#  JWST Photometry of Globular Cluster Populations in Abell 2744 at $z=0.3$

William E. Harris1 and Marta Reina-Campos1,2
1Department of Physics & Astronomy, McMaster University, 1280 Main Street
West, Hamilton, L8S 4M1, Canada
2Canadian Institute for Theoretical Astrophysics (CITA), University of
Toronto, 60 St George St, Toronto, M5S 3H8, Canada
E-mail: harris<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

JWST imaging of the rich galaxy cluster Abell 2744 at $z=0.308$ has been used
by the UNCOVER team to construct mosaic images in the NIRCAM filters. The
exceptionally deep images in the ($F115W$, $F150W$, $F200W$) bands reveal a
large population of unresolved pointlike sources across the field, the vast
majority of which are globular clusters (GCs) or Ultra-Compact Dwarfs (UCDs).
To the limits of our photometry, more than 10,000 such objects were measured,
most of which are in the halos of the five largest A2744 galaxies but which
also include GCs around some satellite galaxies and throughout the
InterGalactic Medium (IGM). The measured luminosity function covers almost
four magnitudes and follows a classic lognormal shape, though the GCLF
turnover point still lies fainter than the photometric completeness limit. The
colour index ($F115W-F200W$) in particular covers an intrinsic spread of $0.5$
mag, clearly resolving the expected range of GC metallicities. The overall
results are consistent with a large, normal GC population seen at a
$3.5~{}$Gyr earlier stage of dynamical evolution.

###### keywords:

galaxies: clusters – galaxies: star clusters – globular clusters

††pubyear: 2023††pagerange: JWST Photometry of Globular Cluster Populations in
Abell 2744 at $z=0.3$–JWST Photometry of Globular Cluster Populations in Abell
2744 at $z=0.3$

##  1 Introduction

Abell 2744 (Pandora’s Cluster), an extremely rich cluster of galaxies at
redshift $z=0.308$, has been the target for intensive imaging campaigns with
HST (Hubble Space Telescope) and now more recently with JWST (James Webb Space
Telescope). As a massive lensing cluster and one of the six Hubble Frontier
Fields (Lotz et al., 2017), it is an attractive testbed for detection and deep
imaging of high-redshift galaxies and for gravitational lensing phenomena in
general.

The UNCOVER project team (Bezanson et al., 2022) has made publicly available a
set of deep mosaic images of A2744 generated from the JWST NIRCAM, HST ACS,
and HST WFC3 cameras. The central part of this field is shown in Figure 1.
This material has been used to extract a catalog of 50,000 galaxies in the
region (Weaver et al., 2023). Close inspection of the NIRCAM SWC (Short
Wavelength Channel) mosaic images also shows the presence of rich populations
of unresolved point sources especially concentrated around the major galaxies
in the cluster. These are the globular clusters (GCs) that are found around
every luminous galaxy (e.g. Harris et al., 2015), along with some probable
Ultra-Compact Dwarfs (UCDs). A small portion of the field is shown in Figure 2
to illustrate the presence of these objects.

A2744 is one of the most well studied clusters of galaxies at intermediate
redshift, having attracted extensive observations across all wavelength
regimes as well as weak and strong lensing analyses. There are five major BCG-
like galaxies in the field, two to the southeast (usually adopted as the
cluster core in previous studies), another pair to the west, and a single one
to the north (Fig. 1). The position and velocity distributions of the member
galaxies show considerable substructure, indicative of highly active merging
in progress (e.g. Owers et al., 2011; Jauzac et al., 2016; Medezinski et al.,
2016). A large X-ray and radio halo is somewhat more symmetric, with a single
major center close to the core BCG pair, but has substructure as well (Kempner
& David, 2004; Boschin et al., 2006; Owers et al., 2011; Eckert et al., 2015;
Jauzac et al., 2016). The overall interpretation is that the subclusters have
already experienced at least one passage, with a final merger into a single
virialized system still very much in progress, though the details of the
merging geometry and history are not yet settled (Merten et al., 2011; Owers
et al., 2011; Eckert et al., 2015; Kimmig et al., 2023).

Accounting for the substructure and globally non-virialized nature of the
system, the total mass of A2744 is determined from recent studies to be
$M_{200}\simeq 2\times 10^{15}M_{\odot}$ (Boschin et al., 2006; Jauzac et al.,
2016; Medezinski et al., 2016). The corresponding virial radius is $R_{200}$ =
2.6 Mpc. By comparison with the two most well known nearby clusters of
galaxies, Virgo has a mass $5.5\times 10^{14}M_{\odot}$ (Durrell et al.,
2014), while Coma is at $\simeq 1.3\times 10^{15}M_{\odot}$ (e.g. Hughes,
1989; Łokas & Mamon, 2003; Kubo et al., 2007; Ho et al., 2022).

At the redshift of A2744 the lookback time is $3.5$ Gyr, a quarter of the way
back to the very first stages of galaxy formation. The exceptionally deep
images from JWST give us an opportunity to observe very directly the
characteristics of entire GC systems at an earlier stage in their evolution.
The ability to study large populations of GCs like this is entirely
complementary to recent JWST observations of objects like the Sparkler, a
lensed galaxy at $z=1.38$ in which a handful of _individual_ GCs or proto-GCs
at even earlier stages of evolution have been seen (Mowla et al., 2022;
Claeyssens et al., 2023; Forbes & Romanowsky, 2023; Adamo et al., 2023); see
also Vanzella et al. (2017, 2019, 2022) for examples in other systems.

The Hubble Space Telescope (HST) has been a powerful instrument for surveying
GC populations around galaxies out to limits of roughly twice the Coma cluster
distance, i.e. $\lesssim 200$ Mpc or $z\lesssim 0.05$ (e.g. Peng et al., 2011;
Lim et al., 2018; Madrid et al., 2018; Amorisco et al., 2018; Harris, 2023;
Hartman et al., 2023; Dornan & Harris, 2023). For all these cases,
cosmological lookback times are $\lesssim 0.6$ Gyr and we are essentially
observing within just the Local Universe. In a few rare cases with very long
exposures, HST photometry has been obtained for GCs and UCDs in more distant
systems including an unnamed elliptical galaxy at $z=0.09$ (Kalirai et al.,
2008), the rich cluster A1689 at $z=0.18$ (Mieske et al., 2004; Alamo-Martínez
et al., 2013; Alamo-Martínez & Blakeslee, 2017), and A2744 itself (Blakeslee
et al., 2015; Lee & Jang, 2016a; Janssens et al., 2017). Even so, in these
cases only the very brightest $\sim 1$ magnitude or so of the GC population is
recovered with any confidence. The first examples of JWST photometry for
entire populations of GCs/UCDs in distant environments are by Faisst et al.
(2022) and Lee et al. (2022) for the cluster SMACS J0723.3-7327 at $z=0.39$.
However, the UNCOVER database for A2744 reaches much deeper in absolute
magnitude into the star cluster population.

An especially interesting new question is the link between the spatial
distribution of GCs and the dark matter (DM) distribution of the galaxy halos
and the cluster they are embedded within. Recent theoretical studies (e.g.
Alonso Asensio et al., 2020; Reina-Campos et al., 2022a, 2023) reinforce the
view that the GC distributions and the IntraCluster Light can be used to
recover the DM profile. Observational tests of such links include the large-
scale survey of the Virgo cluster (Durrell et al., 2014) and JWST imaging of
the cluster SMACS J0723.3-7327 at $z=0.39$ (Lee et al., 2022; Diego et al.,
2023). Carrying out this kind of comparison is opened up by the ability to
measure large-scale spatial distributions of GCs in clusters at significant
redshifts, an observational parameter space well suited to JWST.

In the present study, we describe photometry of the A2744 NIRCAM SWC images
directed specifically at isolating the pointlike sources in the field, which
are dominated by the GCs around the member galaxies. Here, we present the
measurements and give a brief overview of the system. In following studies, we
will analyze the GC spatial distribution and their distributions in
metallicity and luminosity more quantitatively. Section 2 describes the data
and the photometric measurement steps; Section 3 presents the GC colour
distribution function and a brief analysis; and Section 5 presents the
luminosity distribution. Section 6 gives a brief discussion of the adjustments
necessary to normalize the data to zero redshift. Section 7 discusses
connections of our data to a potential UCD population. Finally, Section 8
gives a summary of our findings and prospects for additional work.

We adopt cosmological parameters $H_{0}=67.8$ km s-1 and
$\Omega_{\Lambda}=0.692$, which for $z=0.308$ gives a luminosity distance
$d_{L}=1630$ Mpc or $(m-M)_{0}=41.06$ for A2744, and an angular size distance
of $d_{A}=d_{L}/(1+z)^{2}=952$ Mpc. The foreground extinction (from the NED
database) is $A_{V}=0.036$, which has a negligible effect for the NIR
bandpasses used in the present study.

##  2 Data and Photometry

The mosaic images of the A2744 field and their construction are thoroughly
described in Bezanson et al. (2022). We obtained the NIRCAM SWC images in
$F115W$, $F150W$, and $F200W$, all three of which had closely similar depths
(limiting magnitudes) for objects like GCs with intermediate colours. The
$F090W$ image does not cover as large an area and has shallower depth, and was
not used here. Similarly, the NIRCAM images from the Long Wavelength Channel
(LWC), with their larger pixel scale and lower resolution, also did not reach
sufficient limiting magnitudes for our purposes and were not used. The
mosaics, built from NIRCAM exposures in three different programs (GO-2561,
ERS-1324, DD-2767), have an irregular overall shape with different total
exposure times in various regions (see particularly Fig. 2 of Bezanson et al.,
2022), but the central region thoroughly covering the cluster core is included
by all the programs. Our analysis will concentrate on that central region,
which is marked out in Fig. 1b. The other, outlying wings of the mosaics have
larger levels of sky noise and inhomogeneity and were not used (see Bezanson
et al., 2022).

The mosaic images in $F115W$, $F150W$, and $F150W$ have a resampled pixel size
of $0.02^{\prime\prime}$, smaller than the native SWC camera scale of
$0.03078^{\prime\prime}$ per pixel. The angular scale is therefore 92 pc per
$0.02^{\prime\prime}$ pixel. The mosaics are reoriented to align with the
cardinal directions with EW along the x-axis and NS along the y-axis. Direct
measurements of unsaturated stars in the images give PSF (point spread
function) sizes of _fwhm_ $=1.9$ px ($F115W$), 2.4 px ($F150W$), and 3.0 px
($F200W$).

Photometry was carried out with the tools in daophot (Stetson, 1987) in their
IRAF implementation. The first step was to add the images in the three filters
to produce a very deep stacked image for object finding. On this coadded
image, we used the _daofind_ package to generate a finding list of about
$10^{6}$ candidate objects. Aperture photometry with _phot_ and a 3-px
($0.06^{\prime\prime}$) radius was then carried out with that list on each
filter.

The next stage of the photometry is PSF fitting to the object list. Normally,
bright but unsaturated foreground stars can be used for constructing a PSF,
but they are rare in this high-latitude field. However, the GC/UCD population
in A2744 itself provides a sample of unresolved (starlike) objects; they are
numerous, and the brightest are more than three magnitudes above the
photometric limits. At the distance of A2744, a typical GC with a half-light
diameter $2r_{h}\sim 5$ pc has an angular diameter of $0.0011^{\prime\prime}=$
0.054 px on these images, almost two orders of magnitude below the resolution
limit. Even UCDs with their scale sizes that can be up to $10\times$ larger
(e.g. Drinkwater et al., 2000; Dabringhausen et al., 2008) can be expected to
be unresolved or at worst marginally resolved. About 100 such objects in the
range $F150W$ $<27.5$ scattered across the central region of the field were
carefully selected and confirmed by radial profile measurement. The _pstsel_
and _psf_ tools were then used to construct an empirical PSF from them for
each filter. PSF fitting was then done on the complete photometry list with
_allstar_.

Next, the lists of output photometry from the three filters were matched by
position to within 2 px, accepting only objects that were detected in _all
three_ filters. Though the three images have very similar depths, the triple-
match requirement is useful for rejecting a large proportion of false
detections including pixel artifacts, noise clumps, and the like.

As a final step for reducing sample contamination, the daophot _sharp_
parameter was used to reject remaining objects that were not starlike (the
rejected objects are mainly small, faint background galaxies, severely crowded
objects, or pixel-scale artifacts that do not match the PSF profile) (see
Harris, 2009, 2023, for additional discussion).

Final measured magnitudes were calibrated to the ABMAG system following Weaver
et al. (2023). The fluxes per pixel on the mosaic images are in units of 10
nJy, from which the magnitudes are defined as

$m_{AB}=-2.5\textrm{log}(f/\textrm{10 nJy})+28.90$ (1)

where $f$ is the total flux of the object. We used the PSF encircled-energy
tables as published on the NIRCAM webpages to help estimate the necessary
aperture corrections from the the PSF-fitted instrumental magnitudes to large
radius: direct aperture photometry of the isolated PSF stars on the images was
used to determine the step from the PSF-fitted magnitudes to a radius of
$r=12.5$ px ($0.25^{\prime\prime}$) that encloses 85% of the total profile
light. Lastly, a further $-0.18$ mag was added to step to ‘infinite’ radius.

Figure 1: _Upper panel:_ The central part of the UNCOVER mosaic field of Abell
2744, with North at top and East at left. _Lower panel:_ Spatial distribution
of the candidate globular clusters measured in this study. The red quadrangle
marks the boundary for the central region discussed in the text. As described
in the text, parts of the mosaic image to the lower left and upper right of
the box with shorter total exposures and higher sky noise were not used. The
region shown is $460^{\prime\prime}=2100$ kpc across. Figure 2: A small
portion of the A2744 mosaic field shown at very high contrast, at a location
between the two major galaxies at middle right of Figure 1. The field shown is
$32^{\prime\prime}$ across, equivalent to 150 kpc linear distance. The image
has been median filtered to remove the large-scale light gradients from the
galaxies and to emphasize the point sources. The many small starlike objects
indicate some of the globular cluster and UCD candidates. The thin short
diagonal arcs are strongly lensed background galaxies.

After the photometry and culling steps, the list of GC/UCD candidates consists
of 10617 objects. A final close visual inspection of these objects on the
images showed that the list included virtually all starlike objects that are
clearly detectable, while obviously nonstellar ones were almost all excluded.
The final colour-magnitude diagrams (CMDs) for these matched, starlike sources
appear in Figure 3, where $F150W$ is plotted versus the three different colour
indices that can be obtained from the combination of filters111The third panel
of Fig. 3 has the unusual property for a CMD that the x and y axes are
independent of each other.. Their spatial distribution across the central
field of A2744 is shown in Figure 1b. The concentration of the objects around
the five biggest galaxies is very evident, but smaller galaxies can be spotted
as well, and many GC candidates are also scattered more widely through the ICM
(IntraCluster Medium).

To gauge the effective photometric limits of the data and the internal
measurement uncertainties, artificial-star tests were run. With the daophot
_addstar_ tools, 16000 fake stars covering the magnitude range $26-34$ were
inserted into the three images in series so that no change in the crowding
levels on the images would result (though the absolute crowding level is quite
low to begin with). The synthesized frames were remeasured with exactly the
same procedure as described above. The resulting recovery completeness is
shown in Figure 4, where the recovery fraction $f$ is defined as the number of
artificial stars measured in a given $0.2-$mag bin, divided by the number of
stars originally inserted into that bin. Defined this way, the ratio $f$
implicitly includes the effects of bin-jumping; i.e. a measured star falling
within the bin may have originally been assigned to another adjacent bin
(Alamo-Martínez et al., 2013). Note as well that in Fig. 4, $f$ is plotted
versus the measured (i.e., recovered) magnitude. For $f>0.2$, the trend is
accurately matched by a modified hyperbolic tangent function

$f(m)=\frac{2}{1+\exp\left[{\beta(m-m_{1})}\right]}-1$ (2)

with $\beta=1.70,m_{1}=30.28$.222This function has the unphysical property
that $f$ becomes negative for $m>m_{1}$, but its most important role is to
match the bright end and the downturn region. No part of our analysis depends
on data fainter than F150W $\simeq 30$. The $50~{}$per cent recovery
completeness point is at $F150W$ = 29.63, and $80~{}$per cent at $F150W$ =
28.98. The artificial-star tests were also used to gauge the trend of
photometric measurement uncertainty $\sigma$ with magnitude, as shown in the
second panel of Fig. 4. A simple exponential curve $\sigma(m)\simeq
0.075\exp\left[{0.7(m-29.0)}\right]$ describes the trend well in each filter,
to the useful limits of the data.

##  3 Colour Distributions

The integrated colours of GCs in the NIRCAM filters are relatively new in this
subject, with little available data (Faisst et al., 2022; Lee et al., 2022).
By comparison, there are available observations in many nearby galaxies of HST
photometry of GCs in several ACS and WFC3 filters (e.g. Harris, 2023; Hartman
et al., 2023). GC colours depend primarily on the cluster _metallicity_ and
_age_ ; increases in both quantities drive the cluster to redder colours.
However, as will be seen below, the NIRCAM colour indices in adjacent filters
such as $(F150W-F200W)$ and $(F115W-F150W)$ are not strongly sensitive to
metallicity, so for the CMDs in these colours we should expect to find that
old GCs delineate a narrow, vertical sequence exactly like what is seen in
Fig. 3a-b. The colour $(F115W-F200W)$, however, is about twice as metallicity-
sensitive as either of these and the GC sequence is distinctly broader (Fig.
3c).

Figure 3: CMDs for the unresolved objects in the A2744 field after triple-
matching among the three filters and selection by _allstar/sharp_ to remove
nonstellar objects. This culled sample is dominated by GCs around the A2744
galaxies. Errorbars along the left side of each diagram show the expected $\pm
1\sigma$ spread due to measurement uncertainty. The $50~{}$per cent recovery
completeness level at $F150W=29.6$ is shown as the dashed line.

A basic test of the observed range of colours is shown in Figure 5, displaying
the histograms over the magnitude range $27.0<F150W<28.5$ where the photometry
is the most precise. In this range the recovery completeness is higher than
80%. From many previous studies drawn primarily from optical colour indices,
we expect the GCs to fall into two identifiable metallicity groups, ‘blue’
(metal-poor) and ‘red’ (metal-rich) with a double-Gaussian model usually
providing an accurate match to the colour distribution function (CDF) (e.g.
Larsen et al., 2001; Peng et al., 2006; Harris, 2009; Faifer et al., 2011;
Brodie et al., 2012; Cho et al., 2012; Hargis & Rhode, 2014; Harris, 2023;
Hartman et al., 2023, among many others). For either the index $(F150W-F200W)$
or $(F115W-F150W)$, the observed total colour range is no more than $\sim 0.2$
mag and is not much larger than what would be produced just by random
measurement scatter. In Fig. 5a, the dashed line shows the shape of the CDF
expected if the intrinsic colours of the GCs were dispersionless and the
broadening was equal to the $1\sigma$ colour uncertainty at $F150W=28.0$, i.e.
the _maximum_ colour dispersion over the given magnitude range. For
comparison, the solid line gives a double-Gaussian fit to the CDF determined
from the Gaussian mixture model (GMM) fitting code (Muratov & Gnedin, 2010);
it is scarcely different from the single-Gaussian error distribution, so there
is no compelling evidence for more than one component.

For the broader colour index $(F115W-F200W)$, however (Fig. 5b), the total
width of the CDF is $\sim 0.5$ mag and the rms dispersion is $\pm 0.15$ mag,
larger than the $\pm 0.05-$mag rms spread expected from the measurement
uncertainties alone (dashed line in the Figure). The best-fit double Gaussian
solution performed with GMM gives the results listed in Table 1, where
$\mu_{1},\mu_{2}$ are the means of the bluer and redder subcomponents;
$\sigma_{1},\sigma_{2}$ are their dispersions; $f_{2}$ is the fraction in the
redder component; and $p(uni)$ is the probability that the CDF is a single
Gaussian. Their sum is shown as the solid (magenta) line in Fig. 5b. Clearly,
a single-Gaussian solution is also acceptable. A simpler homoscedastic fit
(enforcing equal variances for the two components) gives
($\mu_{1}=0.244,\mu_{2}=0.393$) and ($\sigma_{1}=\sigma_{2}=0.098$), with
$f_{2}=0.44$. The quality of fit between the two solutions is nearly
identical. The main conclusions drawn from this exercise are that (a) the
intrinsic width of the CDF is resolved by the ($F115W-F200W$) index in
particular; i.e. its spread is distinctly larger than can be accounted for by
measurement scatter alone; and (b) either a single-Gaussian or a conventional
double-Gaussian model can provide an accurate match to the CDF, though the
blue/red fraction in particular is sensitive to the assumptions made about the
parameters.

In Figure 6, theoretically predicted trends of colour versus metallicity are
shown for the three indices used here. These tracks have been generated with
the PARSECv1.2 CMD3.7 stellar models333http://stev.oapd.inaf.it/cgi-bin/cmd
(Bressan et al., 2012) for three different ages (12.5 Gyr, 9.0 Gyr, 7.0 Gyr),
and adopting the standard Kroupa (2001) IMF. Conversions of these models from
their normal output Vegamag magnitude scale to the ABMAG scale have been
applied444https://jwst-crds.stsci.edu. For star clusters in this age range,
colour is insensitive to age, even more so than for optical colour indices.

The best-fit single Gaussians to each of the CDFs give
$\mu=0.088,\sigma=0.072$ for $(F150W-F200W)$, and $\mu=0.290,\sigma=0.14$ for
$(F115W-F200W)$. After K-corrections to the colours (see §6.3 below), these
mean colours adjusted to zero redshift become $\mu_{0}(F150W-F200W)=-0.16$ and
$\mu_{0}(F115W-F200W)=+0.04$. In both cases, comparison with Fig. 6 would give
mean metallicities near [M/H] $\sim-0.4$, though the comparison should be
viewed with caution since it depends on all three of the K-correction
accuracies, the absolute accuracy of the photometry including the aperture
corrections, and the zeropoints of the model colour scales themselves. The
_range_ of colours may be a more robust comparison with the models. These
ranges are equal to $\Delta(F150W-F200W)\simeq 0.2$ mag and
$\Delta(F115W-F200W)\simeq 0.5$ mag (Fig. 5). These correspond to an end-to-
end range of 2.0 dex in metallicity, as observed for the GCs in most large
galaxies (Peng et al., 2006; Harris, 2023).

Table 1: GMM Fits to the Colour Distributions: $N$ is the number of objects, $\mu_{i}$ and $\sigma_{i}$ are the mean colour and its dispersion for the blue ($i=1$) and red ($i=2$) components, $f_{2}$ is the fraction in the redder component, and $p(uni)$ is the probability that the CDF is a single Gaussian. Internal $1\sigma$ fitting uncertainties are given in parentheses. Region | $N$ | $\mu_{1}$ | $\sigma_{1}$ | $\mu_{2}$ | $\sigma_{2}$ | $f_{2}$ | $p(uni)$
---|---|---|---|---|---|---|---
All | 566 | 0.152 (0.084) | 0.106 (0.031) | 0.320 (0.077) | 0.128 (0.030) | 0.82 (0.24) | 0.95
5 BCGs | 413 | 0.166 (0.044) | 0.068 (0.021) | 0.341 (0.071) | 0.112 (0.018) | 0.84 (0.22) | 0.35
IGM | 153 | 0.171 (0.050) | 0.121 (0.029) | 0.353 (0.157) | 0.156 (0.055) | 0.33 (0.28) | 0.29

One additional comparison can be made directly with other JWST photometry:
Faisst et al. (2022) and Lee et al. (2022) have measured the brightest $\sim
1$ mag of the GC population in the $z=0.39$ cluster SMACS J0723.3-7327. The
mean colour (dereddened, but not K-corrected) in $(F150W-F200W)_{0,AB}$ for
their sample is in the range $\simeq 0.05-0.15$ depending on location, in
close agreement with our results for the A2744 population. The brightest GCs
in their data are near $F200W_{0}\simeq 27$, again very consistent with our
A2744 CMD given that SMACSJ0723 is 0.6 mag more distant.

Figure 4: _Upper panel:_ Photometric recovery completeness, measured from the
artificial-star tests. The recovery fraction $f$ is plotted in $0.2-$mag bins.
The solid line shows the tanh function in Eq. 2 with parameters $\beta=1.70$,
$m_{1}=30.28$. _Lower panel:_ Internal measurement uncertainty $\sigma$ versus
magnitude, as determined from the artificial-star tests. The exponential curve
given in the text is shown as the solid line. Figure 5: _Upper panel:_
Histogram of the GC colours in ($F150W$–$F200W$), for objects in the magnitude
range $F150W=27.0-28.5$ for which completeness is $>80~{}$per cent. The solid
line shows the double-Gaussian fit described in the text. The green dashed-
line Gaussian centered on the mean colour shows the expected maximum
dispersion if the colour spread was dominated purely by measurement scatter.
_Lower panel:_ Histogram of GC colours for the same sample in ($F115W-F200W$).
The solid line shows the double-Gaussian fit to the data (either homoscedastic
or heteroscedastic). NB: K-corrections have _not_ been applied to the colour
indices; see text.  Figure 6: Predicted colour-metallicity relations for
globular clusters in the NIRCAM filters, from the PARSEC CMD3.7 stellar
models. Green lines are for an assumed age of 12.5 Gyr, while orange lines are
for 9.0 Gyr and blue lines for 7.0 Gyr. Different linestyles indicate
different filter combinations as noted in the legend. Indices are in the ABMAG
system. Figure 7: Locations of objects in the ‘blue sequence’ described in the
text are shown as blue circles, while the GC candidates brighter than
$F150W=29.0$ are small black dots. The most luminous GC candidates at
$F150W<27.5$ are marked as red crosses. Figure 8: Spatial distributions of GC
and UCD candidates with $F150W<29.0$. _Left panel:_ ‘Blue’ GCs: those with
colours $(F115W-F200W)<0.31$. _Right panel:_ ‘Red’ GCs: those with colours
$(F115W-F200W)>0.31$. The circles mark out the exclusion regions around the
five major galaxies as discussed in the text. Figure 9: _Left panel:_ CMD for
the objects outside the exclusion circles marked in Fig. 8. This sample is
dominated by GCs in the InterGalactic Medium and in a few small satellite
galaxies. _Right panel:_ CMD for the objects inside the circles. These are
dominated by members of the five giant galaxies in the system.  Figure 10:
_Upper panel:_ CDF for the objects inside the exclusion circles in Fig. 8,
mostly belonging to the five major galaxies in the system. As in Fig. 5 above,
this sample is restricted to the range $27.0\leq F50W\leq 28.5$. The solid
line shows the best-fit double Gaussian solution described in the text, while
the dashed blue and red lines show the blue and red subcomponents. _Lower
panel:_ CDF for the objects outside the exclusion circles.

In Fig. 3, just to the left of the major GC sequence, a thin sequence of bluer
objects can be seen, in the colour range $-0.3<(F150W-F200W)<0.0$ and
magnitude range $25<F150W<27$. Close inspection of these objects on the images
shows that almost half of them are in very distant background galaxy pairs or
groups, and some others are located in the bright bulge light of large
galaxies. Some of them may be compact star-forming regions. About 20 of them
are isolated, unresolved objects scattered around the field without showing
any obvious connection with the A2744 galaxies; their distribution across the
field is shown in Figure 7. If guilt by association is relevant, then these
may simply represent other background objects such as remote, high$-z$ galaxy
nuclei that were able to pass through the photometric culling steps. Bright,
unresolved sources sitting to the blue side of the main GC sequence might also
be young massive star clusters that would mark much more recent star
formation, such as those seen in the embedded filamentary structure in the
Perseus giant NGC 1275 (Holtzman et al., 1992; Canning et al., 2014; Lim et
al., 2020). However, we find no noticeable numbers of such young blue GCs in
the current A2744 data.

The bright end of the CMD distribution extends upward to high luminosity
particularly on the red side of the CDF. The spatial distribution of the
luminous, red objects $(F150W<27.5)$ is shown as well in Fig. 7. The majority
of these objects group closely around the major galaxies, consistent with
their being part of the GC/UCD population (see §7 below for further
discussion).

##  4 The InterGalactic Medium

Assuming that GC colour represents metallicity, then an additional test can be
made in terms of their spatial distribution. Much previous photometry for GC
systems in large galaxies shows that the redder, more metal-rich GCs have more
concentrated, steeper radial profiles around their parent galaxies than do the
metal-poor clusters (Zinn, 1985; Geisler et al., 1996; Bassino et al., 2008;
Faifer et al., 2011; Liu et al., 2011; Durrell et al., 2014; Harris et al.,
2017a). In Figure 8, the sample has been subdivided into a ‘blue’ group with
$(F115W-F200W)<0.31$ (the midpoint of the CDF as described above), and a ‘red’
group redder than that dividing line. Only objects with $F150W<29.0$ are
included to guarantee high completeness. As seen in the figure, the bluer and
redder clusters do not show strong differences in their distributions around
the major galaxies. A more noticeable difference is found for the objects
scattered across the IGM and in the smaller satellite galaxies, where the
bluer objects are much more populous than are the redder ones.

To demonstrate this latter effect more clearly, the objects near the five
major galaxies (BCGs) are marked out by the enclosing circles shown in Fig. 8.
The resulting CMDs divided by location are shown in Figure 9, which shows the
objects outside the circles in the left panel, and the ones inside the circles
in the right panel. For the outer population which consists mainly of GCs in
the IGM and a few small satellite galaxies, the red sequence extending to high
luminosity ($F150W$ $<28$) is almost entirely gone, and by default the blue
component is the majority of what remains.

In Figure 10, the CDFs for both populations are shown, for comparison with
Fig. 5. A double-Gaussian fit done with GMM as described above yields the
results summarized in Table 1. Within the uncertainties of the fit, the blue
and red mean colours ($\mu_{1},\mu_{2}$) and their dispersions
($\sigma_{1},\sigma_{2}$) are similar in all three subsamples listed there.
The principal difference is the very much larger blue fraction for the IGM
sample. Similar patterns have been found for the GC populations in the major
nearby clusters of galaxies including Virgo (Durrell et al., 2014), Coma (Peng
et al., 2011), Fornax (Cantiello et al., 2020), and Perseus (Harris et al.,
2020).

The objects in the BCG sample (the ones inside the three exclusion circles)
make up 88% of the total numbers in our photometry. A very rough upper limit
on the IGM population of GCs in A2744 is then that it makes up at most 12% of
the total. Notably, Montes & Trujillo (2014) find that the IntraCluster Light
(ICL) in Abell 2744 makes up $>$6% of the total stellar mass, Morishita et al.
(2017) find an ICL fraction of $8-9$%, while Jiménez-Teja et al. (2018)
estimate a higher value of $\simeq 16-20$%. Our result from GC counts favors
the two lower values, but the range in these different studies appears to
reflect the strong observational challenges in measuring such a wide-field,
low-surface-brightness component (e.g. Furnell et al., 2021). For comparison,
Durrell et al. (2014) estimate that in Virgo the IGM GCs make up 18% of the
total in the entire system, while Peng et al. (2011) find that for Coma, the
IGM population is in the range 30-45% of the total. This contrast adds to the
evidence that A2744 is in an earlier stage of its dynamical history than these
local galaxy clusters. At higher redshift, the intergalactic stellar
population created by tidal stripping from the member galaxies is still
actively developing, and the period since redshift $z\sim 1$ is expected to be
especially important for growing the IGM, including both intergalactic GCs and
more generally the ICL (e.g. Burke et al., 2012; Ramos et al., 2015; Ramos-
Almendares et al., 2018; de Oliveira et al., 2022; Ahvazi et al., 2023).

In some contrast, for the cluster Abell 1689 at $z=0.183$, Alamo-Martínez &
Blakeslee (2017) find that the intergalactic GCs represent as much at 35% of
the total GC population. This cluster appears to be in a more dynamically
evolved state than A2744, since it has a single dominant central BCG with an
extensive cD envelope. Similarly, in the $z=0.39$ cluster SMACS J0723.3-7327,
Lee et al. (2022) find a very extended IGC distribution with a regular,
elongated structure centered on the single dominant BCG, which is again
suggestive of a fairly advanced evolutionary state.

##  5 Luminosity Function

For normal old GCs, the luminosity function (GCLF) follows a lognormal shape
with a peak $m_{0}$ and dispersion $\sigma$ that are known to vary slowly with
host galaxy mass (Jordán et al., 2007; Villegas et al., 2010; Harris et al.,
2014). The GCLF peak (turnover) point for nearby galaxies is near
$M_{I}\simeq-8.3$ and the dispersion $\sigma\simeq 1.2$ mag (Harris et al.,
2014), but the turnover luminosity and dispersion both increase slightly with
galaxy mass. In the A2744 galaxies, the apparent magnitude $m_{0}$ of the GCLF
turnover point is expected to be fainter than our photometric detection limit,
but the data penetrate very much deeper than did the previous HST photometry
and it should therefore be possible to make a basic test of the GCLF shape.

Figure 11 shows the observed numbers of objects as measured in $F150W$. The
basic lognormal shape provides a valid description for the brighter magnitude
range, but for $F150W\gtrsim 29$, the recovery completeness starts having an
important effect on reducing the curve amplitude. For the binned counts shown
in Fig. 11 as grey datapoints, we fit the function

$N(m)=\frac{N_{\rm
tot}}{\sqrt{2\pi}\sigma}e^{-(m-m_{0})^{2}/{2\sigma^{2}}}\cdot f(m)$ (3)

where $f(m)$ is the photometric completeness function given above, $N(m)$ is
the observed number of objects per unit magnitude in each bin, and $(N_{\rm
tot},m_{0},\sigma)$ are the free parameters to be solved for. An unweighted
non-linear least-squares fit gives $m_{0}=(31.05\pm 0.09)$ mag for the
turnover point, $\sigma=(1.25\pm 0.03)$ mag for the dispersion, and a total
population $N_{\rm tot}=78000\pm 6000$ over the entire system. The solid
magenta curve in Fig. 11 shows the intrinsic lognormal LF, while the dashed
curve shows the same lognormal function multiplied by the completeness
function.

The quoted errors on the three parameters reflect only the internal fitting
uncertainties, and are relatively small because the sample size here is large
($10^{4}$ objects), and as shown in Fig. 11, the data match the numerical
model of Eq. (3) extremely closely. An unweighted fit avoids giving too much
emphasis to either the bright end (where the photometry is higher quality but
the bin counts are low) or the faint end (where the counts are far larger but
the photometry is more uncertain). A better idea of the true external
uncertainty of the parameters can be gauged if we weight the datapoints by
either the absolute count uncertainty $\pm N_{\rm bin}^{1/2}$ or the relative
uncertainty $\pm N_{\rm bin}^{-1/2}$. These give results different by an
additional $\pm 0.1$ mag in $m_{0}$, $\pm 0.05$ mag in $\sigma$, and $\pm
10000$ in $N_{\rm tot}$ compared with the unweighted fit.

Though the lognormal model in Eq. 3 fits the observed LF quite well, if the
data fall well short of the true GCLF turnover point, then the solutions for
$m_{0}$ and $\sigma$ become correlated (Hanes & Whittaker, 1987; Harris et
al., 2014) and both are increasingly uncertain. At any magnitudes fainter than
$F150W\gtrsim 30$, the observed counts are steeply choked off by
incompleteness (Fig. 4), and all estimated quantities including the
completeness function itself become very uncertain.

The turnover level of $m_{0}=31.05$ predicted from the fit corresponds to an
absolute magnitude $M_{F150W}=-9.84$, which in turn converts to a mass of
$\simeq 10^{6}M_{\odot}$ using the PARSEC models mentioned above. This level
is a factor of $\sim 3$ higher than the normal GCLF turnover at $L\simeq
10^{5.24}L_{\odot}$ established from nearby galaxies (Jordán et al., 2007;
Villegas et al., 2010; Harris et al., 2014), which would lie at
$M_{F150W}\simeq-8.9$ or $m_{0}\simeq 32.0$ at the distance of A2744. To check
further on the impact of changing the LF parameters, the fit can be redone by
forcing either the dispersion $\sigma$ or the turnover $m_{0}$ to take fixed
values closer to the ones initially expected. If we adopt $\sigma\equiv 1.4$
mag as an appropriate mean for large galaxies (Harris et al., 2014), the
resulting two-parameter solution gives $N_{\rm tot}=116000,m_{0}=31.54$.
Similarly, if we adopt $m_{0}\equiv 32.0$ as a normally expected turnover
luminosity, the resulting solution gives $N_{\rm tot}=167000,\sigma=1.52$ mag.
All three sample solutions are shown in Fig.11, (dashed magenta line for the
three-parameter solution, dashed blue line for fixed $m_{0}=32.0$, dotted
green line for $\sigma=1.4$). There is little to choose among them aross most
of the range, though the restricted two-parameter solutions tend to
overpredict the numbers of the brightest clusters. Arguments can be made for
any of these solutions, and we conclude for the present only that the total GC
population is likely to be at least $\sim 10^{5}$ clusters. We also cannot
rule out a GCLF turnover or intrinsic dispersion close to the standard values
for giant galaxies. Most importantly, we view this comparison primarily as a
test that the standard lognormal LF shape provides a reasonable match to the
data.

It should also be emphasized that the best-fit parameters $(m_{0},\sigma)$ are
an average over the entire A2744 system. The lookback time for A2744 is large
enough that some evolution of the GCLF shape should be expected. Simulations
of evolving GC systems within Milky-Way-sized galaxies with EMP-Pathfinder
(Reina-Campos et al., 2022b) show that by an age of $\sim 6-7$ Gyr, the basic
lognormal shape of the GCLF is well established, but the peak point and spread
(dispersion) continue to evolve slowly as the clusters age and disrupt, in the
sense that the GCLF turnover will gradually become brighter and the spread
narrower (Kruijssen, 2009; Choksi & Gnedin, 2019; Reina-Campos et al., 2022b).

An additional factor to be considered in a more detailed analysis would
involve the effects of differential ages. The GCs in the Milky Way show an
age-metallicity relation (VandenBerg et al., 2013; Forbes & Bridges, 2010;
Dotter et al., 2011) in the sense that the metal-poor ones are 12-13 Gyr old
while the most metal-rich are 9-10 Gyr old (with scatter). Thus if the A2744
GCs have a similar age-metallicity relation, then at a lookback time of 3.5
Gyr the metal-poor ones are seen as $\simeq 9$ Gyr old while the metal-rich
ones are only $\simeq 6$ Gyr old; i.e. the relative age difference was larger
at that time. The red sequence should then be relatively brighter than the
blue sequence for the same GC mass range. A hint of that effect may be visible
in the CMD, where the redder side of the distribution reaches to a much higher
level (cf. the discussion below). Further investigation into these effects
will be done in later work. Deeper photometry would reveal a much clearer
picture, but that is not likely to be achievable in the foreseeable future.

The estimated total GC population from the three-parameter solution of $N_{\rm
tot}\simeq 78000$, as stated above, includes all the cluster galaxies and the
IGM over the central region. It should be viewed as a lower limit, since it
does not include regions outside the central part of the cluster studied here,
and does not account for other locations of area incompleteness such as near
the centers of the large galaxies. This total is nevertheless smaller than the
estimate of $4\times 10^{5}$ GCs from Lee & Jang (2016b) from the HST imaging,
though later discussions (Harris et al., 2017a; Alamo-Martínez & Blakeslee,
2017) revised that downward by at least a factor of two. These HST-based
estimates were based on only the brightest magnitude or so of the GCLF and
thus required a very large extrapolation compared with our present data. As
more relevant comparisons, our estimate for A2744 from the basic three-
parameter GCLF fit for $N_{\rm tot}$ is similar to the total of 67000 GCs in
the entire Virgo cluster (Durrell et al., 2014), and $\simeq 100000$ GCs in
the Coma cluster (Peng et al., 2011), again including both the IGM and the
member galaxies. Notably, however, either of our two-parameter GCLF solutions
stated above would raise $N_{\rm tot}$(A2744) above $10^{5}$, appropriate for
the large total mass of the system (Harris et al., 2017b; Dornan & Harris,
2023).

Figure 11: Luminosity function for the GCs in the A2744 field. The gray
datapoints and errorbars show the observed number of objects per $0.2-$mag bin
in $F150W$, with the $50~{}$per cent recovery completeness level as indicated
by the vertical dashed line. The rising solid line (magenta) shows the best-
fit three-parameter solution for the GCLF with $m_{0}=31.05,\sigma=1.25$,
while the three curves going through the datapoints as described in the text
show three possible solutions for the GCLF now multiplied by the photometric
completeness function. Fainter than $F150W\gtrsim 30$, all numbers are very
uncertain. Figure 12: Predicted GC luminosity versus age in the three NIRCAM
filters. Blue lines are for [M/H] $=-2.0$, orange for $-1.0$, and green for
0.0. These are calculated from the PARSEC CMD3.7 stellar models as described
in the text. These curves track the passive decline in luminosity due only to
stellar evolution, and do not include the effects of mass loss (see text). The
absolute magnitudes are normalized to $1M_{\odot}$.

##  6 Adjustments to Zero Redshift

Comparison of the A2744 GC population with local ($z=0$) GCs requires
estimating the size of three different effects arising from the lookback time
and redshift.

###  6.1 Passive Luminosity Evolution

Any star cluster after its initial formation period will decrease in
luminosity over time due to simple stellar evolution. In Figure 12, predicted
luminosities in the three NIRCAM filters as derived from the PARSEC models are
shown, at three different metallicities. Although the absolute magnitude
depends slightly on metallicity, the relative change in luminosity over the
past 3.5 Gyr is nearly independent of metallicity or filter. The net change
from $z=0.3$ to $z=0$ is an age-fading of $\simeq 0.21$ mag, or about
$20~{}$per cent decrease in luminosity.

This estimate, however, assumes a similar mean age for all the GCs. If as
noted above the red GCs are as much as 3 Gyr younger on average than the blue
GCs, then they would decrease by about $30~{}$per cent in luminosity down to
the present time. A mean age difference of $\sim 3$ Gyr may be an upper limit,
however, since the age/metallicity relation (AMR) for GCs is expected to be
steeper for more massive galaxies (Horta et al., 2021), and most of the A2744
GCs are clearly associated with the giant member galaxies.

###  6.2 Mass Loss

All GCs experience progressive mass loss due to stellar evaporation and tidal
stripping. Clusters located in the IGM far from any major galaxies will be
subject to only slow stellar evaporation. However, most of the GCs in our
observed sample are satellites of the major galaxies (Fig. 1b) and these will
experience larger tidal losses. Tidal disruption times for GCs will be several
Gyr (e.g. Baumgardt & Makino, 2003) but the mass loss rate depends on their
own mass and their local host-galaxy potential. A useful first-order
prescription for the fractional mass loss, averaging over galactocentric
radius, is (Choksi & Gnedin, 2019)

$\frac{\Delta M}{M}=-\frac{\Delta t}{t_{\rm tid}}\simeq-\frac{\Delta
t}{\textrm{5 Gyr}}\cdot\left(\frac{M}{2\times 10^{5}M_{\odot}}\right)^{-2/3}$
(4)

where $t_{\rm tid}$ is the tidal disruption time and the GCLF turnover mass is
$2-3\times 10^{5}M_{\odot}$ (Villegas et al., 2010; Harris et al., 2014).
Baumgardt & Makino (2003) or Lamers et al. (2005) give similar relations. As
discussed above, the A2744 GCs observed in this study are on the bright half
of the the GCLF, with masses extending to $\simeq 10^{6}M_{\odot}$ and above
at the bright end, so with $\Delta t=3.5$ Gyr, the ratio ($-\Delta M/M$) will
range from $\simeq 0.15$ at the high-mass end up to as much as 0.7 at the GCLF
peak; i.e. a dimming of 0.2 to 1.3 mag in absolute magnitude. Stellar
evaporation is negligible by comparison, with dissolution times one or two
orders of magnitude larger (e.g. Baumgardt & Makino, 2003; Lamers et al.,
2005).

###  6.3 K-Corrections

The cosmological K-correction is well known in galaxy studies but relatively
unfamiliar for GC work. The redshift causes any rest-frame wavelength
$\lambda_{0}$ emitted at the source to be measured at
$\lambda=(1+z)\lambda_{0}$, thus both shifting and stretching any given filter
bandpass and reducing the energy of each photon by the same factor. By
definition, the absolute magnitude $M_{\lambda}$ at wavelength $\lambda$ is

$M_{\lambda}=m_{\lambda}-5\log_{10}\left(\frac{d_{L}}{10\,{\rm
pc}}\right)-K_{\lambda}~{}.$ (5)

The redshift factor $K_{\lambda}$ may be positive or negative depending on the
shape of the spectrum in the region of a given filter bandpass. For A2744,
there is an interesting coincidence at play: the ratios of effective
wavelengths between the adjacent NIRCAM/SWC filters almost exactly match its
redshift factor of $(1+z)=1.3$. That is, light observed in $F200W$
($\lambda_{\rm eff}=19680$Å) was emitted very nearly in $F150W$ (14873 Å);
light observed in $F150W$ was emitted in $F115W$ (11434 Å); and light observed
in $F115W$ was emitted in $F090W$ (8985 Å). Thus for the colour indices, our
most metallicity-sensitive index $(F115W-F200W)$ is actually close to the
rest-frame $(F090W-F150W)$, a colour that is similarly metallicity-sensitive.

GCs are good approximations to single stellar populations (SSPs) and their
spectral energy distributions (SEDs) are not the same as those of galaxies.
For galaxies, the $K$-values at a given redshift and wavelength depend on
galaxy type (essentially, star formation history) (e.g. Blanton & Roweis,
2007; O’Mill et al., 2011; Beare et al., 2014), whereas for SSPs the important
parameters are instead age and metallicity. A more general treatment of the
problem is therefore of interest, and this topic is developed further in a
separate discussion (Reina-Campos & Harris 2023, in preparation). For the
purposes of this first look at the A2744 data, we apply mean $K$ corrections
for only a single age and metallicity.

To estimate the $K$-values, model template SEDs were first generated with
E-MILES555http://miles.iac.es (Röck et al., 2016). These have been used to
calculate $K_{\lambda}$ for the three bandpasses here following the method
outlined in Hogg et al. (2002); Blanton & Roweis (2007); Condon & Matthews
(2018). For the SEDs, BaSTI isochrones were adopted with an age of 9 Gyr,
metallicity [Fe/H] = $-1$, and a Chabrier IMF. With these assumptions we
obtain $K_{115}=-0.17$ mag, $K_{150}=-0.17$, and $K_{200}=-0.42$. The values
for $F115W$ and $F150W$ are the same because the redshifted and rest-frame
SEDs are virtually parallel across those two bandpasses. Use of PARSEC
isochrones by comparison gave negligible differences. The true uncertainties
in these estimates are hard to gauge since they rely on model SEDs and also
depend on the adopted age and metallicity, but are likely to be at least $\pm
0.05$ mag (cf. the discussion of Blanton & Roweis, 2007).

Figure 13: Absolute magnitude versus intrinsic colour for the GC population in
A2744. Points are colour-coded by recovery probability as determined from the
artificial-star tests. Luminosities and colours include the $K$-corrections.
The dashed line indicates the approximate UCD luminosity threshold
corresponding to a luminosity of $\simeq 10^{7}L_{\odot}$ (see text).

##  7 A UCD Population

To the measured magnitude in each filter, we derive the absolute magnitude
from Eq. 5 with the appropriate $K$-correction and $d_{L}=1630$ Mpc. In Figure
13, the CMD for the system is shown again, but in the form of luminosity
versus intrinsic colour.

The CMD of Fig. 13 indicates, as mentioned previously, that the luminosity
distribution of our measured objects reaches to very high levels and into the
UCD regime. UCDs have generated an extensive literature since their discovery
in the Fornax cluster (Hilker et al., 1999; Drinkwater et al., 2000):
comprehensive lists of references are given, for example, by Misgeld et al.
(2011); Penny et al. (2012); Zhang et al. (2015); Lee & Jang (2016b); Janssens
et al. (2017) and our current discussion can mention only a few. See also
Hilker (2009); Misgeld & Hilker (2011); Forbes et al. (2014); Norris et al.
(2014); Janz et al. (2016) for overviews of how UCDs fit within the broader
context of hot stellar systems including GCs, cE’s, E galaxies, and nuclear
star clusters and the overlaps among all these categories in terms of scale
size versus luminosity or mass. At least three different plausible formation
mechanisms have been debated including tidal stripping of compact dwarfs or
extensions of the GC sequence (see, e.g., Mieske et al., 2008; Evstigneeva et
al., 2008; Mieske et al., 2012; Lee & Jang, 2016b, as well as the references
cited above) and the UCD population seen in total may be a heterogeneous
combination of all these channels.

UCDs around nearby galaxies have traditionally been identified through
combinations of properties including high luminosities ($M_{\rm
V}\lesssim-11$), large scale radii ($r_{\rm eff}>10$ pc), and internal
dynamics ($M/L\gtrsim 2$) that set them apart from normal GCs. There is no
universal definition of a luminosity or mass threshold, for example, below
which a compact stellar system is a GC and above which it is a UCD; that is,
the GC and UCD regimes overlap (cf. the references cited above). Janssens et
al. (2017, 2019) extract a UCD sample for A2744 from the HST Hubble Frontier
Field imaging data, using stellar models to convert $I-$band luminosity to
mass along with a threshold $M=2\times 10^{6}M_{\odot}$ to set the lower limit
of the UCD regime (see also Mieske et al., 2008, for adoption of the same
threshold). Other studies have used various luminosity-based thresholds
typically in the range $\sim 10^{6-7}L_{\odot}$ (e.g. Mieske et al., 2006;
Chiboucas et al., 2011; Harris et al., 2014; Liu et al., 2015; Evstigneeva et
al., 2008; Wehner & Harris, 2007; Penny et al., 2012; Mieske et al., 2012).

For A2744, all GCs and UCDs are unresolved and we have only the luminosities
and colours to work with. Rather than mass, we prefer to adopt a luminosity-
based UCD threshold here to minimize dependence on the stellar models. The LF
discussed in the previous Section fits a standard lognormal curve rather
seamlessly up to the highest luminosities, so identifying a point at which GCs
‘end’ and UCDs begin is to some degree arbitrary (cf. Mieske et al., 2012).
The CMD does, however, show a change in distribution near
$M_{F150W}\simeq-13.3$ (Fig. 13, $F150W\simeq 27.6$ in Fig. 3), above which
the blue-GC sequence essentially disappears and the red sequence continues
upward. This feature is visible in the present JWST data because of its much
higher precision and depth compared with the shallower HST photometry (Lee &
Jang, 2016b; Janssens et al., 2017), though a hint of it can be seen in Figure
6a of Lee & Jang (2016b). Notably, this same pattern shows up in the GC CMDs
for many other giant galaxies where the red sequence continues to distinctly
higher levels (Mieske et al., 2006; Wehner & Harris, 2007; Harris, 2023). With
$M_{150,AB}(\odot)=4.21$, this level corresponds very nearly to
$10^{7}L_{\odot}$. Accounting for $\simeq 0.4$ mag of luminosity evolution and
mass loss over 3.5 Gyr (see above) would bring the transition point to
$7\times 10^{6}L_{\odot}$ at redshift $z=0$, consistent within factors of two
or three with many of the UCD studies mentioned above. As seen in Fig. 7, most
of these very luminous objects concentrate quite closely around the five major
galaxies in the system (Janssens et al., 2017, 2019), a result that has also
been found for UCDs in nearby clusters such as Virgo and Coma (Chiboucas et
al., 2011; Liu et al., 2015).

In Fig. 13, there are 200 objects higher than the luminosity threshold stated
above, which can plausibly be called UCD candidates. But their scale sizes,
M/L ratios, and ages are unknown, so these may also be a mixture of UCDs and
normal GCs. For comparison, Janssens et al. (2017) found N(UCD) $=385\pm 32$
in the _mass_ range $10^{7}-10^{8}M_{\odot}$, not specifically corrected for
detection incompleteness. Mass-to-light ratios are uncertain and can differ
between UCDs, but for a mean M/L = 4 (e.g. Mieske et al., 2008) this range
would correspond to $L\gtrsim 2.5\times 10^{6}L_{\odot}$, lower than the
transition adopted here. Lee & Jang (2016b) concluded N(UCD) $=147\pm 26$ for
$F814W(\rm Vegamag)<28.6$ ($F150W$ $\lesssim 28.7$) by explicitly subtracting
off a GCLF with an assumed peak and dispersion from the LF of the total
sample, though measured from a much smaller region than ours. Given the
different methods, area coverage, and adopted transition points, these studies
appear to be at least roughly consistent.

##  8 Summary and Conclusions

In this study, we have used the deep UNCOVER mosaic images of Abell 2744 taken
with JWST NIRCAM to construct a catalog of 10,000 pointlike (unresolved)
objects in the central field of the cluster. The vast majority of the detected
objects consists of globular clusters populating the halos of the A2744
galaxies, but many of them also scatter throughout the InterGalactic
(IntraCluster) Medium. PSF fitting with the tools in daophot has been used to
complete the photometry in the $F115W$, $F150W$, and $F200W$ filters, in all
of which the photometric limits are closely similar. Extensive artificial-star
tests are used to determine the recovery completeness and internal measurement
uncertainties.

A brief summary of our findings is as follows:

  1. (1)

After careful rejection of nonstellar or crowded sources, the remaining sample
of starlike (unresolved) sources defines a sharp, well populated sequence in
the CMD. This sample is dominated by GCs, with very little residual
contamination.

  2. (2)

The spatial distribution of the detected sources shows that the majority are
located within the halos of the five biggest A2744 galaxies. The map of their
distribution also marks out many satellites, but there is also a significant
population distributed more widely across the IGM.

  3. (3)

The colour distribution particularly in $(F115W-F200W)$ is much wider (0.5
mag) than the $\lesssim 0.2-$mag spread that would be expected from
measurement scatter alone, and is what would be expected if the GCs span the
full usual range of metallicities from [Fe/H] $\simeq-2$ to 0. There is no
indication of star clusters that were formed much more recently, which would
show up as a population of bright clusters much bluer than the normal GC
sequence.

  4. (4)

The GC luminosity function covers a $2.5-$mag range before it is severely
damped by photometric incompleteness. Over this range, however, it accurately
matches the lognormal shape that is expected for normal old GCs. Extrapolating
to fainter magnitudes, we estimate the total GC population in the region
surveyed here to be $\simeq 10^{5}$ or more objects.

  5. (5)

The metal-poor GCs (defined as the bluer half of the colour range) are less
centrally concentrated to the galaxies than are the metal-richer GCs, and
dominate the IGM population.

The present data strongly suggest that in A2744 we are looking at classic,
normal populations of GCs around its member galaxies, seen at an earlier stage
but well on their way to evolving into the types of distributions that we see
in the Local Universe. Already by this epoch, the lognormal shape of the LF,
at least at the high-luminosity end, has been well established, as have their
fairly regular distributions around the halos of the member galaxies. The
colour distribution function, after adjustment for K-corrections, reflects
that of the full expected metallicity range for old GCs.

Much more detailed followup work is possible and will be addressed in later
studies. Normalizations to the data need to be improved, including
$K$-corrections as a function of colour (metallicity) and age, luminosity
evolution, and dynamical mass loss as a function of both GC mass and spatial
location. Quantitative derivation of the GC radial profiles around the major
A2744 galaxies needs to be done as well. Such work will lead to more detailed
comparison of the overall GC distribution with other indicators of the DM
distribution including the gravitational lensing map and the X-ray gas.

Above all, the A2744 data provide an excellent example of the new ground
opened up by JWST for the study of rich clusters of galaxies and their
embedded GC systems. For the first time, it is possible to investigate
observationally the evolution of entire GC systems over the past several Gyr
leading up to the present day.

## Acknowledgements

We express our sincere thanks to Laura Parker, John Weaver, Laura Greggio, and
Jeremy Webb for helpful discussion, and to Jose Diego for pointing us to this
dataset. The anonymous referee made several helpful suggestions for revisions
and additions to the discussion. We would also like to acknowledge the work of
the UNCOVER team to produce the beautiful mosaic images and to make them
publicly available at such an early stage. MRC gratefully acknowledges the
Canadian Institute for Theoretical Astrophysics (CITA) National Fellowship for
partial support. This work was supported by the Natural Sciences and
Engineering Research Council of Canada (NSERC).

_Facility:_ JWST (NIRCAM)

_Software:_ IRAF (Tody, 1986, 1993), Daophot (Stetson, 1987), Matplotlib
(Hunter, 2007), E-MILES (Röck et al., 2016), PARSECv1.2 (Bressan et al.,
2012), BaSTI (Pietrinferni et al., 2021).

## Data Availability

The mosaics for Abell 2744 from the UNCOVER program are publicly available at:
https://jwst-uncover.github.io/#.

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