership especially for some of
the probed sub-populations, as discussed. We strive to obtain additional
follow-up observations to improve on these specific aspects, thus better
exploiting the characteristics of this cluster sample to investigate the
interplay between star formation quenching and structural evolution in
connection with environmental effects, which is a crucial aspect of galaxy
evolution within the most massive structures.

###### Acknowledgements.

MP and VS acknowledge support by the German Space Agency (DLR) through
Verbundforschung project ID 50OR1603, and by the German Research Foundation
(DFG) through research grant STR 1574/1-1. AS, MP and VS acknowledge support
by the ERC-StG ”ClustersXCosmo” grant agreement 716762. AS acknowledges
support by the FARE-MIUR grant ’ClustersXEuclid’ R165SBKTMA, and by the INFN
InDark grant. CLR acknowledges support from the Australian Research Council’s
Discovery Projects scheme (DP200101068). The South Pole Telescope is supported
by the National Science Foundation through grants PLR-1248097, OPP-1852617,
and OPP-2147371. Based on observations made with the NASA/ESA Hubble Space
Telescope under program GO-14252, obtained from the Data Archive at the Space
Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.
Based on observations made with the Spitzer Space Telescope (program ID 12030)
which is operated by the Jet Propulsion Laboratory, California Institute of
Technology under NASA contract.

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##  Appendix A Estimation of potential bias in the measurements of
morphological parameters of cluster galaxies vs the adopted field reference
measurements

Figure 7: Comparison of effective radii as measured with this work procedures
vs van der Wel et al. (2014) estimates adopted for the field reference sample.
Measurements are compared for a random portion of the control field galaxy
sample (see text), split by Sersic index as indicated. The solid lines show
the bisector (middle), and the expected average uncertainty (1 $\sigma$) on
effective radii from this work, as estimated with simulations (see Sect. 2.4)
for sources at the faint end of the probed magnitude range.

We describe here the assessment of the potential bias between the measured
morphological parameters - in particular Sersic index and effective radius -
for cluster galaxies, and the corresponding measurements adopted for the
control field sample from van der Wel et al. (2014). As discussed in Sect.
2.4, given the lack of overlap between the cluster and control fields, a small
portion of the control field, corresponding to 10 WFC3 fields, is reduced and
analysed with the same procedures we adopted for the cluster fields (also
including PSF modelling), in order to enable a direct comparison of the
measurements for the same sources.

In Figures 7 and 8 we compare our measurements of effective radii with those
from van der Wel et al. (2014) for galaxies in these testing fields. Our
measurements show a systematic offset towards lower values with respect to van
der Wel et al. (2014), possibly dependent on Sersic index. At face value, the
offset is $\sim$3% (5%, 8%) for $n<1.5$ sources ($1.5<n<2.5$, $n>2.5$,
respectively), in the magnitude range relevant to this work. Besides the
systematic offset, the dispersion (rms) between the two measurements is $\sim
4\%$ (7%, 15%, respectively) for the same sub-populations. For reference, our
expected average uncertainty on effective radii, as estimated from simulations
(Sect. 2.4) for sources towards the faint end of our probed range, is within
$\sim$5%. As discussed in Sects. 2.4 and 3.2, we correct our estimates of
effective radii to bring them on the same scale as the van der Wel et al.
(2014) measurements for the purpose of quantitative comparison with field
counterparts.

Figure 8: Comparison of effective radii as measured with this work procedures
vs van der Wel et al. (2014) estimates adopted for the field reference sample.
For the same sources as in Fig. 7, the fractional difference between the two
measurements is shown as a function of Sersic index (two sources (¡1%) falling
outside of the plotted range are not shown).

Figure 9: Comparison of Sersic indices as measured with this work procedures
vs van der Wel et al. (2014) estimates adopted for the field sample, for the
same sources as in Fig. 7 (see text). Left: The direct comparison of the two
measurements. The solid lines show the bisector (middle), and the expected
average uncertainty (1 $\sigma$) on Sersic indices from this work, as
estimated with simulations (see Sect. 2.4) for sources at the faint end of the
probed magnitude range. Right: The fractional difference between the two
measurements as a function of $m_{160}$ magnitude (3% of the sources out of
the plotted range are not shown). Symbols are coded by Sersic index, as in
Fig. 7.

In Fig. 9, we similarly compare our Sersic index measurements versus van der
Wel et al. (2014) for the same sources. We find a systematic offset towards
lower values than those in van der Wel et al. (2014), by $\sim$4% for the
overall population in the magnitude range of interest. At face value, the
offset for sub-samples split by Sersic index is $\sim$4% and 7% for $n<1.5$
and $1.5<n<2.5$ sources, respectively, and consistent with no systematic
offset for $n>2.5$ sources, but possible variation with Sersic index is not
significant with the given statistics. Indeed, Fig. 9 clearly shows the
dispersion between the two measurements, of order 15% for disk-dominated
galaxies and 20-25% for intermediate and bulge-dominated systems. For
reference, the expected average uncertainty on Sersic indices, as estimated
from simulations (Sect. 2.4) for sources towards the faint end of our probed
range, is $\sim$10%. Based on this comparison, with respect to the broad
Sersic index classes considered in this work, and taking van der Wel et al.
(2014) measurements as the reference for the purpose of this assessment, 6% of
$n<1.5$ sources would be misclassified as $n>1.5$, out of which 2% with
$n>2.5$; at the same time, 20% of $n>2.5$ sources would be misclassified as
$n<2.5$, out of which 2% as $n<1.5$. As may be expected, misclassification may
be more severe for intermediate Sersic sources, with almost 40% of $1.5<n<2.5$
sources in van der Wel et al. (2014) being “misclassified” with our
measurements, mostly (25%) as disky $n<1.5$ systems.

Given the intrinsically broad nature of morphology classes used in the
analysis in Sect. 3, the impact of potential systematics at the level
discussed here above on the results presented in this work turns out to be
very marginal. Correcting Sersic indices of cluster galaxies by the amounts
discussed above gives differences on the results and figures presented here
that are always well within the quoted uncertainties, and are actually not
noticeable in most cases. Therefore, as discussed in Sect. 3, Sersic indices
presented throughout and all related results are shown with no corrections
applied.

Figure 10: As Fig. 5, but showing sizes for cluster galaxies as measured (not
corrected for estimated size bias with respect to control field sample, see
text for details). Empty symbols also show the measurement for the full
relevant candidate cluster member samples, not accounting for residual
background contamination (solid symbols account instead for residual
background contamination as in Fig. 5). The three vertical lines on the left
of the control field measurements show the field sample split by redshift
($1.3<z<1.5$, $1.4<z<1.6$, $1.6<z<1.8$), showing no redshift dependence in the
field measurements across the redshift range of interest.

##  Appendix B Additional measurements related to size difference of cluster
versus field galaxies

Figure 10 shows additional measurements related to the investigation of size
differences between cluster and field galaxies for different sub-populations,
as discussed in Sect. 3.2. In particular, Fig. 10 shows 1) analogous
measurements as in Fig. 5, but with average size differences as measured (not
corrected for estimated size bias with respect to control field sample, see
Sects. 2.4 and 3.2); 2) the impact of residual background contamination
correction (see Sects. 2.2.1 and 3.2); 3) the lack of redshift dependence of
average size measurements for the reference field sample (see discussion in
Sect. 3.2).