# Detection of Intracluster Globular Clusters in the First JWST Images of the
Gravitational Lens Cluster SMACS J0723.3-7327 at $z=0.39$

Myung Gyoon Lee Jang Ho Bae Astronomy Program, Department of Physics and
Astronomy, SNUARC, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul
08826, Republic of Korea  In Sung Jang Department of Astronomy & Astrophysics,
University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA

(Accepted ApJL)

###### Abstract

We present a survey of globular clusters (GCs) in the massive gravitational
lens cluster SMACS J0723.3-7327 at $z=0.39$ based on the early released
JWST/NIRCam images. In the color-magnitude diagrams of the point sources we
find clearly a rich population of intracluster GCs that spread in a wide area
of the cluster. Their ages, considering the cluster redshift, are younger than
9.5 Gyr. The F200W (AB) magnitudes of these GCs, $26.5<{F200W_{0}}<29.5$ mag,
correspond to $-15.2<{M_{F200W}}<-12.2$ mag, showing that they belong to the
brightest GCs (including ultracompact dwarfs). The spatial distributions of
these GCs show a megaparsec-scale structure elongated along the major axis of
the brightest cluster galaxy. In addition, they show a large number of
substructures, some of which are consistent with the substructures seen in the
map of diffuse intracluster light. The GC number density map is, in general,
consistent with the dark matter mass density map based on the strong lensing
analysis in the literature. The radial number density profile of the GCs in
the outer region is steeper than the dark matter mass profile obtained from
lensing models. These results are consistent with those for the GCs found in
the deep HST images of Abell 2744, another massive cluster at $z=0.308$, and
in simulated galaxy clusters. This shows that the intracluster GCs are an
excellent independent tool to probe the dark matter distribution in galaxy
clusters as well as to reveal the cluster assembly history in the JWST era.

††facilities: JWST††software:  Numpy (Harris et al., 2020), Matplotlib
(Hunter, 2007), Scipy (Virtanen et al., 2020), Astropy (Astropy Collaboration
et al., 2013, 2018), IRAF(Tody, 1986), PyRAF (Science Software Branch at
STScI, 2012), Photutils (Bradley et al., 2021), Astroalign (Beroiz et al.,
2020), DAOPHOT (Stetson, 1987), and SExtractor (Bertin & Arnouts, 1996)

##  1 Introduction

Massive galaxy clusters that show (strong and weak) gravitational lensing
effects are ideal targets to investigate the large scale distribution of dark
matter and the relation between the dark matter and the baryonic matter (e.g.,
(Lotz et al., 2017; Fox et al., 2022) and references therein). The baryonic
matter in galaxy clusters are composed mainly of galaxies and intracluster
medium (ICM). Primary components in the ICM are X-ray emitting hot gas,
intracluster light (ICL), intracluster globular clusters (GCs), and
intracluster planetary nebulae. Among them, the intracluster GCs are, because
they are compact and abundant, very useful to study the relation between dark
matter and baryonic matter at large scales.

Wide field imaging has been a main tool for the survey of intracluster GCs in
the nearby galaxy clusters (Lee et al., 2010; Durrell et al., 2014; Peng et
al., 2011; Iodice et al., 2017; Harris et al., 2017; Hilker et al., 2018;
Madrid et al., 2018; Harris et al., 2020). High resolution power of the HST
enables us to probe the intracluster GCs in the more distant galaxy clusters,
and study the relation between the intracluster GC and dark matter
distributions (Alamo-Martínez et al., 2013; Alamo-Martínez & Blakeslee, 2017;
Lee & Jang, 2016a).

Using the deep ACS/F814W and WFC3/F105W images of the HST Frontier Fields
(Lotz et al., 2017), Lee & Jang (2016a) presented a survey of GCs including
ultracompact dwarfs (UCDs) in the massive merging cluster Abell 2744 (known as
the Pandora cluster) at $z=0.308$. They found a rich population of GCs and
UCDs in the cluster, a significant fraction of which are intracluster GCs that
spread in the wide area of the cluster. They showed that the number density
map of the intracluster GCs in Abell 2744 is similar to the dark matter mass
map derived from CATS strong lensing models (Jauzac et al., 2015).

In this study, we search for GCs of SMACS J0723.3-7327 (called SMACS 0723
hereafter), a massive cluster at $z=0.39$, which is farther than Abell 2744,
using the first JWST/NIRCam images released on July 12, 2022 as part of the
early released JWST images (Pontoppidan et al., 2022; Rigby et al., 2022).
Recently Mowla et al. (2022) found five GCs that are considered to be
associated with the Sparkler galaxy at $z=1.38$ which is gravitationally
lensed by SMACS 0723 from the JWST NIRCam images and HST/ACS images. Our
primary goal is to find and study the GCs that belong to SMACS 0723. Basic
properties of SMACS 0723 are listed in Table 1.

HST observations of this cluster were included in the HST Snapshot survey
(Repp & Ebeling, 2018) and the RELICS program Coe et al. (2019), providing the
magnitudes of the brightest cluster galaxy (BCG), F814W = 19.14
($M_{F814W}=-22.9$) mag and F606W=20.35 ($M_{F606W}=-22.0$) mag. We checked
first the HST data of SMACS 0723 available in the archive, but found that the
images are too shallow to detect GCs in this cluster. The JWST/NIRCam data go
much deeper for these GCs which are composed of old stars, enabling us to
detect them. SMACS 0723 shows a large number of gravitationally lensed images
of background sources, which were used for tracing dark matter in the cluster
(Pascale et al., 2022; Golubchik et al., 2022; Caminha et al., 2022; Mahler et
al., 2022). The mass of SMACS 0723 based on strong lensing models is
$M(R<400{\rm kpc})\sim 3\times 10^{14}M_{\odot}$ (Mahler et al., 2022), and
the mass derived from PLANCK observations is $M({\rm PLANCK})=8.39\times
10^{14}M_{\odot}$ (Pascale et al., 2022). Mahler et al. (2022) presented a
mean redshift of 26 cluster members located in the central region of SMAC
0723, $z=0.3877$, which is slightly smaller than the redshift of the BCG,
$z=0.3912$. In the following analysis, we adopt $z=0.39$ and the position of
the BCG as the cluster center. We adopt the cosmological parameters: $H_{0}=$
67.8 km s-1 Mpc-1, $\Omega_{\Lambda}=0.7$, and $\Omega_{\Lambda}=0.3$. At the
adopted distance of SMACS 0723 ($d_{L}=2170$ Mpc, $(m-M)_{0}=41.69$), one
arcsec (arcmin) corresponds to 5.453 (327.16) kpc.

This paper is organized as follows. Data and data reduction are described in
Section 2, and main results are given in Section 3. The main results are
discussed in Section 4, and are summarized in the final section.

##  2 Data

In the data set of the first released JWST images of SMACS 0723, we use NIRCam
images obtained with three short wavelength (SW) filters (F090W, F150W, F200W)
and three long wavelength (LW) filters (F277W, F356W, F444W) on June 7, 2022
(see the field locations in Figure 1 of Pontoppidan et al. (2022)). The total
exposure time is 7537 sec for each filter. The SW filter images have an image
scale of $0\farcs 03$ per pixel, and the LW images have a twice larger image
scale of $0\farcs 06$ per pixel.

The released images include two fields: a cluster central field that covers
the central region of the cluster, and a parallel field that covers the
outskirt of the cluster, as shown in Figure 1(a). The field of view for each
of the NIRCam images is $129\arcsec\times 129\arcsec$, and the gap between the
central field and the parallel field is $44\arcsec$. The parallel field is
$\sim 2\farcm 9$ to the southwest from the central field. The radial coverage
of the parallel field is 550 kpc $<R<$ 1.3 Mpc, where $R$ is the projected
radial distance from the cluster center. In Figure 1(a) we display gray scale
maps of F200W images of the two fields. We mark the brightest galaxies (G2,
G3, G4, and G5) including the BCG in the central field. The edge regions of
each field marked by burgundy color have low signal-to-noise ratios in the
combined images so they are not used for the final analysis. In Figure
1(b,c,d, and e) we also display the zoomed-in color image of the central
field, showing the BCG region, and the zoomed-in images of the BCG region that
show GCs clearly, which will be described in the following.

##  3 Data Reduction

We use F200W images, which have the highest sensitivity among the six NIRCam
images, as a reference image for point source detection111JWST user
documentation, https://jwst-docs.stsci.edu. We adopt the AB magnitudes in this
study. The relations between the AB and Vega magnitudes in the JWST
CRDS222https://jwst-crds.stsci.edu are: mag(AB)–mag(Vega)=0.504, 1.243, 1.706,
2.315, 2.824, and 3.242 for F090W, F150W, F200W, F277W, F365W, and F444W.

Mean effective radii of typical globular clusters in the Milky Way are about 3
pc and the FWHM values of the point sources in the JWST/NIRCam/SW images are
about 2.4 pixels ($0\farcs 072$=0.39 kpc). Thus typical GCs appear as point
sources in the JWST/NIRCam images of SMACS 0723 (see also Faisst et al.
(2022)). We select the point sources from which GCs are segregated as follows.

###  3.1 Photometry of the Extended Sources

First we obtain the photometry of the sources (including both extended and
point sources) detected with 10$\sigma$ threshold in the images using Source
Extractor (Bertin & Arnouts, 1996). We carry out dual mode photometry with the
F277W image as a reference image for source detection. As the pixel scales for
LW and SW detector are different, the SW images were reprojected and aligned
with respect to the F277W image using the wregister task in IRAF (Tody, 1986;
Science Software Branch at STScI, 2012) and astroalign (Beroiz et al., 2020),
respectively. For aligning the images, we use the positions of several stars.
We use LW images for the analysis of galaxies because the normal red sequence
of galaxies in galaxy clusters is better distinguishable in the LW color-
magnitude diagrams (CMDs), than in the SW CMDs, as shown in the following.

Figure 2 display effective radius $r_{h}$ vs. F277W (AUTO) magnitudes of the
sources detected with the Source Extractor. We also mark the sources with
small stellarity $<0.4$ (red circles), and the sources with large stellarity
$>0.8$ (blue circles). The prominent narrow slanted sequence dominated by blue
circles represent the point sources with small effective radii. Some of the
bright sources with large effective radii are found to have a large value of
stellarity $>0.8$ so we consider that effective radius is a better indicator
to distinguish extended sources than stellarity. In this study we select
extended sources using the effective radius criterion: $r_{h}>1.8$ pixels in
the F277W image.

The extended sources include galaxies and gravitationally-lensed sources. We
adopt AUTO magnitudes for the extended sources provided by the Source
Extractor, and use them for the analysis of photometric properties of the
galaxies in the following.

###  3.2 Photometry of the Point Sources

For better detection of the point sources in the images that include a number
of bright galaxies, we subtract the diffuse background light from the original
images. First, we derive a smooth background image of the original F200W
image, using a ring median filter with $r_{in}=18$ pixel and $r_{out}=20$
pixel. Then we subtract this smooth background image from the original image,
and use the background-subtracted image for the point source detection.

####  3.2.1 Point Spread Function Fitting Photometry

We obtain the point spread function (PSF) fitting photometry of the sources in
the F150W and F200W images of the central and parallel fields using DAOPHOT
(Stetson, 1987). We derive the PSF using the isolated bright stars in the
images. Among the detected sources we select the point sources using the
sharpness parameter and photometric errors provided by DAOPHOT.

We calibrate the instrumental PSF-fitting magnitudes using the total
magnitudes of bright stars given in the source catalog of SMACS 0723 included
in the released data. We use only the bright stars $21<F150W,F200W<24$ mag
which have small errors.

However, it is noted that this zero-point calibration is preliminary. There
could be a substantial (systematic) error associated with the pre-flight
version of the JWST catalog (Boyer et al., 2022). The catalog of the point
source photometry in this study will be publicly available at
GitHub333https://github.com/hanlbomi/SMACS-J0723.3-7327-GCs.

We calculate the extinction values for the JWST filters from the extinction
value for $V$-band given by Schlegel et al. (1998); Schlafly & Finkbeiner
(2011) using the extinction law (Fitzpatrick, 1999; Indebetouw et al., 2005)
and the filter information in the SVO filter profile service website.(Rodrigo
et al., 2012; Rodrigo & Solano, 2020). The extinction values are listed in
Table 1. We apply the foreground extinction correction to the apparent
magnitudes, use the subscript 0 for the foreground-extinction-corrected
magnitudes.

####  3.2.2 Completeness Tests

We estimate the photometric completeness of the point sources using the
artificial star experiments with DAOPHOT/ADDSTAR. We added 2500 artificial
stars with a range of magnitude and color to each of F150W and F200W images.
We repeat this process 400 times for each set of images so that the total
number of added artificial stars in each band is one million. We obtain the
photometry of these sources using the same procedure as used for the original
images. Then we select the recovered/added stars with the GC color range, and
estimate the completeness from the number ratio of the recovered stars to the
added stars as a function of magnitude. Figure 3 displays the completeness vs.
magnitude for F150W and F200W bands. We fit the data using the interpolation
function given in Harris et al. (2009):
$f(m)=0.5(\beta-\alpha(m-m_{0})/\sqrt{1+\alpha^{2}(m-m_{0})^{2}})$ where
$\beta$ is the maximum completeness, $m_{0}$ is the magnitude for $\beta/2$,
and $\alpha$ represents the slope around the $m_{0}$, as shown by the solid
lines in the figure. The limiting magnitudes for 50% photometric completeness
are F105W=30.44 mag and F220W=30.11 mag.

##  4 Results

###  4.1 CMDs of the Galaxies

In Figure 4 we display the LW CMD (F277W vs (F277W–F356W)) and SW CMD (F200W
vs (F150W–F200W)) (in AUTO magnitudes) of the extended sources in the central
field of SMACS 0723. We also mark the cluster member galaxies (N=26) confirmed
with spectroscopic observations (Mahler et al., 2022), the selected bright
galaxies (including the BCG), and the known gravitational lens image sources
in Mahler et al. (2022).

In the F277W vs (F277W–F356W) CMD, two prominent features are noted: an LW-
blue vertical sequence with $(F277W-F356W)_{0}\approx-0.6$, and an LW-red
slanted sequence with $(F277W-F356W)_{0}\approx+0.1$. The known cluster
members are mostly located in the bright part of the LW-blue sequence. The
known cluster members are mostly early-type galaxies, showing that this
sequence corresponds to the normal red sequence in the optical CMDs of galaxy
clusters. So these member galaxies were plotted in red circles. The selected
bright galaxies including the BCG are also located in the bright part of this
sequence. The presence of a large number of galaxies located in this LW-blue
sequence shows that SMACS 0723 is indeed a rich cluster.

In contrast, the known gravitational lens image sources are mostly located
along the LW-red sequence, but with a larger scatter than the LW-blue
sequence. They look red in the released color images based on the combination
of all SW and LW filter images. The gravitational lens image sources have much
higher redshifts than that of SMACS 0723 so they are not the cluster members.
They are background galaxies most of which show some star formation activity
(i.e., late type galaxies having different colors compared with early-type
galaxies).

However, the F200W vs (F150W–F200W) CMD shows only one notable slanted
sequence at (F150W–F200W)${}_{0}\approx+0.2$. Both the cluster member galaxies
and the lens image sources are located mostly in the same sequence, so they
are hardly distinguished in this sequence.

Therefore, as the red sequence galaxies which are mostly early-type cluster
members, we select those located along the LW-blue sequence as marked in the
LW CMD:$-0.65<(F277W-F356W)_{0}<-0.45$. We use them to check any correlation
between the GCs and the galaxies in the following analysis.

###  4.2 CMDs of the Point Sources: Detection of the GCs

Figure 5 displays F200W vs (F150W–F200W) CMDs of the point sources in the
central and parallel fields. The CMD of the central field shows clearly a
strong concentration of the point sources with GC colors
($-0.2<(F150W-F200W)_{0}<0.6$) in the magnitude range of $26.5<F200W_{0}<30$
mag. In contrast, a much smaller number of the sources are located in the same
region of the CMD of the parallel field. This indicates that most of these
sources in the central field belong to SMACS 0723.

We plot also the GCs and other compact source candidates in the Image 2 field
of Sparkler galaxy ($z=1.38$) located at $R=15\arcsec$ (82 kpc) east of the
BCG in Mowla et al. (2022). We cross-matched the compact sources in Mowla et
al. (2022) with our photometry and found that all the sources (N=12) were
successfully recovered. However, only five of them passed our point source
selection criteria. This indicates that a significant fraction of the compact
sources in Mowla et al. (2022) are at least marginally resolved or do not
follow the clean JWST/NIRCam PSFs. These sources are located in the similar GC
color range, and the matched GCs occupy the brightest part of the GCs
($27<F200W_{0}<28$ mag). Note that there are dozens more sources in the
similar CMD region ($26.5<F200W_{0}<28$ mag) of the central field, but few are
in the CMD of the parallel field. They are probably UCDs, but some of them may
be candidates for background GCs that were gravitationally lensed like the
Sparkler galaxy GCs. The brightest of them are as bright as
F200W${}_{0}\approx 26.5$ mag.

In Figure 5 we also plot the color histograms of the point sources with
$27.5<F200W_{0}<29.5$ mag in the central (thin red line) and parallel (thick
black line) fields. Assuming the parallel field as the background, we subtract
the contribution of the background from the color histogram of the central
field. The resulting net color histogram of the central field (thick red line)
shows a significant excess component that is close to Gaussian with a peak at
$(F150W-F200W)_{0}\approx 0.2$. This indicates that these point sources are
mostly genuine GCs which belong to SMACS 0723.

We select the GC candidate sample using the cyan box marked in the figure
($-0.2<(F150W-F200W)_{0}<+0.6$ and $27.5<F200W_{0}<29.5$ mag) for the
following analysis. We conservatively selected the GC candidates with
photometric completeness higher than 70% ($F200W_{0}<29.5$ mag). The number of
the selected GC candidates in the two fields is about 2500. Figure 1(c,d, and
e) display the zoomed-in images of the sample section of the BCG region that
show these GCs better after subtracting the smooth background image from the
original image.

The apparent magnitude range ($27.5<F200W_{0}<29.5$ mag) of these sources at
the cluster distance corresponds to the absolute magnitude range of
$-14.2<M_{F200W}<-12.2$ mag, so these GCs belong to the bright end of the GCs,
which include the UCDs. Considering the redshift of SMACS 0723, the ages of
these GCs are younger than 9.5 Gyr. The ages of most Milky Way GCs range from
11 Gyr to 13 Gyr, with a mean value of $12.3\pm 0.4$ Gyrs (Oliveira et al.,
2020; Kang & Lee, 2021)). Thus the SMACS 0723 GCs may be about 8 Gyrs old,
assuming that they formed as the Milky Way GCs.

We select two representative regions to check any difference between galaxy
GCs and intracluster GCs: the BCG region (at $R<15\arcsec$ from the BCG
center), and the intracluster GC region (with a radius of $15\arcsec$) that
covers the western loop (Mahler et al., 2022; Pascale et al., 2022; Montes &
Trujillo, 2022) and no bright galaxies, as marked in Figure 1(a). In Figure
6(a,b) we display F200W vs (F150W–F200W) CMDs of the point sources in the BCG
region and the intracluster GC region. We also plot the color histograms of
both regions in Figure 6(c). We derived the color histograms for the BCG and
intracluster GC regions after subtracting the background contribution based on
the parallel field. Note that the color distribution of the intracluster GC
region shows a strong peak at $(F150W-F200W)_{0}=0.05$ and a weaker component
at $(F150W-F200W)_{0}\approx 0.4$. In contrast the color distribution of the
BCG region shows a strong peak at $(F150W-F200W)_{0}=0.15$, which is 0.1
redder than the peak in the intracluster GC region.

We calculate the blue GC fractions, obtaining f(blue GC)=65% for the
intracluster GC region and 54% for the BCG region. Thus the intracluster
region has a higher fraction of blue GCs than the BCG region.

The color distribution for the intracluster GC region is broad across the peak
color, showing that there are not only blue GCs but also red GCs, although the
blue GC fraction is higher. The presence of both subpopulations in this region
implies that the origin of the intracluster GCs is dual: the dominant
progenitors of the intracluster GCs are low mass dwarf galaxies, and the minor
progenitors are massive galaxies, as discussed in the case of Virgo
intracluster GCs by Lee et al. (2010).

Considering these, we divide the GCs in the entire field into two
subpopulations according to their colors: the blue (metal-poor) GCs with
$-0.2<(F150W-F200W)_{0}<+0.2$ and the red (metal-rich) GCs with
$+0.2<(F150W-F200W)_{0}<+0.6$. We use these blue and red GCs for the following
analysis to study any difference between the two subpopulations.

###  4.3 Spatial Distributions of the GCs

Figure 7(a) shows the spatial distribution of the GC candidates selected in
the central field. In Figure 7(b) we plot the number density contours and
color gradient map of these sources on the gray scale map of the F200W image.
The contours were smoothed with a Gaussian smoothing scale, $\sigma_{G}\simeq
3\arcsec$. The lowest level in the contours starts with $2\sigma_{bg}$ where
$\sigma_{bg}$ is estimated from the background fluctuation of the selected GC
candidates in the low density region of the parallel field:
$\sigma_{bg}=0.00052\pm 0.000029$ per kpc2. The step between contours is
$4\sigma_{bg}$. We also mark the locations of the known cluster members, the
selected brightest galaxies (including the BCG), the gravitational lens image
sources (Mahler et al., 2022), and the red sequence galaxies selected in this
study, to check any spatial correlation with the GCs.

Several features are noted in this figure. First, the overall distribution of
the GC candidates shows clearly a central concentration around the BCG that is
located close to the galaxy cluster center. This implies that most of the
selected GC candidates are the members of SMACS 0723, indeed. The strongest
peak of the GC number density is slightly offset to the east direction from
the BCG center, and this can be explained as follows. There are two galaxies
close to the BCG center in the west direction so it is difficult to subtract
completely the stellar light of these galaxies in the central region. This
decreases the detection rate of the GCs in that region, causing the slight
offset from the BCG center. However the center of the contours at
$R>10\arcsec$ is consistent with the BCG center.

Second, the overall distribution of the GCs is elongated along the major axis
of the BCG. Third, the spatial distribution of the GCs is much more extended
than that of the stellar light of the BCG.

Fourth, strong peaks are found at the position of some brightest galaxies. The
second strongest peak of the GC number density is seen at the position of G2,
a bright elliptical member galaxy ($z=0.3841$) at $R\approx 190$ kpc in the
northwest of the BCG. Another weaker peak is seen at the position of G3, a
bright galaxy close to G2. A recognizable clumping of GCs is seen also at the
position of G4, another elliptical member galaxy ($z=0.3845$). There is an
isolated weak GC clump at $R\approx 300$ kpc south of the BCG, at the center
of which one bright red sequence galaxy is located. The rest of the known
cluster member galaxies do not show any strong clumps of GCs.

Fifth, there is a strong concentration of GCs at $R\approx 200$ kpc in the
east of the BCG (called as the GC Clump 1 (GCC 1)). Interestingly there are no
recognizable bright galaxies which can be a host of these GCs. Similarly there
is a weak concentration of GCs at $R\approx 100$ kpc in the west of the BCG
(called as the GC Clump 2 (GCC 2)). There are no recognizable bright galaxies
which can be a host of these GCs.

Sixth, there is seen a concentration of GCs extended to the southwest from the
second strongest G2 peak. This can be a part of the large western loop-like
structure, which will be described in detail later. We selected the
intracluster GC region to cover this substructure, as marked by the large
circle in the figure.

Finally, the GCs located outside the few bright red sequence galaxies
(including the BCG) are considered to be mostly intracluster GCs.

In Figure 8 we display the spatial distributions of the blue GC and red GC
candidates selected in the central field. This figure shows that the central
concentration of the red GCs around the BCG is more prominent than that of the
blue GCs, which will be also shown by their radial number density profiles in
the following. In addition, these maps show a loop-like structure with a
radius of 100 kpc at $R\approx 200$ kpc west of the BCG. The structure is seen
better in the red GC map. This will be compared with the substructure in the
ICL map in the following.

###  4.4 Radial Number Density Profiles of the GCs

Adopting the BCG center as the cluster center we derive the radial number
density profile of the GCs, displaying it in Figure 9(a). The number density
profiles of the GCs derived before background subtraction show a flattening at
$R>90\arcsec$ in the parallel field. We estimate the background level from the
sources at $R>90\arcsec$ in the parallel field, obtaining
$\Sigma_{bg}=0.000831\pm 0.000075$ per kpc2. In the figure the number density
of the GCs deceases as the cluster-centric distance increases, confirming
again that these GCs mostly belong to the galaxy cluster. The radial number
density of the GCs keeps decreasing until $R\approx 600$ kpc. The central
excess component represents the BCG GCs, while the outer part is dominated by
the intracluster GCs.

In Figure 9(b) we also plot the radial number density profiles of the blue and
red GCs. The radial profile of the red GCs shows a stronger excess in the
central region than the blue GCs, and it shows an opposite trend in the outer
region.

We fit the radial number density profiles of the GCs with the two component
Sérsic law (the BCG component plus the intracluster GC component):
$\Sigma_{GC}(R)=\Sigma_{\rm eff}\exp{\\{-b_{n}[(R/R_{\rm eff})^{1/n}-1]\\}}$
and $(b_{n}=2n-0.3271)$ (Sérsic, 1963; Graham & Driver, 2005). We also fit the
data with the power law for the outer region of the intracluster GC component
($158<R<631$): $\Sigma_{GC}(R)\propto R^{\alpha}$. Table 2 lists a summary of
the fitting results. The radial profile of all GCs is fit well with the Sérsic
parameters, $R_{\rm eff,1}=28.5\pm 3.2$ pc and $n_{1}=0.1\pm 0.1$ for the BCG
component, and $R_{\rm eff,2}=224.5\pm 22.1$ pc, $n_{2}=1.3\pm 0.3$ for the
intracluster component. The outer region is also fit well with a power law
index $\alpha=-2.0\pm 0.2$. The radial profiles of the blue GCs and red GCs
are also fit with similar parameters: in the case of the blue GC, $R_{\rm
eff,1}=29.5\pm 6.5$ pc, $n_{1}=0.1\pm 0.2$ for the BCG component, and $R_{\rm
eff,2}=213.7\pm 22.1$ pc, $n_{2}=1.1\pm 0.3$ for the intracluster GC
component, and $\alpha=-2.2\pm 0.2$ for the outer region; in the case of the
red GCs, $R_{\rm eff,1}=26.7\pm 3.4$ pc, $n_{1}=0.1\pm 0.1$ for the BCG
component $R_{\rm eff,2}=241.7\pm 48.6$ pc, $n_{2}=1.5\pm 0.6$ for the
intracluster GC component, and $\alpha=-1.9\pm 0.3$ for the outer region.

Thus the effective radius of the intracluster GC system is about eight times
larger than that of the BCG GC system. The outermost region of the
intracluster GC system is also represented well by the power law with an index
of $\alpha=-2.0\pm 0.2$. This profile is slightly steeper than that of the
intracluster GC system in the Virgo cluster, $\alpha=-1.5\pm 0.1$(Lee et al.,
2010).

##  5 Discussion

###  5.1 Comparison with ICL Distribution

From the JWST/NIRCam images of SMACS 0723, Pascale et al. (2022) and Mahler et
al. (2022) derived a smooth map of the diffuse light using a median box car
filter with $21\times 21$ pixels and $100\times 100$ pixels, respectively,
showing the distribution of the ICL. They noted that the diffuse ICL is
elongated along the major axis of the BCG, but in a much more extended way.
Also they found two interesting substructures of the ICL: a large scale loop
in the west of the BCG and a large lobe-like feature in the east component.

To compare the distributions of the GCs and ICL, we derive similarly a smooth
map of the diffuse light applying a median boxcar smoothing with $51\times 51$
pixels to the F277W image, and display it in Figure 10(a). We overlay the GC
number density contour maps (all GCs, blue GCs, and red GCs) to the smooth map
of the ICL in Figure 10(b,c, and d). We also mark the positions of bright
stars, known cluster member galaxies, and gravitational lens image sources
(Mahler et al., 2022) in the figure.

Figure 10 shows several distinguishable features. First, the spatial
distributions of the GCs and ICL are consistent in general. However, the GCs
are found farther than the ICL boundary. Second, the western large scale loop
structure seen in the GC number density map is consistent with that of the
ICL. A number of GCs are located along the loop of the diffuse ICL. Third, the
GC number density map shows also an extended structure in the east of the BCG,
which is consistent with the lobe-like diffuse component of the ICL. However,
the GC Clump 1 (the strongest clump of GCs at $R\approx 200$ kpc east of the
BCG) does not have a bright counterpart in the ICL map, although it is close
to the boundary of the east loop. The GC Clump 1 is better seen in the blue GC
map, indicating that it is composed mainly of the blue GCs.

###  5.2 Formation of SMACS 0723

The existence of a number of substructures with varying scales (in addition to
the BCG) in the GC map and ICL map indicates that a large number of galaxy
groups with diverse masses are falling to the cluster center, and they are in
the middle of merging process now. The elongated structure seen in the maps of
the GCs and ICL indicates that most galaxies are falling to the cluster center
along the east-west direction. These maps illustrate the distribution of the
stars and GCs that are stripped off from their host galaxies or are the
remnant of disrupted galaxies.

Considering the distributions of the GCs and ICL, G2 is probably a main host
of a galaxy group that includes G3 (called the G2 group). Figure 10 shows that
the G2 group and the BCG are connected not only in the GC map but also in the
ICL map. The existence of the GCs and diffuse light between the G2 group and
the BCG implies that both systems are physically interacting. This is similar
to the case of the NGC 4839 group that is known to be falling to the Coma
center, as shown in the observations of galaxies and various ICM including the
GCs (Briel et al., 1992; White et al., 1993; Colless & Dunn, 1996; Lyskova et
al., 2019; Churazov et al., 2021; Oh et al., 2022). The loop structure might
have formed when the G2 group is falling to the cluster center, which needs to
be investigated further in the future.

###  5.3 Comparison with X-ray Brightness Distribution

Chandra X-ray brightness map of SMACS 0723 is given in Mahler et al. (2022)
(their Figs. 1 and 9). Comparing the GC number density map in this study with
the X-ray map of SMACS 0723 given in Mahler et al. (2022), we find both maps
display generally similar structures in the sense that both show a large scale
elongated distribution. Interestingly the X-ray contour map of the central
region of SMACS 0723 (Fig. 1 in Mahler et al. (2022)) shows a distinguishable
component at the position of the western loop structure in addition to the
strongest peak at the BCG center. The location of this component is consistent
with the center of the western loop in the GC number density map and ICL map.

###  5.4 Comparison with Dark Matter Distribution

Dark matter mass density maps (and radial profiles) of SMACS 0723 derived from
the strong lensing analysis were presented by Mahler et al. (2022); Pascale et
al. (2022); Caminha et al. (2022); Golubchik et al. (2022) who used the
JWST/NIRCam images and HST/ACS/WFC3 images. In Figure 11 we overlay the GC
number density contour maps on the dark matter surface mass density map (the
convergence ($\kappa$=surface mass density normalized to the critical mass
density) map) provided by (Mahler et al., 2022) (pseudo color maps). The GC
maps and dark matter mass maps show remarkably similar structures in the sense
that both show a large scale structure that is elongated along the major axis
of the BCG, but much more extended than the BCG. They show also similar
substructures.

Mahler et al. (2022) present a comparison of the dark matter radial density
profiles of SMACS 0723 they derived from the JWST/NIRCam images with those
derived using different lensing models in the literature: RELICS-lenstool (Coe
et al., 2019), RELICS-GLAFIC (Coe et al., 2019), LTM (Golubchik et al., 2022)
(their Fig. 6). In this comparison, the first three models produce similar
profiles extending out to $R\approx 1$ Mpc, while the LTM profile is much more
steeply declining in the outer region ($R\approx 500$ kpc).

In Figure 12 we present a comparison of the radial number density profiles of
the GCs with the dark matter mass density profiles based on the lensing
analysis (Mahler et al., 2022). This figure shows that the radial density
profile of the GCs is very similar to those of the dark matter in the inner
range of $R=50-200$ kpc. However it becomes steeper in the outer region at
$R=200-600$ kpc, deviating from the three lens models (RELICS-lenstool,
RELICS-GLAFIC, and Mahler et al. (2022)) and getting closer to the LTM model.
However, the outermost GC profile is between the two model groups.

These results are consistent with those for the GCs found in the deep HST
images of Abell 2744, another massive cluster at $z=0.308$ that is known as
one of the most GC-abundant galaxy clusters (Lee & Jang, 2016a). Similar
trends are also seen in the radial profiles of the intracluster GC number
density and the dark matter mass derived from the simulated galaxy clusters
selected from the cosmological simulations (Ramos-Almendares et al., 2018,
2020).

##  6 Summary

In the search of the GCs in the massive galaxy cluster SMACS 0723 using the
early released JWST/NIRCam images, we find a large population of GCs which
spread over the cluster. These GCs are mostly intracluster GCs as well as the
BCG GCs. The ages of these GCs, considering the cluster redshift, are younger
than 9.5 Gyr. These GCs are about 8 Gyr old, if they formed as the Milky Way
GCs.

Primary results are summarized as follows.

  1. 1.

The F200W magnitudes of these GCs, $26.5<F200W_{0}<29.5$ mag, correspond to
$-15.2<M_{F200W}<-12.2$ mag, showing that they belong to the brightest GCs
(including the UCDs)).

  2. 2.

The spatial distributions of these GCs show a megaparsec-scale structure that
is elongated along the major axis of the brightest cluster galaxy, but is much
extended than the stellar light of the BCG. In addition, they show a large
number of substructures with various scales, some of which are consistent with
the substructures in the map of the diffuse ICL.

  3. 3.

The existence of the GCs and ICL between the G2 group and the BCG indicates
that the G2 group is falling to the cluster center, as in the case of the NGC
4839 group in the Coma cluster. The large scale loop structure in the west of
the BCG might have formed when the G2 group is falling to the cluster center.

  4. 4.

The GC number density map is, in general, consistent with that of the dark
matter mass density map based on the strong lensing analysis in the literature
in the sense both show a large-scale elongated structure.

  5. 5.

The radial number density profiles of the GCs are fit reasonably by the two
component Sérsic law: the BCG component and the intracluster GC component. The
effective radius of the intracluster GC system is about eight times larger
than that of the BCG GC system.

  6. 6.

The radial number density profile of the GCs in the inner region at $R=50-200$
kpc is very similar to the dark matter mass profile obtained from strong
lensing models. However it becomes steeper in the outer region at $R=200-600$
kpc, deviating from the three lens models and getting closer to the LTM model.
However, the outermost GC profile is between the two model groups.

All these results, based on the excellent data obtained with the JWST/NIRCam,
show that the intracluster GCs are an excellent independent tool to probe the
dark matter distribution in galaxy clusters as well as to reveal the cluster
assembly history. SMACS 0723 is only the first case of distant galaxy clusters
showing the power of the JWST, and many more will come in the JWST era.

The authors are grateful to the anonymous referee for useful comments. This
work was supported by the National Research Foundation grant funded by the
Korean Government (NRF-2019R1A2C2084019). We thank Brian S. Cho for improving
the English in the original manuscript. This work is based on observations
made with the NASA/ESA/CSA James Webb Space Telescope. The data were obtained
from the Mikulski Archive for Space Telescopes at the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. Some/all of the
data presented in this paper were obtained from the Mikulski Archive for Space
Telescopes (MAST) at the Space Telescope Science Institute. The specific
observations analyzed can be accessed via https://doi.org/DOI (catalog DOI).

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Table 1: Basic Properties of SMACS 0723

Parameter | Value | References
---|---|---
Heliocentric Velocity | 116919 km s-1 | 1,2
Redshift | $z=0.39$ | 1,2
Luminosity Distancea |  $2170$ Mpc | 1
Distance Modulusa | $(m-M)_{0}=41.69\pm 0.15$ | 1
Image Scalea | 5.453 kpc arcsec-1 = 327.16 kpc arcmin-1 | 1
Age at Redshifta | 9.474 Gyr | 1
Foreground Extinction |  $A_{V}=0.585$, $A_{I}=0.328$ | 3
|  $A_{F090W}=0.296$, $A_{F150W}=0.134$, $A_{F200W}=0.083$ | 3
|  $A_{F277W}=0.053$, $A_{F356W}=0.039$, $A_{F444W}=0.031$ | 3
Velocity Dispersion |  $\sigma_{v}=1,180\pm 170$ km s-1 | 2
Mass | $M(R<400{\rm kpc})=3\times 10^{14}M_{\odot}$ | 2 (Lensing)
| $M(R<1{\rm Mpc})=8\times 10^{14}M_{\odot}$ | 4 (PLANCK)

aafootnotetext: NED values for $H_{0}=67.8$ km s-1 Mpc-1, $\Omega_{M}=0.308$,
$\Omega_{\Lambda}=0.692$.

Note. — References: (1) the NASA/IPAC Extragalactic Database (NED); (2) Mahler
et al. (2022); (3) Schlegel et al. (1998); Schlafly & Finkbeiner (2011); (4)
Pascale et al. (2022).

Table 2: Fitting Results of the GC Radial Number Density Profiles

GC sample | BCG componenta | Intracluster GC componenta | Power Law Slopeb
---|---|---|---
All GC |  $R_{\rm eff,1}=28.5\pm 3.2$ pc, $n_{1}=0.1\pm 0.1$ |  $R_{\rm eff,2}=224.5\pm 22.1$ pc, $n_{2}=1.3\pm 0.3$ | $\alpha=-2.0\pm 0.2$
Blue GC |  $R_{\rm eff,1}=29.3\pm 7.0$ pc, $n_{1}=0.1\pm 0.2$ |  $R_{\rm eff,2}=238.9\pm 29.1$ pc, $n_{2}=1.3\pm 0.3$ | $\alpha=-2.1\pm 0.2$
RGC GC |  $R_{\rm eff,1}=26.7\pm 3.4$ pc, $n_{1}=0.1\pm 0.1$ |  $R_{\rm eff,2}=241.7\pm 48.6$ pc, $n_{2}=1.5\pm 0.6$ | $\alpha=-1.9\pm 0.3$

aafootnotetext: Fitting with the two component Sérsic law (the BCG component
plus the intracluster GC component): $\Sigma_{GC}(R)=\Sigma_{\rm
eff}\exp{\\{-b_{n}[(R/R_{\rm eff})^{1/n}-1]\\}}$ and $b_{n}=2n-0.3271$
(Sérsic, 1963; Graham & Driver, 2005).

bbfootnotetext: Fitting with the power law for the outer region ($158<R<631$
kpc) of the intracluster GC component: $\Sigma_{GC}(R)\propto R^{\alpha}$.

Figure 1: (a) Gray scale maps of the F200W images of the central (left) and
parallel (right) fields of SMACS 0723 (see also Figure 1 of Pontoppidan et al.
(2022)). Two large circles with radius of $15\arcsec$ represent the BCG region
and intracluster GC region, and the brightest galaxies including the BCG are
labeled. Burgundy color denotes the edge regions with low signal to noise
ratios in the combined images, which were not used for analysis. (b) A zoomed-
in view of the BCG region in the central field of SMACS 0723: the Sparkler
galaxy ($z=1.38$, with a red linear shape embedding several red point sources)
is at $15\arcsec$ east of the BCG. (c, d, and e) Zoomed-in views of the
original F200W image of the red box region in (b), the same image smoothed
with a ring median filter, and the background-subtracted image. Red circles
represent the point sources (thin dotted line) and GC candidates (thick solid
line) found in this study, which are visible more clearly in the background-
subtracted image. Figure 2: Effective radius $r_{h}$ vs. F277W (AUTO)
magnitudes of the sources detected with the Source Extractor. Red circles
represent the sources with stellarity $<0.4$, and blue circles denote the
sources with stellarity$>0.8$. The narrow slanted line dominated by the blue
circles represent the point sources. Note that some bright sources
($F277W_{0}<22.5$ mag) with stellarity$>0.8$ have large effective radii,
$r_{h}>1.8$ pixels. In this study we select extended sources using the
effective radius criterion: $r_{h}>1.8$ pixels in the F277W image, as marked
by the vertical black line.

Figure 3:  Completeness (recovery fraction) vs. F150W (a) and F200W (b)
magnitudes of the point sources. Blue solid lines denote the fitting results.
The vertical black lines mark 50% completeness limits: $F150W_{\rm lim}=30.44$
mag, and $F200W_{\rm lim}=30.11$ mag.

Figure 4: LW CMD (F277W vs. (F277W–F356W)) and SW CMD (F200W vs. (F150W–F200W)
of the extended sources with AUTO magnitudes in the central field of SMACS
0723. Red circles denote the spectroscopically confirmed cluster member
galaxies, and blue circles represent the gravitational lens image sources
(Mahler et al., 2022). The yellow starlet is the BCG, and cyan starlets
represent the bright galaxies (G2, G3, G4, and G5) marked in Figure 1. The red
box in the left CMD represents the selection criteria for the optically-red
sequence galaxies which are mostly early-type members of the cluster. Note
that the blue member galaxies in (F277W–F356W) colors are optically red
galaxies so they are plotted with red circles.

Figure 5:  F200W vs. (F150W–F200W) CMDs of the point sources in the central
(a) and parallel (b) fields of SMACS 0723. Magenta and orange circles,
respectively, represent the GCs and other compact sources of the Sparkler
galaxy ($z=1.38)$ in Mowla et al. (2022). The sources inside the cyan box of
the central field are mostly GCs belonging to SMACS 0723. Cyan boxes represent
the boundary for selecting the GC candidates in this study. The curved yellow
dashed lines mark the 50% completeness limit. In (c) the thick red line
denotes the net color histogram of the point sources with $27.5<F200_{0}<29.5$
mag in the central field (thin red line) after subtracting the contribution of
the background based on the parallel field (black line).  Figure 6: (a,b)
F200W vs. (F150W–F200W) CMDs of the point sources in the BCG region and the
intracluster GC region in the central field of SMACS 0723, as marked in Figure
1. The curved yellow dashed lines mark the 50% completeness limit. (c) Color
histograms of the BCG region (black line) and the intracluster GC region (blue
line) after subtracting the contribution of the background based on the
parallel field. Note that the color distribution of the intracluster GC region
shows a strong peak at $(F150W-F200W)_{0}=0.05$, while that of the BCG region
shows a strong peak at 0.1 redder color, $(F150W-F200W)_{0}=0.15$. Note also
both regions show a broad color distribution across the peak. Cyan boxes
represent the boundary for selecting GC candidates, and green dashed lines
mark the boundary for separating blue and red GCs.

Figure 7: (a) Spatial distribution of the GCs (green squares) in the gray
scale map of the F200W image for the central field of SMACS 0723. Red
triangles represent the confirmed cluster member galaxies, and dark red
diamonds denote the selected bright red sequence galaxies (with
$-0.65<(F277W-F356W)_{0}<-0.45$ and F277W${}_{0}<22.5$ mag). Blue open circles
represent the gravitational lens image sources (Mahler et al., 2022). Yellow
and cyan starlets denote the BCG, and other bright galaxies. Two large circles
mark the BCG region and the intracluster GC region. (b) The contour map and
color gradient map of the GC number density in the gray scale map of the F200W
image. The contours were plotted from 2$\sigma_{bg}$ level with $4\sigma_{bg}$
step. The color scale bar represents the GC number density per kpc2. GCC1 and
GCC2 denote GC clumps.

Figure 8: Same as Figure 7(b) but for blue GCs ($-0.2<(F150W-F200W)_{0}<0.2$)
and red GCs ($0.2<(F150W-F200W)_{0}<0.6$).

Figure 9: Radial number density profiles of the GCs (all GCs (black circles),
blue GCs (blue circles) and red GCs (red circles). Solid lines represent the
two component Sérsic law fitting results for the central plus intracluster GC
components (dashed lines for individual components). The black, blue, and red
lines, denote, respectively, fitting results for the all GCs, blue GCs, and
red GCs. Thick dot-dashed lines denote the power law fitting results for the
outer region ($158<R<631$ kpc).

Figure 10: Comparison of the GC (all GC, blue GC, and red GC) number density
contour maps with the ICL map (pseudo color map) of the F277W image of the
central field that was derived from a median boxcar ($51\times 51$ pixels)
smoothing filter. Red triangles and blue circles represent the known cluster
member galaxies and the gravitational lens sources (Mahler et al., 2022),
respectively. Black circles denote the bright stars with $F200W_{0}<22$ mag,
the sizes of which are scaled according to relative magnitudes. The yellow
starlet mark is the center of the BCG. The color scale bars represent the ICL
surface brightness.

Figure 11:  Comparison of the GC number density contour maps for the central
field of SMACS 0723 with the dark matter surface mass density map (the
convergence map) from strong lensing models given by Mahler et al. (2022)
(pseudo color map). Red triangles and blue circles represent the known cluster
member galaxies and the gravitational lens sources (Mahler et al., 2022),
respectively. The color scale bars denote the convergence (the dark matter
surface mass density normalized to the critical surface mass density).  Figure
12: Comparison of radial number density profiles of the GCs in SMACS 0723
(black circles for the data and the thick black line for the fitting result of
the intracluster component) and the dark matter mass density profiles from
four strong lensing models given in Mahler et al. (2022) (their Fig. 6):
RELICS-lenstool (Coe et al., 2019) (light green line), RELICS-GLAFIC (Coe et
al., 2019) (yellow line), LTM (Golubchik et al., 2022) (blue line), and Mahler
et al. (2022) (red line). The lensing model profiles were arbitrarily shifted
to match the GC data for $50<R<200$ kpc.