11institutetext: Ruhr University Bochum, Faculty of Physics and Astronomy,
Astronomical Institute, Universitätsstr. 150, 44801 Bochum, Germany
11email<EMAIL_ADDRESS>22institutetext: European Southern Observatory,
Karl-Schwarzschild-Str. 2, 85748, Garching, Germany
22email<EMAIL_ADDRESS>33institutetext: Univ. Lyon, ENS de Lyon, Univ. Lyon
1, CNRS, Centre de Recherche Astrophysique de Lyon, UMR5574, 69007, Lyon,
France
33email<EMAIL_ADDRESS>44institutetext: Cosmic Dawn Center (DAWN),
Denmark 55institutetext: Niels Bohr Institute, University of Copenhagen,
Lyngbyvej 2, DK-2100 Copenhagen, Denmark 66institutetext: Department of
Physics and Astronomy, York University, 4700, Keele Street, Toronto, Ontario,
ON MJ3 1P3, Canada

# Low Surface Brightness Galaxies in $z>1$ Galaxy Clusters:
HST approaches the Progenitors of Local Ultra Diffuse Galaxies

Aisha Bachmann 112As part of the 1st ESO Summer Research Programme2As part of
the 1st ESO Summer Research Programme Remco F. J. van der Burg 22 Jérémy
Fensch 3322 Gabriel Brammer 4455 Adam Muzzin 66

(Submitted 9 December 2020; accepted 15 January 2021 )

Ultra Diffuse Galaxies (UDGs), a type of large Low Surface Brightness (LSB)
galaxies with particularly large effective radii ($r_{\mathrm{eff}}>1.5$ kpc),
are now routinely studied in the local ($z$¡0.1) universe. While they are
found to be abundant in clusters, groups, and in the field, their formation
mechanisms remain elusive and an active topic of debate. New insights may be
found by studying their counterparts at higher redshifts ($z$¿1.0), even
though cosmological surface brightness dimming makes them particularly
difficult to detect and study there. This work uses the deepest Hubble Space
Telescope (HST) imaging stacks of $z$ ¿ 1 clusters, namely: SPT-CL J2106-5844
and MOO J1014+0038. These two clusters, at $z$=1.13 and $z$=1.23, were
monitored as part of the HST See-Change program. Compared to the Hubble
Extreme Deep Field (XDF) as reference field, we find statistical over-
densities of large LSB galaxies in both clusters. Based on stellar population
modelling and assuming no size evolution, we find that the faintest sources we
can detect are about as bright as expected for the progenitors of the
brightest local UDGs. We find that the LSBs we detect in SPT-CL J2106-5844 and
MOO J1014-5844 already have old stellar populations that place them on the red
sequence. Correcting for incompleteness, and based on an extrapolation of
local scaling relations, we estimate that distant UDGs are relatively under-
abundant compared to local UDGs by a factor $\sim$3\. A plausible explanation
for the implied increase with time would be a significant size growth of these
galaxies in the last $\sim$ 8 Gyr, as also suggested by hydrodynamical
simulations.

###### Key Words.:

galaxies: clusters: general – galaxies: dwarfs – galaxies: formation

##  1 Introduction

Dwarf galaxies are showing a vast range of properties in size and luminosity.
Twenty particularly large (~10 kpc) dwarfs with low surface brightness (LSB)
were discovered through extensive photometric studies of the Virgo cluster by
Sandage & Binggeli (1984). An additional 27 examples were found in the Virgo
cluster (Impey et al., 1988) as well as in the Fornax cluster (Ferguson &
Sandage, 1988). While these objects were found in high density environments,
similar low surface brightness objects were also discovered in lower density
environments such as the field (Dalcanton et al., 1997; Román et al., 2019).

More recently, after discovering 47 similar LSB objects (reff
~$3-10^{\prime\prime}$ , or reff ¿ 1.5 kpc, and $\mu(g,0)=24-26$ mag arcsec-2)
in the Coma cluster, the term ”Ultra Diffuse Galaxies” (UDGs) was introduced
for these objects (van Dokkum et al., 2015a). Due to their projected density,
and their spatial coincidence with the Coma cluster, van Dokkum et al. (2015a)
concluded these objects to be a part of the Coma cluster, a statement that was
confirmed by a follow-up spectroscopic study (van Dokkum et al., 2015b).

Even though it is still a challenge to obtain redshift measurements of sizable
samples of UDGs, their overdensity in galaxy clusters allows us to study their
properties in such over-dense environments. An approximately linear dependence
between the abundance of UDGs in galaxy clusters, and the cluster mass was
found (van der Burg et al., 2017; Janssens et al., 2017; Román & Trujillo,
2017). UDGs within clusters appear to be found on the red sequence (van Dokkum
et al., 2015a; van der Burg et al., 2016), while UDG-like galaxies found in
the field appear to be typically bluer (Leisman et al., 2017; Prole et al.,
2019).

Important open questions surrounding the study of UDGs are related to their
origin, for which different theories have been proposed in the literature. van
Dokkum et al. (2015a) suggest that (some) UDGs may have formed in haloes with
masses similar to the Milky Way, but “failed” to form an L* galaxy. UDGs may
also be the extremes in a continuous distribution in dwarf galaxy properties,
having acquired their expanded sizes due to internal (Amorisco & Loeb, 2016;
Di Cintio et al., 2017), or external (Bennet et al., 2018) processes.

Given the suggested low dark-matter content of some field UDGs (van Dokkum et
al., 2018), they may also have formed as tidal dwarf galaxies (Bennet et al.,
2018; Fensch et al., 2019). Since these formation processes happen over
different time scales, observing the evolving properties of UDGs may help
distinguish between different scenarios. To this end, we search for LSB
galaxies in the two galaxy clusters SPTCL-2106-5844 ($z$ = 1.13) and
MOO-1014+0038 ($z$ = 1.23). Using deep HST image stacks for those clusters, we
reach the spatial resolution required to measure their sizes. We discuss our
results in the context of the UDGs found in the local Universe.

This paper is organized as follows. Section 2 provides an overview of the data
we used. Section 3 describes how we select our sample of UDGs. In Sect. 4 we
discuss our results regarding abundance and colour of the sample, and we
summarize in Sect. 5. We adopt the $\Lambda$CDM cosmology with $\Omega_{m}$ =
0.3, $\Omega_{\Lambda}$ = 0.7 and H0 = 70 km s-1 Mpc-1. At the redshift of our
clusters, 1 arcsec corresponds to ~8.2 - 8.4 kpc. For stellar masses we assume
the Initial Mass Function (IMF) from Chabrier (2003). All magnitudes we quote
are in the AB magnitude system.

##  2 Data

We are making use of HST photometry taken as part of the See Change program
(HST GO 13677, 14327; PI: Perlmutter), which targeted galaxy clusters in the
range $1.13<z<1.75$. The main goal of their program was to find high-$z$
supernovae (SN) type Ia, and to use these to constrain the expansion rate of
the universe. The survey strategy has therefore been to take data with a
$\sim$ monthly cadence (e.g. Williams et al., 2020). Rather than using the
individual exposures, we use the image stacks, which reach a combined exposure
time from 3.99 to 5.13 hours in F140W per cluster we examined. In this work we
focus on the two lowest-$z$ clusters from their sample.

The first cluster we analyze is SPT-CL J2106-5844 (hereafter SPTCL-2106) at
redshift $z$=1.13. It was discovered with the South Pole Telescope (SPT),
thanks to its strong Sunyaev-Zel’dovich effect (SZ) signal, yielding a mass
estimate of M200 = (1.27 $\pm$ 0.21) $\times$ $10^{15}$ M⊙ (Foley et al.,
2011). The second cluster is MOO J1014+0038 (MOO-1014) at redshift z = 1.23,
discovered by the Massive and Distant Clusters of WISE Survey (MaDCoWS) based
on a rich overdensity of galaxies (Gonzalez et al., 2019). It has a mass
estimate of M200 = (5.6 $\pm$ 0.6) $\times$ $10^{14}$ Msun and a strong SZ
signature (Brodwin et al., 2015). RGB images of the two clusters are shown in
Figs. 6 & 7.

Figure 1: RGB (red = F140W, green = F105W, blue = F814W) images of members of
the studied clusters. Top: Two spectroscopically-confirmed bright members of
SPTCL-2106 (on the left) and three LSB galaxies that are likely members of
SPTCL-2106 (based on a reference field comparison, on the right). Bottom:
Three LSB galaxies that are likely members of the cluster MOO-1014 (based on a
reference field comparison).

To create the full-depth mosaics of both clusters we start by aligning each of
the multiple SN monitoring “visits” first internally to a catalog of sources
detected in a single F140W visit and then globally to sources matched in the
GAIA DR2 catalog (Gaia Collaboration et al., 2018). We use the AstroDrizzle
software package (Gonzaga & et al., 2012) to identify and mask cosmic rays and
bad pixels in the aligned individual exposures and perform source detection on
the final combined F140W (WFC3/IR) mosaic generated with 60 mas pixels. We
further use F814W (WFC3/UVIS) stacks to provide basic colour information (or
limits on the inferred colour based on the F814W detection limit). The
combination of these filters bridge the 4000Å break at the redshifts of our
clusters, hence providing clues on stellar populations and a way to help
assess the sample purity.

###  2.1 Reference field

To estimate the level of contamination of the sample by foreground and
background objects, we require a field survey with the same filter bands and
image depth. We therefore utilise the

data stacks taken in the Hubble eXtreme Deep
Field111https://archive.stsci.edu/prepds/xdf/ (XDF). These deep stacks are
composed of data from 19 different HST programs covering the Hubble Ultra Deep
Field from 2002 to 2012. For details on the data reduction we refer to
Illingworth et al. (2013).

To ensure similar source detection limits as for the clusters, we add
artificial noise so that the recovered fraction of simulated sources were
similar between the reference and cluster fields (see Sect. 3.3).

Figure 2: Left: Recovery fractions for the simulated sources in SPTCL-2106.
Middle: Same for MOO-1014. Right: Same for the XDF reference field, with noise
level matched to the cluster fields. The colourbar shows the recovery
fractions. While the detection limits are comparable between the panels, the
XDF shows overall a better recovery fraction for brighter targets than in the
clusters due to a higher source crowding in the cluster fields. Also
highlighted is the regime of objects with a surface brightness from 24.0 to
26.5 mag arcsec-2 in F140W and a radius from 1.5 to 7.0 kpc.

##  3 Analysis

###  3.1 Source detection

Sources are detected by running SExtractor (Bertin & Arnouts, 1996) on the
F140W images of the clusters and the XDF. The parameters used to ensure
optimal detection of faint and extended sources in the clusters can be found
in Appendix B, and an identical setup was used for the XDF images. We only
consider sources in the relatively central regions of the cluster stacks,
where exposure time is nearly uniform (cf. Figs. 6 & 7). Examples of detected
objects in each of the two clusters are shown Fig. 1.

###  3.2 Structural parameters

For the detected sources, structural parameters such as magnitude, radius,
ellipticity and Sérsic index of the detected objects are determined using
GALFIT (Peng et al., 2002) on the F140W image after masking neighbouring
objects that are detected by SExtractor. GALFIT is also allowed to
simultaneously fit a constant value to the sky background to improve the
overall fit. In order to measure reliable colours, the F814W fluxes of the
detected objects are measured on the corresponding stack by forcing GALFIT to
use the morphological parameters obtained from the F140W stack, and only fit
the flux normalisation.

To estimate the measurement uncertainty, the GALFIT models are injected on a
hundred different random locations in the corresponding cluster, requiring
that there were no prior detections, and measured exactly as before. In this
way the 1-$\sigma$-uncertainties for size and magnitude in F140W, and
magnitude in F814W, are obtained. We note that GALFIT measured a slightly
lower flux (by about 0.2 mag) and smaller size (by about 0.3 kpc) than the
simulated inputs. In the following, we correct for this small bias.

###  3.3 Image simulations

To assess the completeness of our UDG progenitor selection, we perform all
processing steps also on a range of image simulations. For this we inject
objects with Sérsic profiles on random locations in the HST stacks. We choose
a constant Sérsic-$n$ parameter of unity, which corresponds to typical light
profiles of UDGs measured in the local Universe (e.g. van Dokkum et al.,
2015a; Koda et al., 2015; van der Burg et al., 2016). Sizes are drawn
uniformly between 0$\aas@@fstack{\prime\prime}$1 and
1$\aas@@fstack{\prime\prime}$0, and ellipticities $f$, defined as $f=1-b/a$
with b/a the axis ratio, uniformly between 0.0 and 0.2. Each step was
performed identically on the cluster- and on the reference field image.

Fig. 2 shows the recovered fractions of the inserted objects, for the two
clusters and the reference field. While the detection limits in the different
panels looks similar overall, we note that there is a substantial difference
between the clusters and the reference field. Even for relatively bright
sources, the recovery fraction is lower in the cluster than in the field. This
is expected given the relatively high number of large and bright sources
crowding the cluster stacks. These recovery fractions are used to determine
the limits of our analysis, and to correct the detected sources for
incompleteness, both due to limiting depth and due to crowding/obscuration.

###  3.4 Sample selection

While the definition of UDGs is rather arbitrary, we initially filter the
sample by using a definition similar to that used in the Local Universe:

  * •

surface brightness in F140W $\geq$ 24.0 mag arcsec-2 (i.e., not corrected for
surface brightness dimming),

  * •

effective radius between 1.5 and 7.0 kpc,

  * •

Sérsic index $\leq$ 4.0 to increase the sample purity in favour of sources
reminiscent of UDGs in the local universe,

  * •

distance between SExtractor detection and GALFIT position of measurement ¡ 3.0
pixels to ensure that both consider the same object.

A fainter limit for the surface brightness is not included as one purpose of
the study is to test the detection limits of LSB galaxies with the available
data. After detecting sources in direction of the cluster we assume that each
source is at the redshift of the cluster to infer their physical parameters.
This is a valid assumption since we subsequently perform a statistical
subtraction of fore- and background objects, thereby making the same
assumption for sources detected in the reference field.

After discarding failed detections with a by-eye scan we find 95 objects (10
discarded) in SPTCL-2106 (70 in reference field, 6 discarded) and 111 objects
(10 discarded) in MOO-1014 (72 in reference field, 9 discarded). We note that
the number of objects in the reference field depends on the assumed angular
diameter distance, and thus the redshift of the cluster. We conservatively
only consider sources that would have had a detection probability of at least
50$\%$ in the reference field for both cluster and reference field objects and
only count the objects above this limit to ensure a reasonable completeness
correction. For the remaining sources we apply a completeness correction that
is thus at most a factor 2 based on the determined recovery fractions (see
Sect. 3.3). We also apply a correction based on the different sky area covered
by the cluster and reference field. We are left with a statistical count of 99
$\pm$ 10 objects in SPTCL-2106 (67 $\pm$ 8 in reference field) and 90 $\pm$ 10
in MOO-1014 (70 $\pm$ 8 in reference field).

Colour-Magnitude diagrams for all the detected sources falling within the
50$\%$-limit (see Fig. 8) in both clusters and the reference field are shown
in the Appendix C. We subtract the reference field galaxies from the nearest
cluster object in regards of colour (F814W-F140W) and magnitude (F140W). For
this we use the colour and magnitude measurements for each cluster object as
coordinates and subtracted the reference field object from the nearest cluster
object. The relative weights, which include corrections for incompleteness and
different covered sky areas, are taken into account. For more details on the
subtraction of the reference field we refer to van der Burg et al. (2016).
After the subtraction we are left with a statistical count of 32 $\pm$ 13 in
SPTCL-2106 and 20 $\pm$ 13 in MOO-1014.

Figure 3: A selection by size and apparent magnitude, in F140W, of our LSB
galaxies. The panels show the different clusters. Red: LSB galaxies detected
following our selection criteria and with a weight higher than 0.5. Blue and
Grey: the samples by van Dokkum et al. (2015a) and Mobasher et al. (2001),
both shifted to our observed redshift by accounting for an E+K correction (see
Sect. 4). We plot curves of constant surface brightness,
$\mathrm{\mu(r_{eff,circ}})$ = 24.0, 26.0 mag arcsec-2 evolved from the Coma
cluster redshift to the high-$z$ clusters. Average errorbars for our sample
are shown. Figure 4: Same es Fig. 3 but for both clusters combined and with
the sample by van Dokkum et al. (2015a) with the size evolution taken out.
Cyan: the sample by van Dokkum et al. (2015a), where the suggested size
evolution since $z\sim 1$ (cf. Sect. 4.3) is taken out.  Figure 5: Colour-
Magnitude diagrams for the sample of LSB candidates in the clusters after
correcting for fore- and background interlopers and incompleteness. The
colourbar gives the residual weight of the data points (as detailed in Sect.
3.4). The left panel shows the cluster SPTCL-2106 and the right panel the
cluster MOO-1014. Additionally shown in the left panel are the positions in
the colour-magnitude diagram of spectroscopically-confirmed members of
SPTCL-2106, and an extrapolation of the red sequence as defined by the
confirmed members of SPTCL-2106, ignoring some of the data points that may be
part of a bluer/starforming cluster population to guide the reader’s eye. This
line has a slope of -0.12.

##  4 Results and Discussion

###  4.1 Comparison with local UDGs

To be able to compare our LSB candidates to likely progenitors of UDGs studied
in the local universe, we evolve local UDGs back to the redshift of our
clusters following a simple stellar population model. The model assumes a
passively-evolving stellar population that was formed at
$z_{\mathrm{form}}=1.5$, which is in line with intermediately old ages of UDGs
measured locally (Ferré-Mateu et al., 2018; Ruiz-Lara et al., 2018; Fensch et
al., 2019). It is based on stellar population synthesis models from Bruzual &
Charlot (2003), a star formation history $\mathrm{SFR}\propto e^{-t/\tau}$
with a short e-folding time of $\tau$ = 10 Myr, a Chabrier (2003) initial mass
function and no dust extinction. We use the magnitudes, physical sizes and
filters of van Dokkum et al. (2015a) as anchor point, and estimate how those
UDGs would appear at the redshift of our cluster as observed through the
WFC3/F140W filter. This estimate accounts, by construction, for surface
brightness dimming. The 47 UDG candidates are shown in Fig. 3. Additionally we
evolved the dwarf and giant galaxies found by Mobasher et al. (2001) in the
Coma cluster back to the redshift of our clusters in the same way and plotted
them as well in Fig. 3.

Figure 3 shows that the LSB samples of our clusters lie in the area between
the samples by van Dokkum et al. (2015a) and Mobasher et al. (2001), making
them fainter than the progenitors of normal dwarf and giant galaxies in the
Coma cluster, and almost as faint as the expected progenitors of the UDGs
studied by van Dokkum et al. (2015a). We can see a small overlap between our
samples and the compared objects from both other studies. As a reference, we
also plot the curves of constant surface brightness,
$\mu(r,r_{\mathrm{eff,circ}})=24.0,26.0$ mag arcsec-2, which is a common
selection boundary for UDGs in the local universe, also evolved to the
redshifts of our clusters. This indicates that only half of the objects we are
able to detect in both clusters could classify as progenitors of the brightest
UDGs known in the local universe, based on this evolution model.

We note that, while projecting the local Coma galaxies back to higher
redshift, we have only evolved their fluxes and ignored any potential size
evolution.However, numerical simulations suggest that a typical UDG may see
its radius increase with age from around 2.5 - 3 kpc at $z$ = 1 to 4 - 5 kpc
at $z$ = 0 (Martin et al., 2019; Wright et al., 2021). Accounting for such an
expansion would bring the data points from van Dokkum et al. (2015a), when
evolved to the redshift of our clusters, downward, and thus closer to our data
points. A possible size evolution is described in Sect. 4.3 and the sample by
van Dokkum et al. (2015a) effected by it is plotted in Fig. 4.

###  4.2 Colour

Figure 5 shows the colours and magnitudes of the sample of LSB galaxies. The
residual weight shows the number of galaxies we expect in the observed cluster
area per detected object after accounting for the subtraction of the reference
field. Also shown in Fig. 5 are the positions in the colour-magnitude diagram
of galaxies which were spectroscopically confirmed as members of SPTCL-2106
(by the GOGREEN collaboration, Balogh et al., 2021). The colours were measured
in the same filter bands and following an identical method as for the LSB
candidates. Ignoring some of the data points that may be part of a bluer/star-
forming cluster population, we note that the bulk of the LSB galaxies lie on
an extended red-sequence, shown as a pink-dashed line, as defined by the
brighter cluster galaxies. We note that the slope of this estimate red-
sequence, -0.12, is consistent with $z\sim 1$ estimates by e.g. Bell et al.
(2004). No similar population of bright cluster members has been
spectroscopically identified for MOO-1014, so that we plot the same red-
sequence estimate for this cluster, ignoring the small redshift difference
between the two clusters. The LSB galaxies of SPTCL-2106 and MOO-1014 show
colours that are consistent with the red sequence, suggesting that these
galaxies are likely quenched and have thus already stopped forming stars.

###  4.3 Abundance comparison with local universe UDGs

To put the measured abundance of LSB galaxies in our clusters into context, we
compare it to the abundance of UDGs in local clusters, within projected
$R<R_{200}$. For this, we have to make assumptions regarding the underlying
magnitude and size distribution of dwarf galaxies, and how these evolve with
redshift. We assume a flat magnitude distribution for different size bins
(consistent with what is observed in the Coma cluster, by Danieli & van
Dokkum, 2019), and the same size distribution as measured for UDGs in local
clusters (for radii between 1.5 and 7.0 kpc van der Burg et al., 2016). Based
on Fig. 2 we can also assume that our samples in the range with surface
brightness from 24.0 to 26.5 mag in F140W and a radius from 1.5 to 7.0 kpc are
mostly complete for the parameter range studied of both clusters.

The available HST imaging does not allow us to probe radii out to $R_{200}$,
but only to radii corresponding to $\sim 0.35\cdot R_{200}$ for SPTCL-2106 and
$\sim 0.50\cdot R_{200}$ for MOO-1014. To correct for the missing area, we
assume that LSBs approximately trace the overall matter distribution in the
cluster, which is described by an NFW (Navarro et al., 1997) profile with
concentration $c_{200}$=3 (e.g. Duffy et al., 2008). Integrating this profile
along the line-of-sight indicates that we probe a fraction of $\sim 0.4\pm
0.1$ of the LSB population in SPTCL-2106 and $\sim 0.55\pm 0.1$ in MOO-1014.
Based on the assumed magnitude and size distribution222We considered
uncertainties in the assumed size distribution (as measured in van der Burg et
al., 2016) and magnitude distribution (as measured in Danieli & van Dokkum,
2019), finding that these affect our estimated number of high-z UDGs by at
most 14%, hence not impacting our conclusions., and after applying the needed
correction for missed area, we would estimate a total number of 80 $\pm$ 38
UDGs in SPTCL-2106 and 36 $\pm$ 25 UDGs in MOO-1014. Studies of local clusters
suggest an abundance of $\sim$100-200 in clusters of this mass, being three
times higher than our best estimate for the clusters we study. This thus
implies a substantial increase in the UDG abundance with time since $z\sim 1$.
A possible explanation for this implied evolution is that we are assuming the
UDG progenitors to be of the same size as local Universe UDGs. If their
progenitors were actually smaller at $z$ = 1 (as suggested by several
simulations, cf. Martin et al., 2019; Wright et al., 2021) they would not fall
into our selection criteria and thus be missed in the current analysis.

Assuming the size distribution of UDGs in the local universe, as described by
the power law shown in Fig. 7 of van der Burg et al. (2016), we find that a
size growth by a factor $\sim$1.4 of all galaxies may have boosted the number
of galaxies classified as UDGs by a factor $\sim$3 since $z\sim 1$.
Hydrodynamical simulations by Martin et al. (2019) would predict a slightly
larger size growth by a factor $\sim$1.8. This suggests that size evolution is
sufficient to explain the observed underabundance of UDGs.

##  5 Summary and outlook

This paper studies the abundance of LSB galaxies in two $z>1$ clusters,
SPTCL-2106 and MOO-1014, down to the detection limit of the available deep HST
imaging data. We correct for background objects by comparing the detections
with those measured in the XDF as reference field. Simulations are run to
estimate completeness limits, and to tailor the depth of the reference field
to the cluster imaging. We summarise our main conclusions as follows:

  * •

Within the parameter space we defined, we find a statistical overdensity of 32
$\pm$ 13 LSB galaxies in SPTCL-2106 and 20 $\pm$ 13 in MOO-1014.

  * •

We find the colours of those LSB galaxies in SPTCL-2106 and MOO-1014 to be
consistent with an extension of the red sequence, as defined by
spectroscopically identified brighter cluster members. This suggests that the
LSB galaxies in both clusters are already evolving passively.

  * •

Based on a simple stellar population evolution model, we compare our detected
LSB galaxies with the expected progenitors of local UDGs in the Coma cluster.
This suggests that the faintest sources we can detect approximate the expected
progenitors of local UDGs.

  * •

Based on an extrapolation, motivated by local scaling relations, we estimate
an overall abundance of 80 $\pm$ 38 UDGs in SPTCL-2106 and 36 $\pm$ 25 UDGs in
MOO-1014. We note that this is about three times lower than the abundance of
UDGs in local galaxy clusters having similar masses.

  * •

One way to interpret the implied evolution is by assuming a substantial size
growth of dwarf galaxies since $z\sim 1$, which would then increase the
numbers of those that classify as UDGs. As we discuss, this is qualitatively
consistent with results from hydrodynamical simulations.

We stress that this study uses the deepest data available for galaxy clusters
at $z$ ¿ 1 that still allow to spatial resolve galaxies of 1-2 kpc, and thus
reaches the limit of current instrumentation. For further studies on the
existence and properties of distant UDGs, data with higher spatial resolution
and depth is needed, being within reach of the next generation of telescopes.

###### Acknowledgements.

We thank the anonymous referee for their useful comments that substantially
clarified the paper. AB acknowledges a 6-week ESO summer studentship during
which a substantial part of this research was done.

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##  Appendix A RGB images of the clusters

Figure 6: RGB (red = F140W, green = F105W, blue = F814W) image of the cluster
SPTCL-2106. Figure 7: RGB (red = F140W, green = F105W, blue = F814W) image of
the cluster MOO-1014.

##  Appendix B SExtractor parameters

Table 1: SExtractor parameters used. All other parameters were left to their defaults. Parameter | Value
---|---
DETECT_MINAREA | 7
DETECT_THRESH | 1.1
ANALYSIS_THRESH | 1.1
BACK_TYPE | MANUAL
BACK_VALUE | 0
FILTER_TYPE | GAUSSIAN
FILTER | default

##  Appendix C Additional Figures

Figure 8: Colour-Magnitude diagrams for the sample of LSB candidates in the
clusters and the reference field that fall within the 50% detection limit.
These are the raw numbers, without accounting for incompleteness, or
background interlopers. The left panel shows the cluster SPTCL-2106 and the
right panel shows the cluster MOO-1014. Additionally shown in the left panel
are the positions in the colour-magnitude diagram of spectroscopically-
confirmed members of SPTCL-2106 and the same extrapolation of the red-sequence
as described in Fig. 5.