# JWST reveals a possible $z\sim 11$ galaxy merger in triply-lensed
MACS0647–JD

Tiger Yu-Yang Hsiao Center for Astrophysical Sciences, Department of Physics
and Astronomy, The Johns Hopkins University, 3400 N Charles St. Baltimore, MD
21218, USA  Dan Coe Space Telescope Science Institute (STScI), 3700 San Martin
Drive, Baltimore, MD 21218, USA  Association of Universities for Research in
Astronomy (AURA), Inc. for the European Space Agency (ESA)  Center for
Astrophysical Sciences, Department of Physics and Astronomy, The Johns Hopkins
University, 3400 N Charles St. Baltimore, MD 21218, USA  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
Lily Whitler Steward Observatory, University of Arizona, 933 N Cherry Ave,
Tucson, AZ 85721 USA  Intae Jung Space Telescope Science Institute (STScI),
3700 San Martin Drive, Baltimore, MD 21218, USA  Gourav Khullar Department of
Physics and Astronomy and PITT PACC, University of Pittsburgh, Pittsburgh, PA
15260, USA  Ashish Kumar Meena Physics Department, Ben-Gurion University of
the Negev, P.O. Box 653, Be’er-Sheva 84105, Israel  Pratika Dayal Kapteyn
Astronomical Institute, University of Groningen, P.O. Box 800, 9700 AV
Groningen, The Netherlands  Kirk S. S. Barrow Department of Astronomy,
University of Illinois at Urbana-Champaign, 1002 W Green St, Urbana, IL 61801,
USA  Lillian Santos-Olmsted Kavli Institute for Particle Astrophysics and
Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94305-4085, USA
Adam Casselman Department of Aerospace Engineering, University of Illinois at
Urbana, Champaign 104 S Wright St, Urbana, IL 61801, USA  Eros Vanzella INAF –
OAS, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, via
Gobetti 93/3, I-40129 Bologna, Italy  Mario Nonino INAF-Trieste Astronomical
Observatory, Via Bazzoni 2, 34124, Trieste, Italy  Yolanda Jiménez-Teja
Instituto de Astrofísica de Andalucía, Glorieta de la Astronomía s/n, 18008
Granada, Spain  Observatório Nacional - MCTI (ON), Rua Gal. José Cristino 77,
São Cristóvão, 20921-400, Rio de Janeiro, Brazil  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  Daniel P. Stark  Steward
Observatory, University of Arizona, 933 N Cherry Ave, Tucson, AZ 85721 USA
Lukas J. Furtak Physics Department, Ben-Gurion University of the Negev, P.O.
Box 653, Be’er-Sheva 84105, Israel  Adi Zitrin Physics Department, Ben-Gurion
University of the Negev, P.O. Box 653, Be’er-Sheva 84105, Israel  Angela Adamo
Department of Astronomy, Oskar Klein Centre, Stockholm University, AlbaNova
University Centre, SE-106 91 Stockholm, Sweden  Gabriel Brammer Cosmic Dawn
Center (DAWN), Copenhagen, Denmark  Niels Bohr Institute, University of
Copenhagen, Jagtvej 128, Copenhagen, Denmark  Larry Bradley Space Telescope
Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA
Jose M. Diego Instituto de Física de Cantabria (CSIC-UC). Avda. Los Castros
s/n. 39005 Santander, Spain  Erik Zackrisson Observational Astrophysics,
Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20
Uppsala, Sweden  Steven L. Finkelstein Department of Astronomy, The University
of Texas at Austin, Austin, TX 78712  Rogier A. Windhorst School of Earth and
Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA
Rachana Bhatawdekar European Space Agency, ESA/ESTEC, Keplerlaan 1, 2201 AZ
Noordwijk, NL  Taylor A. Hutchison NASA Postdoctoral Fellow  Observational
Cosmology Lab, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Tom
Broadhurst Department of Theoretical Physics, University of the Basque Country
UPV/EHU, Bilbao, Spain  Donostia International Physics Center (DIPC), 20018
Donostia, Spain  IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
Paola Dimauro INAF - Osservatorio Astronomico di Roma, via di Frascati 33,
00078 Monte Porzio Catone, Italy  Felipe Andrade-Santos Department of Liberal
Arts and Sciences, Berklee College of Music, 7 Haviland Street, Boston, MA
02215, USA  Center for Astrophysics $\|$ Harvard $\&$ Smithsonian, 60 Garden
Street, Cambridge, MA 02138, USA  Jan J. Eldridge Department of Physics,
University of Auckland, Private Bag 92019, Auckland, New Zealand  Ana Acebron
Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16,
I-20133 Milano, Italy  INAF - IASF Milano, via A. Corti 12, I-20133 Milano,
Italy  Roberto J. Avila Space Telescope Science Institute (STScI), 3700 San
Martin Drive, Baltimore, MD 21218, USA  Matthew B. Bayliss Department of
Physics, University of Cincinnati, Cincinnati, OH 45221, USA  Alex Benítez
King’s College London, University of London, Strand, London WC2R 2LS, UK
Christian Binggeli Observational Astrophysics, Department of Physics and
Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden  Patricia
Bolan Department of Physics and Astronomy, University of California, Davis, 1
Shields Ave, Davis, CA 95616, USA  Maruša Bradač Department of Mathematics and
Physics, University of Ljubljana, Jadranska ulica 19, SI-1000 Ljubljana,
Slovenia  Department of Physics and Astronomy, University of California,
Davis, 1 Shields Ave, Davis, CA 95616, USA  Adam C. Carnall Institute for
Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ, UK
Christopher J. Conselice Jodrell Bank Centre for Astrophysics, University of
Manchester, Oxford Road, Manchester UK  Megan Donahue Michigan State
University, Physics & Astronomy Department, East Lansing, MI, USA  Brenda Frye
Department of Astronomy, Steward Observatory, University of Arizona, 933 North
Cherry Avenue, Tucson, AZ 85721, USA  Seiji Fujimoto Hubble Fellow  Department
of Astronomy, The University of Texas at Austin, Austin, TX 78712  Cosmic Dawn
Center (DAWN), Copenhagen, Denmark  Niels Bohr Institute, University of
Copenhagen, Jagtvej 128, Copenhagen, Denmark  Alaina Henry Space Telescope
Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA
Center for Astrophysical Sciences, Department of Physics and Astronomy, The
Johns Hopkins University, 3400 N Charles St. Baltimore, MD 21218, USA  Bethan
L. James Space Telescope Science Institute (STScI), 3700 San Martin Drive,
Baltimore, MD 21218, USA  Susan A. Kassin Space Telescope Science Institute
(STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA  Center for
Astrophysical Sciences, Department of Physics and Astronomy, The Johns Hopkins
University, 3400 N Charles St. Baltimore, MD 21218, USA  Lisa Kewley Center
for Astrophysics $\|$ Harvard $\&$ Smithsonian, 60 Garden Street, Cambridge,
MA 02138, USA  Rebecca L. Larson NSF Graduate Fellow  Department of Astronomy,
The University of Texas at Austin, Austin, TX 78712  Tod Lauer NSF’s National
Optical-Infrared Astronomy Research Laboratory, 950 North Cherry Avenue,
Tucson, AZ 85719, USA  David Law Space Telescope Science Institute (STScI),
3700 San Martin Drive, Baltimore, MD 21218, USA  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  Ramesh Mainali Observational Cosmology Lab, NASA Goddard Space Flight
Center, Greenbelt, MD 20771, USA  Stephan McCandliss Center for Astrophysical
Sciences, Department of Physics and Astronomy, The Johns Hopkins University,
3400 N Charles St. Baltimore, MD 21218, USA  David Nicholls Research School of
Astronomy and Astrophysics, Australian National University, Canberra, ACT,
Australia  ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions
(ASTRO 3D), Australia  Norbert Pirzkal Space Telescope Science Institute
(STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA  Marc Postman Space
Telescope Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD
21218, USA  Jane R. Rigby Observational Cosmology Lab, NASA Goddard Space
Flight Center, Greenbelt, MD 20771, USA  Russell Ryan Space Telescope Science
Institute (STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA  Peter
Senchyna Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 91101,
USA  Keren Sharon Department of Astronomy, University of Michigan, 1085 S.
University Ave, Ann Arbor, MI 48109, USA  Ikko Shimizu  Department of
Literature, Shikoku Gakuin University, 3-2-1 Bunkyocho, Zentsuji, Kagawa
765-8505, Japan  Victoria Strait Cosmic Dawn Center (DAWN), Copenhagen,
Denmark  Niels Bohr Institute, University of Copenhagen, Jagtvej 128,
Copenhagen, Denmark  Mengtao Tang Department of Physics and Astronomy,
University College London, Gower Street, London WC1E 6BT, UK  Michele Trenti
School of Physics, University of Melbourne, Parkville VIC 3010, Australia  ARC
Centre of Excellence for All-Sky Astrophysics in 3 Dimensions, University of
Melbourne, Parkville VIC 3010, Australia  Anton Vikaeus Observational
Astrophysics, Department of Physics and Astronomy, Uppsala University, Box
516, SE-751 20 Uppsala, Sweden  Brian Welch Department of Astronomy,
University of Maryland, College Park, MD 20742, USA  Observational Cosmology
Lab, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Center for
Research and Exploration in Space Science and Technology, NASA/GSFC,
Greenbelt, MD 20771

###### Abstract

MACS0647–JD is a triply-lensed $z\sim 11$ galaxy originally discovered with
the _Hubble Space Telescope_. The three lensed images are magnified by factors
of $\sim$8, 5, and 2 to AB mag 25.1, 25.6, and 26.6 at 3.5 $\mu$m. The
brightest is over a magnitude brighter than other galaxies recently discovered
at similar redshifts $z>10$ with JWST. Here we report new JWST imaging clearly
resolves MACS0647–JD as having two components that are either merging galaxies
or stellar complexes within a single galaxy. The brighter larger component “A”
is intrinsically very blue ($\beta\sim-2.6\pm 0.1$), likely due to very recent
star formation and no dust, and is spatially extended with an effective radius
$\sim 70$$\pm 24$ pc. The smaller component “B” ($r\sim
20$${}^{+8}_{-5}\,$${\rm pc}$) appears redder ($\beta\sim-2\pm 0.2$), likely
because it is older (100–200 Myr) with mild dust extinction ($A_{V}\sim 0.1$
mag). With an estimated stellar mass ratio of roughly 2:1 and physical
projected separation $\sim 400\,{\rm pc}$, we may be witnessing a galaxy
merger 430 million years after the Big Bang. We identify galaxies with similar
colors in a high-redshift simulation, finding their star formation histories
to be dissimilar, which is also suggested by the SED fitting, suggesting they
formed further apart. We also identify a candidate companion galaxy “C”
$\sim$3 kpc away, likely destined to merge with A and B. Upcoming JWST NIRSpec
observations planned for January 2023 will deliver spectroscopic redshifts and
more physical properties for these tiny magnified distant galaxies observed in
the early universe.

Galaxies (573), High-redshift galaxies (734), Strong gravitational lensing
(1643), Galaxy clusters (584), Early universe (435)

††journal: ApJ††facilities: JWST(NIRCam), HST(ACS, WFC3)††software: astropy
(Astropy Collaboration et al., 2022, 2018, 2013), photutils (Bradley et al.,
2022), grizli (Brammer et al., 2022), eazypy (Brammer et al., 2008), piXedfit
(Abdurro’uf et al., 2021, 2022) Bagpipes (Carnall et al., 2018),
Cloudy(Ferland et al., 1998, 2013, 2017), Prospector (Leja et al., 2017;
Johnson et al., 2021), beagle (Chevallard & Charlot, 2016), Jdaviz (JDADF
Developers et al., 2022)

##  1 Introduction

Galaxies have formed from the repeated mergers of small star-forming clumps
over cosmic time, with some small galaxies left over even today, such as the
Magellanic clouds. JWST has now discovered two such small galaxies within the
first 430 million years, that are seen close to the very start of this
process. Studies have shown that up to $85\%$ of present-day massive galaxies
went through a galaxy merger in their lifetime, indicating that galaxy mergers
play an important role in the formation and evolution of galaxies (e.g., Bell
et al., 2006; Stewart et al., 2009; Hopkins et al., 2010b; Lotz et al., 2011;
Rodriguez-Gomez et al., 2015; Duncan et al., 2019; Sotillo-Ramos et al.,
2022). The Milky Way itself likely experienced a major merger at $z\sim 2$
with the so-called Gaia-Sausage-Enceladus galaxy (Helmi et al., 2018;
Belokurov et al., 2018; Bonaca et al., 2020; Naidu et al., 2021; Xiang & Rix,
2022). Based on reconstructions of this event, Naidu et al. (2021) concluded
that $\approx 50\%$ of the stellar mass of the current halo of the Milky Way
came from this galaxy. More generally speaking, mergers build up the stellar
content and transform galaxy morphology (e.g., Toomre & Toomre, 1972; Barnes,
1992; Mihos & Hernquist, 1996; Huško et al., 2023) Mergers are also believed
to affect the kinematics and distribution of stars (e.g., Naab et al., 2009;
van Dokkum et al., 2010; Newman et al., 2012), and play a key role in the
growth of supermassive black holes (e.g., Treister et al., 2012; Ellison et
al., 2019; Zhang et al., 2023).

JWST (Gardner et al. 2006) is a state-of-the-art infrared space-based
telescope which was launched in December 2021 and started scientific
observations recently in July 2022 (Rigby et al., 2022). Numerous high-
redshift candidates have been discovered based on their photometric redshifts
and drop-out selections (e.g., Naidu et al., 2022; Castellano et al., 2022;
Adams et al., 2022; Yan et al., 2022; Donnan et al., 2022; Harikane et al.,
2022; Atek et al., 2022; Finkelstein et al., 2022; Whitler et al., 2022a;
Bradley et al., 2022; Castellano et al., 2022). Within its first few months,
JWST is quickly transforming our understanding of the early Universe (e.g.,
with flat / disky galaxies reported at $z\sim 2$ – 6: Ferreira et al. 2022;
Nelson et al. 2022).

Gravitational lensing by massive galaxy clusters magnifies the light and sizes
of distant objects. Thanks to these cosmic telescopes, not only are the fluxes
of faint objects in the early Universe are boosted to the observable regime,
the sizes of small-scale structures are amplified (e.g., Welch et al., 2022a;
Vanzella et al., 2022; Meštrić et al., 2022; Welch et al., 2022b; Claeyssens
et al., 2022). Thus, lensing has enabled us to discover early galaxies and
study their properties (e.g, Coe et al., 2013). In order to study several key
scientific topics in the early Universe, several lensing cluster surveys have
been conducted, including the Cluster Lensing and Supernova survey with Hubble
(CLASH111https://www.stsci.edu/~postman/CLASH/; Postman et al., 2012a), the
Hubble Frontier Fields (Lotz et al., 2017), and the Reionization Lensing
Cluster Survey (RELICS222https://relics.stsci.edu Coe et al., 2019).

CLASH is one of the large Hubble treasury programs which adopted the lensing
technique to study distant galaxies (e.g., Zheng et al., 2012; Coe et al.,
2013; Bouwens et al., 2014; Smit et al., 2014; Bradley et al., 2014),
supernovae and cosmology (e.g., Graur et al., 2014; Patel et al., 2014; Rodney
et al., 2014; Strolger et al., 2015; Riess et al., 2018; Gómez-Valent &
Amendola, 2018), dark matter in clusters (e.g., Pacucci et al., 2013; Eichner
et al., 2013; Sartoris et al., 2014; Umetsu et al., 2014; Merten et al.,
2015), and galaxies in clusters (e.g., Postman et al., 2012b; Burke et al.,
2015; Donahue et al., 2015; Fogarty et al., 2017; Connor et al., 2017).

CLASH imaged 25 massive galaxy clusters in 16 filters with HST from near-UV
($\sim 200\,{\rm nm}$) to near-IR ($\sim 1.6\,{\rm\mu m}$). Five of the
clusters were selected for their strong lensing strength, including
MACSJ0647.7+7015 (MACS0647; $z=0.591$; Ebeling et al., 2007) modeled by Zitrin
et al. (2011). CLASH observations of MACSJ0647.7+7015 revealed 32 lensed
$z\sim 6$ – 8 candidates (Bradley et al., 2014) and a triply-lensed $z\sim 11$
candidate MACS0647–JD (Coe et al., 2013).

MACS0647–JD had a photometric redshift $z=10.7^{+0.6}_{-0.4}$ based on HST
images, where it was detected in only the two reddest filters F140W and F160W,
dropping out of 15 bluer filters, including $J$ F125W, hence the name JD
(J-band dropout). Despite lensing magnifications up to a factor of 8,
MACS0647–JD was spatially unresolved in HST imaging.

MACS0647–JD was the first robust $z\sim 11$ candidate of the HST era, followed
by GN-z11, which surpassed it at $z=11.1$ (Oesch et al., 2016) and is
similarly bright (F160W AB mag $\sim$26) without the benefit of lensing
magnification. Lensed as brightly as F356W AB mag 25.1, MACS0647–JD is 1 – 5
magnitudes brighter than recently discovered $z\sim 8$ – 16 candidates
reported in JWST imaging (Figure 1; Bradley et al., 2022; Naidu et al., 2022;
Adams et al., 2022; Atek et al., 2022; Leethochawalit et al., 2022; Donnan et
al., 2022; Harikane et al., 2022; Finkelstein et al., 2022). Because it is so
bright, we can study its physical properties in more detail. More detail about
the photometry measurement and the lensing will be later described in Section
2 and 3.1.

Pirzkal et al. (2015) analyzed HST WFC3/IR G141 grism spectroscopy of
MACS0647–JD, concluding that any emission line bright enough to reproduce the
observed photometry was ruled out by the observations. Any line or combination
of emission lines with a flux of $10^{-17}$ erg/s/cm2/Å would have been
detected at the 5$\sigma$ level, adding further support for $z\sim 11$
excluding a lower redshift interloper, as in Brammer et al. (2013).

Lens modeling contributes geometric redshift corroboration based on the
measured separations between the lensed images. The models in Coe et al.
(2013) and Chan et al. (2017) both supported $z\sim 11$.

Lam et al. (2019) analyzed deep Spitzer imaging (50 hours / band), modeling
and subtracting light of nearby galaxies to arrive at tentative detections of
MACS0647–JD. Photometry varied between the three lensed images, yielding
estimates of stellar mass $M_{*}/M_{\odot}\sim 10^{8}$ – $10^{9}$, specific
star formation rates $\sim$ 3 – 10 Gyr-1, and ages ranging between $\sim$ 10
Myr – 400 Myr (the age of the universe at $z\sim 11$).

JWST observing program GO 1433 (PI Coe) aims at studying MACS0647–JD in more
detail, obtaining higher resolution images, measuring colors, and obtaining
spectroscopy to more precisely measure the redshift and constrain other
physical properties including metallicity. NIRCam imaging was obtained in 6
filters spanning 1.0–5.0 $\mu$m, out to $\sim$4300 Å rest-frame at $z=10.6$.
The second epoch of observations planned for January 2023 will obtain NIRSpec
MSA PRISM observations and add the NIRCam F480M filter, fully redward of the
Balmer break to obtain better measurements of ages and stellar masses at
$z\sim 11$. All data from this program are public. We are releasing high-level
science products and analysis tools online.333https://cosmic-spring.github.io

In this paper, we report new observations of MACS0647–JD with 6 JWST NIRCam
filters and derive physical properties including the stellar mass and dust
content, while constraining the star formation history. This paper is
organized as follows. In §2, we describe the JWST and HST observational data
and the data reduction. In §3, we present the detected objects and their sizes
and separations based on lens modeling. We detail photometry measurements in
§4 and SED fitting in §5. In §6, we discuss our results, including
measurements of physical parameters from SED fitting. We also present
properties of analog galaxies identified with similar colors in a hydrodynamic
simulation. We summarize our conclusions in §7.

We adopt the AB magnitude system ($m_{\rm AB}=31.4-2.5\log(f_{\nu}/{\rm
nJy})$; Oke, 1974; Oke & Gunn, 1983) and the Planck 2018 flat $\Lambda$CDM
cosmology (Planck Collaboration et al., 2020) with $H_{0}=67.7$ km s-1 Mpc-1,
$\Omega_{\rm M}=0.31$, and $\Omega_{\Lambda}=0.69$, for which the universe is
13.8 billion years old, and $1\arcsec\sim 4$ kpc at $z\sim 11$.

Figure 1: F356W AB magnitude vs. redshift for MACS0647–JD and $z\sim 8$ – 16
candidates recently discovered in JWST imaging (Bradley et al., 2022; Naidu et
al., 2022; Adams et al., 2022; Leethochawalit et al., 2022; Donnan et al.,
2022; Harikane et al., 2022; Finkelstein et al., 2022). MACS0647–JD is shown
both as observed (magnified) and delensed (intrinsic) according to our models.
Figure 2: JWST NIRCam color image of MACS0647+70 with the three lensed images
of MACS0647–JD labeled in red. Also circled in orange are the lensed images of
a candidate companion galaxy C.

##  2 Observational Data

We analyze new JWST NIRCam images (GO 1433, PI Coe) shown in Figure 2, as well
as archival HST images described below and detailed in Table 1. All of the
data are publicly available in the Mikulski Archive for Space Telescopes
(MAST; DOI: 10.17909/d2er-wq71). We also provide reduced data products aligned
to a common pixel grid (§2.3).

###  2.1 HST observations

MACS0647+70 has been observed with 39 orbits of HST imaging in 17 filters. It
was first observed by programs GO 9722 (PI Ebeling) and GO 10493, 10793 (PI
Gal-Yam) in the ACS F555W and F814W filters. Then CLASH (GO 12101, PI Postman)
obtained imaging in 15 additional filters with WFC3/UVIS, ACS, and WFC3/IR,
spanning 0.2–1.7$\mu$m. Additional imaging in WFC3/IR F140W was obtained as
part of a grism spectroscopy program (GO 13317, PI Coe).

###  2.2 JWST observations

Here we present new JWST NIRCam imaging in 6 filters, F115W, F150W, F200W,
F277W, F365W, and F444W spanning 1–5$\,\mu$m. These public data were obtained
2022 September 23 as part of Cycle 1 program GO 1433 (PI Coe). Total exposure
times of 2104 s in each filter achieve 5$\sigma$ depths of AB mag 28.0 to 29.0
for small sources ($r=0.1^{\prime\prime}$ aperture). Depths were measured by
placing circular apertures in blank regions of the image using the photutils
ImageDepth
routine444https://photutils.readthedocs.io/en/stable/api/photutils.utils.ImageDepth.html.

In each filter, we obtained 4 dithered exposures using INTRAMODULEBOX primary
dithers to cover the 4-5$\arcsec$ gaps between the short wavelength detectors,
while maximizing image area observed at full depth. Dithering also mitigates
bad pixels and image artifacts, while improving resolution of the final
drizzled images. Each exposure uses the SHALLOW4 readout pattern with ten
groups and one integration.

Backgrounds were relatively high that time of year for this target ($\sim$80%
higher than minimum). The telescope was rolled to Position Angle 280$\degree$.
We observed the cluster in NIRCam module A and a nearby “blank” field with
module B. The brighter lensed images MACS0647–JD1 and JD2 were observed with
NIRCam SW detector A3, while JD3 was observed with A1.

This program GO 1433 will obtain additional public data expected in January
2023: NIRCam imaging in F200W and F480M and NIRSpec MSA PRISM spectroscopic
observations.

Table 1: HST and JWST Exposure Times and Depths |  | $\lambda$ | Exp. | Depthaa5$\sigma$ point source AB magnitude limit (within a 0.2″ diameter aperture).
---|---|---|---|---
Camera | Filter | ($\mu$m) | Time (sec) | (AB)
HST WFC3/UVIS | F275W | 0.23–0.31 | 3879 | 27.4
HST WFC3/UVIS | F336W | 0.30–0.37 | 2498 | 27.6
HST WFC3/UVIS | F390W | 0.33–0.45 | 2545 | 28.1
HST ACS/WFC | F435W | 0.36–0.49 | 2124 | 28.0
HST ACS/WFC | F475W | 0.39–0.56 | 2248 | 28.2
HST ACS/WFC | F555W | 0.46–0.62 | 7740 | 28.7
HST ACS/WFC | F606W | 0.46–0.72 | 2064 | 28.3
HST ACS/WFC | F625W | 0.54–0.71 | 2131 | 27.9
HST ACS/WFC | F775W | 0.68–0.86 | 2162 | 27.8
HST ACS/WFC | F814WbbWe excluded one dataset (J8QU04020: 3960 s) because it is contaminated by scattered light from the WFPC2 internal lamp, which was in use for a parallel program. | 0.69–0.96 | 8800 | 28.5
HST ACS/WFC | F850LP | 0.80–1.09 | 4325 | 27.3
HST WFC3/IR | F105W | 0.89–1.21 | 2914 | 28.3
HST WFC3/IR | F110W | 0.88–1.41 | 1606 | 28.7
HST WFC3/IR | F125W | 1.08–1.41 | 2614 | 28.3
HST WFC3/IR | F140W | 1.19–1.61 | 2411 | 28.7
HST WFC3/IR | F160W | 1.39–1.70 | 5229 | 28.4
JWST NIRCam | F115W | 1.0–1.3 |  2104 | 28.1
JWST NIRCam | F150W | 1.3–1.7 |  2104 | 28.3
JWST NIRCam | F200W | 1.7–2.2 |  2104 | 28.4
JWST NIRCam | F277W | 2.4–3.1 |  2104 | 28.9
JWST NIRCam | F356W | 3.1–4.0 |  2104 | 29.0
JWST NIRCam | F444W | 3.8–5.0 |  2104 | 28.8

###  2.3 Data Reduction

We process imaging data from MAST from all the programs above. The reduced
images, along with source catalogs, are publicly available
online555https://s3.amazonaws.com/grizli-v2/JwstMosaics/v4/index.html along
with public data from other JWST programs.

We retrieve the individual calibrated exposures processed by the HST and JWST
pipelines (FLT and Level 2b CAL images, respectively). We then process all of
these using the grizli pipeline (Brammer et al., 2022), co-adding all
exposures in each filter, and aligning all stacked images to a common
$0.04^{\prime\prime}$ pixel grid with coordinates registered to the GAIA DR3
catalogs (Gaia Collaboration et al., 2021). The NIRCam short wavelength images
are drizzled to $0.02^{\prime\prime}$ pixels (on the same pixel grid
supersampled $2\times$) to provide the highest possible resolution. We leave
out the bluest filter HST WFC3/UVIS F225W image, which contains very few
sources making it difficult to process.

We make use of the latest NIRCam calibrations jwst_0995.pmap, based on data
from NIRCam CAL program data and made operational 2022 October 6. These were
not available at the time of processing, so we recalibrate our data in several
steps. The JWST pipeline used NIRCam calibrations first made available July 29
in jwst_0942.pmap; these were the first photometric calibrations based on in-
flight data. Subsequently in late August, updated NIRCam
calibrations666https://zenodo.org/record/7143382 were calculated independently
and utilized in grizli v4 image processing of many public datasets, including
this one. These calibrations are consistent to within $<5\%$ of the most
recent jwst_0995.pmap calibrations in each filter and detector. We measure
photometry (§4) in the grizli v4 images, then finally apply the necessary flux
corrections (Table 2) to JD1 and JD2 observed in NIRCam detectors A3 and A5,
and JD3 in detectors A1 and A5.

The grizli pipeline applies corrections for $1/f$ noise striping and masks
“snowballs”777https://jwst-docs.stsci.edu/data-artifacts-and-
features/snowballs-artifact caused by high-energy cosmic rays. It also
corrects for stray light features known as “wisps” that are static and have
been modeled in the A3, B3, and B4 detectors in F150W and F200W
images.888https://jwst-docs.stsci.edu/jwst-near-infrared-camera/nircam-
features-and-caveats/nircam-claws-and-wisps

Finally, the grizli pipeline combines all images in each filter, drizzling
them to a common pixel grid using astrodrizzle (Koekemoer et al., 2003;
Hoffmann et al., 2021). The NIRCam short wavelength images F115W, F150W, and
F200W are drizzled to 0$\farcs$02 pixels, and all other images are drizzled to
0$\farcs$04 pixels (on the same grid at half the resolution). All HST and JWST
images are aligned to a common world coordinate system (WCS) registered to the
GAIA DR3 catalogs (Gaia Collaboration et al., 2021). We create color images
using Trilogy999https://github.com/dancoe/trilogy (Coe et al., 2012).

Table 2: Photometric Recalibration

Filter | JD1, JD2 | JD3
---|---|---
F115W | A3 0.9687 | A1 0.9826
F150W | A3 0.9536 | A1 0.9777
F200W | A3 0.9658 | A1 0.9891
F277W | A5 1.0239 | A5 1.0239
F356W | A5 0.9763 | A5 0.9763
F444W | A5 1.0073 | A5 1.0073

Note. — We multiply JD1,2,3 fluxes and uncertainties by these values to
correct from grizli v4 calibration to jwst_0995.pmap.

###  2.4 JWST Stellar Diffraction Spikes and Scattered Light Artifacts

At relatively low Galactic latitude $b=25\degree$, there are many stars
affecting the image. One particularly bright $\sim$ 8th magnitude star $\sim$
2$\arcmin$ southwest of JD1 and JD2 (observed in module B) produces a
diffraction spike that crosses the entire module A image of the cluster.
Fortunately, none of the lensed images JD1, 2, 3 are impacted by the spikes,
with the possible exception of one that comes close to JD2 in F277W.

Other scattered light artifacts are isolated and do not impact the lensed
images of MACS0647–JD. “Claws”101010https://jwst-docs.stsci.edu/jwst-near-
infrared-camera/nircam-features-and-caveats/nircam-claws-and-wisps are visible
as horizontal stripes in our F200W image well south of JD3. These are
presumably due to an extremely bright ($K\lesssim 3$ Vega mag) star very far
from the field of view ($10\degree$ in the telescope V3 direction). They do
not move significantly between dithers and cannot be modeled or subtracted.

Dragon’s Breath Type II111111https://jwst-docs.stsci.edu/jwst-near-infrared-
camera/nircam-features-and-caveats/nircam-dragon-s-breath-type-ii is visible
as vertical stripes in our F200W image, near the west edge, extending south of
center in the A4 detector, also far from JD1, 2, 3.

Figure 3: MACS0647–JD observed in the NIRCam SW color image (B=F115W, G=F150W,
R=F200W) and in each NIRCam filter. Each image stamp is $1\arcsec$ across.
Grayscale images for all filters are scaled to the same flux densities per
$0\farcs 02$ pixel, as shown in the colorbar. Data are recalibrated to
jwst_0995.pmap.  Figure 4: Candidate companion galaxy MACS0647–JDc. Color and
grayscale images as in Figure 3.

##  3 Three Stellar Components

The JWST NIRCam images clearly resolve MACS0647–JD into two galaxies or
components: A and B (Figure 3). Component A is brighter and spatially
extended, while B is fainter, more compact, and redder in the short wavelength
filters. These two components are clearly seen in each of the three lensed
images JD1, 2, 3. Both are J-band dropouts, not detected in F115W.

Additionally, we identify a candidate companion galaxy C, another J-band
dropout (Figure 4) observed 2.2″, 2.2″, and 0.9″ from JD1A, JD2A, and JD3A,
respectively (see Figure 2). It is fainter than A and B and even more compact.

###  3.1 Lens Modeling

A first lens model for this cluster, prior to CLASH imaging, was presented by
Zitrin et al. (2011). Lens modeling enabled by the CLASH HST images has been
presented in Coe et al. (2013); Zitrin et al. (2015); Chan et al. (2017) using
various methods: Lenstool (Jullo et al., 2007; Jullo & Kneib, 2009), Zitrin-
LTM (Zitrin et al., 2009; Broadhurst et al., 2005), and WSLAP+ (Diego et al.,
2005, 2007). Magnification estimates range from 6.0–8.4, 5.5–7.7, and 2.1–2.8
for JD1, 2, 3, respectively. Uncertainties are thus roughly $\pm 17$%, similar
to performances modeling simulated lenses with excellent constraints. These
models have decent constraints with between 9 and 12 multiply-lensed galaxies,
however none have spectroscopic redshift.

JWST imaging reveals more multiply-lensed image systems which will be
published alongside a new lens model in Meena et al. (in preparation). The
model was obtained using a revised, analytic version of the parametric method
presented in Zitrin et al. (2015) and was recently used, for example, in
Pascale et al. (2022). This preliminary, new parametric lens model yields
magnification estimates of $\sim$6.9, 6.3, and 2.1 for JD1, 2, 3, with
tangential (linear) magnifications of $\sim$4.7, 4.4, and 1.8. Another
preliminary new mass model using GLAFIC (Oguri, 2010) predicts magnifications
of $\sim 9.1$, $5.5$, and $1.8$ for JD1, 2, 3, respectively.

JWST imaging also yields direct new measurements of the observed flux ratios
$\sim$ 3.5 : 2.3 : 1 for JD1, 2, 3 based on NIRCam photometry measured in
F200W and redward, averaging 340, 223, 97 nJy (AB mag 25.1, 25.5, 26.4). Based
on these measured flux ratios, we adopt fiducial magnification estimates of
$\sim$ 8.0, 5.3, and 2.2 for JD1, 2, 3, respectively, with tangential
magnifications of $\sim$ 5, 4 and 2. These are roughly consistent with
previous estimates121212Previous magnification estimates for JD1, JD2, and JD3
were 8, 7, 3 (Coe et al., 2013); 6, 6, 2 (Zitrin et al., 2015); and 8, 8, 3
(Chan et al., 2017).  and the total magnification $\sim$ 15.5 is roughly equal
to the total in our new preliminary lens model. The average delensed flux in
F200W, F277W, F356W, F444W is 43 nJy (AB mag 27.3, $M_{UV}=-20.4$) with an
uncertainty of $\sim$ 17%.

###  3.2 Sizes and Separations

Figure 5:  GALFIT modeling (center) of JD1ABC in the F150W and F200W images
(left) with residuals shown at right. Sérsic model parameters are fit in F150W
and held constant (aside from flux) in F200W. A possible noise fluctuation
A$\arcmin$ apparent only in the F150W image was included as a 4th model
component so as not to bias the fitting. A$\arcmin$ and C are compact and
modeled as point sources (convolved with the image PSF). Based on this model
combined with our lens model, we measure A and B have radii of $\sim$
70${}^{+24}_{-24}\,$ and 20${}^{+8}_{-5}\,$pc, respectively (§3.2).  Figure 6:
Delensed images of JD1, 2, 3 based on our Zitrin-analytic lens model (Meena et
al. in preparation) compared to a pair of merging galaxies in the Renaissance
simulations (Barrow et al., 2017) shown at bottom on the same physical scale.
Galaxies A & B are separated by $\sim 0.1\arcsec\sim 400$ pc in the delensed
source plane. The candidate companion C is $\sim 0.63\arcsec\sim 2.5$ kpc
away. Note the relative positions are reproduced well here assuming A, B, and
C are all at $z=10.6$. The reconstruction is similar for C at $z\sim 9$, with
delensed positions changing slightly. Redshifts $z<5$ are ruled out for B and
C (assuming A is at $z\sim 11$), as the relative separations would change
significantly.

We use GALFIT (Peng et al., 2010) to model JD1 A & B in the sharpest image,
F150W. Galaxy A is fit well by a 2-component Sérsic model (see Figure 5),
including a compact core and a more extended host with a radius of $4.4\pm
1.5$ pixels = $0.09\arcsec$ (adopting a Gaussian profile for both, Sérsic
index n=0.5). De-lensing that by the tangential linear magnification $\sim$ 5,
yields a radius $\sim$ 70${}^{+24}_{-24}\,$pc. Galaxy B is well-fitted by a
single compact source with a radius of 1.3${}^{+0.5}_{-0.3}$ pixels, with a
de-lensed radius $\sim$ 20${}^{+8}_{-5}\,$pc. This analysis method was tested
and validated with simulations in Meštrić et al. (2022). Note that we use the
morphology measurements from F150W to model the F200W image as shown in Figure
5 and is well-fitted.

A similar independent analysis with IMFIT (Erwin, 2015) fitting galaxy A to a
single component yields a radius of 3 pixels (with higher Sérsic index $n\sim
2$ vs. 0.5 for the GALFIT extended component). This yields a smaller delensed
radius $\sim$ 45 pc for A.

A third analysis measuring the curve of growth (flux vs. radius) yields
delensed effective radii $\sim$ 70 and 50 pc for A and B, respectively.

To measure separations between A, B, and C, we delens images JD1, 2, 3 to the
source plane (Figure 6). We find the cores of A and B are separated by $\sim
0.1\arcsec(\sim 400$ pc) in both the Zitrin-analytic GLAFIC models. The
candidate companion C is $\sim$ 3 kpc away.

##  4 Photometry Measurements

Table 3: Coordinates and multiwavelength photometry of MACS0647–JD

Filter | JD1 | JD2 | JD3 |
---|---|---|---|---
RA(J2000) | 101.9822676 | 101.971326 | 101.9811153 |
DEC(J2000) | 70.24328239 | 70.2397157 | 70.26059029 |
F275W | $-31\pm 35$ | $11\pm 30$ | $43\pm 27$ |
F336W | $-8\pm 27$ | $32\pm 24$ | $-24\pm 21$ |
F390W | $-12\pm 17$ | $-5\pm 44$ | $24\pm 23$ |
F435W | $-25\pm 21$ | $70\pm 18$ | $-23\pm 21$ |
F475W | $7\pm 15$ | $-26\pm 113$ | $21\pm 12$ |
F555W | $-2\pm 10$ | $15\pm 8$ | $8\pm 7$ |
F606W | $-16\pm 10$ | $4\pm 12$ | $-1\pm 28$ |
F625W | $-38\pm 20$ | $-24\pm 17$ | $15\pm 17$ |
F775W | $24\pm 28$ | $-16\pm 21$ | $-18\pm 17$ |
F814W | $-8\pm 9$ | $0\pm 8$ | $-3\pm 7$ |
F850LP | $-55\pm 33$ | $-11\pm 30$ | $29\pm 30$ |
F105W | $3\pm 19$ | $4\pm 16$ | $-1\pm 14$ |
F110W | $-25\pm 13$ | $5\pm 12$ | $7\pm 10$ |
F115W | $-1\pm 8$ | $-35\pm 7$ | $-2\pm 6$ |
F125W | $-13\pm 19$ | $-9\pm 17$ | $6\pm 14$ |
F140W | $126\pm 11$ | $97\pm 12$ | $59\pm 9$ |
F150W | $304\pm 7$ | $173\pm 6$ | $92\pm 5$ |
F160W | $301\pm 17$ | $203\pm 17$ | $85\pm 13$ |
F200W | $354\pm 6$ | $227\pm 6$ | $115\pm 4$ |
F277W | $351\pm 6$ | $248\pm 5$ | $93\pm 3$ |
F356W | $322\pm 6$ | $203\pm 5$ | $86\pm 3$ |
F444W | $330\pm 9$ | $214\pm 7$ | $95\pm 5$ |

††footnotetext: Note. All fluxes are given in $\rm nJy$.

The grizli pipeline uses SEP (Barbary, 2016), a Python implementation of
SourceExtractor (Bertin & Arnouts, 1996), to detect sources in a stacked
NIRCam image and measure aperture-matched photometry in all filters.
Photometry is measured in circular apertures with radii $0.5\arcsec$.

JD1, 2, 3 are detected as objects #3593, 3349, 4871 in the public v4 catalog
(§2.3). Table 3 provides their measured coordinates and photometry
recalibrated using Table 2. These are total fluxes measured for galaxies A+B.
To measure photometry of these components individually, we use the methods
below. The photometry of individual galaxies A and B is organized in Table 4.

The candidate companion galaxy C is detected as objects #3621, 3314, 4858.

###  4.1 piXedfit

Table 4: Multiwavelength photometry of two individual galaxies in MACS0647–JD
(i.e., JDa and JDb).

Filter | JD1a | JD1b | JD2a | JD2b | JD3a | JD3b
---|---|---|---|---|---|---
F435W | $-16\pm 6$ | $-2\pm 5$ | $4\pm 5$ | $8\pm 5$ | $-5\pm 4$ | $-3\pm 4$
F475W | $-9\pm 5$ | $-2\pm 3$ | $-10\pm 4$ | $-9\pm 3$ | $-3\pm 3$ | $0\pm 2$
F555W | $-10\pm 3$ | $-5\pm 2$ | $-3\pm 3$ | $-5\pm 2$ | $-1\pm 2$ | $-2\pm 1$
F606W | $-6\pm 7$ | $-2\pm 4$ | $0\pm 4$ | $-1\pm 3$ | $6\pm 14$ | $1\pm 3$
F625W | $-19\pm 7$ | $-4\pm 4$ | $2\pm 5$ | $-6\pm 4$ | $8\pm 5$ | $-3\pm 2$
F775W | $-23\pm 9$ | $-6\pm 8$ | $-25\pm 6$ | $3\pm 5$ | $-8\pm 5$ | $-3\pm 3$
F814W | $-15\pm 4$ | $-5\pm 3$ | $-8\pm 3$ | $-4\pm 2$ | $-1\pm 2$ | $-1\pm 2$
F115W | $-18\pm 3$ | $-2\pm 2$ | $-10\pm 3$ | $-7\pm 2$ | $-2\pm 2$ | $-3\pm 1$
F150W | $144\pm 3$ | $27\pm 2$ | $91\pm 3$ | $16\pm 2$ | $55\pm 2$ | $7\pm 1$
F200W | $160\pm 3$ | $43\pm 2$ | $115\pm 2$ | $27\pm 2$ | $60\pm 2$ | $13\pm 1$
F277W | $143\pm 2$ | $37\pm 2$ | $90\pm 2$ | $27\pm 1$ | $43\pm 1$ | $8\pm 1$
F356W | $106\pm 2$ | $39\pm 1$ | $64\pm 2$ | $25\pm 1$ | $30\pm 1$ | $9\pm 1$
F444W | $97\pm 3$ | $44\pm 2$ | $59\pm 2$ | $26\pm 1$ | $28\pm 1$ | $8\pm 1$

††footnotetext: Note. All fluxes are described in $\rm nJy$ and were measured
using piXedfit (Abdurro’uf et al., 2021).

To spatially resolve the SEDs of the two galaxies, we use piXedfit(Abdurro’uf
et al., 2021). For this resolved SED analysis, we use 13-band imaging from ACS
and NIRCam (excluding ACS F850LP and WFC3/IR filters with broader PSF, as well
as the lower wavelength WFC3/UVIS filters), similar to the analyses carried
out in Abdurro’uf et al. (2023). First, all images are resampled to
$0.02^{\prime\prime}$ pixels using reproject (Robitaille et al., 2020). Then,
we use SEP (Barbary, 2016) to detect objects in the NIRCam images, generating
a segmentation map defining pixels belonging A+B.

Photometry is measured in elliptical apertures defined within the segments and
without overlap. Aperture A is an ellipse with semi-major axis 0.2$\arcsec$
and semi-minor axis 0.1$\arcsec$. Aperture B is a circle with radius
0.1$\arcsec$. Radial profiles decrease within these apertures, reaching a
minimum between them that defines their boundary.

We initially forgo PSF-matching to retain spatial resolution. However, we note
measured colors may be affected by lost and/or blended flux in the redder
filters. The F444W PSF FWHM is 0.14$\arcsec$ with 54% encircled energy within
$r=0.1\arcsec$, compared to 70% for F150W.131313https://jwst-
docs.stsci.edu/jwst-near-infrared-camera/nircam-performance/nircam-point-
spread-functions We perform aperture corrections based on point source
encircled energy and discuss how this affects results below. The effect is to
make colors redder, though we note this may be an overcorrection with flux
also blending between A and B.

Aside from A and B, there are no other nearby objects affecting the
photometry. Local backgrounds are small, consistent with zero, and not
subtracted.

###  4.2 IMFIT

IMFIT (Erwin, 2015) has been used to perform 2D fitting to MACS0647-JD. The
PSF used in the fitting has been generated, for each filter, using isolated
stars. The two clumps have been fitted separately, alternately masking them,
followed by a simultaneous fitting step with the parameters for clump A kept
fixed. A Sérsic profile has been used for clump A, while for clump B both
Sérsic and pointlike profiles resulted in similar values for the reduced
$\chi^{2}$. Photometry has then been performed on the models generated from
the results from the 2D fitting, using an elliptical aperture for clump A.

###  4.3 CHEFs

CHEFs (from Chebyshev-Fourier functions, Jiménez-Teja & Benítez, 2012) are
mathematical orthonormal basis specially designed to model the surface
luminous distribution of galaxies. First, a segmentation map is created using
SourceExtractor (Bertin & Arnouts, 1996) to identify the regions that are
dominated by each object. Then, objects are sorted by magnitude and fitted
with CHEFs, so the light contribution from the brightest objects is removed
previous to the modeling of the fainter objects. As CHEF are orthonormal
basis, they can fit any shape, thus recovering all the light even in the case
of irregular morphologies. The CHEFs model of each object is calculated in a
circular region with radius twice the equivalent radius of the area assigned
to the object by the segmentation map. However, the flux is measured up to the
radius where the profile of the model either converges to zero or submerges
into the sky noise.

##  5 SED fitting

Table 5: SED fitting methods, templates, and assumptions used Method | SEDs | IMF | SFH | Dust | Ionization log($U$)
---|---|---|---|---|---
EAZY | SFHZ |  |  |  |
Bagpipes | BPASS+Cloudy | Kroupa et al. (1993) | delayed tau | Salim et al. (2018) |  $-4$ to $-1$
piXedfit | FSPS+Cloudy | Chabrier (2003) | double power-law | Charlot & Fall (2000) | $-2$
Prospector | FSPS+Cloudy | Chabrier (2003) | constant / non-parametric | SMC (Pei, 1992) |  $-4$ to $-1$
BEAGLE | BC03+Cloudy | Chabrier (2003) | constant | SMC (Pei, 1992) |  $-4$ to $-1$

We perform spectral energy distribution (SED) fitting with various methods to
estimate the photometric redshift and physical parameters of MACS0647–JD. The
various methods adopt different SED templates and assumptions about physical
parameters summarized in Table 5. We also match the observed clump colors to
simulated galaxies with realistic bursty star formation histories (§5.6).

###  5.1 EAZY

Our public dataset includes SED fitting results from EAZY (Brammer et al.,
2008) using recently implemented SFHZ templates with redshift-dependent star
formation histories.141414https://github.com/gbrammer/eazy-
photoz/tree/master/templates/sfhz EAZY fits non-negative linear combinations
of these templates to the observed photometry. The code is fast, analyzing
thousands of galaxies in minutes. It estimates photometric redshifts
$z=10.6^{+0.3}_{-0.2}$, $z=10.6^{+0.3}_{-0.4}$, $z=10.2^{+0.5}_{-0.6}$ (95%
C.L.) for JD1, 2, 3, respectively (A+B components combined, with F200W AB mag
25.0, 25.5, 26.2).

The fainter companion galaxy C (F200W AB mag 28.0, 27.3, 27.8 with large
uncertainties) is also a J-dropout that can be well fit to SEDs at $z=10.6$
given its larger photometric uncertainties, as we show in §6.6. The
photometric redshifts are highly uncertain, with 95% confidence ranges
0.5–10.2, 2.2–10.3, and 9.8–11.5 for JD1C, JD2C, and JD3C, respectively.

While EAZY also provides quick estimates of physical parameters, we turn to
other methods to more fully explore the parameter space and estimate values
with uncertainties for the individual clumps A and B.

###  5.2 Bagpipes

Bagpipes151515https://bagpipes.readthedocs.io (Carnall et al., 2018) fits
redshift along with a multidimensional space of physical parameters using the
MultiNest nested sampling algorithm (Feroz & Hobson, 2008; Feroz et al., 2009;
Feroz & Skilling, 2013). We run Bagpipes with various sets of assumptions.

We use BPASS v2.2.1 SED templates (Eldridge & Stanway, 2009), importantly
including binary stars, resulting in brighter rest-UV flux (Eldridge, 2020;
Eldridge & Stanway, 2022). We use the fiducial BPASS IMF imf135_300: Kroupa et
al. (1993) slope $\alpha=-2.35$ between 0.5 – 300 $M_{\odot}$ and shallower
$\alpha=-1.3$ for lower mass stars 0.1 – 0.5 $M_{\odot}$. This is close to the
shallower upper mass slope IMF of Kroupa (2002). Metallicities range from
(0.0005 – 2) $Z_{\odot}$.

We reprocess the templates using the photoionization code Cloudy c17.03
(Ferland et al., 1998, 2013, 2017) to include nebular continuum and emission
lines. We generate templates for ionization parameter $U$ ranging between
log($U$) = $-4$ to $-1$.

We assume an analytic star formation history (SFH) model “delayed $\tau$”:
SFR$(t)\propto t\ \exp{(-t/\tau)}$. SFR rises linearly, then slows before
declining exponentially, unless the free parameter $\tau$ is larger than the
formation age (as in our fits), in which case there is no decline.

For dust attenuation, we use the Salim et al. (2018) parameterization with
slope $\delta$ allowed to vary between 0 (Milky Way) and steeper $-0.45$
(Small Magellanic Cloud; SMC), and 2175Å bump strength $B$ allowed to vary
between 0 and 5 (where the Milky Way has $B=3$ and SMC has $B\sim 0$). Young
stars (age $<10$ Myr) residing in stellar birth clouds experience more dust
extinction by a factor $\eta$ in the range 1 to 3.

###  5.3 piXedfit

As an independent comparison, we also perform SED fitting using
piXedfit(Abdurro’uf et al., 2021). For SED modelling, we use Flexible Stellar
Population Synthesis (FSPS161616https://github.com/cconroy20/fsps; Conroy et
al., 2009; Leja et al., 2017), initial mass function of Chabrier (2003),
Padova isochrones (Girardi et al., 2000; Marigo & Girardi, 2007; Marigo et
al., 2008), MILES stellar spectral library (Sánchez-Blázquez et al., 2006;
Falcón-Barroso et al., 2011), and the two-component dust attenuation law by
Charlot & Fall (2000). We assume a parametric SFH model in the form of double
power-law. FSPS incorporates Cloudy code for modeling the nebular emission. We
model the attenuation due to intergalactic medium using Inoue et al. (2014)
model. We assume uniform priors for redshift ($2.0-15.0$), age ($0.01-10.0$
Gyr), $Z$ ($\log(Z/Z_{\odot}):[-2.0,0.2]$), and SFH time scale $\tau$
($0.1-32$ Gyr). The fitting with double power law SFH has two more free
parameters that control the slopes of the rising and falling star formation
episodes ($\beta$ and $\alpha$). We assume a uniform prior for these
parameters with the range of $10^{-2.0}-10^{2.0}$. For the fitting method, we
apply the Markov Chain Monte Carlo (MCMC) and set the number of walkers and
steps to be 100 and 1000, respectively.

###  5.4 Prospector

To get an independent comparison with non-parametric SFH models, we run SED
fitting using Prospector (Leja et al., 2017; Johnson et al., 2021), adopting
both constant and non-parametric SFHs. Similar to piXedfit, this code uses
FSPS stellar population synthesis models and Cloudy code to account for the
nebular emission. We assume a Chabrier (2003) IMF with mass range
$0.1-300~{}M_{\odot}$ the IGM attenuation model of Inoue et al. (2014). We
assume a uniform prior for redshift ($z=6-15$), and log-uniform priors for
stellar mass ($5\leq\log(M/M_{\odot})\leq 12$), $V$-band optical depth
assuming an SMC dust extinction law ($-3\leq\log(\tau_{V})\leq 0.7$; Pei,
1992), stellar metallicity ($-2.2\leq\log(Z/Z_{\odot})\leq-0.3$, and we assume
that the interstellar gas-phase metallicity is equal to the stellar
metallicity), and ionization parameter ($-4\leq\log(U)\leq-1$). For our
constant SFH model, we assume a log-uniform prior on formation age from 1 Myr
to the age of the universe at the redshift under consideration. Throughout
this process, we remove Ly$\alpha$ from the fitting templates.

The non-parametric SFH models implemented in Prospector are piecewise constant
functions in time. We adopt eight time bins spanning from the time of
observation to a formation redshift, $z_{\rm form}=15-30$ (uniform prior),
where the two most recent bins range from $0-3$ Myr and $3-10$ Myr and the
remaining six are spaced evenly in logarithmic lookback time. We adopt the
“continuity” prior in Prospector, which tends to weight against sharp changes
in SFR between adjacent time bins, though we note that the choice of non-
parametric prior can have a significant influence on the inferred physical
parameters (e.g., Leja et al., 2019; Tacchella et al., 2022; Whitler et al.,
2022b).

###  5.5 BEAGLE

We also perform SED fitting using BEAGLE tool (Chevallard & Charlot, 2016).
BEAGLE uses templates by Gutkin et al. (2016) which combines the 2016 version
of BC03 with the Cloudy code to incorporate nebular emission. We assume a
constant SFH model and fit for age with a uniform prior ranging from 1 Myr to
the age of the universe at the redshift under consideration. We adopt the same
priors on redshift, stellar mass, $\tau_{V}$, $Z$, and $\log(U)$ as for the
non-parametric Prospector models. We assume that the total interstellar (dust-
and gas-phase) metallicity is equal to the stellar metallicity, but note that
BEAGLE self-consistently accounts for the depletion of metals onto dust
grains, regulated in part by the dust-to-metal mass ratio ($\xi_{d}$), which
we fix to $\xi_{d}=0.3$.

###  5.6 GAINN

Finally, we identified simulated galaxies with colors similar to those
observed for MACS0647–JD to estimate its redshift and star formation history.
We analyzed detailed ENZO (Bryan et al., 2014) star-forming radiative-
hydrodynamic simulations of the early universe with synthetic photometry
generated by Barrow et al. (2020). The simulated galaxy redshifts and colors
were used as a training set for the Galaxy Assembly and Interaction Neural
Network (GAINN; Santos-Olmsted et al., 2023). Additional details are provided
in §A.3 and results are presented below.

Figure 7: Redshift likelihood distributions $P(z)$ of JD1 A+B estimated by
various methods (§6.1). Also shown are Bagpipes results for the individual
clumps A and B.  Figure 8:  Photometry and Bagpipes BPASS SED fits for JD1, 2,
3, both as observed and delensed by fiducial magnifications $\mu=8.0$, $5.3$,
$2.2$. Filled circles with errorbars give measured photometry in each filter,
and open boxes show model fluxes for each best fit SED model spectrum shown.
JWST photometry are highlighted by magenta stars. $P(z)$ of JD1, 2, 3, and the
stack one is shown in the small box in the upper panel.  Figure 9:  Star
formation rate (SFR) vs. stellar mass for MACS0647–JD and recently discovered
$z\sim 9$ – 12 candidates analyzed in JWST imaging (Furtak et al., 2022;
Bradley et al., 2022; Naidu et al., 2022; Leethochawalit et al., 2022). We
plot Bagpipes results for JD1 (A+B). The results lie along predictions for the
$z=10$ star-formation main sequence from semi-analytic modeling Yung et al.
(2019) and the DELPHI simulations (Dayal et al., 2014, 2022). Note that we
show the stellar mass estimated from delayed $\tau$ SFH for JD1 (A+B).
Possible systematic uncertainty from different assumed SFH is shown in a
dotted line.  Figure 10: Specific star-formation rate as a function of
redshift. We show the Bagpipes result for the JD1 photometry, while
acknowledging the results vary from different methods. We compare with
published results from Tasca et al. (2015, ${\rm log}(M_{*}/M_{\odot})>9.7$);
Khusanova et al. (2021, $9.6<{\rm log}(M_{*}/M_{\odot})<9.8$); Stefanon et al.
(2022, ${\rm log}(M_{*}/M_{\odot})\sim 8.4$); Topping et al. (2022); Furtak et
al. (2022); and Di Cesare et al. (2022). We also compare with predictions from
Dekel et al. (2013); Whitaker et al. (2014); Tacchella et al. (2018) and
DELPHI (Dayal et al., 2014, 2022). Note that we show the stellar mass
estimated from delayed $\tau$ SFH for JD1 (A+B). Possible systematic
uncertainty from different assumed SFH is shown in a dotted line. Figure 11:
Bagpipes SED fits to photometry of individual clumps A and B measured by
piXedfit with 3% uncertainty added in quadrature.

Figure 12:  Constraints on age, stellar mass, metallicity, and dust for JD1A
(left) and JD1B (right) from Bagpipes with $+3\%$ uncertainty. Note that the
mass estimates shown here are not delensed.  Figure 13:  Star formation
histories (SFH) of clumps A and B for the median ages estimated by each
method. The various SFH parameterizations and assumptions are summarized in
Table 7. For Bagpipes, we plot results from adding 3% photometric uncertainty.
Shaded regions indicate the 68 percentile confidence intervals.  Figure 14:
Star formation histories of simulated galaxies with colors similar to clumps A
(top) and B (bottom). Note the anti-correlation: A analogs form most stars
while most B analogs are less active, and vice versa. Time scales are the same
on both $x$ axes. Mass-weighted ages and $\chi^{2}$ values from SED fits are
given in the legend. Photometry of the simulated galaxies was measured by
Barrow et al. (2020) and matched to the observations using the GAINN deep
learning network (Santos-Olmsted et al., 2023).  Table 6: Physical properties
of MACS0647–JD estimated from Bagpipes corrected for magnification (flux
ratio).

| JD1 | JD2 | JD3 | Combined |
---|---|---|---|---|---
Formation age ($\rm Myr$) | $160^{+69}_{-69}$ | $151^{+60}_{-74}$ | $153^{+121}_{-75}$ | $177^{+73}_{-71}$ |
Mass-weighted age ($\rm Myr$) | $54^{+24}_{-23}$ | $51^{+20}_{-25}$ | $51^{+43}_{-25}$ | $59^{+25}_{-24}$ |
Stellar Mass (${\rm log}(M_{*}/M_{\odot})$) | $8.62^{+0.11}_{-0.15}$ | $8.61^{+0.10}_{-0.18}$ | $8.51^{+0.18}_{-0.22}$ | $8.65^{+0.11}_{-0.14}$ |
SFR ($M_{\odot}/{\rm yr}$) within 100 Myr | $4^{+1}_{-1}$ | $4^{+1}_{-1}$ | $3^{+1}_{-1}$ | $4^{+1}_{-1}$ |
log sSFR (${\rm yr}^{-1}$) | $-7.98^{+0.05}_{-0.09}$ | $-7.96^{+0.04}_{-0.08}$ | $-7.97^{+0.04}_{-0.16}$ | $-8.00^{+0.07}_{-0.10}$ |
Photometric Redshift | $10.64^{+0.06}_{-0.07}$ | $10.76^{+0.08}_{-0.09}$ | $10.50^{+0.14}_{-0.16}$ | $10.65^{+0.09}_{-0.10}$ |
Relative flux ($\geq\rm F200W$) | 1 | 0.66 | 0.28 | 1.94 |
Magnification (flux ratio) | 8 | 5.3 | 2.2 | 15.5 |
Magnification (lens model) | 6.9 | 6.3 | 2.1 | 15.3 |
Tangential Magnification | 4.7 | 4.4 | 1.8 |  |

††footnotetext:  Note. Magnification uncertainties are on the order of 15%
(Meneghetti et al., 2017) and are not included in the uncertainties quoted
above for stellar mass and SFR.

Table 7: Physical properties of A and B analyzed individually by various
methods assuming $z=10.6$. Photometry is measured in the brightest image JD1
by piXedfit, analyzed with and without inflated uncertainties and corrected
for magnification.

| Photometric |  |  | Agea | Stellar Mass | specific SFRb | Dust |
---|---|---|---|---|---|---|---|---
Clump | Uncertainty | Method | Star Formation History | Myr | log($M_{*}/M_{\odot}$) | Gyr-1 |  $A_{V}$ mag | $\chi^{2}$
JD1A |  $\cdots$ | Bagpipes | delayed $\tau$ exponential | $1.3\pm 0.2$ | $7.2\pm 0.1$ | $101^{+1}_{-1}$ | $0.00^{+0.01}_{-0.00}$ | $93$
| +3% | Bagpipes | delayed $\tau$ exponential | $1^{+1}_{-1}$ | $7.2^{+0.1}_{-0.1}$ | $101^{+1}_{-1}$ | $0.00^{+0.01}_{-0.00}$ | $82$
| +10% | Bagpipes | delayed $\tau$ exponential | $14^{+14}_{-9}$ | $7.7^{+0.2}_{-0.3}$ | $48^{+52}_{-22}$ | $0.01^{+0.02}_{-0.01}$ | $67$
|  $\cdots$ | piXedfit | double power-law | $23^{+19}_{-9}$ | $8.2^{+0.1}_{-0.1}$ | $8^{+9}_{-7}$ | $0.34^{+0.22}_{-0.21}$ | $105$
|  $\cdots$ | Prospector | non-parametric cont. | $43^{+25}_{-20}$ | $8.3\pm 0.1$ | $0$ | $0.01^{+0.02}_{-0.01}$ | $18^{c}$
|  $\cdots$ | Prospector | constant | $35^{+8}_{-6}$ | $8.0\pm 0.1$ | $14\pm 3$ | $0.00^{+0.00}_{-0.00}$ | $90^{c}$
|  $\cdots$ | beagle | constant | $35\pm 7$ | $8.1\pm 0.1$ | $14^{+4}_{-3}$ | $0.00^{+0.00}_{-0.00}$ | $103^{c}$
JD1B |  $\cdots$ | Bagpipes | delayed $\tau$ exponential | $70^{+49}_{-44}$ | $7.8^{+0.1}_{-0.3}$ | $11^{+16}_{-4}$ | $0.10^{+0.06}_{-0.03}$ | $15$
| +3% | Bagpipes | delayed $\tau$ exponential | $67^{+45}_{-40}$ | $7.8^{+0.2}_{-0.3}$ | $12^{+16}_{-5}$ | $0.10^{+0.07}_{-0.04}$ | $14$
| +10% | Bagpipes | delayed $\tau$ exponential | $81^{+41}_{-50}$ | $7.8^{+0.1}_{-0.3}$ | $10^{+14}_{-3}$ | $0.10^{+0.08}_{-0.05}$ | $12$
|  $\cdots$ | piXedfit | double power-law | $111^{+32}_{-30}$ | $8.3^{+0.1}_{-0.3}$ | $0^{+2}_{-0}$ | $0.25^{+0.14}_{-0.15}$ | $20$
|  $\cdots$ | Prospector | non-parametric cont. | $127^{+50}_{-58}$ | $8.1\pm 0.2$ | $3^{+10}_{-2}$ | $0.12^{+0.12}_{-0.08}$ | $2.9^{c}$
|  $\cdots$ | Prospector | constant | $3^{+35}_{-2}$ | $6.9\pm 0.2$ | $185^{+319}_{-171}$ | $0.03^{+0.03}_{-0.02}$ | $1.5^{c}$
|  $\cdots$ | beagle | constant | $10^{+49}_{-8}$ | $7.3\pm 0.6$ | $51^{+198}_{-42}$ | $0.01^{+0.03}_{-0.01}$ | $0.6^{c}$

aafootnotetext: Mass-weighted.

bbfootnotetext: Within recent 10 Myr.

ccfootnotetext: Calculated in F200W and redder photometry.

Note. Most of these SED fitting methods assume a Chabrier (2003) IMF (Table
5). BAGPIPES assumes Kroupa et al. (1993); to renormalize those results, we
multiplied the stellar masses by 0.94 (Madau & Dickinson, 2014).

##  6 Results and Discussion

###  6.1 Photometric Redshift

MACS0647–JD is confidently at $z=10.6\pm 0.3$ (Figure 7), with this range
spanning the most likely redshifts from 5 SED fitting packages as well as the
GAINN deep learning network, which estimates $z=10.48$, 10.81, 10.54 for JD1,
2, 3, respectively. The components A and B are also each independently strong
$z\sim 11$ candidates (with no significant likelihood below $z<9.5$), despite
lower SNR photometry in each individual object.

We also tried restricting $z<9$ with Bagpipes, finding significantly worse
($\chi^{2}\sim 500$) fits at $z\sim 0.2$ for JD1, 2, 3 (that reproduce the
flat NIRCam colors at 2–5 $\mu$m but miss the NIRCam F150W and F115W
photometry, also failing to drop out in bluer filters). Dusty / old galaxies
at $z\sim 2$ – 5 have SEDs that are far too red, with SEDs rising through the
near-IR.

###  6.2 Physical properties

In Table 6, we report the physical properties of MACS0647–JD treated as a
single galaxy analyzed by Bagpipes with photometry from the grizli v4 catalog
(recalibrated). SED fits are shown in Figure 8. We report results for each of
the 3 lensed images JD1, 2, 3 and for the stacked photometry, correcting SFR
and mass for magnification. Assuming A+B had the same star formation history,
this analysis estimates a mass-weighted age $60\pm 25$ Myr, with SFR $4\pm 1$
$M_{\odot}$ yr-1 averaged over 100 Myr, stellar mass between 3–6$\times
10^{8}~{}M_{\odot}$, and specific SFR $\sim$ 10 Gyr-1($\pm 10\%$). We
acknowledge the stellar masses estimates are subject to uncertainties in the
star formation history, stellar mass function, stellar metallicities, and dust
properties.

The SFR and stellar mass are consistent with the predicted stellar main
sequence from semi-analytic models Dayal et al. (2014); Yung et al. (2019);
Dayal et al. (2022) and simulations (Dekel et al., 2013; Whitaker et al.,
2014; Tacchella et al., 2018; Behroozi et al., 2019). We plot these relations
and results from other $z\sim 9$ – $12$ candidates measured in JWST
observations in Figure 9.

The specific SFR is also consistent with predictions at this redshift as shown
in Figure 10. Note in these model predictions (Dekel et al., 2013; Whitaker et
al., 2014; Tacchella et al., 2018; Behroozi et al., 2019; Dayal et al., 2022),
sSFR is relatively flat at high redshifts, increasing only 0.2 dex from $z=6$
to 11. This suggests a significant role for mergers in the early universe;
sSFR(z) would continue to rise more as $\propto(1+z)^{2.25}$ if growth were
dominated by cold-mode accretion (e.g., Dekel et al., 2009).

###  6.3 Components A and B: Ages, Dust, and Mass

In Table 7, we report results for components A and B analyzed individually by
various SED fitting methods with photometry from piXedfit. The fiducial values
are organized in Table 8. SED fits from Bagpipes are plotted in Figure 11. The
corner plots of A and B are provided in Figure 12. Star formation histories
from SED fitting methods are plotted in Figure 13. Star formation histories
from simulated galaxies matching the colors of A and B using GAINN are plotted
in Figure 14.

B’s redder color may be explained by age and/or dust. Results vary depending
on the method and assumptions, including star formation history. Dust is
negligible ($A_{V}<0.02$ mag) for A in most analyses, and slightly higher
($A_{V}\sim 0.1$ mag) for B, assuming steep SMC-like attenuation strongly
suppressing the rest-UV.

Stellar mass estimates are on the order of $10^{8}M_{\odot}$ with some
agreement on higher mass for clump A by a factor of 2 or more (e.g., A
$\sim$$2\times 10^{8}~{}M_{\odot}$; B $\sim$$10^{8}~{}M_{\odot}$).

Mass-weighted ages from the SED fitting methods range up to $\sim$ 50 Myr and
$\sim$ 100 Myr for A and B, respectively. GAINN analog simulated galaxies,
similarly, have mass-weighted ages $50\pm 5$ Myr and $125^{+24}_{-12}$ Myr for
A and B, respectively.

B’s SED was relatively rare among the simulated galaxies. It was best matched
by galaxies that formed most of their stars over 80 Myr prior to observation,
then either remained less active ($<0.01~{}M_{\odot}$ yr-1) or perhaps had
some shorter burst of star formation. The simulated galaxies with colors
similar to A had star formation dissimilar: bursty during that period when B
was less active.

JD1A is intrinsically very blue ($\beta\sim-2.6\pm 0.1$) as measured with a
power-law fit to the F200W, F277W, and F356W photometry measured by piXedfit,
where $\beta$ is the rest-frame UV continuum slope
$F_{\lambda}\propto\lambda^{\beta}$ (or $F_{\nu}\propto\lambda^{\beta+2}$). We
measure $\beta=-2.69$ without PSF correction and $\beta=-2.54$ after
correcting for point source encircled energy within $r=0.2\arcsec$ (see §4.1).

Other recent JWST observations have revealed even bluer slopes ($\beta\sim-3$)
in galaxies at $z\sim 7$ – 8.5 (Topping et al., 2022) and in a candidate
$z\sim 16$ galaxy (Furtak et al., 2022), all with stellar masses of the order
of $10^{8}~{}M_{\odot}$. Topping et al. (2022) found these blue colors
required large escape fractions $f_{\rm esc,H\,{\sc ii}}\sim 0.6$ – 0.8 of
photons leaking directly from stellar H ii regions, bypassing nebular
reprocessing. Our measured $\beta\sim-2.6\pm 0.1$ is slightly redder and can
be fit by our SED models that all assume $f_{\rm esc}=0$. Nevertheless, it is
in the regime where some significant $f_{\rm esc}$ should be considered to
avoid biasing age and mass measurements.

Binary stars are important to include in SED modeling as in BPASS, especially
for such blue galaxies (Eldridge, 2020; Eldridge & Stanway, 2022). Binary
interactions produce more Wolf–Rayet / helium stars at later ages, generating
more energetic photons. Thus blue observed SEDs may be fit well by older (tens
of Myr) BPASS templates including binaries, whereas templates without binaries
may require very young ages ($<10$ Myr).

We also note uncertainty in the photometry and some variation in $\beta$
measured by the various methods and in the three lensed images. Ultimately,
upcoming NIRSpec spectroscopy will improve measures of $\beta$, age, and
reveal other signatures of large escape fractions.

Table 8: Estimated clump properties adopting fiducial stellar mass and star
formation rate

Clump | Radius | Stellar Mass | Stellar Mass Density | SFR | SFR Density
---|---|---|---|---|---
JD1A | 70${}^{+24}_{-24}\,$pc | $10^{8}M_{\odot}$ | 1800 $M_{\odot}$ pc-2 | 1 $M_{\odot}$ yr-1 | 18 $M_{\odot}$ yr-1 kpc-2
JD1B | 20${}^{+8}_{-5}\,$pc | $6\times 10^{7}M_{\odot}$ | 12000 $M_{\odot}$ pc-2 | 0.6 $M_{\odot}$ yr-1 | 120 $M_{\odot}$ yr-1 kpc-2

††footnotetext:  Note. The estimated stellar mass and SFR vary from different
SED fitting packages under different assumptions (e.g., star formation
history). The uncertainties of stellar mass density and SFR density may be up
to 200%.

###  6.4 Stellar Mass and SFR Densities

The stellar complexes in MACS0647–JD are very dense with $\sim
10^{8}\,M_{\odot}$ stellar mass packed into effective radii of $\sim$
70${}^{+24}_{-24}\,$ and 20${}^{+8}_{-5}\,$ pc for A and B, respectively.
Assuming fiducial masses $10^{8}$ and $6\times 10^{7}\,M_{\odot}$ for A and B,
respectively, the stellar mass surface densities $\Sigma_{\rm eff}$ are
roughly on the order of $\sim$2000 and $\sim$12000 $M_{\odot}$ pc-2, where
$\Sigma_{\rm eff}=(M/2)/(\pi R_{M/2}^{2})$ and the half-mass radius
$R_{M/2}=(4/3)R_{\rm eff}$.171717The factor of $4/3$ might not be warranted
since these are much larger than star clusters, in which case the densities
would increase by a factor of $\sim$ 2\. See Portegies Zwart et al. (2010).
These are higher than the highest density $\sim$1800 $M_{\odot}$ pc-2 reported
by Chen et al. (2022) because their size measurements, unaided by lensing,
were only sensitive to structures with radii $>150$ pc. The density for clump
B is just an order of magnitude less than the maximal density
$10^{5}~{}M_{\odot}$ pc-2 reported by Hopkins et al. (2010a).

A similar rough estimate of SFR densities yields $\sim$ 20 and $\sim$ 120
$M_{\odot}\,$yr-1 kpc-2. These are high values, though less than the highest
values $>1000~{}M_{\odot}$ yr-1 kpc-2 reported for SMGs.

###  6.5 Galaxy clumps or merger?

The stellar components A and B may be two merging galaxies, or they may be two
clumps that formed together in situ $\sim 400\,{\rm pc}$ apart within a single
galaxy. We cannot distinguish these scenarios with the current data.

Given their masses $\sim 10^{8}\,M_{\odot}$, they would affect their
surroundings such that we would expect them to form at the same time within a
galaxy. A significant age difference would suggest they are separate galaxies
now merging. We cannot conclusively distinguish the ages of A and B given the
current data, though the simulated analog galaxies at similar redshfit and SED
fitting do strongly suggest star formation to be dissimilar (see A.3).

MACS0647–JD was discovered in CLASH imaging with a search volume of a few
times 1000 Mpc3 = (10 cMpc)3 at $z\sim 11$ (Coe et al., 2013). We employ the
Astraeus cosmological simulations (Hutter et al., 2021) to calculate the
likelihood of finding such a merger within that search volume. With a box-size
of (230 cMpc)3 and a minimum resolved halo mass of $M_{h}\sim
10^{8.6}~{}M_{\odot}$, these simulations are ideally suited for such
statistics. We find 0.176 mergers in a (10 cMpc)3 volume for systems such as
JD1 and JD2 and 0.056 mergers per (10 cMpc)3 for three clumps with $M_{*}$
$\sim$ $10^{8-9}\,M_{\odot}$ (Legrand et al., 2022).

Dust may also contribute to the different colors observed between A and B.
Clumps are often obscured by different amounts of dust within a galaxy.
Atacama Large Millimeter/submillimeter Array (ALMA) observations of $z\sim 7$
galaxies reveal spatially varying dust that is sometimes even offset from the
stars observed in the rest-UV (Bowler et al., 2022; Dayal et al., 2022). JWST
observations of $z\sim 6-8$ galaxies in blank fields reveal clumpy
morphologies are common; each galaxy has a few multi-colored star-forming
complexes separated by $\sim 300$ – $4300\,{\rm pc}$ with various ages, dust
reddening, and masses (Chen et al., 2022).

The ground-based spectroscopic survey VIMOS UltraDeep Survey (VUDS) found
21–25% of $z\sim 2-6$ galaxies are dominated by two massive clumps, each
$\sim$$10^{9}-10^{10}~{}M_{\odot}$, with smaller fractions of galaxies having
3, 4, or more clumps (Ribeiro et al., 2017). Major mergers are invoked to
explain the galaxies with two massive clumps, while disk instability can
explain the formation of 3 or more smaller clumps in situ.

Figure 15: Candidate companion C is fainter and the photometric redshift is
less clear, but its photometry can be well fit by SEDs at $z=10.6$. EAZY SED
fits are shown for JD1C, JD2C, and JD3C, left to right. Their redshift
likelihood distributions $P(z)$ are shown in the insets before fixing their
redshifts to $z=10.6$ for the SED fits shown.

###  6.6 A possible companion

The candidate companion galaxy C is also a J-band dropout with three lensed
images at the predicted locations for a galaxy 3 kpc away at $z\sim 11$. It is
$>2$ mags fainter, so the photometric redshifts are more uncertain. In Figure
15, we show the photometry for JD1C, JD2C, and JD3C can all be well fit with
EAZY SEDs assuming $z=10.6$. (This is also the most likely redshift for JD3C,
though it is not for JD1C and JD2C.)

The redshift can also be constrained from strong lens mass modeling. Both of
our lens models (§3.1) find the observed lensed image locations are best fit
by high-redshift solutions $z\sim 11$.

###  6.7 Comparisons to Simulated Galaxies

We compare our results to various expectations from large cosmological semi-
analytic models (SAMs), an N-body cosmological simulation, and high-resolution
zoom-in hydrodynamic simulations of the early universe.

We first compare to the DELPHI semi-analytic model (Dayal et al., 2014, 2022).
In brief, this model reconstructs galaxy halo assembly histories from $z\sim
40$ – 4.5, tracking buildup of gas and star formation, including feedback.
With minimal free parameters and calibration, it reproduces observed high-$z$
luminosity functions, stellar mass functions, and ALMA dust estimates. Details
are provided in §A.2.

Given a stellar mass of $10^{8}$ ($10^{9}$) $M_{\odot}$ at $z\sim 10.6$,
DELPHI predicts a host halo mass $M_{h}\sim 10^{10}$ ($10^{11}$) $M_{\odot}$,
absolute UV magnitude $M_{\rm UV}\sim-19.5$ ($-20$), dust $A_{V}\sim 0.03$
(0.12) mag, and a stellar radius $\sim$ 70 (350) pc for galaxies at $z\sim
10$, consistent with our observations, especially for the lower end stellar
mass $10^{8}~{}M_{\odot}$. Finally, this model predicts stellar mass-weighted
ages that range between 35–180 Myr for galaxies of a similar mass at $z\sim
10$; the range of ages reflects the varied assembly histories.

These small amounts of dust are also consistent with recent modeling by
Ferrara et al. (2022) suggesting that negligible dust at these redshifts could
help explain the unexpectedly large numbers of $z\sim 10$ – 14 candidates
reported in early JWST observations.

Next, we consider the merging galaxies from a hydrodynamic simulation (Barrow
et al., 2017) presented in Figure 6 that bears a resemblance to MACS0647–JD
A+B and C. This was the most massive halo in that simulation, and it has a
total stellar mass $4\times 10^{7}~{}M_{\odot}$. The analog C is connected by
a faint filament of stars and gas. This configuration was likely the result of
previous galaxy mergers, including A+B, as evidenced by hot regions tracing
supernova remnants.

Within a separate hydrodynamic simulation of a 66 Mpc3 co-moving volume with
adaptive mesh refinement resolution sufficient to track gas down to 0.25 pc at
$z=12$ and form individual Population III stars as well as metal-enriched star
clusters (Santos-Olmsted et al., 2023), we perform a more thorough search for
simulated galaxies with colors similar to A and B. The best-matching analogs
have mass-weighted ages of $\sim$ 50 and $\sim$ 125 Myr, with B having little
or no SFR within the past 100 Myr before observation. Bursty SFHs with dormant
periods of several 10 Myr are common in these simulations. Observationally,
the question is whether we observe them when they are active with SFR in the
past 10 Myr and thus brightest in the rest-UV.

JD1A’s photometry was well matched to SEDs from the simulation (Santos-Olmsted
et al., 2023) showing routine bursts of star formation, while JD1B showed
clear evidence of suppressed star formation with a relatively flat UV slope
and weaker evidence for the presence of emission lines. The close projected
distance of only 400 pc in a halo that should be several kpc wide for stellar
population of this mass might imply that the two regions formed in the same
halo, but the SED fits SFHs with suppressed star formation for several
dynamical times in only B. The difference in SFHs implies that both halos were
subject to independent radiative and dynamical environments and likely formed
much farther apart than 400 pc before coming closer or alternatively, both
objects may be farther apart than their projected separation despite their
coincident redshift. Both scenarios, the SED model and the simulation suggest
an in-progress merger. This interaction merits further study with models tuned
to investigate bursty star formation events and may yield more insight into
high-redshift galaxy interactions and mergers.

###  6.8 Prospects of future JWST observations

The physical properties of MACS0647–JD inferred by our JWST NIRCam
observations indicate that future JWST spectroscopy should allow the detection
of several strong emission lines which would make it possible to improve
constraints on the metallicity, gas ionization state, dust reddening, and star
formation history of this intriguing $z\approx 11$ system. Based on the
photometric redshift, the planned JWST/NIRSpec prism observations extending to
5.3$\mu$m ($\sim$4300Å rest-frame) may detect strong emission lines like [C
iii] $\lambda$1908, [O ii] $\lambda$3727, H$\gamma$ and [Ne iii]
$\lambda$3869+H$\zeta$+HeI $\lambda$3889 (blended).

Other strong rest-frame optical emission lines like [O iii] $\lambda$5007 and
H$\alpha$ will fall in the wavelength domain of JWST MIRI. The inferred SFR of
MACS0647–JD suggests that both [O iii] $\lambda$5007 and H$\alpha$ may be
detected with MIRI medium-resolution spectroscopy (MRS) targeting JD1, which
would then also allow simultaneous MIRI imaging of part of the MACS0647
cluster field. Such MIRI imaging could, depending on the position angle, also
cover JD3, which is predicted to be sufficiently bright for detection in both
F560W and F770W.

##  7 Conclusions

In this study, we report on public JWST imaging observations of the $z\sim 11$
galaxy MACS0647–JD taken with 6 NIRCam filters (F115W, F150W, F200W, F277W,
F356W, and F444W) by GO program 1433 (PI Coe). Three lensed images are
observed with magnifications $\sim$ 8, 5, and 2 and F356W AB mags of 25.1,
25.6, 26.6. The delensed F356W magnitude is 27.3, with $M_{UV}=-20.4\pm 17\%$.
MACS0647–JD is a J-band dropout appearing in all filters redward of F115W. Its
photometric redshift is $z=10.6\pm 0.3$ as estimated by 6 different methods.

MACS0647–JD is spatially resolved into two components A and B separated by
$\sim$ 400 pc in projection. They may be merging galaxies or two clumps that
formed in situ within one galaxy.

Component A is brighter and very blue ($\beta\sim-2.6\pm 0.1$), dust-free with
a delensed radius $\sim$ 70${}^{+24}_{-24}\,$pc and mass-weighted age $\sim$
50 Myr. Component B is smaller and redder with perhaps some dust $A_{V}\sim
0.1$ mag, a delensed radius $\sim$ 20${}^{+8}_{-5}\,$pc, and mass-weighted age
$\sim$ 100 Myr. Simulated galaxies with similar colors as observed for A and B
at similar redshift have star formation histories to be dissimilar despite
their proximity, which is consistent with our SED fitting results, suggesting
they formed some distance apart, perhaps as separate galaxies observed now as
they were on their way to merge.

Both have stellar masses $\sim$$10^{8}\,M_{\odot}$ with A likely more massive
by a factor of 2 or so. With star formation rates on the order of 1
$M_{\odot}$ yr-1 averaged over the past 10 Myr and specific SFRs $\sim$10
Gyr-1, these galaxies are consistent with expectations for the stellar main
sequence at $z\sim 11$. Given their small radii $<100$ pc, they have very high
stellar mass surface densities, up to $\sim$$10^{4}\,M_{\odot}$ pc-2, with
correspondingly large SFR surface densities up to $\sim$$~{}100\,M_{\odot}$
yr-1 kpc-2. These are large, though not exceeding theoretical limits or values
measured for other extreme objects.

A small candidate companion galaxy C is identified $\sim$ 3 kpc away. Three
lensed images of C are at the expected locations are all J-band dropouts.
While fainter (F356W AB mag $\sim$28) with more uncertain photometry, its SED
consistent with $z\sim 10.6$.

The NIRCam imaging spans 1–5 $\mu$m to rest-frame 4300 Å at $z=10.6$. F444W is
only partially redward of the Balmer break, limiting our ability to estimate
ages and stellar masses. Additional observations with the reddest NIRCam
filter F480M and the NIRSpec MSA PRISM are upcoming and planned for January
2023.

##  8 Acknowledgments

We are grateful and indebted to all 20,000 people who worked to make JWST an
incredible discovery machine.

We dedicate these JWST observations to Rob Hawkins, former lead developer of
the Astronomer’s Proposal Tool (APT). Rob lost his life in November 2020 while
astronomers around the world were using APT to prepare observations we
proposed for JWST Cycle 1.

This work is based on observations made with the NASA/ESA/CSA James Webb Space
Telescope (JWST) and Hubble Space Telescope (HST). The data were 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), Inc., under NASA contract NAS
5-03127 for JWST. These observations are associated with program JWST GO 1433
and HST GO 9722, 10493, 10793, and 12101.

TH and A were funded by a grant for JWST-GO-01433 provided by STScI under NASA
contract NAS5-03127. LW acknowledges support from the National Science
Foundation Graduate Research Fellowship under Grant No. DGE-2137419. AA
acknowledges support from the Swedish Research Council (Vetenskapsrådet
project grants 2021-05559). PD acknowledges support from the NWO grant
016.VIDI.189.162 (“ODIN”) and the European Commission’s and University of
Groningen’s CO-FUND Rosalind Franklin program and warmly thanks the Institute
for Advanced Study (IAS) Princeton, where a part of this work was carried out,
for their generous hospitality and support through the Bershadsky Fund. The
Cosmic Dawn Center is funded by the Danish National Research Foundation (DNRF)
under grant #140. EZ and AV ackowledge support from the Swedish National Space
Agency. MB acknowledges support from the Slovenian national research agency
ARRS through grant N1-0238. MO acknowledges support from JSPS KAKENHI Grant
Numbers JP22H01260, JP20H05856, JP20H00181, JP22K21349. AZ, AKM and LJF
acknowledge 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), and by the Ministry of Science &
Technology, Israel. EV and MN acknowledge financial support through grants
PRIN-MIUR 2017WSCC32, 2020SKSTHZ and INAF “main-stream” grants 1.05.01.86.20
and 1.05.01.86.31. Y.J-T acknowledges financial support from the European
Union’s Horizon 2020 research and innovation programme under the Marie
Sklodowska-Curie grant agreement No 898633, the MSCA IF Extensions Program of
the Spanish National Research Council (CSIC), and the State Agency for
Research of the Spanish MCIU through the Center of Excellence Severo Ochoa
award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709). ACC thanks
the Leverhulme Trust for their support via a Leverhulme Early Career
Fellowship.

##  Appendix A Appendix

###  A.1 Photometry measurement for individual clumps

In Section. 4, we measure the photometry for components A and B using
different methods including piXedfit, IMFIT, and CHEFs. Only the photometry
from piXedfit was used for SED fitting to estimate physical properties. Here
we provide the comparison among three different methods, which is shown in
Figure 16. We also test the SED fitting for the photometry from IMFIT and
CHEFs. The results are similar to the result using piXedfit photometry.

Figure 16:  Photometry of JD1A and JD1B measured from different methods,
piXedfit, IMFIT, and CHEFs. With 3% and 10% uncertainty added in quadrature
are shown for piXedfit.

###  A.2 DELPHI Semi-Analytic Model

In brief, the DELPHI semi-analytic model (Dayal et al., 2014, 2022) uses a
binary merger tree approach to build the dark matter assembly histories of
$z\sim 4.5$ galaxies with halo masses ${\rm log}(M_{h}/M_{\odot})$ = 8 – 14 up
to $z\sim 40$. It then jointly tracks the build-up of dark matter halos and
their baryonic components (gas, stellar, metal and dust mass) between $z\sim
40-4.5$ including the impact of both internal (supernova) and external
(reionziation) feedback; here we consider a case that ignores reionization
feedback since reionization affects $\lesssim 20$% of the volume of the
Universe at $z\sim 10.5$ (Dayal et al., 2020). The key strength of this model
lies in its minimal free parameters (the star formation efficiency and
fraction of supernova energy coupling to gas) and the fact that is it
baselined against all available high-$z$ datasets including the evolving
ultra-violet luminosity function, the stellar mass function and against the
most recent dust estimates at $z\sim 7$ from the REBELS (Reionization Era
Bright Emission Line Survey) ALMA large program (Bouwens et al., 2022).

###  A.3 GAINN Analog Simulated Galaxies

Synthetic fluxes from JWST’s wideband filters F115W, F150W, F200W, F277W,
F356W, and F444W were used as a training set for photometric redshift
predictions of the combined fluxes of the A and B objects using the Galaxy
Assembly and Interaction Neural Network (GAINN) method (Santos-Olmsted et al.,
2023), which trains deep convolutional neural networks on synthetic photometry
created in post processing from in-situ star-forming ENZO (Bryan et al., 2014)
radiative-hydrodynamic simulations. GAINN was originally designed for
redshifts higher than 11.4 and so star formation histories were shifted
forward in time by 50, 100, and 150 Myr to produce a training set. Then a
20-layer network was trained on the approximately 12,000 SEDs in the set that
fell between $z=12$ and $z=10$ to accommodate the likely redshift of
MACS0647–JD, and achieved a mean absolute error of 0.0261 in the validation
set. Predicted redshifts for MACS0647–JD were consistent with galaxies at
$z\sim 10.6$, returning a value of $z=10.6417$ for object A and a value of
$z=10.5614$ for object B.

Additionally, $\chi^{2}$ SED-fitting to GAINN simulated galaxies was performed
on JD1A and JD1B’s fluxes in F200W, F277W, F356W, and F444W, which focus on
the rest-UV slope of both objects. Fitting was accomplished by first shifting
over 10,000 synthetic observations in GAINN to $z=10.6$ and then using
relative synthetic flux to create a mass and redshift-independent comparison.
Then, the synthetic flux of the SED was scaled to the observed flux of JD1A
and JD1B and $\chi^{2}$ values were calculated for the other three bands. We
report four star formation histories corresponding to the lowest values of
$\chi^{2}$ for both JD1A and JD1B along with their mass weighted mean stellar
age after restricting our output to the best fit result in any particular halo
tree branch.

JD1B’s spectra was relatively rare in the simulation, resulting in various
predictions with higher squared error, but it often matched to star formation
histories with the strongest episodes of star formation ending earlier than
100 Myr before the observation, with some results showing a more recent burst.
Predicted mean stellar ages were between 100 and 160 Myr, which is consistent
with an absence of young stars and the flat UV slope of JD1B.

All histories matched to JD1A featured bursty episodes of star formation
peaking between 50 and 100 Myr before the observation, followed by a turn off
and a resumption of star formation at the time of observation. Predictions for
mean stellar age also converged between 45 and 80 Myr, which was consistent
with the observed blue UV slope. All matched SED’s had strong emission lines,
implying that previous episodes of star formation well-enriched the ISM.

## References

  * Abdurro’uf et al. (2021) Abdurro’uf, Lin, Y.-T., Wu, P.-F., & Akiyama, M. 2021, ApJS, 254, 15, doi: 10.3847/1538-4365/abebe2
  * Abdurro’uf et al. (2022) —. 2022, piXedfit: Analyze spatially resolved SEDs of galaxies, Astrophysics Source Code Library, record ascl:2207.033.  http://ascl.net/2207.033
  * Abdurro’uf et al. (2023) Abdurro’uf, Coe, D., Jung, I., et al. 2023, ApJ, 945, 117, doi: 10.3847/1538-4357/acba06
  * Adams et al. (2022) Adams, N. J., Conselice, C. J., Ferreira, L., et al. 2022, arXiv e-prints, arXiv:2207.11217.  https://arxiv.org/abs/2207.11217
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f
  * Astropy Collaboration et al. (2022) Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, ApJ, 935, 167, doi: 10.3847/1538-4357/ac7c74
  * Atek et al. (2022) Atek, H., Shuntov, M., Furtak, L. J., et al. 2022, arXiv e-prints, arXiv:2207.12338.  https://arxiv.org/abs/2207.12338
  * Barbary (2016) Barbary, K. 2016, Journal of Open Source Software, 1, 58, doi: 10.21105/joss.00058
  * Barnes (1992) Barnes, J. E. 1992, ApJ, 393, 484, doi: 10.1086/171522
  * Barrow et al. (2020) Barrow, K. S. S., Robertson, B. E., Ellis, R. S., et al. 2020, ApJ, 902, L39, doi: 10.3847/2041-8213/abbd8e
  * Barrow et al. (2017) Barrow, K. S. S., Wise, J. H., Norman, M. L., O’Shea, B. W., & Xu, H. 2017, MNRAS, 469, 4863, doi: 10.1093/mnras/stx1181
  * Behroozi et al. (2019) Behroozi, P., Wechsler, R. H., Hearin, A. P., & Conroy, C. 2019, MNRAS, 488, 3143, doi: 10.1093/mnras/stz1182
  * Bell et al. (2006) Bell, E. F., Phleps, S., Somerville, R. S., et al. 2006, ApJ, 652, 270, doi: 10.1086/508408
  * Belokurov et al. (2018) Belokurov, V., Erkal, D., Evans, N. W., Koposov, S. E., & Deason, A. J. 2018, MNRAS, 478, 611, doi: 10.1093/mnras/sty982
  * Bertin & Arnouts (1996) Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393, doi: 10.1051/aas:1996164
  * Bonaca et al. (2020) Bonaca, A., Conroy, C., Cargile, P. A., et al. 2020, ApJ, 897, L18, doi: 10.3847/2041-8213/ab9caa
  * Bouwens et al. (2014) Bouwens, R. J., Bradley, L., Zitrin, A., et al. 2014, ApJ, 795, 126, doi: 10.1088/0004-637X/795/2/126
  * Bouwens et al. (2022) Bouwens, R. J., Smit, R., Schouws, S., et al. 2022, ApJ, 931, 160, doi: 10.3847/1538-4357/ac5a4a
  * Bowler et al. (2022) Bowler, R. A. A., Cullen, F., McLure, R. J., Dunlop, J. S., & Avison, A. 2022, MNRAS, 510, 5088, doi: 10.1093/mnras/stab3744
  * Bradley et al. (2014) Bradley, L. D., Zitrin, A., Coe, D., et al. 2014, ApJ, 792, 76, doi: 10.1088/0004-637X/792/1/76
  * Bradley et al. (2022) Bradley, L. D., Coe, D., Brammer, G., et al. 2022, arXiv e-prints, arXiv:2210.01777.  https://arxiv.org/abs/2210.01777
  * Brammer et al. (2022) Brammer, G., Strait, V., Matharu, J., & Momcheva, I. 2022, grizli, 1.5.0, Zenodo, doi: 10.5281/zenodo.6672538
  * Brammer et al. (2008) Brammer, G. B., van Dokkum, P. G., & Coppi, P. 2008, ApJ, 686, 1503, doi: 10.1086/591786
  * Brammer et al. (2013) Brammer, G. B., van Dokkum, P. G., Illingworth, G. D., et al. 2013, ApJ, 765, L2, doi: 10.1088/2041-8205/765/1/L2
  * Broadhurst et al. (2005) Broadhurst, T., Benítez, N., Coe, D., et al. 2005, ApJ, 621, 53, doi: 10.1086/426494
  * Bryan et al. (2014) Bryan, G. L., Norman, M. L., O’Shea, B. W., et al. 2014, ApJS, 211, 19, doi: 10.1088/0067-0049/211/2/19
  * Burke et al. (2015) Burke, C., Hilton, M., & Collins, C. 2015, MNRAS, 449, 2353, doi: 10.1093/mnras/stv450
  * Carnall et al. (2018) Carnall, A. C., McLure, R. J., Dunlop, J. S., & Davé, R. 2018, MNRAS, 480, 4379, doi: 10.1093/mnras/sty2169
  * Castellano et al. (2022) Castellano, M., Fontana, A., Treu, T., et al. 2022, arXiv e-prints, arXiv:2207.09436.  https://arxiv.org/abs/2207.09436
  * Chabrier (2003) Chabrier, G. 2003, PASP, 115, 763, doi: 10.1086/376392
  * Chan et al. (2017) Chan, B. M. Y., Broadhurst, T., Lim, J., et al. 2017, ApJ, 835, 44, doi: 10.3847/1538-4357/835/1/44
  * Charlot & Fall (2000) Charlot, S., & Fall, S. M. 2000, ApJ, 539, 718, doi: 10.1086/309250
  * Chen et al. (2022) Chen, Z., Stark, D. P., Endsley, R., et al. 2022, arXiv e-prints, arXiv:2207.12657.  https://arxiv.org/abs/2207.12657
  * Chevallard & Charlot (2016) Chevallard, J., & Charlot, S. 2016, MNRAS, 462, 1415, doi: 10.1093/mnras/stw1756
  * Claeyssens et al. (2022) Claeyssens, A., Adamo, A., Richard, J., et al. 2022, arXiv e-prints, arXiv:2208.10450.  https://arxiv.org/abs/2208.10450
  * Coe et al. (2012) Coe, D., Umetsu, K., Zitrin, A., et al. 2012, ApJ, 757, 22, doi: 10.1088/0004-637X/757/1/22
  * Coe et al. (2013) Coe, D., Zitrin, A., Carrasco, M., et al. 2013, ApJ, 762, 32, doi: 10.1088/0004-637X/762/1/32
  * Coe et al. (2019) Coe, D., Salmon, B., Bradač, M., et al. 2019, ApJ, 884, 85, doi: 10.3847/1538-4357/ab412b
  * Connor et al. (2017) Connor, T., Donahue, M., Kelson, D. D., et al. 2017, ApJ, 848, 37, doi: 10.3847/1538-4357/aa8ad5
  * Conroy et al. (2009) Conroy, C., Gunn, J. E., & White, M. 2009, ApJ, 699, 486, doi: 10.1088/0004-637X/699/1/486
  * Dayal et al. (2014) Dayal, P., Ferrara, A., Dunlop, J. S., & Pacucci, F. 2014, MNRAS, 445, 2545, doi: 10.1093/mnras/stu1848
  * Dayal et al. (2020) Dayal, P., Volonteri, M., Choudhury, T. R., et al. 2020, MNRAS, 495, 3065, doi: 10.1093/mnras/staa1138
  * Dayal et al. (2022) Dayal, P., Ferrara, A., Sommovigo, L., et al. 2022, MNRAS, 512, 989, doi: 10.1093/mnras/stac537
  * Dekel et al. (2013) Dekel, A., Zolotov, A., Tweed, D., et al. 2013, MNRAS, 435, 999, doi: 10.1093/mnras/stt1338
  * Dekel et al. (2009) Dekel, A., Birnboim, Y., Engel, G., et al. 2009, Nature, 457, 451, doi: 10.1038/nature07648
  * Di Cesare et al. (2022) Di Cesare, C., Graziani, L., Schneider, R., et al. 2022, arXiv e-prints, arXiv:2209.05496.  https://arxiv.org/abs/2209.05496
  * Diego et al. (2005) Diego, J. M., Protopapas, P., Sandvik, H. B., & Tegmark, M. 2005, MNRAS, 360, 477, doi: 10.1111/j.1365-2966.2005.09021.x
  * Diego et al. (2007) Diego, J. M., Tegmark, M., Protopapas, P., & Sandvik, H. B. 2007, MNRAS, 375, 958, doi: 10.1111/j.1365-2966.2007.11380.x
  * Donahue et al. (2015) Donahue, M., Connor, T., Fogarty, K., et al. 2015, ApJ, 805, 177, doi: 10.1088/0004-637X/805/2/177
  * Donnan et al. (2022) Donnan, C. T., McLeod, D. J., Dunlop, J. S., et al. 2022, arXiv e-prints, arXiv:2207.12356.  https://arxiv.org/abs/2207.12356
  * Duncan et al. (2019) Duncan, K., Conselice, C. J., Mundy, C., et al. 2019, ApJ, 876, 110, doi: 10.3847/1538-4357/ab148a
  * Ebeling et al. (2007) Ebeling, H., Barrett, E., Donovan, D., et al. 2007, ApJ, 661, L33, doi: 10.1086/518603
  * Eichner et al. (2013) Eichner, T., Seitz, S., Suyu, S. H., et al. 2013, ApJ, 774, 124, doi: 10.1088/0004-637X/774/2/124
  * Eldridge (2020) Eldridge, J. J. 2020, Astronomy and Geophysics, 61, 2.24, doi: 10.1093/astrogeo/ataa029
  * Eldridge & Stanway (2009) Eldridge, J. J., & Stanway, E. R. 2009, MNRAS, 400, 1019, doi: 10.1111/j.1365-2966.2009.15514.x
  * Eldridge & Stanway (2022) —. 2022, ARA&A, 60, 455, doi: 10.1146/annurev-astro-052920-100646
  * Ellison et al. (2019) Ellison, S. L., Viswanathan, A., Patton, D. R., et al. 2019, MNRAS, 487, 2491, doi: 10.1093/mnras/stz1431
  * Erwin (2015) Erwin, P. 2015, ApJ, 799, 226, doi: 10.1088/0004-637X/799/2/226
  * Falcón-Barroso et al. (2011) Falcón-Barroso, J., Sánchez-Blázquez, P., Vazdekis, A., et al. 2011, A&A, 532, A95, doi: 10.1051/0004-6361/201116842
  * Ferland et al. (1998) Ferland, G. J., Korista, K. T., Verner, D. A., et al. 1998, PASP, 110, 761, doi: 10.1086/316190
  * Ferland et al. (2013) Ferland, G. J., Porter, R. L., van Hoof, P. A. M., et al. 2013, Rev. Mexicana Astron. Astrofis., 49, 137.  https://arxiv.org/abs/1302.4485
  * Ferland et al. (2017) Ferland, G. J., Chatzikos, M., Guzmán, F., et al. 2017, Rev. Mexicana Astron. Astrofis., 53, 385\.  https://arxiv.org/abs/1705.10877
  * Feroz & Hobson (2008) Feroz, F., & Hobson, M. P. 2008, MNRAS, 384, 449, doi: 10.1111/j.1365-2966.2007.12353.x
  * Feroz et al. (2009) Feroz, F., Hobson, M. P., & Bridges, M. 2009, MNRAS, 398, 1601, doi: 10.1111/j.1365-2966.2009.14548.x
  * Feroz & Skilling (2013) Feroz, F., & Skilling, J. 2013, in American Institute of Physics Conference Series, Vol. 1553, Bayesian Inference and Maximum Entropy Methods in Science and Engineering: 32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. U. von Toussaint, 106–113, doi: 10.1063/1.4819989
  * Ferrara et al. (2022) Ferrara, A., Pallottini, A., & Dayal, P. 2022, arXiv e-prints, arXiv:2208.00720.  https://arxiv.org/abs/2208.00720
  * Ferreira et al. (2022) Ferreira, L., Adams, N., Conselice, C. J., et al. 2022, arXiv e-prints, arXiv:2207.09428.  https://arxiv.org/abs/2207.09428
  * Finkelstein et al. (2022) Finkelstein, S. L., Bagley, M. B., Arrabal Haro, P., et al. 2022, arXiv e-prints, arXiv:2207.12474.  https://arxiv.org/abs/2207.12474
  * Fogarty et al. (2017) Fogarty, K., Postman, M., Larson, R., Donahue, M., & Moustakas, J. 2017, ApJ, 846, 103, doi: 10.3847/1538-4357/aa82b9
  * Furtak et al. (2022) Furtak, L. J., Shuntov, M., Atek, H., et al. 2022, arXiv e-prints, arXiv:2208.05473.  https://arxiv.org/abs/2208.05473
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1, doi: 10.1051/0004-6361/202039657
  * Gardner et al. (2006) Gardner, J. P., Mather, J. C., Clampin, M., et al. 2006, Space Sci. Rev., 123, 485, doi: 10.1007/s11214-006-8315-7
  * Girardi et al. (2000) Girardi, L., Bressan, A., Bertelli, G., & Chiosi, C. 2000, A&AS, 141, 371, doi: 10.1051/aas:2000126
  * Gómez-Valent & Amendola (2018) Gómez-Valent, A., & Amendola, L. 2018, J. Cosmology Astropart. Phys, 2018, 051, doi: 10.1088/1475-7516/2018/04/051
  * Graur et al. (2014) Graur, O., Rodney, S. A., Maoz, D., et al. 2014, ApJ, 783, 28, doi: 10.1088/0004-637X/783/1/28
  * Gutkin et al. (2016) Gutkin, J., Charlot, S., & Bruzual, G. 2016, MNRAS, 462, 1757, doi: 10.1093/mnras/stw1716
  * Harikane et al. (2022) Harikane, Y., Ouchi, M., Oguri, M., et al. 2022, arXiv e-prints, arXiv:2208.01612.  https://arxiv.org/abs/2208.01612
  * Helmi et al. (2018) Helmi, A., Babusiaux, C., Koppelman, H. H., et al. 2018, Nature, 563, 85, doi: 10.1038/s41586-018-0625-x
  * Hoffmann et al. (2021) Hoffmann, S. L., Mack, J., Avila, R., et al. 2021, in American Astronomical Society Meeting Abstracts, Vol. 53, American Astronomical Society Meeting Abstracts, 216.02
  * Hopkins et al. (2010a) Hopkins, P. F., Murray, N., Quataert, E., & Thompson, T. A. 2010a, MNRAS, 401, L19, doi: 10.1111/j.1745-3933.2009.00777.x
  * Hopkins et al. (2010b) Hopkins, P. F., Bundy, K., Croton, D., et al. 2010b, ApJ, 715, 202, doi: 10.1088/0004-637X/715/1/202
  * Hutter et al. (2021) Hutter, A., Dayal, P., Yepes, G., et al. 2021, MNRAS, 503, 3698, doi: 10.1093/mnras/stab602
  * Huško et al. (2023) Huško, F., Lacey, C. G., & Baugh, C. M. 2023, MNRAS, 518, 5323, doi: 10.1093/mnras/stac3152
  * Inoue et al. (2014) Inoue, A. K., Shimizu, I., Iwata, I., & Tanaka, M. 2014, MNRAS, 442, 1805, doi: 10.1093/mnras/stu936
  * JDADF Developers et al. (2022) JDADF Developers, Averbukh, J., Bradley, L., et al. 2022, Jdaviz, 2.10.0, doi: https://doi.org/10.5281/zenodo.5513927
  * Jiménez-Teja & Benítez (2012) Jiménez-Teja, Y., & Benítez, N. 2012, ApJ, 745, 150, doi: 10.1088/0004-637X/745/2/150
  * Johnson et al. (2021) Johnson, B. D., Leja, J., Conroy, C., & Speagle, J. S. 2021, ApJS, 254, 22, doi: 10.3847/1538-4365/abef67
  * Jullo & Kneib (2009) Jullo, E., & Kneib, J. P. 2009, MNRAS, 395, 1319, doi: 10.1111/j.1365-2966.2009.14654.x
  * Jullo et al. (2007) Jullo, E., Kneib, J. P., Limousin, M., et al. 2007, New Journal of Physics, 9, 447, doi: 10.1088/1367-2630/9/12/447
  * Khusanova et al. (2021) Khusanova, Y., Bethermin, M., Le Fèvre, O., et al. 2021, A&A, 649, A152, doi: 10.1051/0004-6361/202038944
  * Koekemoer et al. (2003) Koekemoer, A. M., Fruchter, A. S., Hook, R. N., & Hack, W. 2003, in HST Calibration Workshop : Hubble after the Installation of the ACS and the NICMOS Cooling System, 337
  * Kroupa (2002) Kroupa, P. 2002, Science, 295, 82, doi: 10.1126/science.1067524
  * Kroupa et al. (1993) Kroupa, P., Tout, C. A., & Gilmore, G. 1993, MNRAS, 262, 545, doi: 10.1093/mnras/262.3.545
  * Lam et al. (2019) Lam, D., Bouwens, R. J., Coe, D., et al. 2019, arXiv e-prints, arXiv:1903.08177.  https://arxiv.org/abs/1903.08177
  * Leethochawalit et al. (2022) Leethochawalit, N., Trenti, M., Santini, P., et al. 2022, arXiv e-prints, arXiv:2207.11135.  https://arxiv.org/abs/2207.11135
  * Legrand et al. (2022) Legrand, L., Dayal, P., Hutter, A., et al. 2022, arXiv e-prints, arXiv:2207.06786.  https://arxiv.org/abs/2207.06786
  * Leja et al. (2019) Leja, J., Carnall, A. C., Johnson, B. D., Conroy, C., & Speagle, J. S. 2019, ApJ, 876, 3, doi: 10.3847/1538-4357/ab133c
  * Leja et al. (2017) Leja, J., Johnson, B. D., Conroy, C., van Dokkum, P. G., & Byler, N. 2017, ApJ, 837, 170, doi: 10.3847/1538-4357/aa5ffe
  * Lotz et al. (2011) Lotz, J. M., Jonsson, P., Cox, T. J., et al. 2011, ApJ, 742, 103, doi: 10.1088/0004-637X/742/2/103
  * Lotz et al. (2017) Lotz, J. M., Koekemoer, A., Coe, D., et al. 2017, ApJ, 837, 97, doi: 10.3847/1538-4357/837/1/97
  * Madau & Dickinson (2014) Madau, P., & Dickinson, M. 2014, ARA&A, 52, 415, doi: 10.1146/annurev-astro-081811-125615
  * Marigo & Girardi (2007) Marigo, P., & Girardi, L. 2007, A&A, 469, 239, doi: 10.1051/0004-6361:20066772
  * Marigo et al. (2008) Marigo, P., Girardi, L., Bressan, A., et al. 2008, A&A, 482, 883, doi: 10.1051/0004-6361:20078467
  * Meneghetti et al. (2017) Meneghetti, M., Natarajan, P., Coe, D., et al. 2017, MNRAS, 472, 3177, doi: 10.1093/mnras/stx2064
  * Merten et al. (2015) Merten, J., Meneghetti, M., Postman, M., et al. 2015, ApJ, 806, 4, doi: 10.1088/0004-637X/806/1/4
  * Meštrić et al. (2022) Meštrić, U., Vanzella, E., Zanella, A., et al. 2022, MNRAS, 516, 3532, doi: 10.1093/mnras/stac2309
  * Mihos & Hernquist (1996) Mihos, J. C., & Hernquist, L. 1996, ApJ, 464, 641, doi: 10.1086/177353
  * Naab et al. (2009) Naab, T., Johansson, P. H., & Ostriker, J. P. 2009, ApJ, 699, L178, doi: 10.1088/0004-637X/699/2/L178
  * Naidu et al. (2021) Naidu, R. P., Conroy, C., Bonaca, A., et al. 2021, ApJ, 923, 92, doi: 10.3847/1538-4357/ac2d2d
  * Naidu et al. (2022) Naidu, R. P., Oesch, P. A., van Dokkum, P., et al. 2022, arXiv e-prints, arXiv:2207.09434.  https://arxiv.org/abs/2207.09434
  * Nelson et al. (2022) Nelson, E. J., Suess, K. A., Bezanson, R., et al. 2022, arXiv e-prints, arXiv:2208.01630.  https://arxiv.org/abs/2208.01630
  * Newman et al. (2012) Newman, A. B., Ellis, R. S., Bundy, K., & Treu, T. 2012, ApJ, 746, 162, doi: 10.1088/0004-637X/746/2/162
  * Oesch et al. (2016) Oesch, P. A., Brammer, G., van Dokkum, P. G., et al. 2016, ApJ, 819, 129, doi: 10.3847/0004-637X/819/2/129
  * Oguri (2010) Oguri, M. 2010, PASJ, 62, 1017, doi: 10.1093/pasj/62.4.1017
  * Oke (1974) Oke, J. B. 1974, ApJS, 27, 21, doi: 10.1086/190287
  * Oke & Gunn (1983) Oke, J. B., & Gunn, J. E. 1983, ApJ, 266, 713, doi: 10.1086/160817
  * Pacucci et al. (2013) Pacucci, F., Mesinger, A., & Haiman, Z. 2013, MNRAS, 435, L53, doi: 10.1093/mnrasl/slt093
  * Pascale et al. (2022) Pascale, M., Frye, B. L., Diego, J., et al. 2022, ApJ, 938, L6, doi: 10.3847/2041-8213/ac9316
  * Patel et al. (2014) Patel, B., McCully, C., Jha, S. W., et al. 2014, ApJ, 786, 9, doi: 10.1088/0004-637X/786/1/9
  * Pei (1992) Pei, Y. C. 1992, ApJ, 395, 130, doi: 10.1086/171637
  * Peng et al. (2010) Peng, C. Y., Ho, L. C., Impey, C. D., & Rix, H.-W. 2010, AJ, 139, 2097, doi: 10.1088/0004-6256/139/6/2097
  * Pirzkal et al. (2015) Pirzkal, N., Coe, D., Frye, B. L., et al. 2015, ApJ, 804, 11, doi: 10.1088/0004-637X/804/1/11
  * Planck Collaboration et al. (2020) Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6, doi: 10.1051/0004-6361/201833910
  * Portegies Zwart et al. (2010) Portegies Zwart, S. F., McMillan, S. L. W., & Gieles, M. 2010, ARA&A, 48, 431, doi: 10.1146/annurev-astro-081309-130834
  * Postman et al. (2012a) Postman, M., Coe, D., Benítez, N., et al. 2012a, ApJS, 199, 25, doi: 10.1088/0067-0049/199/2/25
  * Postman et al. (2012b) Postman, M., Lauer, T. R., Donahue, M., et al. 2012b, ApJ, 756, 159, doi: 10.1088/0004-637X/756/2/159
  * Ribeiro et al. (2017) Ribeiro, B., Le Fèvre, O., Cassata, P., et al. 2017, A&A, 608, A16, doi: 10.1051/0004-6361/201630057
  * Riess et al. (2018) Riess, A. G., Rodney, S. A., Scolnic, D. M., et al. 2018, ApJ, 853, 126, doi: 10.3847/1538-4357/aaa5a9
  * Rigby et al. (2022) Rigby, J., Perrin, M., McElwain, M., et al. 2022, arXiv e-prints, arXiv:2207.05632.  https://arxiv.org/abs/2207.05632
  * Robitaille et al. (2020) Robitaille, T., Deil, C., & Ginsburg, A. 2020, reproject: Python-based astronomical image reprojection, Astrophysics Source Code Library, record ascl:2011.023.  http://ascl.net/2011.023
  * Rodney et al. (2014) Rodney, S. A., Riess, A. G., Strolger, L.-G., et al. 2014, AJ, 148, 13, doi: 10.1088/0004-6256/148/1/13
  * Rodriguez-Gomez et al. (2015) Rodriguez-Gomez, V., Genel, S., Vogelsberger, M., et al. 2015, MNRAS, 449, 49, doi: 10.1093/mnras/stv264
  * Salim et al. (2018) Salim, S., Boquien, M., & Lee, J. C. 2018, ApJ, 859, 11, doi: 10.3847/1538-4357/aabf3c
  * Sánchez-Blázquez et al. (2006) Sánchez-Blázquez, P., Peletier, R. F., Jiménez-Vicente, J., et al. 2006, MNRAS, 371, 703, doi: 10.1111/j.1365-2966.2006.10699.x
  * Santos-Olmsted et al. (2023) Santos-Olmsted, L., Barrow, K., & Hartwig, T. 2023, arXiv e-prints, arXiv:2305.17158, doi: 10.48550/arXiv.2305.17158
  * Sartoris et al. (2014) Sartoris, B., Biviano, A., Rosati, P., et al. 2014, ApJ, 783, L11, doi: 10.1088/2041-8205/783/1/L11
  * Smit et al. (2014) Smit, R., Bouwens, R. J., Labbé, I., et al. 2014, ApJ, 784, 58, doi: 10.1088/0004-637X/784/1/58
  * Sotillo-Ramos et al. (2022) Sotillo-Ramos, D., Pillepich, A., Donnari, M., et al. 2022, MNRAS, 516, 5404, doi: 10.1093/mnras/stac2586
  * Stefanon et al. (2022) Stefanon, M., Bouwens, R. J., Labbé, I., et al. 2022, arXiv e-prints, arXiv:2206.13525.  https://arxiv.org/abs/2206.13525
  * Stewart et al. (2009) Stewart, K. R., Bullock, J. S., Barton, E. J., & Wechsler, R. H. 2009, ApJ, 702, 1005, doi: 10.1088/0004-637X/702/2/1005
  * Strolger et al. (2015) Strolger, L.-G., Dahlen, T., Rodney, S. A., et al. 2015, ApJ, 813, 93, doi: 10.1088/0004-637X/813/2/93
  * Tacchella et al. (2018) Tacchella, S., Bose, S., Conroy, C., Eisenstein, D. J., & Johnson, B. D. 2018, ApJ, 868, 92, doi: 10.3847/1538-4357/aae8e0
  * Tacchella et al. (2022) Tacchella, S., Finkelstein, S. L., Bagley, M., et al. 2022, ApJ, 927, 170, doi: 10.3847/1538-4357/ac4cad
  * Tasca et al. (2015) Tasca, L. A. M., Le Fèvre, O., Hathi, N. P., et al. 2015, A&A, 581, A54, doi: 10.1051/0004-6361/201425379
  * Toomre & Toomre (1972) Toomre, A., & Toomre, J. 1972, ApJ, 178, 623, doi: 10.1086/151823
  * Topping et al. (2022) Topping, M. W., Stark, D. P., Endsley, R., et al. 2022, MNRAS, 516, 975, doi: 10.1093/mnras/stac2291
  * Treister et al. (2012) Treister, E., Schawinski, K., Urry, C. M., & Simmons, B. D. 2012, ApJ, 758, L39, doi: 10.1088/2041-8205/758/2/L39
  * Umetsu et al. (2014) Umetsu, K., Medezinski, E., Nonino, M., et al. 2014, ApJ, 795, 163, doi: 10.1088/0004-637X/795/2/163
  * van Dokkum et al. (2010) van Dokkum, P. G., Whitaker, K. E., Brammer, G., et al. 2010, ApJ, 709, 1018, doi: 10.1088/0004-637X/709/2/1018
  * Vanzella et al. (2022) Vanzella, E., Castellano, M., Bergamini, P., et al. 2022, A&A, 659, A2, doi: 10.1051/0004-6361/202141590
  * Welch et al. (2022a) Welch, B., Coe, D., Zitrin, A., et al. 2022a, arXiv e-prints, arXiv:2207.03532.  https://arxiv.org/abs/2207.03532
  * Welch et al. (2022b) Welch, B., Coe, D., Zackrisson, E., et al. 2022b, arXiv e-prints, arXiv:2208.09007.  https://arxiv.org/abs/2208.09007
  * Whitaker et al. (2014) Whitaker, K. E., Franx, M., Leja, J., et al. 2014, ApJ, 795, 104, doi: 10.1088/0004-637X/795/2/104
  * Whitler et al. (2022a) Whitler, L., Endsley, R., Stark, D. P., et al. 2022a, arXiv e-prints, arXiv:2208.01599.  https://arxiv.org/abs/2208.01599
  * Whitler et al. (2022b) Whitler, L., Stark, D. P., Endsley, R., et al. 2022b, arXiv e-prints, arXiv:2206.05315.  https://arxiv.org/abs/2206.05315
  * Xiang & Rix (2022) Xiang, M., & Rix, H.-W. 2022, Nature, 603, 599, doi: 10.1038/s41586-022-04496-5
  * Yan et al. (2022) Yan, H., Ma, Z., Ling, C., et al. 2022, arXiv e-prints, arXiv:2207.11558.  https://arxiv.org/abs/2207.11558
  * Yung et al. (2019) Yung, L. Y. A., Somerville, R. S., Popping, G., et al. 2019, MNRAS, 490, 2855, doi: 10.1093/mnras/stz2755
  * Zhang et al. (2023) Zhang, H., Behroozi, P., Volonteri, M., et al. 2023, MNRAS, 518, 2123, doi: 10.1093/mnras/stac2633
  * Zheng et al. (2012) Zheng, W., Postman, M., Zitrin, A., et al. 2012, Nature, 489, 406, doi: 10.1038/nature11446
  * Zitrin et al. (2011) Zitrin, A., Broadhurst, T., Barkana, R., Rephaeli, Y., & Benítez, N. 2011, MNRAS, 410, 1939, doi: 10.1111/j.1365-2966.2010.17574.x
  * Zitrin et al. (2009) Zitrin, A., Broadhurst, T., Umetsu, K., et al. 2009, MNRAS, 396, 1985, doi: 10.1111/j.1365-2966.2009.14899.x
  * Zitrin et al. (2015) Zitrin, A., Fabris, A., Merten, J., et al. 2015, ApJ, 801, 44, doi: 10.1088/0004-637X/801/1/44