# Unveiling the Cosmic Gems Arc at $z\sim 10.2$ with JWST

Larry D. Bradley Space Telescope Science Institute (STScI), 3700 San Martin
Drive, Baltimore, MD 21218, USA  Angela Adamo The Oskar Klein Centre,
Department of Astronomy, Stockholm University, AlbaNova, SE-106 91 Stockholm,
Sweden  Eros Vanzella INAF–OAS, Osservatorio di Astrofisica e Scienza dello
Spazio di Bologna, via Gobetti 93/3, I-40129 Bologna, Italy  Keren Sharon
Department of Astronomy, University of Michigan, 1085 S. University Ave, Ann
Arbor, MI 48109, USA  Gabriel Brammer Cosmic Dawn Center (DAWN), Copenhagen,
Denmark  Niels Bohr Institute, University of Copenhagen, Jagtvej 128, DK-2200
N, Copenhagen, Denmark  Dan Coe Space Telescope Science Institute (STScI),
3700 San Martin Drive, Baltimore, MD 21218, USA  Association of Universities
for Research in Astronomy (AURA) for the European Space Agency (ESA), STScI,
Baltimore, MD, USA  Center for Astrophysical Sciences, Department of Physics
and Astronomy, The Johns Hopkins University, 3400 N Charles St. Baltimore, MD
21218, USA  Jose M. Diego Instituto de Física de Cantabria (CSIC-UC). Avda.
Los Castros s/n. 39005 Santander, Spain  Vasily Kokorev Kapteyn Astronomical
Institute, University of Groningen, P.O. Box 800, 9700AV Groningen, The
Netherlands  Guillaume Mahler Institute for Computational Cosmology, Durham
University, South Road, Durham DH1 3LE, UK  Centre for Extragalactic
Astronomy, Durham University, South Road, Durham DH1 3LE, UK  STAR Institute,
Quartier Agora - Allée du six Août, 19c B-4000 Liège, Belgium  Masamune Oguri
Center for Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba
263-8522, Japan  Department of Physics, Graduate School of Science, Chiba
University, 1-33 Yayoi-Cho, Inage-Ku, Chiba 263-8522, Japan  Abdurro’uf Center
for Astrophysical Sciences, Department of Physics and Astronomy, The Johns
Hopkins University, 3400 N Charles St. Baltimore, MD 21218, USA  Space
Telescope Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD
21218, USA  Rachana Bhatawdekar European Space Agency (ESA), European Space
Astronomy Centre (ESAC), Camino Bajo del Castillo s/n, 28692 Villanueva de la
Cañada, Madrid, Spain  Lise Christensen Cosmic Dawn Center (DAWN), Copenhagen,
Denmark  Niels Bohr Institute, University of Copenhagen, Jagtvej 128, DK-2200
N, Copenhagen, Denmark  Seiji Fujimoto Hubble Fellow  Department of Astronomy,
The University of Texas at Austin, Austin, TX 78712, USA  Takuya Hashimoto
Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1
Tennodai, Tsukuba, Ibaraki 305-8571, Japan  Tomonaga Center for the History of
the Universe, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki
305-8571, Japan  Tiger Y.-Y Hsiao Center for Astrophysical Sciences,
Department of Physics and Astronomy, The Johns Hopkins University, 3400 N
Charles St. Baltimore, MD 21218, USA  Akio K. Inoue Department of Physics,
School of Advanced Science and Engineering, Faculty of Science and
Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan
Waseda Research Institute for Science and Engineering, Faculty of Science and
Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan
Yolanda Jiménez-Teja Instituto de Astrofísica de Andalucía–CSIC, Glorieta de
la Astronomía s/n, E–18008 Granada, Spain  Observatório Nacional, Rua General
José Cristino, 77 - Bairro Imperial de São Cristóvão, Rio de Janeiro,
20921-400, Brazil  Matteo Messa INAF–OAS, Osservatorio di Astrofisica e
Scienza dello Spazio di Bologna, via Gobetti 93/3, I-40129 Bologna, Italy
Colin Norman Department of Physics and Astronomy, The Johns Hopkins
University, 3400 N Charles St. Baltimore, MD 21218, USA  Space Telescope
Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA
Massimo Ricotti Department of Astronomy, University of Maryland, College Park,
20742, USA  Yoichi Tamura Department of Physics, Graduate School of Science,
Nagoya University Furo, Chikusa, Nagoya, Aichi 464-8602, Japan  Rogier A.
Windhorst School of Earth and Space Exploration, Arizona State University,
Tempe, AZ 85287-1404, USA  Xinfeng Xu Department of Physics and Astronomy,
Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, USA  Center
for Interdisciplinary Exploration and Research in Astrophysics (CIERA),
Northwestern University, 1800 Sherman Avenue, Evanston, IL, 60201, USA  Adi
Zitrin Department of Physics, Ben-Gurion University of the Negev, P.O. Box
653, Be’er-Sheva 84105, Israel

###### Abstract

We present recent JWST NIRCam imaging observations of SPT0615-JD (also known
as the Cosmic Gems Arc), lensed by the galaxy cluster SPT-CL J0615$-$5746\.
The 5″-long arc is the most highly magnified $z>10$ galaxy known, straddling
the lensing critical curve and revealing five star clusters with radii $\sim
1$ pc or less. We measure the full arc to have F200W 24.5 AB mag, consisting
of two mirror images, each 25.3 AB mag with a magnification $\mu\sim 60$
(delensed 29.7 AB mag, $M_{UV}=-17.8$). The galaxy has an extremely strong
Lyman break F115W$-$F200W $>3.2$ mag ($2\sigma$ lower limit), is undetected in
all bluer filters ($<2\sigma$), and has a very blue continuum slope redward of
the break ($\beta=-2.7\pm 0.1$), resulting in a photometric redshift $z_{\rm
phot}=10.2\pm 0.2$ (95% confidence) with no significant likelihood below
$z<9.8$. Based on SED fitting to the total photometry, we estimate an
intrinsic stellar mass of $M_{*}\sim 2.4-5.6\times 10^{7}M_{\odot}$, young
mass-weighted age of $\sim 21-79$ Myr, low dust content ($A_{V}<0.15$), and a
low metallicity of $\lesssim 1\%~{}Z_{\odot}$. We identify a fainter third
counterimage candidate within 2$\farcs$2 of the predicted position, lensed to
AB mag 28.4 and magnified by $\mu\sim 2$, suggesting the fold arc may only
show $\sim 60$% of the galaxy. SPT0615-JD is a unique laboratory to study star
clusters observed within a galaxy just 460 Myr after the Big Bang.

Early Universe (435), Galaxy formation (595), Galaxy evolution (594), High-
redshift galaxies (734), Strong gravitational lensing (1643), Galaxy clusters
(584)

††journal: ApJ††facilities: JWST(NIRCam, NIRSpec), HST(ACS, WFC3)††software:
astropy (Astropy Collaboration et al., 2022, 2018), photutils (Bradley et al.,
2024), grizli (Brammer et al., 2022), eazypy (Brammer et al., 2008), bagpipes
(Carnall et al., 2018),

##  1 Introduction

The James Webb Space Telescope (JWST) was designed to peer into the distant
Universe and study galaxies near the beginning of time. Early in its mission,
JWST observations have already prompted us to reevaluate our understanding of
the first phases of galaxy build-up, eventually leading to the reionization of
the Universe. At early cosmic times and throughout the reionization era,
galaxies appear to experience rapid starburst phases (Endsley et al., 2023;
Boyett et al., 2024) and metal enrichment (Curti et al., 2023), merger events
(Hsiao et al., 2023a; Asada et al., 2023), and harbor massive stars producing
extreme ionization (e.g., Matthee et al., 2023; Atek et al., 2023). At
redshift $z>10$ ($t_{\rm Universe}<470$ Myr), early galaxies appear to be more
luminous than expected, suggesting conditions for which we have not accounted.
Several explanations have so far been explored, including significantly higher
star formation efficiency during their early assembly stages, a top-heavy
initial mass function (IMF), and stochastic burst events (e.g, Adams et al.,
2023a; Harikane et al., 2023; McLeod et al., 2023; Finkelstein et al., 2023a,
among many others).

While JWST has already discovered many galaxies at $z>9$ (e.g., Castellano et
al., 2022; Naidu et al., 2022; Finkelstein et al., 2022; Adams et al., 2023a;
Harikane et al., 2023; Bradley et al., 2023; Donnan et al., 2023; Atek et al.,
2023; Finkelstein et al., 2023a; Robertson et al., 2023; Castellano et al.,
2024; Hainline et al., 2024), most are too faint and small to be studied in
detail. Most of these early galaxies will remain unresolved, with their
stellar populations only inferred and never observed directly. Highly-lensed
and spatially-resolved early galaxies (e.g., Bradley et al., 2023; Hsiao et
al., 2023a; Roberts-Borsani et al., 2023; Stiavelli et al., 2023; Vanzella et
al., 2023; Bradač et al., 2024) will provide the only chance to directly study
the engines that reionized the Universe.

The combined powers of JWST and gravitational lensing have revealed small star
clusters in a precious few highly-magnified distant galaxies at $4<z<8$ (e.g.,
Mowla et al., 2022; Claeyssens et al., 2023; Vanzella et al., 2022, 2023;
Mowla et al., 2024). Star clusters with radii as small as $\sim 1$ pc were
recently discovered in a highly-magnified distant galaxy at $z_{\rm
spec}=5.93$, dubbed the “Sunrise Arc” (Vanzella et al., 2023). Some of these
are observed to be young massive star clusters (a few Myr old) with intense
ionizing emission, while others are somewhat older (a few hundred Myr) and
already gravitationally bound (Vanzella et al., 2023).

SPT0615-JD (also known as Cosmic Gems Arc), discovered by Salmon et al. (2018)
in the Reionization Lensing Cluster Survey (RELICS) Hubble Treasury program
(Coe et al., 2019), holds the record for being the most highly magnified and
second-brightest galaxy known at $z\gtrsim 10$. Magnified to 24.5 AB mag,
SPT0615-JD is several magnitudes brighter than most new $z\gtrsim 10$
candidates being discovered by JWST. Hubble Space Telescope (HST) imaging at
1.6 $\micron$ (rest-frame UV at $\sim$1500 Å) identified SPT0615-JD as a
2$\farcs$5-long arc (Salmon et al., 2018) and revealed small structures with
radii $25-70$ pc (Welch et al., 2023). The superb resolution offered by NIRCam
has enabled to resolve the Cosmic Gems Arc into 5 young massive star clusters
(YSCs) which dominate the light of the galaxy (Adamo et al., 2024). The
combination of magnified brightness and resolution make the Cosmic Gems Arc a
unique laboratory to conduct spatially-resolved studies with JWST not possible
in any other galaxy at this distance.

In this paper, we present JWST NIRCam imaging observations of the SPT-CL
J0615$-$5746 galaxy cluster and the Cosmic Gems Arc (SPT0615-JD), and the
redshift estimate and the derived physical properties of the latter. We
describe the observations in Section 2. Section 3 presents the data reduction,
photometric catalogs, and photometric redshifts. Section 4 presents the lens
models of the foreground galaxy cluster. Section 5 presents the results and
discussion. Section 6 summarizes the results and conclusions. We use the
absolute bolometric (AB) magnitude system, $m_{\rm AB}=31.4-2.5\log(f_{\nu}\
/{\rm nJy})$ (Oke, 1974; Oke & Gunn, 1983). Where needed, we adopt a
concordance cosmology with $H_{0}=70$ km s-1 Mpc-1, $\Omega_{\rm m}=0.3$, and
$\Omega_{\Lambda}=0.7$, for which $1\arcsec\sim 4.1$ kpc at $z=10.2$. All
photometric redshift uncertainties are given at the 95% confidence level.

Table 1: HST and JWST Exposure Times and Depths  |  |  |  | Cluster | Parallel
---|---|---|---|---|---
|  | Wavelength | Exposure Time |  $m_{\mathrm{lim}}$aa5$\sigma$ limiting AB magnitude in a $r=0\farcs 1$ circular aperture measured on the background-subtracted data. |  $m_{\mathrm{lim}}$aa5$\sigma$ limiting AB magnitude in a $r=0\farcs 1$ circular aperture measured on the background-subtracted data.
Camera | Filter | (µm) | (s) | (AB) | (AB)
HST ACS/WFC | F435W | 0.37–0.47 |  2249 | 27.8 | 28.1bbOnly a small corner of the F435W image covers the parallel field.
HST ACS/WFC | F606W | 0.47–0.7 |  8880ccTotal exposure time includes an overlapping $2\times 2$ mosaic centered on the cluster (GO 12477; 1920 s each) and a pointing centered on ESO 121$-$20 in the parallel field (GO 9771; 1200 s). The quoted depths represent an average over the mosaic. | 28.7 | 28.7
HST ACS/WFC | F814W | 0.7–0.95 | 12720ddTotal exposure time includes an overlapping $2\times 2$ mosaic centered on the cluster (GO 12757; 2476 s each), a single pointing centered on the cluster (GO 12477; 1916 s), and a pointing centered on ESO 121$-$20 in the parallel field (GO 9771; 900 s). The quoted depths represent an average over the mosaic. | 28.7 | 28.3
HST WFC3/IR | F105W | 0.9–1.2 |  4166eeTotal exposure time after removing MULTIACCUM reads affected by scattered earthshine. | 28.6 |  $\cdots$
HST WFC3/IR | F125W | 1.1–1.4 |  3464eeTotal exposure time after removing MULTIACCUM reads affected by scattered earthshine. | 28.6 |  $\cdots$
HST WFC3/IR | F140W | 1.2–1.6 |  5874eeTotal exposure time after removing MULTIACCUM reads affected by scattered earthshine. | 29.1 |  $\cdots$
HST WFC3/IR | F160W | 1.4–1.7 |  7374eeTotal exposure time after removing MULTIACCUM reads affected by scattered earthshine. | 28.8 |  $\cdots$
JWST NIRCam | F090W | 0.8–1.0 |  2920 | 28.9 | 29.0
JWST NIRCam | F115W | 1.0–1.3 |  2920 | 28.9 | 29.0
JWST NIRCam | F150W | 1.3–1.7 |  2920 | 29.2 | 29.2
JWST NIRCam | F200W | 1.7–2.2 |  2920 | 29.4 | 29.4
JWST NIRCam | F277W | 2.4–3.1 |  2920 | 29.7 | 29.7
JWST NIRCam | F356W | 3.1–4.0 |  2920 | 29.7 | 29.7
JWST NIRCam | F410M | 3.8–4.3 |  2920 | 29.0 | 29.0
JWST NIRCam | F444W | 3.8–5.0 |  2920 | 29.3 | 29.3

##  2 Observations

###  2.1 JWST Data

We obtained JWST NIRCam imaging of the galaxy cluster SPT-CL J0615$-$5746
(also known as PLCKG266.6$-$27.3) in 2023 September (JWST GO 4212; PI
Bradley). The cluster has a redshift of $z_{\rm spec}=0.972$, and has a very
large mass of $M_{500}=7.1\times 10^{14}M_{\odot}h_{70}^{-1}$ (Williamson et
al., 2011) for its distance.

The NIRCam observations include four short-wavelength (SW) filters (F090W,
F115W, F150W, and F200W) and four long-wavelength (LW) filters (F277W, F356W,
F410M, and F444W) spanning $0.8-5.0~{}\micron$ with 2920.4 s of exposure time
in each filter. Each exposure uses the MEDIUM8 readout pattern with seven
groups/integration and one integration. Four dithers were obtained with the
INTRAMODULEBOX dither pattern, designed to fill the 5″ gaps in the NIRCam SW
detectors and maximize the area with full exposure time. The dithers mitigate
the effects of bad pixels, image artifacts, and flat-field uncertainties. They
also improve the spatial resolution of the resampled/drizzled images. The
NIRCam imaging includes two $2\farcm 3\times 2\farcm 3$ fields separated by
40$\farcs$5, covering 10.2 arcmin2 in total. The SPT-CL J0615$-$5746 cluster
was centered on NIRCam module B while NIRCam module A obtained observations on
a nearby field centered $\sim$ 2$\farcm$9 north-northwest of the cluster
center. The JWST observations are shown in Figures 1 and 2 and summarized in
Table 1.

Figure 1:  JWST NIRCam color image of the SPT-CL J0615$-$5746 cluster field
(red: F115W + F150W, green: F200W + F277W, blue: F356W + F444W). The field of
view is $\sim 2\farcm 3\times 2\farcm 3$ and the image is shown with north up
and east left. The $z=10.2$ critical curve of our fiducial LENSTOOL-A model
(see Section 4) is shown in gold. The location of the Cosmic Gems Arc is shown
in the left-hand white box, with a zoomed inset figure ($8\arcsec\times
8\arcsec$) outlining the galaxy with a red ellipse. The $z=10.2$ critical
curves of the LENSTOOL-A (gold), LENSTOOL-B (dark orange), Glafic (cyan), and
WSLAP+ (magenta) lens models (described in Section 4) bisect the Cosmic Gems
Arc. The right-hand white box and zoomed inset ($8\arcsec\times 8\arcsec$)
shows the candidate counterimage of the arc, which is located near (within
2$\farcs$2) the position predicted by the lens models.  Figure 2:  JWST NIRCam
color image of the SPT-CL J0615$-$5746 parallel field, located north-northwest
of the cluster field (red: F115W + F150W, green: F200W + F277W, blue: F356W +
F444W). The field of view is $\sim 2\farcm 3\times 2\farcm 3$ and the image is
shown with north up and east left. The field partially includes ESO 121$-$20
(outlined in red), an isolated dwarf irregular galaxy at a distance of 6.05
Mpc (Karachentsev et al., 2006).

###  2.2 HST Data

We supplement the JWST NIRCam observations with archival HST optical and near-
infrared imaging of SPT-CL J0615$-$5746\. Both the South Pole Telescope Survey
(GO 12477; Williamson et al., 2011) and Planck collaboration (GO 12757; Planck
Collaboration et al., 2011) obtained HST imaging of SPT-CL J0615$-$5746 with
ACS/WFC F606W and F814W in 2013 January. The Reionization Lensing Cluster
Survey (RELICS) HST Treasury program (GO 14096; Coe et al., 2019) obtained HST
imaging of SPT-CL J0615$-$5746 with ACS/WFC F435W (1 orbit) and WFC3/IR F105W,
F125W, F140W, and F160W (2 orbits total) in 2017. Additional HST WFC3/IR
imaging was obtained in F105W (1 orbit), F125W (1 orbit), F140W (2 orbits),
and F160W (2 orbits) by the RELICS team in 2020 (GO 15920; PI Salmon).

The HST observations are summarized in Table 1. In total, the JWST and HST
observations of SPT-CL J0615$-$5746 include imaging in 15 filters spanning
$0.4-5.0~{}\micron$.

##  3 Methods

###  3.1 Data Reduction

We reduced the pipeline-calibrated HST data and the JWST level-2 imaging
products using the grizli (version 1.9.5) reduction package (Brammer et al.,
2022). The JWST data were processed with version 1.11.4 of the calibration
pipeline with CRDS context jwst_1123.pmap, which includes photometric
calibrations based on in-flight data.

The grizli pipeline reprocesses the HST WFC3/IR data to correct exposures
affected by time-variable sky backgrounds caused by scattered earthshine. For
the NIRCam data, the grizli pipeline applies a correction to reduce the effect
of $1/f$ noise, masks “snowballs” caused by large cosmic-ray impacts, and
subtracts templates to remove the “wisp” stray-light features from the NIRCam
SW detectors. We aligned the HST and JWST data to a common world coordinate
system registered to the GAIA DR3 catalogs (Gaia Collaboration et al., 2021).
We then combined and resampled the fully-calibrated images in each filter to a
common pixel grid using astrodrizzle (Koekemoer et al., 2003; Hoffmann et al.,
2021). The HST and JWST NIRCam LW filter images were drizzled to a grid with
0$\farcs$04 per pixel, while the JWST NIRCam SW filter images, with their
smaller native pixel scale, were drizzled to a grid with 0$\farcs$02 per
pixel.

Our NIRCam SW images show the presence of stronger-than-usual wisp features
that were not sufficiently removed by the wisp-template subtraction. Wisps are
caused by off-axis light from bright stars reflecting off the top secondary
mirror strut of JWST and entering into the aft-optics-system mask. The wisp
geometry and intensity can vary significantly depending on the exact telescope
pointing. Wisps are present only in NIRCam SW images and are most prominent in
the A3, A4, B3, and B4 detectors (Rigby et al., 2023).

To remove the residual wisps, we use an iterative two-dimensional (2D)
background procedure using the photutils Background2D and SourceFinder
classes. We start by computing a 2D background from the drizzled image using
the Background2D class with large box sizes ($100\times 100$ pixels), median-
filtering over $3\times 3$ boxes, and a sigma-clipping threshold of 3$\sigma$.
We then use the SourceFinder class (with deblending turned off) to detect
sources in the image larger than 50 pixels with a 2D threshold image
calculated as the 2D background image plus a multiple of the background root-
mean-square (rms) image. We then create a source mask from the segmentation
image and dilate it using a circular footprint with a radius of 31 pixels. The
dilated source mask is then input into the Background2D class with a smaller
box size to compute a new background-subtracted image, from which a new source
mask is created. This iterative process was repeated three times with box
sizes of 100, 50, and 25 pixels, detection thresholds of 3.0, 3.0, and
1.8$\sigma$, detection pixel sizes of 50, 9, and 9 pixels, and dilation sizes
of 31, 21, and 15 pixels, respectively. The final source mask was then used to
compute and subtract the final background image using the Background2D class
with a box size of $10\times 10$ and median-filtered over $5\times 5$ boxes.

###  3.2 Photometric Catalog of sources in the SPT-CL J0615$-$5746 region

Sources were identified in a detection image composed of an inverse variance-
weighted sum of the F277W, F356W, and F444W NIRCam LW images using photutils
(Bradley et al., 2024) image-segmentation tools. Before performing photometry,
we rebinned the NIRCam SW images to a pixel scale of 0$\farcs$04 per pixel to
put the images for all 15 filters on the same pixel-registered grid.

Photometry was measured in all bands using photutils SourceCatalog with the
segmentation image and catalog produced from the detection image. Source
colors were measured in elliptical Kron apertures with a scale factor of 1.5
to accurately recover the colors of distant galaxies. Each source has a
different elliptical-aperture size and orientation based on the central
moments of its flux distribution in the detection image. We derived aperture
corrections by computing the ratio of the flux in a larger Kron aperture (with
a Kron scale factor of 2.5) to that in the smaller aperture for each source,
as measured in the detection image. We applied this aperture correction to the
fluxes and uncertainties for all filters to compute total Kron fluxes.
Isophotal fluxes were also calculated by summing the fluxes within the source
segments defined by the segmentation image. Additional correction factors are
not applied to the isophotal fluxes.

###  3.3 Photometric Redshifts

We measure photometric redshifts using eazypy (Brammer et al., 2008) for all
sources in our catalog using the photometry measured in the elliptical Kron
apertures. eazypy fits the observed photometry of each galaxy with a non-
negative linear combination of templates to derive a probability distribution
function of the redshift. We use a template set composed of the 12
“tweak_fsps_QSF_12_v3” templates derived from the Flexible Stellar Population
Synthesis (FSPS) library (Conroy et al., 2009, 2010; Conroy & Gunn, 2010),
which include a range of galaxy types (e.g., star-forming, quiescent, dusty)
and realistic star formation histories (e.g., bursts, slowly rising, slowly
falling). We also include six additional templates (sets 1 and 4) from Larson
et al. (2023) that are based on a combination of BPASS and CLOUDY models.
These templates have bluer colors than the fiducial FSPS templates and match
the predicted rest-UV colors of simulated galaxies at $z>8$. The inclusion of
these additional templates provides improvements in the photometric redshift
accuracy for bluer galaxies at $z>8$ (Larson et al., 2023).

We assume a flat luminosity prior, similar to recent JWST high-redshift
studies (e.g., Finkelstein et al., 2022; Adams et al., 2023b; Finkelstein et
al., 2023b), to prevent bias against selecting bright high-redshift galaxies,
whose luminosity function is poorly known. We apply an error floor of 5% to
the flux uncertainties to account for photometric calibration uncertainties.
We allow the redshifts to span from $0.1<z<20$, in steps of 0.01. We also
perform a second run of eazypy with the redshift range restricted to $z<7$ to
compare the fiducial results with the best-fit low-redshift solutions.

A recent study comparing photometric and spectroscopic redshifts for 43
$z=7-13$ galaxies measured with eazypy from the JWST JADES (Rieke et al.,
2023) and CEERS (Finkelstein et al., 2023b) surveys found that the photometric
redshifts show exceptional agreement with the spectroscopic redshifts (Duan et
al., 2024). Overall, 4.6% (2 of 43) of the sources qualify as outliers,
defined as having $z_{\rm phot}>1.15(z_{\rm spec}+1)$ or $z_{\rm
phot}<0.85(z_{\rm spec}+1)$ (Duan et al., 2024). Both of the outlier sources
were at $7<z_{\rm phot}<8$. None of the sources at $z>8$ were classified as
outliers.

The photometric redshift catalog is available on our Cosmic Spring
website.111https://cosmic-spring.github.io The grizli reduced images and
catalogs are available online at the DAWN JWST Archive222https://dawn-
cph.github.io/dja.

##  4 Cluster Lens Models

We generated four independent lensing models for the foreground strong-lensing
galaxy cluster SPT-CL J0615$-$5746 to estimate source magnifications using
LENSTOOL, Glafic, and WSLAP+. These new models are improvements over the
previous SPT-CL J0615$-$5746 lens models presented in Paterno-Mahler et al.
(2018) and Salmon et al. (2018), which were based only on HST imaging data.
The different models not only span a range of modeling algorithms. Their
independent construction also gives us leverage over systematic uncertainties
that are due to modeling choices. The models differed in how they considered
the observational constraints (e.g., whether to include candidate lensed
images; photometric redshifts; including clumps within images of lensed
galaxies as individual constraints; astrometric uncertainty), and choices for
the parameterization of the lens plane (number of halos, substructure, and
interloping masses). A more detailed comparison between the lens models will
be presented in a forthcoming paper (Resseguier et al. in prep). We provide a
short summary of each model below.

###  4.1 LENSTOOL Models

We generated two different lensing models using LENSTOOL (Jullo et al., 2007)
that we refer to as LENSTOOL-A and LENSTOOL-B. LENSTOOL employs a parametric
approach and MCMC sampling of the parameter space to identify the best-fit
model and associated uncertainties.

For the LENSTOOL-A model, the cluster lens is represented by a combination of
three main halos with contribution from cluster member galaxies, all
parameterized as pseudo-isothermal ellipsoidal mass distributions (Limousin et
al., 2005). Galaxy-scale halo parameters are determined using scaling
relations (Jullo et al., 2007). The parameters of the two cluster-scale halos
are allowed to vary, except for the cut radius that is larger than the strong
lensing region and thus cannot be constrained by strong lensing evidence. The
positional parameters of the brightest cluster galaxy (BCG) halo are fixed to
observed values, while its slope parameters are allowed to vary. The model
incorporates constraints from the positions of 43 multiple images belonging to
14 clumps from 9 distinct source galaxies. Redshifts of two spectroscopically
confirmed sources at $z=1.358$ and $z=4.013$ (Paterno-Mahler et al., 2018) and
the Cosmic Gems Arc at $z=10.2$ are used as constraints (the A, B, and C star
clusters from Adamo et al. (2024); see Figure 4). The redshifts of arcs
without spectroscopic redshifts are treated as free parameters with very broad
priors. While the model predicts a counterimage at (RA, Dec)=($93.9490607$,
$-57.7701814$), a potential candidate (see Figure 1) observed near this
location ($\sim 1\farcs 8$) was not used as a constraint.

External shear is not required. However, one of the cluster-scale halos is
generally aligned with the galaxy distribution of the foreground group at
$z=0.42$ (Jiménez-Teja et al., 2023), possibly accounting for contributions
from this structure. All observed lensed features are well-reproduced by this
model. The image-plane rms of the best-fit LENSTOOL-A model is 0$\farcs$36\.
The LENSTOOL-A model is used as the reference model for the analysis presented
in this paper.

The LENSTOOL-B cluster lens model uses a different set of input assumptions,
including a different position of the mass distribution of the lens. This
model uses 43 multiple images from 11 unique sources as constraints. A
secondary cluster-scale halo is placed around the location of dusty galaxies
nearly 50″ north of the BCG. The position of this halo is allowed to move
within a 20″ box around this position. The image-plane rms of the best-fit
LENSTOOL-B model is 0$\farcs$68.

###  4.2 Glafic Model

We construct another mass model using Glafic (Oguri, 2010, 2021). We follow
the methodology described in Kawamata et al. (2016) to determine a set of lens
mass components used for mass modeling. Our mass model consists of three
elliptical Navarro–Frenk–White (NFW) halos (Navarro et al., 1997), external
shear, and cluster member galaxies modeled by pseudo-Jaffe ellipsoids. We fix
positions of two NFW halos at the locations of bright cluster member galaxies
at (RA, Dec) = ($93.9663980$, $-57.7791580$) and ($93.9705078$,
$-57.7753866$), while the center of the third NFW mass halo is left as a free
parameter. For all the three elliptical NFW components, we leave their masses,
ellipticities, position angles, and concentration parameters as free
parameters. In order to reduce the number of parameters, we adopt the standard
scaling relations between the luminosities, velocity dispersions, and
truncation radii of cluster member galaxies (see Kawamata et al., 2016, for
more details). The observational constraints consist of the positions of 44
multiple images from 15 background sources. Spectroscopic redshifts are
available for five of the 15 background sources (Paterno-Mahler et al., 2018).
We fix the source redshift of Cosmic Gems Arc to $z=10.2$. In addition, we
include constraints on redshifts of six background sources based on their
photometric redshifts, with a conservative error on the photometric redshifts
of $\sigma_{z}=0.5$ assuming the Gaussian distribution. In order to better
reproduce the shape of the Cosmic Gems Arc, we also include the positions of
the star cluster systems A.1/A.2 and B.1/B.2 (see Figure 4) in the Cosmic Gems
Arc as constraints. We assume a positional error of 0$\farcs$4, except for the
positions of A.1/A.2 and B.1/B.2, for which we assume a smaller positional
errors of 0$\farcs$04.

The best-fitting model has $\chi^{2}=52.7$ for 37 degrees of freedom, and
reproduces all multiple image positions well, with a rms of image positions of
0$\farcs$41.

###  4.3 WSLAP+ Model

The WSLAP+ model (Diego et al., 2005, 2007) is a hybrid model combining a
large-scale component for the mass and a small-scale component. The large-
scale distribution of the mass is described by a predetermined grid (uniform
or multi-resolution) of 2D Gaussian functions. The small-scale component
follows directly the light distribution of member galaxies. The WSLAP+ lens
model offers an alternative to parametric models and is free of assumptions
made about the distribution of dark matter.

For the small scale, we select the most luminous elliptical member galaxies
and assume their mass follows the distribution of light in the F356W filter.
All galaxies are distributed in three groups, each group with a fixed light-
to-mass ratio that is optimized by WSLAP+. The first group contains the
central BCG. The second group contains bright member galaxies at $z=0.972$
($N\approx 70$). Finally, the third group contains two foreground galaxies at
$z=0.42$ that are near other arcs in the background. This third group has
negligible impact in the Cosmic Gems Arc, but it is added to the lens model to
increase its precision in other portions of the image.

The smooth component is composed of either a $20\times 20$ regular grid of 2D
Gaussians or a 158 grid of 2D Gaussians. The second grid is derived from a
solution obtained with the regular grid and has increased resolution in the
central region of the cluster. In both cases, the amplitudes of the Gaussians
are optimized by WSLAP+. We use a set of 14 multiple images as constraints
from 11 individual galaxies. As in other lens models in this work, we use
multiply lensed knots in several galaxies as additional constraints. The rms
of the model is $\approx 1\arcsec$ (image plane) although for two systems we
find a rms of $\approx 2\arcsec$, indicating a possible tension in that
portion of the lens plane. These two systems are far from the $z\sim 10.2$
Cosmic Gems Arc.

##  5 Results and Discussion

This section focuses on the analysis of the galaxy appearing as the Cosmic
Gems Arc. We first present its photometric properties and discuss its
photometric redshift. We describe the estimated magnifications of the arc and
the detection of a candidate counterimage. Finally, we perform spectral energy
distribution (SED) fitting to the multiband photometry of the Cosmic Gems Arc
and discuss the intrinsic physical properties of the galaxy.

Figure 3:  Cutout images of the Cosmic Gems Arc in the observed HST and JWST
filters. The cutout field of view is 4$\farcs$8 $\times$ 4$\farcs$8 and the
images are shown with north up and east left. Filters are labeled in the
upper-left corner of each panel with white text for HST images and gold for
JWST images. The Cosmic Gems Arc extends to 5″ long in the JWST NIRCam images
and is centered in the cutout images. The galaxy is undetected in F115W and
all bluer filters. It is weakly detected in F125W and clearly detected in
F140W and all redder filters. The JWST NIRCam F150W image (PSF FWHM
0$\farcs$05) provides the best resolution of the Cosmic Gems Arc, revealing
star clusters down to 1 pc in intrinsic size (Adamo et al., 2024). The nearby
arc to the north has a photometric redshift of $z\sim 2.6$.  Figure 4:  Cutout
images (4$\farcs$8 $\times$ 4$\farcs$8) of the Cosmic Gems Arc in the NIRCam
F150W and detection (F277W + F356W + F444W) image. The segments S1–S7 were
defined from the detection image and are outlined in gold. The Kron ellipse
defined from the central moments of the flux distribution in the combined
segments is shown in red. In the F150W image, we also label the two mirrored
images of the arc, Images 1 and 2, as well as the star clusters A through E
analyzed by Adamo et al. (2024).

###  5.1 The Cosmic Gems Arc (SPT0615-JD)

In Figure 3, we show cutout images ($4\farcs 8\times 4\farcs 8$) of the Cosmic
Gems Arc in the observed HST and JWST filters. The galaxy is weakly detected
in the WFC3/IR F125W image and clearly detected in F140W and all redder
filters. The Cosmic Gems Arc is undetected in the JWST NIRCam F115W image and
all bluer filters. While Salmon et al. (2018) reported the length of the
Cosmic Gems Arc to be 2$\farcs$5 from the HST WFC3/IR F160W data, the JWST
data reveal faint emission that extends to 5.0″ long in the NIRCam images.

The JWST NIRCam F150W image provides the best resolution of the Cosmic Gems
Arc, revealing at least nine observed bright knots along the arc (see Figures
3 and 4). Overall, there is a distinctive symmetry of the knot locations from
the center of the extended arc, suggesting that the observed arc represents
two mirror images of the lensed galaxy. This is confirmed by our cluster lens
models (see Section 4), all of which predict the $z=10.2$ critical curve
crossing the arc (see Figure 1 inset).

The bright knots in the Cosmic Gems Arc have been identified as individual
star clusters, resolved down to 1 pc in intrinsic size in the JWST NIRCam
F150W image (Adamo et al., 2024). This is the first such detection of star
clusters at $z>10$, only 460 Myr after the Big Bang, made possible by the
combination of JWST’s high sensitivity and spatial resolution and the
gravitational lensing magnification of the Cosmic Gems Arc. The clusters have
very large stellar surface densities of $\sim 10^{5}~{}M_{\odot}/pc^{2}$ and
are consistent with gravitationally-bound YSCs (Adamo et al., 2024). These
clusters could be the progenitors of metal-poor globular clusters at $z=0$.
The possibility that some progenitors of today’s globular clusters have formed
in low-mass galaxies at $z>7$ is particularly interesting also because it is
somewhat at odds with the predictions of several theoretical models (e.g.,
Reina-Campos et al., 2019), with a few exceptions (Katz & Ricotti, 2013,
2014). Importantly, the high stellar densities within these systems pave the
way to massive stars and stellar black hole runway collisions, which might
lead to the formation of intermediate-mass black hole seeds (Gieles et al.,
2018; Antonini et al., 2019).

Table 2: Measured Photometry of SPT0615-JD with HST

IDaaFigure 4 shows the Kron aperture and segments S1 – S7 overplotted on the arc. |  $z_{phot}$bbPhotometric redshift measured with eazypy. Errors are 95% confidence intervals. | F435W | F606W | F814W | F105W | F125W | F140W | F160W
---|---|---|---|---|---|---|---|---
|  | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$
Kron Ellipse | $10.19_{-0.16}^{+0.16}$ | $5.1\pm 32.7$ | $-17.4\pm 19.9$ | $-8.0\pm 18.0$ | $38.1\pm 24.1$ | $123.8\pm 24.8$ | $292.4\pm 16.1$ | $543.0\pm 21.2$
Sum S1–S7 | $10.18_{-0.16}^{+0.16}$ | $12.0\pm 26.0$ | $-0.6\pm 15.9$ | $-3.2\pm 14.3$ | $33.0\pm 19.2$ | $96.1\pm 19.7$ | $248.1\pm 12.9$ | $447.9\pm 16.9$
Sum S2–S6 | $10.18_{-0.16}^{+0.16}$ | $7.3\pm 24.7$ | $3.0\pm 15.0$ | $-9.5\pm 13.6$ | $28.3\pm 18.3$ | $95.7\pm 18.7$ | $236.0\pm 12.2$ | $433.4\pm 16.1$
Sum S4–S5 | $10.18_{-0.17}^{+0.16}$ | $25.7\pm 18.7$ | $11.0\pm 11.4$ | $-8.9\pm 10.2$ | $6.6\pm 13.8$ | $61.8\pm 14.1$ | $185.8\pm 9.3$ | $319.0\pm 12.2$
S4 | $10.25_{-0.23}^{+0.33}$ | $14.5\pm 11.7$ | $3.0\pm 7.1$ | $4.0\pm 6.7$ | $2.5\pm 8.5$ | $25.4\pm 8.8$ | $75.7\pm 5.7$ | $130.7\pm 7.5$
S5 | $10.22_{-0.19}^{+0.21}$ | $11.2\pm 14.6$ | $8.0\pm 8.9$ | $-12.9\pm 7.7$ | $4.1\pm 10.9$ | $36.4\pm 11.1$ | $110.1\pm 7.3$ | $188.3\pm 9.6$
CounterimageccPhotometry measured in the Kron aperture described in Section 3.2. | $10.8_{-1.4}^{+0.6}$ | $2.8\pm 7.2$ | $-3.9\pm 4.2$ | $-2.5\pm 4.7$ | $1.5\pm 6.2$ | $-0.6\pm 5.7$ | $7.8\pm 3.5$ | $9.7\pm 5.3$

Note. — Observed fluxes, uncorrected for magnification. $m_{\rm
AB}=31.4-2.5\log(f_{\nu}/{\rm nJy}).$

Table 3: Measured Photometry of SPT0615-JD with JWST/NIRCam

ID | F090W | F115W | F150W | F200W | F277W | F356W | F410M | F444W
---|---|---|---|---|---|---|---|---
| $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$ | $\mathrm{(nJy)}$
Kron Ellipse | $1.9\pm 14.0$ | $-4.8\pm 12.9$ | $508.5\pm 11.6$ | $574.0\pm 9.1$ | $457.3\pm 8.0$ | $368.5\pm 7.9$ | $357.1\pm 15.3$ | $402.2\pm 12.5$
Sum S1–S7 | $-7.5\pm 11.1$ | $4.2\pm 10.3$ | $442.3\pm 9.2$ | $491.4\pm 7.4$ | $396.3\pm 6.5$ | $321.6\pm 6.3$ | $302.2\pm 12.3$ | $350.3\pm 10.0$
Sum S2–S6 | $-3.9\pm 10.6$ | $6.9\pm 9.8$ | $424.1\pm 8.8$ | $468.9\pm 7.0$ | $381.0\pm 6.2$ | $306.5\pm 6.1$ | $291.8\pm 11.8$ | $333.4\pm 9.6$
Sum S4–S5 | $-0.3\pm 8.0$ | $10.6\pm 7.4$ | $289.4\pm 6.6$ | $337.7\pm 5.3$ | $279.6\pm 4.9$ | $230.4\pm 4.8$ | $221.4\pm 9.3$ | $254.0\pm 7.5$
S4 | $1.8\pm 5.0$ | $4.7\pm 4.7$ | $119.7\pm 4.2$ | $137.1\pm 3.4$ | $118.8\pm 3.1$ | $95.5\pm 3.0$ | $95.1\pm 5.9$ | $111.0\pm 4.8$
S5 | $-2.1\pm 6.2$ | $6.0\pm 5.8$ | $169.8\pm 5.1$ | $200.5\pm 4.2$ | $160.9\pm 3.8$ | $134.9\pm 3.7$ | $126.3\pm 7.2$ | $143.0\pm 5.8$
CounterimagebbPhotometry measured in the Kron aperture described in Section 3.2. | $1.9\pm 3.1$ | $0.2\pm 3.0$ | $13.5\pm 2.5$ | $15.3\pm 2.0$ | $11.0\pm 1.5$ | $8.4\pm 1.5$ | $8.8\pm 3.0$ | $6.5\pm 2.4$

Note. — Observed fluxes, uncorrected for magnification. $m_{\rm
AB}=31.4-2.5\log(f_{\nu}/{\rm nJy}).$

###  5.2 Photometry of the Cosmic Gems Arc

In our initial extraction of sources in the SPT-CL J0615$-$5746 field, the
Cosmic Gems Arc is segmented into seven separate components, labeled S1–S7,
which are shown in Figure 4. We subsequently combined these segments into a
single source within the segmentation image. We then measured the photometry
of the Cosmic Gems Arc in all the observed HST and JWST filters using the
photutils SourceCatalog class as described in Section 3.2. As before, we
measured the photometry of the Cosmic Gems Arc in both an elliptical Kron
aperture with a scale factor of 1.5 and applied an aperture correction to the
fluxes and uncertainties for all filters to compute total Kron fluxes. The
size and shape of the elliptical Kron aperture are determined by the central
moments of the flux distribution of the Cosmic Gems Arc in the detection
image. This elliptical Kron aperture is shown in Figure 4. We also calculate
isophotal fluxes by summing the fluxes within the combined source segments
defined by the segmentation image. No additional correction factors were
applied, and no additional local background was subtracted.

The measured photometry of the Cosmic Gems Arc in the observed HST and JWST
filters is summarized in Tables 2 and 3. We also include the photometry for a
few different segment sums and the brightest two individual segments (S4 and
S5) to illustrate the photometric properties of the Cosmic Gems Arc in
different locations. The arc (and each of its segments) is brightest in the
JWST NIRCam F200W image, with an observed magnitude of $m_{\rm AB}=24.5$ in
the Kron aperture (including the correction to total flux) and $m_{\rm
AB}=24.7$ in the sum of segments S1–S7. Each of the two lensed mirror images
is $m_{\rm AB}=25.3$, similar to that observed for the brightest lensed image
of MACS0647–JD at $z_{spec}=10.17$ (Hsiao et al., 2023b) with an observed
F200W magnitude of $m_{\rm AB}=25.1$ (Hsiao et al., 2023a). With a more modest
magnification $\mu\sim 8$, MACS0647–JD is intrinsically brighter ($m_{\rm
AB}=27.3$ delensed) than the Cosmic Gems Arc (see Section 5.4). MACS0647–JD is
also observed to be slightly brighter when adding the flux from all three
lensed images: $m_{\rm AB}=24.2$, compared to the Cosmic Gems Arc with $m_{\rm
AB}=24.5$ (the counterimage contributing negligibly).

For comparison, the exceptionally luminous unlensed galaxy GN-z11 at
$z_{spec}=10.60$ (Bunker et al., 2023) has an observed magnitude of $m_{\rm
AB}=26.0$ in the NIRCam F200W data (Tacchella et al., 2023). With a few
exceptions of lensed galaxies, most other galaxy candidates at $z>10$ being
discovered by JWST are several magnitudes fainter (e.g., Finkelstein et al.,
2023a).

Figure 5:  Best-fit eazypy photometric redshifts for the Cosmic Gems Arc as a
whole (Kron Ellipse and Sum S1–S7) and various component segments. The
measured fluxes are shown as blue data points or triangle upper limits.
Nondetections are plotted as upper limits at the $2\sigma$ level. The best-fit
eazypy SED model is shown in orange, with squares indicating the expected
photometry in a given band. The best-fit eazypy SED for the low-redshift
($z<7$) solution is shown in green. To the right of each SED, we also plot the
P($z$) posterior redshift probability distributions. The Cosmic Gems Arc has a
best-fit photometric redshift of $z_{\rm phot}=10.2$, with low-redshift
solutions ruled out high significance.

###  5.3 Photometric Redshifts

The Cosmic Gems Arc has an extremely strong F115W$-$F200W break of $>3.2$ mag
($2\sigma$ lower limit) and is completely undetected ($<2\sigma$) in all bluer
filters. These properties, combined with a very blue continuum redward of the
break, are consistent with a high-redshift Lyman-break galaxy at $z\gtrsim
10$.

We measure the photometric redshift of the Cosmic Gems Arc using eazypy using
the same procedure described in Section 3.3. We use the photometry of the
Cosmic Gems Arc in the elliptical Kron aperture, the sum of all segments
(S1–S7), plus other segment sums and the brightest two individual segments (S4
and S5).

We measure the photometric redshift of the Cosmic Gems Arc to be $z_{\rm
phot}=10.19\pm 0.16$ in the elliptical Kron aperture and $z_{\rm
phot}=10.18\pm 0.16$ in the sum of segments S1–S7. The photometric redshifts
in the various segments are all consistent with each other at $z\sim 10.2$.
The photometric redshifts in the individual segments S4 and S5 are also
completely consistent at $10.25_{-0.23}^{+0.33}$ and $10.22_{-0.19}^{+0.21}$,
respectively, but have larger uncertainties due to the lower signal-to-noise
flux ratios in the smaller segments.

We present the best-fit SED templates and the posterior redshift
distributions, P($z$), in Figure 5. We also show the best-fitting SED template
where we restrict the redshift to be $0.972<z<7$. We restrict the redshift to
$z>0.972$ as the arc is clearly lensed and thus must lie behind the galaxy
cluster. The best-fit low-redshift models attempt to fit the very strong
observed spectral break with a Balmer break at $z\sim 2.5$, but are unable to
match the observed photometry. In all cases, the best-fit $\chi^{2}$ for these
“low-redshift” solutions are significantly worse than the best-fit high-
redshift solutions, ruling out the low-redshift models at high significance.
Formally, 97% of the P($z$) probability distribution function is at $z>10$ and
increases to 100% for $z>9.8$. The photometric redshift measurements of the
Cosmic Gems Arc are summarized in Table 2.

While the photometric redshift of the Cosmic Gems Arc is highly robust,
definitive confirmation of the redshift requires spectroscopic observations.
In 2023 December, we also obtained JWST NIRSpec high-resolution G395H/F290LP
spectroscopy (8928 s total) from the same JWST Cycle 2 program (JWST GO 4212)
in several multi-shutter array slitlets along the Cosmic Gems Arc. The primary
goals of these observations were to obtain a spectroscopic redshift of the
galaxy and to detect and resolve the [O ii] $\lambda$$\lambda$3726, 3729
doublet, measuring electron densities along the arc. Incidentally, the first
such detection of the resolved [O ii] $\lambda$$\lambda$3726, 3729 doublet at
$z>8$ was recently made from NIRSpec G395H observations of the lensed galaxy
MACS0647-JD at $z=10.17$ (Abdurro’uf et al. in prep).

Unfortunately, the spectroscopic data does not reveal any strong emission
lines over the wavelength range of the observations (2.9 – 5.3 µm), which
covers rest-frame 2636 – 4818 Å at $z=10.2$. The continuum was also not
detected, as expected for the high-resolution G395H grating setting. Our team
was recently awarded JWST cycle 3 (PI: Vanzella) observing time that includes
NIRSpec prism observations of the Cosmic Gems Arc, which will be used to
confirm the redshift using the Lyman-alpha break of the continuum, a technique
recently used to spectroscopically confirm the redshifts of four galaxies at
$10.3\leq z\leq 13.2$ (Curtis-Lake et al., 2023).

###  5.4 Magnifications

All four of our independent lens models produce excellent results consistent
with the $z=10.2$ critical curve crossing the Cosmic Gems Arc, which confirms
that the observed symmetry of the arc is indeed the result of seeing two
lensed mirror images of the galaxy (denoted in Figure 4). The $z=10.2$
critical curve for our fiducial LENSTOOL-A model is shown in Figure 1 overlaid
on the SPT-CL J0615$-$5746 cluster image. The Cosmic Gems Arc inset image
(Figure 1) shows the critical curves from all four lens models bisecting the
arc.

To verify that our results are not biased by a misinterpretation of the
lensing symmetry of the arc, we ran a consistency check by excluding the
positional constraints of the Cosmic Gems Arc from the lens models. For the
Glafic and LENSTOOL-A lens models, even without this constraint, the critical
curve still passes through the center of the Cosmic Gems Arc, confirming our
interpretation of it being a pair of multiple images.

For the WSLAP+ lens model, when the $z=10.2$ arc is not included as a
constraint, the model predicts the critical curve passing $\sim 1\arcsec$ from
the Cosmic Gems Arc. When the arc is included as a constraint, the predicted
critical curve passes between the star clusters C.1 and D.1, just 0$\farcs$3
from the alleged symmetry point in the arc and within the uncertainties
typical of WSLAP+ models.

While the star clusters in the arc appear overall to be symmetric, the
distance between A.1 and B.1 is greater than the distance between A.2 and B.2
by a factor of $\sim 1.4$. The appearance of Image 2 is likely affected by
additional lensing effects from the $z_{phot}=2.6$ arc immediately to the
north of the Cosmic Gems Arc (see Figure 3). We investigated this possibility
by running a WSLAP+ model that includes the $z=2.6$ arc. While the agreement
improves, it is not yet sufficient to completely explain the observed
perturbation in the arc. Adding at least one other small-scale dwarf galaxy
near the Cosmic Gems Arc below our current detection limit could explain the
perturbed magnification of Image 2. We are exploring this possibility with a
new WSLAP+ model that includes additional perturbers, but defer such analysis
to future work.

Because the arc lies on the critical curve, it also has a very large
magnification. The arc is highly magnified in the tangential direction along
the arc, with only modest magnification in the radial direction ($\mu\sim
1.3$). The magnifications also vary along the arc, with higher values near the
critical curve, and are consistent among our lens models (see values reported
in Adamo et al. (2024) at the star cluster positions). For our reference
LENSTOOL-A model, the star cluster E.1 has the highest magnification of
$\mu=419$, while the star cluster A.1 has the lowest magnification of
$\mu=57$.

The light-weighted magnification of each mirrored image is $\mu\sim 60$.
Assuming that we are observing two lensed images of the same galaxy, in total,
the portion of the galaxy that is lensed to form the Cosmic Gems Arc is
magnified by $\mu=120$. We use this value to compute the intrinsic properties
of the whole galaxy from the measured values.

The Cosmic Gems Arc has an intrinsic F200W apparent magnitude of $m_{\rm
AB}=29.7$. This corresponds to an absolute magnitude of $M_{\rm AB}=-17.8$ in
the rest-frame UV. This makes the Cosmic Gems Arc less luminous than the
typical $M^{*}$ galaxy at $z\sim 10$ (e.g. Finkelstein et al., 2023a; Adams et
al., 2023b), placing it in the category of galaxies likely to have driven
cosmic reionization. This is especially true if the escape fraction of
ionizing radiation from compact star clusters is close to unity, as suggested
by some theoretical models (see, Ricotti, 2002; He et al., 2020).

Figure 6:  Cutout images of the Cosmic Gems Arc (top) and the candidate
counterimage (bottom), showing the Lyman-$\alpha$-break using the JWST bands
only. The field of view of the cutouts is $5\arcsec\times 6\arcsec$ and the
images are shown with north up and east left. The stacked images blueward
(F090W \+ F115W) and redward (F150W + F200W + F356W + F410M + F444W) of the
Lyman-$\alpha$-break are shown in the left and central panels, respectively.
The right panels show color composites in the NIRCam filters. The Cosmic Gems
Arc has an extremely strong NIRCam F115W$-$F200W break of $>3.2$ mag
($2\sigma$ lower limit), is undetected ($<2\sigma$) in all bluer filters, and
has a very blue continuum slope redward of the break. The candidate
counterimage has similar colors to the arc, but is 3.9 mag fainter, with an
observed F200W magnitude of $m_{\rm AB}=28.4$, fully consistent with the
LENSTOOL-A model prediction of the counterimage being $\sim 3.7-4.7$ mag
fainter. The predicted locations of the counterimage from the LENSTOOL-A and
Glafic models (star symbols in the bottom-center panel) are within 1$\farcs$8
and 2$\farcs$2 of the candidate counterimage, respectively.  Figure 7:  Best-
fit eazypy photometric redshift for the candidate counterimage. The measured
fluxes are shown as blue data points or triangle upper limits. Nondetections
are plotted as upper limits at the $2\sigma$ level. The best-fit eazypy SED
model is shown in orange, with squares indicating the expected photometry in a
given band. In the right-hand panel, we plot the P($z$) posterior redshift
probability distribution. The candidate counterimage has a best-fit
photometric redshift of $z_{\rm phot}=10.8_{-1.4}^{+0.6}$, which is consistent
with the redshift of the Cosmic Gems Arc of $z_{\rm phot}=10.2\pm 0.2$.

###  5.5 Candidate Counterimage

All four of our independent lens models predict a fainter counterimage of the
Cosmic Gems Arc at similar locations. The reference LENSTOOL-A model predicts
the counterimage at (R.A., Decl.) = ($93.9490607$, $-57.7701814$). The
LENSTOOL-B predicted location is $\sim$2″ away. The Glafic best model
prediction is also nearby at (R.A., Decl.) = ($93.9504865$, $-57.7696559$).
The WSLAP+ prediction is consistent with the other models. All the models
predict a much lower magnification for the counterimage than the Cosmic Gems
Arc, in the range $\mu\sim 1.5-2.0$.

We identify a potential candidate counterimage with the same colors of the
Cosmic Gems Arc at (R.A., Decl.) = ($93.95000245$, $-57.77021846$), as shown
in Figure 1. This is within $\sim 1\farcs 8$ and 2$\farcs$2 of the predictions
from LENSTOOL-A and Glafic, respectively, as shown in Figure 6. The measured
photometry of the candidate counterimage in the observed HST and JWST filters
is summarized in Tables 2 and 3. The candidate counterimage is 3.9 mag fainter
than the Cosmic Gems Arc, with an observed F200W magnitude of $m_{\rm
AB}=28.4$, consistent with the expectation from the lens models. Earlier lens
models based only on HST data (Paterno-Mahler et al., 2018; Salmon et al.,
2018) predicted a counterimage in proximity to our candidate, but those works
were unable to identify the counterimage at the shallower depth of the HST
data.

Assuming the LENSTOOL-A magnification estimate of $\mu=2.0\pm 0.1$ for the
counterimage yields a delensed magnitude $m_{\rm AB}=29.2$, which is 60%
brighter than the delensed magnitude estimate for the Cosmic Gems Arc of
$m_{\rm AB}=29.7$. This may be explained by the portion of the galaxy missing
in the fold of the lensing critical curve in the Cosmic Gems Arc image,
whereas the counterimage is a complete image of the source galaxy. Lens model
magnification uncertainties may contribute as well.

We measure a photometric redshift of $z_{phot}=10.8_{-1.4}^{+0.6}$ for the
candidate counterimage, which is consistent with the redshift of the Cosmic
Gems Arc given the larger uncertainties. We present its best-fit eazypy SED
model and the posterior redshift distribution in Figure 7.

Finally, we note according to the LENSTOOL-A model, each star cluster is
magnified $\sim 3.7-4.7$ mag brighter in the Cosmic Gems Arc compared to the
counterimage. Thus, with intrinsic magnitudes $\sim 31$ and fainter, none of
the star clusters can be individually detected in the counterimage. Nor would
they be detected without lensing in a blank field. They are only discernible
thanks to the very strong lensing of the Cosmic Gems Arc.

Table 4: bagpipes photometric redshifts and physical properties of SPT0615-JD

Object ID |  $z_{\rm phot}$aaFigure 4 shows the Kron aperture and segments S1 – S7 overplotted on the arc. | $\log M_{\star}/M_{\odot}$ | SFRbbStar formation rate during the past 100 Myr. |  $\log$ sSFR/Gyr-1 | AgeccMass-weighted age. | $A_{V}$ |  $t_{\rm form}$ddFormation time in Myr after the Big Bang based on the mass-weighted age.
---|---|---|---|---|---|---|---
|  |  | $M_{\odot}/yr$ |  | Myr | mag | Myr
Delayed-$\tau$ SFH model, SMC dust extinction
Kron Ellipse | $10.2_{-0.1}^{+0.1}$ | $7.47_{-0.18}^{+0.18}$ | $0.33_{-0.09}^{+0.03}$ | $1.05_{-0.14}^{+0.03}$ | $49_{-22}^{+40}$ | $0.02_{-0.01}^{+0.01}$ | $406_{-41}^{+24}$
Sum S1–S7 | $10.2_{-0.1}^{+0.1}$ | $7.38_{-0.21}^{+0.18}$ | $0.28_{-0.10}^{+0.03}$ | $1.06_{-0.13}^{+0.03}$ | $44_{-22}^{+39}$ | $0.03_{-0.01}^{+0.01}$ | $411_{-40}^{+24}$
Delayed-$\tau$ SFH model, SMC dust extinction, BPASS stellar models
Kron Ellipse | $10.1_{-0.1}^{+0.1}$ | $7.53_{-0.19}^{+0.12}$ | $0.28_{-0.03}^{+0.01}$ | $0.93_{-0.12}^{+0.13}$ | $78_{-36}^{+36}$ | $0.01_{-0.01}^{+0.01}$ | $380_{-36}^{+35}$
Sum S1–S7 | $10.1_{-0.1}^{+0.1}$ | $7.47_{-0.17}^{+0.12}$ | $0.24_{-0.02}^{+0.01}$ | $0.93_{-0.12}^{+0.13}$ | $79_{-34}^{+38}$ | $0.01_{-0.01}^{+0.01}$ | $378_{-37}^{+34}$
Delayed-$\tau$ SFH model, Calzetti dust extinction
Kron Ellipse | $10.2_{-0.1}^{+0.1}$ | $7.49_{-0.20}^{+0.17}$ | $0.34_{-0.11}^{+0.04}$ | $1.05_{-0.14}^{+0.03}$ | $47_{-23}^{+41}$ | $0.06_{-0.03}^{+0.03}$ | $407_{-40}^{+25}$
Sum S1–S7 | $10.2_{-0.1}^{+0.1}$ | $7.40_{-0.22}^{+0.20}$ | $0.29_{-0.11}^{+0.05}$ | $1.06_{-0.13}^{+0.02}$ | $40_{-21}^{+43}$ | $0.07_{-0.03}^{+0.03}$ | $415_{-45}^{+22}$
Exponential SFH model, SMC dust extinction
Kron Ellipse | $10.2_{-0.1}^{+0.1}$ | $7.45_{-0.13}^{+0.17}$ | $0.35_{-0.10}^{+0.07}$ | $1.08_{-0.08}^{+0.02}$ | $36_{-13}^{+30}$ | $0.03_{-0.01}^{+0.01}$ | $419_{-30}^{+14}$
Sum S1–S7 | $10.2_{-0.1}^{+0.1}$ | $7.39_{-0.15}^{+0.18}$ | $0.30_{-0.10}^{+0.06}$ | $1.08_{-0.10}^{+0.02}$ | $36_{-14}^{+32}$ | $0.03_{-0.01}^{+0.01}$ | $419_{-34}^{+16}$
Constant SFH model, SMC dust extinction
Kron Ellipse | $10.1_{-0.1}^{+0.1}$ | $7.75_{-0.09}^{+0.05}$ | $0.68_{-0.13}^{+0.09}$ | $1.08_{-0.01}^{+0.01}$ | $22_{-4}^{+5}$ | $0.14_{-0.04}^{+0.03}$ | $435_{-8}^{+7}$
Sum S1–S7 | $10.1_{-0.1}^{+0.1}$ | $7.68_{-0.10}^{+0.06}$ | $0.58_{-0.12}^{+0.09}$ | $1.08_{-0.01}^{+0.01}$ | $21_{-4}^{+6}$ | $0.15_{-0.04}^{+0.03}$ | $436_{-8}^{+7}$

aafootnotetext: Photometric redshift with 95% confidence interval.

Note. — Properties are quoted as the median and the 68% range of the joint
posterior distributions. Stellar masses and SFRs are corrected for
magnification. Multiply these values by 120 / $\mu$ to apply a different
magnification. We did not propagate magnification uncertainties to those
parameter uncertainties.

Figure 8:  Best-fit bagpipes photometric redshifts for the Cosmic Gems Arc.
The top panels show the fits to fluxes measured in the Kron Ellipse, while the
bottom panels show the fits to the sum of all segments (S1–S7). The left
panels show the best fits using the default BC03 stellar population models,
while the right panels show the best fits using the BPASS stellar population
models. The measured fluxes are shown as blue data points or triangle upper
limits. Nondetections are plotted as upper limits at the $2\sigma$ level. The
best-fit bagpipes SED model is shown in orange, with squares indicating the
expected photometry in a given band. To the right of each SED, we also plot
the P($z$) posterior redshift probability distributions with the median
$z_{\rm phot}$ and 95% confidence interval.

###  5.6 Physical Properties

The physical properties of the Cosmic Gems Arc were estimated using the
Bayesian Analysis of Galaxies for Physical Inference and Parameter EStimation
(bagpipes) SED-fitting code (Carnall et al., 2018). bagpipes fits the observed
photometry of a galaxy by generating model galaxy spectra over the
multidimensional space of physical parameters. The fits are performed using
the multinest nested sampling algorithm (Feroz et al., 2009).

By default, bagpipes uses the stellar population synthesis models from the
2016 version of the BC03 (Bruzual & Charlot, 2003) models with a Kroupa (2002)
IMF. These models also include nebular line and continuum emission based on
Cloudy (Ferland et al., 2013) with the logarithm of ionization parameter
($\log$ U) allowed to vary between $-4$ and $-2$. We vary metallicity in
logarithmic space from $\log Z/Z_{\odot}=-4$ to $-0.7$. Formation ages vary
from 1 Myr to the age of the Universe.

We also explore the effect of using the Binary Population and Spectral
Synthesis (BPASS) stellar population models (Eldridge & Stanway, 2009) on the
derived physical properties. The BPASS models include binary stellar evolution
and account for the effects of binary interactions on the stellar population
(Eldridge et al., 2017). We use the BPASS v2.2.1 models (Stanway & Eldridge,
2018) with an IMF slope of $-1.30$ for stars with masses
$0.1-0.5~{}M_{\odot}$, $-2.35$ for stars with masses $0.5-300~{}M_{\odot}$,
and a maximum stellar mass of $300~{}M_{\odot}$.

We explore several star formation histories (SFHs) to estimate the physical
properties of the Cosmic Gems Arc. The SFHs include delayed exponentially
declining $\tau$ models, constant star formation rate (SFR) models, and
exponentially declining models. For the delayed-$\tau$ model, the SFR is of
the form SFR$(t)\propto t\ \exp{(-t/\tau)}$, where $\tau$ is the e-folding
time. This SFR rises linearly with time and then exponentially declines if
$\tau$ is less than the formation age.

We generally assume a Small Magellanic Cloud (SMC) dust extinction law (Salim
et al., 2018). However, we also investigate the effect of using the Calzetti
extinction law (Calzetti et al., 2000). For both extinction laws, we also add
a second component to the dust model that includes birth-cloud dust
attenuation. This attenuation is a factor of two larger around H ii regions,
as in the general ISM within the galaxy’s first 10 Myr. We allow dust
extinction to range from $A_{V}$ = $0-1$ magnitudes.

We fit the observed photometry using the Kron ellipse and the sum of all
segments (S1–S7) of the Cosmic Gems Arc. As with the eazypy fits, we apply an
error floor of 5% to the flux uncertainties to account for photometric
calibration uncertainties. The redshifts are allowed to span from
$9.9<z<10.5$, based on the measured eazypy $z_{\rm phot}=10.2\pm 0.2$.

The physical properties of the Cosmic Gems Arc are presented in Table 4. The
reported stellar masses and SFRs are corrected for magnification and assume
that we are observing two mirror images of a galaxy, as suggested by the lens
models (see Section 5.4). In Figure 8, we show the best-fit bagpipes SED
models for the Cosmic Gems Arc, fitting both the fluxes from the Kron Ellipse
and sum of segments S1–S7. Fits for both are shown for the default BC03 models
and BPASS models.

For most bagpipes models the best-fit photometric redshift for the Cosmic Gems
Arc is $z_{\rm phot}=10.2\pm 0.1$, in agreement with the eazypy photometric
redshift of $z_{\rm phot}=10.2\pm 0.2$. Some models yield a slightly lower
$z_{\rm phot}=10.1\pm 0.1$, but all are consistent with the eazypy redshift.

The intrinsic stellar masses of the Cosmic Gems Arc are consistent among the
different models, with typical $\log M_{\star}/M_{\odot}$ values of $7.4-7.5$
($M_{*}=2.5-3.2\times 10^{7}~{}M_{\odot}$). The constant SFR models yield
slightly larger intrinsic stellar masses of $\log M_{\star}/M_{\odot}=7.7-7.8$
($M_{*}=4.7-5.6\times 10^{7}~{}M_{\odot}$). These stellar masses are lower
than the typical stellar masses of $10^{8}-10^{9}~{}M_{\odot}$ found for
galaxies at $z\sim 10$ (Finkelstein et al., 2022; Naidu et al., 2022; Bradley
et al., 2023; Bunker et al., 2023; Hsiao et al., 2023a; Stiavelli et al.,
2023).

The mass-weighted ages of the Cosmic Gems Arc indicate a relatively young
stellar population, with ages typically $\sim 36-49$ Myr. These galaxy ages
are slightly older than the ages derived for the individual star clusters,
which range from 9 to 35 Myr (Adamo et al., 2024), suggesting they formed only
a few tens of Myr after the galaxy and, indeed, constitute a significant
fraction of the galaxy mass ($\sim 30$% Adamo et al., 2024). The constant SFR
models yield even younger ages of $\sim 21-22$ Myr, while the BPASS models
prefer older ages of $\sim 78-79$ Myr. The formation time of the Cosmic Gems
Arc is $t_{\rm form}=378-436$ Myr after the Big Bang.

Most models yield similar SFRs of $\sim 0.2-0.3~{}M_{\odot}/yr$ (averaged over
the last 100 Myr), with the constant SFR models yielding larger SFRs of $\sim
0.6-0.7~{}M_{\odot}/yr$ with corresponding younger ages of only $\sim 22$ Myr.
This same effect of younger ages and larger SFRs for constant SFR models was
observed for a sample of four high-redshift galaxies at $z\sim 9-10$ by
Bradley et al. (2023).

We also find very low dust content with $A_{V}<0.07$ mag for most models. For
the constant SFR models, the dust extinction is slightly larger with
$A_{V}=0.14-0.15$ mag. The low dust content is consistent with the very blue
rest-frame UV slope ($\beta=-2.7\pm 0.1$) measured from a power-law fit to the
F200W, F277W, and F356W photometry. These results are also consistent with the
low dust extinction found in the individual star clusters from SED fitting
(Adamo et al., 2024).

Finally, the best-fitting bagpipes results suggest a very low metallicity of
$\lesssim 1\%~{}Z_{\odot}$. While it is difficult to constrain the metallicity
with the current photometric data alone, the low metallicity is consistent
with the low dust content and young stellar population inferred from the SED
fitting. The low metallicity is also consistent with the low metallicity
($\sim$ 5% $Z_{\odot}$) found in the individual star clusters of the Cosmic
Gems Arc (Adamo et al., 2024). The inferred low metallicity is interesting in
the context of the reionization-era galaxies, as it suggests that the Cosmic
Gems Arc may be a low-metallicity or Population III (PopIII) star-forming
galaxy.

The low dust content and low metallicity are also consistent with the non-
detection of the dust continuum and the [O iii] 88$\mu$m line from deep ALMA
cycle 6 and 7 observations (PI: Tamura; program IDs 2018.1.00295.S and
2019.1.00327.S) of the Cosmic Gems Arc covering $z=9.5-10.7$. The lack of any
bright emission lines (including [O ii] $\lambda$$\lambda$3726, 3729) in the
JWST NIRSpec G395H MOS observations could also be explained by low
metallicity. The apparent excess of flux in the NIRCam F200W band (see Figure
8) could be due to the presence of the He ii $\lambda$1640 Å line, which is
expected to be strong in low-metallicity or PopIII galaxies (e.g., Nakajima &
Maiolino, 2022). If the Cosmic Gems Arc is a low-metallicity or PopIII galaxy,
the He ii $\lambda$1640 Å line will be clearly detected (EW $>$ 30 Å) in the
upcoming JWST Cycle 3 NIRSpec IFU prism observations of the Cosmic Gems Arc.

##  6 Conclusions

We present a detailed analysis of the Cosmic Gems Arc (SPT0615-JD), a galaxy
candidate at $z\sim 10.2$, using a combination of recent JWST NIRCam imaging
data in eight bands and archival HST imaging data in seven bands, in total
spanning $0.4-5.0$ µm. The Cosmic Gems Arc is the most highly magnified
($\mu=120$) and second-brightest observed galaxy known at $z\gtrsim 10$,
magnified to 24.5 AB mag in the NIRCam F200W band. The combination of
magnified brightness and resolution make the Cosmic Gems Arc a unique
laboratory to perform spatially-resolved studies not possible in any other
galaxy at this distance.

The Cosmic Gems Arc extends 5″ in the JWST NIRCam images. There is a
distinctive symmetry of bright knots from the center of the extended arc,
suggesting that the observed arc represents two mirror images of the lensed
galaxy. This is confirmed by our four independent cluster lens models (see
Section 4), all of which predict the $z=10.2$ critical curve crossing the arc
(see Figure 1 inset). The bright knots in the Cosmic Gems Arc have been
identified as five individual star clusters, resolved down to 1 pc in
intrinsic size in the JWST NIRCam F150W image (Adamo et al., 2024). This is
the first such detection of star clusters at $z>10$, only 460 Myr after the
Big Bang.

The arc has an extremely strong NIRCam F115W$-$F200W break of $>3.2$ mag
($2\sigma$ lower limit), is undetected ($<2\sigma$) in all bluer filters, and
has a very blue continuum slope redward of the break. Using eazypy, the best-
fit photometric redshift for the Cosmic Gems Arc is $z_{\rm phot}=10.2\pm
0.2$. This is in agreement with the best-fit bagpipes photometric redshift of
$z_{\rm phot}=10.2\pm 0.1$. We find that the arc is a low-luminosity galaxy
($M_{UV}=-17.8$) with a very blue rest-frame UV slope ($\beta=-2.7\pm 0.1$).
Thus, the Cosmic Gems Arc less luminous than the typical $M^{*}$ galaxy at
$z\sim 10$ (e.g. Finkelstein et al., 2023a; Adams et al., 2023b), placing it
in the category of galaxies likely to have driven cosmic reionization.

We use the bagpipes code to estimate the physical properties of the Cosmic
Gems Arc. Assuming a total magnification of $\mu=120$, the intrinsic stellar
mass of the Cosmic Gems Arc is $\log M_{\star}/M_{\odot}=7.4-7.8$
($M_{*}=2.4-5.6\times 10^{7}~{}M_{\odot}$), with a mass-weighted age of $\sim
21-79$ Myr. The star formation rate of the Cosmic Gems Arc is $\sim
0.2-0.7~{}M_{\odot}/yr$, with a very low dust content of $A_{V}<0.15$ mag and
a very low metallicity of $\lesssim 1\%~{}Z_{\odot}$. The low metallicity is
consistent with the low dust content and young stellar population inferred
from the SED fitting, and suggests that the Cosmic Gems Arc may be a low-
metallicity or PopIII star-forming galaxy.

Upcoming JWST Cycle 3 NIRSpec IFU prism observations of the Cosmic Gems Arc
will provide a spectroscopic redshift and a definitive test of the low-
metallicity or PopIII nature of the Cosmic Gems Arc via the He ii
$\lambda$1640 Å emission line. The JWST Cycle 3 observations also include MIRI
MRS observations that will measure H$\alpha$ emission, providing spatially-
resolved maps of the star formation rates and, when combined with the NIRSpec
FUV spectroscopy, the ionizing photon production efficiency, $\xi_{ion}$, in a
young galaxy 460 Myr after the Big Bang.

##  7 Acknowledgments

Based on observations with the NASA/ESA/CSA James Webb Space Telescope
obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space
Telescope Science Institute (STScI), which is operated by the Association of
Universities for Research in Astronomy (AURA), Incorporated, under NASA
contract NAS5-03127. Support for Program number JWST-GO-04212 was provided
through a grant from the STScI under NASA contract NAS5-03127. The data
described here may be obtained from the MAST archive at
https://dx.doi.org/10.17909/tcje-1780 (catalog doi:10.17909/tcje-1780). Also
based on observations made with the NASA/ESA Hubble Space Telescope, obtained
at STScI, which is operated by AURA under NASA contract NAS5-26555. The HST
observations are associated with programs HST-GO-14096, HST-GO-15920, HST-
GO-9771, HST-GO-12757, and HST-GO-12477. Cloud-based data processing and file
storage for this work is provided by the AWS Cloud Credits for Research
program. The Cosmic Dawn Center is funded by the Danish National Research
Foundation (DNRF) under grant #140. A.A. acknowledges support by the Swedish
research council Vetenskapsrådet (2021-05559). T.H. is supported by the
Leading Initiative for Excellent Young Researchers, MEXT, Japan (HJH02007) and
by JSPS KAKENHI grant No. 22H01258. A.K.I. is supported by JSPS KAKENHI grant
No. 23H00131. M.O. acknowledges the support of JSPS KAKENHI grant numbers
JP22H01260, JP20H05856, and JP22K21349. Y.T. is supported by JSPS KAKENHI
grant No. 22H04939. R.A.W. acknowledges support from NASA JWST
Interdisciplinary Scientist grants NAG5-12460, NNX14AN10G, and 80NSSC18K0200
from GSFC. A.Z. acknowledges support by grant No. 2020750 from the United
States-Israel Binational Science Foundation (BSF) and grant No. 2109066 from
the United States National Science Foundation (NSF); by the Ministry of
Science & Technology, Israel; and by the Israel Science Foundation grant No.
864/23. E.V. and M.M. acknowledge financial support through grants PRIN-MIUR
2020SKSTHZ, the INAF GO Grant 2022 “The revolution is around the corner: JWST
will probe globular cluster precursors and Population III stellar clusters at
cosmic dawn” and by the European Union – NextGenerationEU within PRIN 2022
project n.20229YBSAN - “Globular clusters in cosmological simulations and in
lensed fields: from their birth to the present epoch”.

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