#  NIRSpec spectroscopy of the triply-lensed $z=10.17$ galaxy MACS0647–JD

Tiger Yu-Yang Hsiao Both lead authors contributed equally  Center for Astrophysical Sciences, Department of Physics and Astronomy, The Johns Hopkins University, 3400 N Charles St. Baltimore, MD 21218, USA  Abdurro’uf Both lead authors contributed equally  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  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  Rebecca L. Larson NSF Graduate Fellow  The University of Texas at Austin, Department of Astronomy, Austin, TX, United States  Intae Jung Space Telescope Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA  Matilde Mingozzi Space Telescope Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA  Pratika Dayal Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, 9700AV Groningen, The Netherlands  Nimisha Kumari 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)  Vasily Kokorev Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, 9700AV Groningen, The Netherlands  Anton Vikaeus Observational Astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden  Gabriel Brammer Cosmic Dawn Center (DAWN), Copenhagen, Denmark  Niels Bohr Institute, University of Copenhagen, Jagtvej 128, Copenhagen, Denmark  Lukas J. Furtak 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  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  Jacqueline Antwi-Danso George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX 78743, USA  Department of Physics and Astronomy, Texas A&M University, 4242 TAMU, College Station, TX 78743, 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  Larry D. Bradley Space Telescope Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA  Tom Broadhurst Department of Theoretical Physics, University of the Basque Country UPV-EHU, E-48040 Bilbao, Spain  Donostia International Physics Center (DIPC), 20018 Donostia, The Basque Country, Spain  IKERBASQUE, Basque Foundation for Science, Alameda Urquijo, 36-5 E-48008 Bilbao, Spain  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 M13 9PL, UK  Jose M. Diego Instituto de Física de Cantabria (CSIC-UC). Avda. Los Castros s/n. 39005 Santander, Spain  Megan Donahue Michigan State University, Physics & Astronomy Department, East Lansing, MI, USA  Jan J. Eldridge Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand  Seiji Fujimoto Hubble Fellow  The University of Texas at Austin, Department of Astronomy, Austin, TX, United States  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  Svea Hernandez Association of Universities for Research in Astronomy (AURA), Inc. for the European Space Agency (ESA)  Space Telescope Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA  Taylor A. Hutchison NASA Postdoctoral Fellow  Observational Cosmology Lab, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Bethan L. James 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)  Colin Norman 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  Hyunbae Park Lawrence Berkeley National Laboratory, CA 94720, USA  Berkeley Center for Cosmological Physics, UC Berkeley, CA 94720, USA  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  Massimo Ricotti Department of Astronomy, University of Maryland, College Park, 20742, USA  Jane R. Rigby Observational Cosmology Lab, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Eros Vanzella INAF – OAS, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, via Gobetti 93/3, I-40129 Bologna, Italy  Brian Welch Observational Cosmology Lab, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Department of Astronomy, University of Maryland, College Park, 20742, USA  Stephen M. Wilkins Astronomy Centre, University of Sussex, Falmer, Brighton BN1 9QH, UK  Institute of Space Sciences and Astronomy, University of Malta, Msida MSD 2080, Malta  Rogier A. Windhorst School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA  Xinfeng Xu Center for Astrophysical Sciences, Department of Physics and Astronomy, The Johns Hopkins University, 3400 N Charles St. Baltimore, MD 21218, USA  Erik Zackrisson Observational Astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden  Adi Zitrin Physics Department, Ben-Gurion University of the Negev, P.O. Box 653, Be’er-Sheva 84105, Israel

###### Abstract

We present /NIRSpec prism spectroscopy of MACS0647$-$JD, the triply-lensed
$z\sim 11$ candidate discovered in HST imaging and spatially resolved by
imaging into two components A and B. Spectroscopy of component A yields a
spectroscopic redshift $z=10.17$ based on 7 detected emission lines: C iii]
$\lambda\lambda$1907,1909, [O ii] $\lambda$3727, [Ne iii] $\lambda$3869, [Ne
iii] $\lambda$3968, H$\delta$ $\lambda$4101, H$\gamma$ $\lambda$4340, and [O
iii] $\lambda$4363\. These are the second-most distant detections of these
emission lines to date, in a galaxy observed just 460 million years after the
Big Bang. Based on observed and extrapolated line flux ratios we derive a gas-
phase metallicity $Z=$ 12+log(O/H) = 7.5 – 8.0, or (0.06 – 0.2) $Z_{\odot}$,
ionization parameter $\log(U)$ $\sim$ $-1.9\pm 0.2$, and an ionizing photon
production efficiency ${\rm log}(\xi_{\rm ion})=25.2\pm 0.2\,$erg-1 Hz. The
spectrum has a softened Lyman-$\alpha$ break, evidence for a strong Ly$\alpha$
damping wing, suggesting that MACS0647$-$JD was unable to ionize its
surroundings beyond its immediate vicinity ($R_{\text{HII}}\ll 1$ pMpc). The
Ly$\alpha$ damping wing also suppresses the F150W photometry, explaining the
slightly overestimated photometric redshift $z=10.6\pm 0.3$. MACS0647$-$JD has
a stellar mass log($M/M_{\odot}$) = $8.1\pm 0.3$, including
$\sim$6$\times$$10^{7}$ $M_{\odot}$ in component A, most of which formed
recently (within $\sim$20 Myr) with a star formation rate $2\pm 1$ $M_{\odot}$
yr-1, all within an effective radius $70\pm 24\,$pc. The smaller component B
($r\sim 20$) pc is likely older ($\sim$100 Myr) with more dust ($A_{V}\sim
0.1$ mag), as found previously. Spectroscopy of a fainter companion galaxy C
separated by a distance of $\sim$ 3 kpc reveals a Lyman break consistent with
$z=10.17$. MACS0647$-$JD is likely the most distant galaxy merger known.
MACS0647$-$JD offers a unique opportunity to study properties of a $z>10$
galaxy.

Galaxies (573), High-redshift galaxies (734), Early universe (435), Strong
gravitational lensing (1643), Galaxy spectroscopy (2171)

††journal: ApJ††facilities: JWST(NIRCam, NIRSpec), HST(ACS, WFC3)††software:
STScI JWST pipeline; msaexp; grizli (Brammer et al., 2022); eazypy (Brammer et
al., 2008); astropy (Astropy Collaboration et al., 2022, 2018, 2013);
photutils (Bradley et al., 2022); piXedfit (Abdurro’uf et al., 2021, 2022);
bagpipes (Carnall et al., 2018, 2019); beagle (Chevallard & Charlot, 2016);
Cloudy (Ferland et al., 1998, 2013, 2017); pyneb (Luridiana et al., 2015);
hii-chi-mistry (Pérez-Montero, 2014)

##  1 Introduction

Spectroscopy using the NIRSpec instrument (Jakobsen et al., 2022; Ferruit et
al., 2022; Böker et al., 2023) onboard (Gardner et al., 2023; Rigby et al.,
2023) is beginning to confirm distant galaxy candidates and reveal their
properties in the early universe ($z>8$; e.g., Fujimoto et al., 2023; Roberts-
Borsani et al., 2022; Bunker et al., 2023; Arrabal Haro et al., 2023a;
Harikane et al., 2023; Curtis-Lake et al., 2023). With coverage out to
$5.3\,$$\mu$m, NIRSpec can detect the strong emission lines [O iii]
$\lambda$4959,$\lambda$5007 and H$\beta$ in galaxies as distant as $z\sim
9.5$, confirming redshifts and constraining properties such as metallicity and
ionization parameter when combined with other emission lines (e.g., Williams
et al., 2022; Nakajima et al., 2023; Boyett et al., 2023; Cameron et al.,
2023b; Tang et al., 2023; Sanders et al., 2023; Jung et al., 2023).

At $z>10$ within the first 500 million years, spectroscopic confirmations and
detailed studies are more challenging because [O iii]+H$\beta$ is redshifted
out of the NIRSpec wavelength range, and fainter emission lines are difficult
to detect in low-luminosity $z>10$ galaxies. Brighter galaxies or longer
exposure times are required. Curtis-Lake et al. (2023) presented deep spectra
with a spectral resolution of $R\sim 100$ that impressively confirmed galaxies
with redshifts $z=10.4$, 11.6, 12.6, and 13.2 based on significant Lyman break
detections and an absence of definitive emission lines in long exposures of 9
– 28 hours for these faint candidates (AB mag 28 – 29). Similarly, Arrabal
Haro et al. (2023a) confirmed galaxies at $z=10.1$ and $z=11.4$ based on Lyman
break detections with no emission lines in 5-hour NIRSpec prism spectra that
also revised the redshift of a $z\sim 16$ candidate down to $z=4.912$.

Over a decade of Hubble Space Telescope (HST) WFC3/IR observations yielded two
$z>10$ galaxies bright enough (AB mag 26) for more detailed study. GN-z11 was
one of the most distant galaxies ever discovered in HST imaging (Oesch et al.,
2016). They noted that given the search area, it was surprising to discover a
galaxy so bright. NIRCam (Rieke et al., 2023) imaging photometry yields F200W
AB mag of 26.0 and $M_{UV}=-21.6$, or $M_{UV}=-21.8$ corrected for dust
(Tacchella et al., 2023). NIRSpec spectroscopy has now confirmed GN-z11 at
$z=10.603$ and revealed 12 emission lines (Bunker et al., 2023).

MACS0647$-$JD was the other similarly bright $z\sim 11$ candidate discovered
in HST imaging (Coe et al., 2013), supported by HST grism observations
(Pirzkal et al., 2015), Spitzer imaging (Lam et al., 2019), and gravitational
lens modeling (Chan et al., 2017). MACS0647–JD is triply-lensed by a massive
foreground galaxy cluster, MACSJ0647.7+7015 ($z=0.591$; Ebeling et al., 2007).
Despite lensing magnifications of $\sim$8, 5, and 2 (Meena et al., 2023), the
three lensed images JD1, JD2, and JD3 were spatially unresolved in HST
imaging.

/NIRCam imaging resolved MACS0647$-$JD as having two small components in a
possible galaxy merger at $z=10.6\pm 0.3$ (Hsiao et al., 2022). The brighter
component A has an effective radius $r\sim 70\pm 24\,$pc and appears bluer,
likely due to its young stellar population ($\sim$50 Myr old) and no dust. The
other component, JDB, has a smaller radius of $r\sim 20^{+8}_{-5}\,$pc and
appears redder, likely due to an older stellar population ($\sim$100 Myr old)
and mild dust ($A_{V}\sim 0.1\,$mag). The different inferred star formation
histories suggest these two components formed separately and are in the
process of merging. A third triply-lensed component C was also identified 2″
away ($\sim$3 kpc in the delensed source plane). With similar colors and a
consistent photometric redshift, C may be destined to merge with A and B.

Compared to GN-z11, MACS0647$-$JD is intrinsically fainter ($M_{UV}=-20.3$),
yet observed to be brighter; the brightest lensed image JD1 is F200W AB mag
25.0. The brightest clump A is $M_{UV}=-19.5$ and lensed to F200W AB mag of
25.8 in JD1. This enables detailed study with .

In this paper, we report NIRSpec and NIRCam observations of MACS0647–JD
obtained by observation program GO 1433 (PI Coe). Most of the NIRCam images
were analyzed previously by Hsiao et al. (2022). This work includes a new
F480M image, deeper F200W data, and updated image reductions and photometry
(§2). Based on NIRSpec prism ($R\sim 100$) spectroscopy spanning 0.7 – 5.3
$\mu$m, we detect nebular emission lines, measure the spectroscopic redshift,
and derive physical properties including the ionization parameter and
metallicity using various emission line ratios as well as photometric spectral
energy distribution (SED) fitting (§3). We present conclusions in §4.

##  2 Observations

program GO 1433 (PI Coe) observed MACS0647$-$JD as summarized in Table 1. We
also analyze archival HST imaging from programs GO 9722, 10493, 10793, 12101,
and 13317, described in Hsiao et al. (2022). All and HST data are publicly
available in the Mikulski Archive for Space Telescopes (MAST). We also provide
reduced data products111https://cosmic-spring.github.io along with our data
analysis scripts.222https://github.com/cosmic-spring/MACS0647-JD-NIRSpec

###  2.1 NIRSpec MOS prism spectroscopy

There were two separate NIRSpec multi-object spectroscopy (MOS) observations
(Obs 21 and Obs 23) using the microshutter assembly (MSA). Both used the low-
resolution $R\sim 30-300$ prism yielding data from 0.6 – 5.3 $\mu$m. Obs 23
was performed with standard 3-slitlet nods used to subtract backgrounds
measured near each target. The total exposure time was 1.8 hours. Obs 21 was
performed with single slitlets, requiring backgrounds to be measured in nearby
slitlets designed to observe “blank” sky and intracluster light. Two MSA
configurations were executed in Obs 21 with a total exposure time of 1.8
hours. The two configurations were similar with small dithers between them and
most targets included in both.

The two brightest lensed images of MACS0647$-$JD (JD1 and JD2) were observed
in all exposures of all observations for a total exposure time of 3.6 hours.
The slitlets primarily captured light from the brightest clump A. The
brightest lensed images of the companion galaxy C (JD1C and JD2C) were also
observed in all exposures. Since JD1 and JD2 are multiple images of the same
object with JD2 magnified $\sim$70% as bright ($\mu\sim 5.3$) as JD1, the
resulting stacked spectra have signal-to-noise ratio (SNR) similar to 6-hour
total effective exposure times on JD1A and JD1C.

Clump B was observed only in Observation 21 of JD2. Given its proximity to
clump A, it is difficult to spatially resolve its contribution to the JD2
spectrum. They are separated by only one or two 0.1″ pixels in the cross-
dispersion direction. We do perhaps detect some emission line flux from JD2B
as we discuss in §3.4.

We retrieved NIRSpec Level 1 data products from MAST and processed them with
the STScI JWST pipeline333https://github.com/spacetelescope/jwst version 1.9.2
and msaexp444https://github.com/gbrammer/msaexp version 0.6.0. First, msaexp
corrects for 1/$f$ noise555While the observations were obtained in IRS2
readout mode to mitigate the effect of 1/$f$ noise, NIRSpec data still exhibit
this characteristic to some extent, motivating the correction., masks
snowballs666Snowballs are now masked by the JWST Level 1 pipeline as well.,
corrects bias levels in individual exposures, and rescales the noise array
RNOISE based on measurements in blank regions. Next, we run JWST pipeline
Stage 2 routines to perform WCS registration, flat-fielding, pathloss
corrections, and flux calibration.

For the 3-slitlet data, background subtraction is performed locally before
drizzling the 3 exposures onto a common 2D pixel grid. For the single-slitlet
data, we drizzle-combined data from the 2 exposures (MSA configurations). Then
we subtracted the 2D background spectrum in a nearby slit (#50981) that
observed a relatively blank region of the image.

To extract each 1D spectrum, msaexp uses a Gaussian profile in the cross-
dispersion direction, derived from an inverse-weighted sum of the 2D spectrum
in the dispersion direction, based on the optimal extraction described in
Horne (1986). The results are shown in Figure 1 for each observation.

Finally, we stacked the 1D spectra, adding flux uncertainties in quadrature,
yielding the spectrum shown in Figure 2. This spectrum includes the total flux
observed in all 4 exposures for JD1A and JD2A.

###  2.2 NIRCam imaging

NIRCam imaging was obtained first in 6 filters, F115W, F150W, F200W, F277W,
F365W, and F444W spanning 1–5$\,\mu$m, and the results were studied and
presented in Hsiao et al. (2022). Additional NIRCam imaging has since been
obtained in F200W and F480M, concurrent with the NIRSpec observation 21. The
F480M observation was included to observe MACS0647$-$JD redward of the Balmer
break to better constrain its stellar age and mass. Each NIRCam image has an
exposure time of 35 minutes, split between 4 INTRAMODULEBOX dithers that cover
the short-wavelength gaps.

We process the NIRCam images using the STScI pipeline and grizli (Brammer et
al., 2022). In Hsiao et al. (2022), we analyzed grizli v4 images then
performed zeropoint corrections based on updated calibrations that remain
robust today (Boyer et al., 2022). Those updated zeropoints were implemented
in grizli v5. In this work, we analyze grizli v6 image
mosaics777https://github.com/gbrammer/grizli/blob/master/docs/grizli/image-
release-v6.rst featuring improved sky flats, bad pixel tables, wisp templates,
and long-wavelength zeropoints.

Briefly, in each NIRCam exposure, the grizli pipeline applies corrections for
$1/f$ noise striping and masks “snowballs”888https://jwst-docs.stsci.edu/data-
artifacts-and-features/snowballs-artifact and “wisps”999https://jwst-
docs.stsci.edu/jwst-near-infrared-camera/nircam-features-and-caveats/nircam-
claws-and-wisps. Then grizli drizzle-combines all exposures in each filter on
to a common pixel grid using astrodrizzle (Koekemoer et al., 2003; Hoffmann et
al., 2021). The NIRCam short wavelength images are drizzled to 0$\farcs$02
pixels, and all other images are drizzled to 0$\farcs$04 pixels. All images
are aligned with coordinates registered to GAIA DR3 (Gaia Collaboration et
al., 2021). We create color images using
trilogy101010https://github.com/dancoe/trilogy (Coe et al., 2012).

We measure photometry of the lensed images JD1 and JD2 using grizli with
circular apertures of 0$\farcs$25 radius. We then measure the photometry of
the JD components A and B individually using piXedfit (Abdurro’uf et al.,
2023) within elliptical apertures as described in Hsiao et al. (2022).
Additionally, we create rectangular photometric apertures that match the
NIRSpec slitlets in size, position, and orientation in each of our 4
observations for JD1 and JD2 (Figure
1)111111https://github.com/aabdurrouf/JWST-
HST_resolvedSEDfits/tree/main/MACS0647-JD. We find this photometry is very
similar to the photometry of component A, which tracks because the NIRSpec
slitlets primarily targeted A with occasional small contributions from the
fainter clump B. All resulting NIRCam photometry is presented in Table 2 and
plotted along with the NIRSpec spectrum in Figure 3.

We note the photometry of clump A is slightly redder than the observed
spectrum. Both measurements present challenges, including the proximity of the
A and B clumps, and variable slit loss corrections as a function of wavelength
applied by the JWST pipeline to the NIRSpec spectrum.

Table 1:  Observations of MACS0647

Observation | Date (UT) | Mode | Exposures | Filters $/$ Element | Exposure Timea
---|---|---|---|---|---
10 | 2022-09-23 | NIRCam imaging | 3 filter pairs | F115W, F150W, F200W, | 2104 s
|  |  |  | F277W, F356W, F444W |
20 | 2023-01-08 | NIRCam imaging | 1 filter pair | F200W, F480M | 2104 s
21 | 2023-01-08 | NIRSpec MOS | 1 slitlet; 2 dithersb | prism | 6420 s
23 | 2023-02-20 | NIRSpec MOS | 3 slitlet nods | prism | 6567 s

aafootnotetext: Exposure time per imaging filter; total exposure times for
NIRSpec

bbfootnotetext: Each dither requires its own MSA configuration.

Table 2: NIRCam photometry of MACS0647$-$JD

Object | Magnif.a | Photometry | Aperture | F115W | F150W | F200W | F277W | F356W | F444W | F480M
---|---|---|---|---|---|---|---|---|---|---
JD1 |  $\sim$8 | grizli | circular | $1\pm 8$ | $297\pm 7$ | $368\pm 5$ | $309\pm 6$ | $306\pm 6$ | $317\pm 8$ | $314\pm 18$
JD2 |  $\sim$5.3 | grizli | circular | $12\pm 7$ | $178\pm 6$ | $255\pm 4$ | $229\pm 5$ | $205\pm 5$ | $209\pm 7$ | $185\pm 16$
JD1A |  $\sim$8 | piXedfit | elliptical | $-8\pm 4$ | $146\pm 3$ | $169\pm 2$ | $135\pm 2$ | $120\pm 2$ | $116\pm 3$ | $124\pm 8$
JD2A |  $\sim$5.3 | piXedfit | elliptical | $-2\pm 3$ | $90\pm 3$ | $125\pm 2$ | $95\pm 2$ | $82\pm 2$ | $77\pm 3$ | $87\pm 7$
JD1B |  $\sim$8 | piXedfit | elliptical | $1\pm 2$ | $26\pm 2$ | $40\pm 2$ | $31\pm 2$ | $39\pm 2$ | $44\pm 2$ | $45\pm 5$
JD2B |  $\sim$5.3 | piXedfit | elliptical |  $-3\pm$3 | $17\pm 2$ | $31\pm 1$ | $27\pm 1$ | $27\pm 1$ | $28\pm 2$ | $29\pm 5$
JDAb |  $\sim$26.6 | piXedfit | rectangular | $-35\pm 10$ | $450\pm 8$ | $623\pm 5$ | $509\pm 6$ | $461\pm 6$ | $441\pm 9$ | $446\pm 21$

aafootnotetext: Lensing magnification estimates (Meena et al., 2023)

bbfootnotetext: Photometric apertures designed to match the 4 observed NIRSpec
slitlets that primarily observe JDA. Flux densities include the sum of all 4.

††footnotetext: Note. All flux densities are given in $\rm nJy$. Photometry is
plotted in Figure 3 along with the spectrum.

Figure 1: Individual NIRSpec spectra of MACS0647$-$JD lensed images JD1 and
JD2 (#3593 and #3349, respectively, in the catalog used to prepare NIRSpec
Observations 21 and 23). Left: Slitlets in red are overlaid on 2″$\times$2″
NIRCam color images (blue F115W; cyan F150W; green F200W; red F277W, F356W,
F444W, F480M). Note that most of the observations target the brighter
component A. Right: 2D spectra vs. rest-frame wavelength for $z=10.17$ (top)
and 1D spectra $F_{\nu}$ ($\mu$Jy) vs. observed wavelength in microns
(bottom). In each 1D plot, the gray line shows the spectrum, and the red line
shows the uncertainty. Faint vertical colored shaded regions mark wavelengths
of common emission lines: Ly$\alpha$ $\lambda$1216 (pink), C iii]
$\lambda\lambda$1907,1909 (green), Mg ii $\lambda$2800 (blue), and [O ii]
$\lambda$3727 (purple). Only two of those (C iii] and [O ii]) appear in
MACS0647$-$JD, along with others revealed in the stacked spectrum (Figure 2)
and listed in Table 3.  Figure 2: Spectrum and photometry of MACS0647$-$JD
component A in the sum of both lensed images in both observations (i.e., JD1
Obs 21 + JD1 Obs 23 + JD2 Obs 21 + JD2 Obs 23), with a total magnification
$\sim$$26.6=8+8+5.3+5.3$. The spectrum is the stacked sum of all 4 observed
spectra. The photometry shown here is measured within rectangular apertures
resembling the NIRSpec slits in the 4 exposures. The red line is the piXedfit
model fit to the spectrum with emission lines masked out. After subtracting
this continuum (bottom panels), detected emission lines are fit with Gaussian
functions (blue) to measure fluxes. (Other undetected emission lines are
labeled in gray.)  Figure 3: MACS0647$-$JD NIRSpec stacked spectrum (divided
by 4; gray) compared with photometry presented in Table 2. Black points show
the photometry measured in rectangular apertures that mimic the observed
NIRSpec slits. These synthetic colors match the JD1A and JD2A photometry
measured within elliptical apertures by piXedfit (blue and cyan). The smaller
clump B is redder (JD1B red, JD2B pink). Photometry of the entire galaxy
MACS0647$-$JD lensed images JD1 and JD2 (dark and light green), including
clumps A and B plus additional diffuse light, was measured by grizli with
circular apertures of 0$\farcs$25 radius.

##  3 Results and Discussion

Table 3: Measured emission line fluxes for JDA

Emission Lines | Rest wavelength | Observed wavelength | Line fluxesa | SNR | Equivalent width
---|---|---|---|---|---
| $\rm\AA$ | $\rm\mu m$ |  $10^{-20}\,$erg/s/cm2 |  | (rest-frame) $\rm\AA$
C iii] | 1907, 1909 | 2.13 | $310\pm 60$ | $5.7$ | 14$\pm 3$
[O ii] | 3726, 3729 | 4.16 | $42\pm 5$ | $8.9$ | 13$\pm 2$
[Ne iii] | 3869 | 4.32 | $76\pm 6$ | $13.8$ | 25$\pm 2$
[Ne iii] | 3968 | 4.43 | $41\pm 6$ | $7.3$ | 15$\pm 2$
H$\delta$ | 4101 | 4.58 | $40\pm 7$ | $6.1$ | 17$\pm 3$
H$\gamma$ | 4340 | 4.85 | $74\pm 10$ | $7.7$ | 42$\pm 6$
[O iii] | 4363 | 4.87 | $25\pm 6$ | $4.4$ | 14$\pm 3$
HeI | 4473 | 5.00 | $24\pm 9$ | $2.8$ | 16$\pm 5$

aafootnotetext: As observed in the stack of 4 observations divided by 2 with a
total magnification $\sim$13.3

We obtain four spectra of MACS0647$-$JD component A in the lensed images JD1
and JD2 (Figure 1). Obs 21 of JD2 also includes flux from the fainter
component B. We have not attempted to extract signal from component B that
might be isolated from A in the cross-dispersion direction. That analysis will
be presented by Topping et al. (in preparation).

The stacked spectrum of all four observations (JD1 Obs 21, JD1 Obs 23, JD2 Obs
21, and JD2 Obs 23) is shown in Figure 2, with a total magnification of
$26.6=8+8+5.3+5.3$. We detect the continuum between 1.5 and 5.3 $\mu$m with
SNR $>$ 10 per spectral resolution element out to $\sim$3 $\mu$m; flux
decreases and noise increases to longer wavelengths. Rather than a sharp Lyman
break, the spectrum rolls off gradually from 1.5 $\mu$m (1343Å rest-frame) to
the Lyman break observed at 1.36 $\mu$m (1216Å rest-frame). In §3.7 we show
that this attenuation is consistent with a Lyman damping wing.

We detect seven emission lines (including unresolved doublets): C iii]
$\lambda\lambda$1907,1909, [O ii] $\lambda\lambda$3727,3729, [Ne iii]
$\lambda$3869, [Ne iii] $\lambda$3968, H$\delta$ $\lambda$4101, H$\gamma$
$\lambda$4340, and [O iii] $\lambda$4363, all with SNR $>$ 4\. We also
marginally detect HeI $\lambda$4473 with SNR $\sim$ 2.8. Based on the observed
wavelengths of these lines, we measure a spectroscopic redshift $z_{\rm
spec}=10.17$. Harikane et al. (2023) recently reported the same redshift for
MACS0647$-$JD based on a fraction of the data: JD1 Obs 23.

The spectroscopic redshift is slightly lower (consistent within 2$\sigma$)
than the photometric redshifts estimated previously: $z_{\rm
phot}=10.7^{+0.6}_{-0.4}$ (95% C.L.) from HST imaging (Coe et al., 2013) and
$z_{\rm phot}=10.6\pm 0.3$ from +HST imaging (Hsiao et al., 2022). This may be
explained by the Lyman damping wing reducing flux between 1.35 – 1.5 $\mu$m
(in the F150W and HST F140W filters) more than expected for a sharp Lyman
break, as assumed in the photometric redshift fitting based on spectral energy
distribution (SED) modeling.

We measure the emission line fluxes and report them in Table 3. To measure the
fluxes, we fit each line with a Gaussian after modeling and subtracting the
continuum using piXedfit (Abdurro’uf et al., 2023). The continuum model is fit
to the NIRSpec spectrum while masking out the emission lines. The unresolved
doublets C iii] and [O ii] are each fitted with a single Gaussian. Flux
uncertainties are estimated using the Monte Carlo method.

Recently, Bunker et al. (2023) presented deeper NIRSpec
spectroscopy121212Exposure times of 6.9 hours with the low-resolution ($R\sim
100$) prism and 3.45 hours in each of three medium resolution ($R\sim 1000$)
gratings: G140M/F070LP, G235M/F170LP, and G395M/F290LP of GN-z11 at $z=10.603$
that featured all the lines above, plus additional lines that are not detected
in MACS0647-JD: Ly$\alpha$ $\lambda$1216, N iv] $\lambda$1486, C iv
$\lambda$1549, HeII $\lambda$1640, N iii] $\lambda$1748, and Mg ii
$\lambda$2800\. The nitrogen lines N iv] and N iii] were surprising detections
rarely observed in any galaxy (Cameron et al., 2023a; Charbonnel et al.,
2023). The measured line fluxes were $\sim$$10^{-18}$ erg s${}^{-1}\,$cm-2.
Nitrogen lines that strong would have also been detected in our observations
of MACS0647$-$JD. Note the continuum brightness of GN-z11 is comparable to
JD1A (F200W AB mag 26), so similar line fluxes would correspond to similar
equivalent widths (generated by similar physical properties).

###  3.1 Spectral modeling

We perform spectrophotometric SED fitting using piXedfit (Abdurro’uf et al.,
2021, 2022, 2023). This code fits the spectral continuum (with emission lines
masked out) and photometry simultaneously. We use the stacked spectrum and the
total photometry measured with rectangular apertures resembling the NIRspec
slits in the four exposures. This code uses Flexible Stellar Population
Synthesis (FSPS; Conroy et al., 2009; Leja et al., 2017) SED models, which
have nebular emission incorporated using Cloudy (Ferland et al., 2017). We
assume a Chabrier (2003) initial mass function, Charlot & Fall (2000) dust
attenuation law, and the intergalactic absorption based on Inoue et al. (2014)
model. The dust optical depth is denoted $\hat{\tau}_{2}$. We assume a double
power-law star formation history (SFH) with rising slope $\beta$, declining
slope $\alpha$, and timescale $\tau$: SFR($t$)
$=[(t/\tau)^{\alpha}+(t/\tau)^{-\beta}]^{-1}$. Please refer to Abdurro’uf et
al. (2023, Table 2 therein) for more information on the definition of these
parameters and associated priors.

Gas-phase metallicity $Z_{\rm gas}$ and stellar metallicity $Z_{*}$ are
modeled independently. To reduce the number of free parameters, we fix the
ionization parameter $\log(U)=-2.0$ and the gas-phase metallicity $Z_{\rm
gas}$ to 12+log(O/H) $=7.5$ based on our estimate from emission lines (see
§3.6, §3.5 and Table 7). Varying these values within the uncertainties does
not significantly change the results that follow.

First, we use piXedfit to fit the spectral continuum after masking out the
emission lines. Then we subtract this best-fit continuum and fit Gaussians to
the emission lines to measure their fluxes and equivalent widths, reported in
Table 3.

The spectrum has no Balmer break with $F_{\nu}(4200$Å$)/F_{\nu}(3500$Å$)\sim
0.77\pm 0.06$, measured as in Binggeli et al. (2019), suggesting a young age.
Spectral continuum fitting suggests a very young mass-weighted age of
$8^{+3}_{-2}\,$Myr for component A. However, these spectral models do not
account for the Lyman damping wing. SED fitting to the photometry (§3.2)
yields a similarly young age until we omit the F150W flux measurement affected
by the Lyman damping. Our measured photometry is also slightly redder than the
spectrum, contributing to slightly older age measurements, though still young
as we discuss next in §3.2.

Table 4: Physical properties of JD1, JD1A, JD1B from SED fitting using various
methods

|  |  | Agea | Stellar Mass | SFR | specific SFR | Dust
---|---|---|---|---|---|---|---
Component | Code | Star Formation History | Myr | log($M_{*}/M_{\odot}$) |  $M_{*}$/yr | Gyr-1 |  $A_{V}$ mag
JD1 | bagpipes | constant | $8^{+3}_{-2}$ | $8.1\pm 0.3$ | $10\pm 3$ | $-7.1\pm 0.3$ | $0.09\pm 0.02$
| bagpipes | non-parametric | $6^{+12}_{-1}$ | $8.0\pm 0.1$ | $10\pm 1$ | $-7.0\pm 0.1$ | $0.09\pm 0.01$
| bagpipes | delayed $\tau$ | $3^{+3}_{-2}$ | $7.7^{+0.2}_{-0.1}$ | $5.5^{+0.8}_{-1.0}$ | $-7.0\pm 0.1$ | $0.02^{+0.02}_{-0.01}$
| beagle | delayed $\tau$ | $40^{+85}_{-25}$ | $8.2\pm 0.1$ | $10\pm 1$ | $-7.2\pm 0.1$ | $0.11\pm 0.03$
| piXedfit | double power-law | $30^{+53}_{-20}$ | $8.4\pm 0.3$ | $4.4^{+2.5}_{-1.2}$ | $-7.7^{+0.1}_{-0.2}$ | $0.05\pm 0.04$
JD1A | bagpipes | constant | $8^{+3}_{-2}$ | $7.6\pm 0.1$ | $3\pm 1$ | $-7.0\pm 0.3$ | $<0.01$
| bagpipes | delayed $\tau$ | $5^{+2}_{-1}$ | $7.5\pm 0.1$ | $2.4\pm 0.1$ | $-7.0\pm 0.1$ | $<0.01$
| beagle | delayed $\tau$ | $14^{+6}_{-3}$ | $7.9\pm 0.1$ | $3.3\pm 0.1$ | $-7.3\pm 0.1$ | $0.05\pm 0.01$
| piXedfit | double power-law | $38^{+28}_{-20}$ | $8.1\pm 0.3$ | $1.3\pm 0.6$ | $-8.0\pm 0.1$ | $0.03^{+0.04}_{-0.03}$
JD1B | bagpipes | delayed $\tau$ | $50^{+60}_{-40}$ | $7.7\pm 0.3$ | $1.0\pm 0.3$ | $-7.7\pm 0.3$ | $0.13\pm 0.07$
| piXedfit | double power-law | $15^{+40}_{-10}$ | $7.3\pm 0.3$ | $0.7^{+0.5}_{-0.3}$ | $-7.4^{+0.1}_{-0.2}$ | $0.06\pm 0.04$

aafootnotetext: Ages are mass-weighted. This equals half the formation age for
a constant star formation history.

Note. Stellar mass and SFR estimates are delensed by a magnification $\mu=8\pm
1$ (Meena et al., 2023). Magnification uncertainties are not included in the
uncertainties quoted in the table for stellar mass and SFR. Most of these SED
fitting methods assume a Chabrier (2003) IMF. bagpipes assumes Kroupa et al.
(1993); to renormalize those results, we multiplied the stellar masses by 0.94
(Madau & Dickinson, 2014).

###  3.2 Photometric SED modeling

We perform spectral energy distribution (SED) fitting to the NIRCam photometry
of the brightest lensed image JD1 (magnified by $\mu=8\pm 1$) for the full
galaxy and then for the individual clumps A and B, as reported in Table 2. We
exclude the F150W photometry because our spectral models do not include Lyman
damping. (Including the F150W photometry results in artificially low ages.) We
perform SED modeling using 3 methods: piXedfit (Abdurro’uf et al., 2021, 2022,
2023); bagpipes131313https://bagpipes.readthedocs.io (Carnall et al., 2018,
2019); and beagle (Chevallard & Charlot, 2016). We describe our methods in
§3.1 for piXedfit and below for bagpipes and beagle. We summarize our results
in Table 4.

Our bagpipes (Carnall et al., 2018, 2019) method is described in detail in
Hsiao et al. (2022). Briefly, we use Binary Population and Stellar Synthesis
(BPASS) v2.2.1 templates (Stanway & Eldridge, 2018) including binary
evolution, with a Kroupa (2001) IMF and upper mass cutoff of 300 M⊙. Nebular
emission is included by processing these stellar models through the
photoionization code Cloudy (Ferland et al., 2017). Dust attenuation is
modeled with the Salim et al. (2018) flexible parameterization, including a
variable slope and additional dust within star-forming regions $<10$ Myr old.
Based on our spectroscopic results below, we fix gas metallicity to $Z_{\rm
gas}$ = 0.1$Z_{\odot}$ and ionization parameter $\log(U)=-2$. Varying these
values within their uncertainties does not significantly affect our derived
physical parameters.

We explore various star formation histories: constant, “delayed $\tau$”, and
non-parametric. The delayed $\tau$ SFH allows for a linear rise followed by an
exponential decline: SFR($t$) $\propto t\,\exp(-t/\tau)$. Most of our fits
only have the linear rise with $\tau>1$ Gyr. We explore non-parametric star
formation histories with constant SFR in 4 time bins (e.g., 0 – 10 – 50 – 150
– 300 Myr). With these models, we find almost all the SFR ends up in our
youngest bin 0 – 10 Myr, with negligible older populations.

We also use beagle (Chevallard & Charlot, 2016) to derive an independent fit
to both the photometry and the measured emission line equivalent widths (see
Table 3). beagle assumes a Chabrier (2003) IMF and also uses Cloudy to account
for nebular emission. We further assume a delayed $\tau$ SFH with an ongoing
starburst over the last 10 Myr, an SMC dust attenuation law, and the Inoue et
al. (2014) IGM attenuation models. We apply a similar setup and and parameter
space as in Furtak et al. (2023), though without the external priors and
fixing the redshift to the measured spectroscopic value. Here we also leverage
the additional information provided by the numerous emission lines to also
leave the gas-phase metallicity and the dust-to-metal ratio as free
parameters. These are modeled with uniform priors
$\log(Z_{\mathrm{gas}}/\mathrm{Z}_{\odot})\in[-2.2,-0.3]$ and
$\xi_{\mathrm{d}}\in[0.1,0.5]$.

Based on these various methods, we obtain results summarized in Table 4. We
find MACS0647$-$JD has a stellar mass log($M_{*}$/$M_{\odot}$) $=8.1\pm 0.3$;
SFR $10\pm 3$ $M_{\odot}$ yr-1; and high sSFR $\sim$ 80 Gyr-1, where the
specific star formation rate sSFR = SFR / stellar mass.

The clump A photometry can be well fit by constant star formation for
$17^{+5}_{-4}$ Myr, corresponding to mass-weighted ages $8^{+3}_{-2}$ Myr,
according to bagpipes. Age estimates from the various methods range between 1
– 50 Myr, consistent with the results from Hsiao et al. (2022). We estimate
clump A contains about 1/3 the stellar mass of MACS0647$-$JD.

The smaller redder component B photometry is best fit by a linearly rising SFR
for 40 – 300 Myr, with a mass-weighted age 10 – 110 Myr, stellar mass
log($M_{*}$/$M_{\odot}$) $=7.9\pm 0.3$, and dust $A_{V}=0.10\pm 0.05$ mag.
Based on similar age estimates in Hsiao et al. (2022), they suggested clump B
may have formed separately and merged with the younger clump A, though
different star formation histories in situ are also possible.

MACS0647$-$JD has an absolute UV magnitude $M_{UV}=-20.3\pm 0.2$, including
$M_{UV}=-19.5\pm 0.2$ for clump A and $M_{UV}=-17.9\pm 0.2$ for clump B. These
are based on the JD1 F200W photometry in Table 2 delensed by a magnification
$\mu=8\pm 1$.

Table 5: Derived emission line ratios and expected values

Line or line ratio | Equation / Derivation | Flux or flux ratioa
---|---|---
H$\beta$ |  $2.14$ H$\gamma$ | ($160\pm 20$) $\times$ $10^{-20}$ erg s${}^{-1}\,$cm-2
H$\alpha$ |  $6.11$ H$\gamma$ | ($460\pm 60$) $\times$ $10^{-20}$ erg s${}^{-1}\,$cm-2
Ne3O2 | [Ne iii] $\lambda$3869 $/$ [O ii] $\lambda$3727 | $1.8\pm 0.2$
O32 | from Ne3O2b; [O iii] $\lambda$5007 $/$ [O ii] | $30\pm 6$
[O iii] $\lambda$5007 | O32 $\times$ [O ii] | ($1300\pm 300$) $\times$ $10^{-20}$ erg s${}^{-1}\,$cm-2
auroral line ratio | [O iii] $\lambda$5007$/$ [O iii] $\lambda$4363 | $50\pm 16$
[O iii] $\lambda$4959,$\lambda$5007 | 1.34 $\times$ [O iii] $\lambda$5007 | ($1700\pm 400$) $\times$ $10^{-20}$ erg s${}^{-1}\,$cm-2
R23 | ([O ii] + [O iii] $\lambda$4959,$\lambda$5007) $/$ H$\beta$ | $11\pm 3$

aafootnotetext: Measured fluxes in the stacked spectra are magnified by
$\sim$13.3

bbfootnotetext: We estimate O32 based on our measured Ne3O2. The two line
ratios are strongly correlated at these high values.

###  3.3 Star formation rate and history

Hydrogen Balmer line strengths yield robust estimates of recent star formation
history within the past $\lesssim$ 10 Myr. These measurements commonly utilize
the strongest Balmer line H$\alpha$ or second strongest H$\beta$. Both of
these are redshifted beyond our observed wavelength range, however we detect
both H$\gamma$ and H$\delta$.

Intrinsic Balmer line strength ratios are dictated by atomic physics. For Case
B recombination at $T=10000\,$K, we expect H$\gamma$ / H$\delta$ $=1.81$
(e.g., Dopita & Sutherland, 2003; Groves et al., 2012). In MACS0647$-$JD, we
measure H$\gamma$ / H$\delta$ $\sim 1.88\pm 0.43$, consistent with
expectations (H$\gamma$ / H$\delta$ $=1.81$) within the uncertainties. Dust
reddening may artificially increase observed Balmer line ratios. We cannot
place meaningful constraints on the dust extinction, given the large
uncertainties in the flux ratio and the similar wavelengths of H$\gamma$ and
H$\delta$. Note that Balmer line stellar absorption might affect our
measurement of H$\gamma$ and H$\delta$ of $0-5\,$Å, which is within our
uncertainty of $6\,$Å. We assume no dust, consistent with the result
$A_{V}<0.02$ mag from SED fitting to the photometry of component A in Hsiao et
al. (2022) and similarly in our updated analysis of the latest photometry
§3.2. Finally, we note the measured H$\gamma$ rest-frame equivalent width EW
42$\pm$6 Å may be slightly suppressed by photospheric absorption lines with EW
$<5$Å, but that is within our measurement uncertainty.

Assuming no dust, we estimate the H$\beta$ and H$\alpha$ line fluxes using the
expected line ratios H$\beta$ = 2.14 H$\gamma$ and H$\alpha$ = 6.11 H$\gamma$
(see Table 5). Converting our inferred H$\alpha$ line flux to luminosity,
including a de-lensing correction for magnification, we estimate $L_{\rm
H\alpha}=(4.5\pm 0.2)\times 10^{41}\,{\rm erg\,s^{-1}}$. Adopting an SFR
conversion factor of 3.2 $\times$ $10^{-42}$ suitable for high-redshift
galaxies (Reddy et al., 2018), we estimate SFR $=1.4\pm 0.2\,$$M_{\odot}$
yr-1. Note that the SFR will be higher if there is dust, and the conversion
factor is sensitive to the IMF, star formation history, and metallicity
assuming that the escape fraction is zero (e.g., Wilkins et al., 2019).

Similarly, [O ii] $\lambda$3727 can also be used to estimate the SFR for
distant galaxies (e.g., Kennicutt, 1998). This yields a slightly lower ${\rm
SFR_{OII}}=0.6\pm 0.2\,$$M_{\odot}$ yr-1. However, we note that this empirical
calibration was derived for low-redshift galaxies and depends on metallicity
and dust, which are lower for high-redshift galaxies like MACS0647$-$JD.

###  3.4 Strong C iii] $\lambda\lambda$1907,1909 emission

We detect strong emission of C iii] $\lambda\lambda$1907,1909 (blended) with a
line flux of $(3.1\pm 0.6)\times 10^{-18}$ erg s-1 cm-2 and rest-frame
equivalent width 14$\pm 3\,$Å. Such high equivalent width C iii]
$\lambda\lambda$1907,1909 is associated with low metallicity galaxies
experiencing an intense burst of star formation (Rigby et al., 2015); it is
predicted for BPASS models only when they include very recent star formation
within the past Myr (Jaskot & Ravindranath, 2016), consistent with our young
age estimates §3.2. We use the measured equivalent width as a metallicity
diagnostic in §3.6.

We note additional C iii] emission appears to come from the B component, which
is marginally spatially resolved in the 2D spectrum of JD2 in Obs 21 (Figure
1). This would suggest a young age for B, or at least very recent star
formation perhaps in addition to the older star formation and age ($\sim$100
Myr) estimated from the photometry.

Strong C iii] emission with high rest-frame equivalent widths of 10 – 20 Å or
more has been observed in $z\sim 0$ – 6 galaxies, often associated with high
observed or inferred [O iii]+H$\beta$ equivalent widths $\sim$ 1000Å – 2000Å
(e.g., Stark et al., 2017; Berg et al., 2019; Hutchison et al., 2019; Mainali
et al., 2020; Tang et al., 2021; Mingozzi et al., 2022; Vanzella et al.,
2020a, 2023) or even higher than $2000\,$Å (Tang et al., 2023). This is
consistent with our expectation based on our extrapolated [O iii]+H$\beta$
flux (Table 5), which roughly corresponds to an equivalent width $\sim$ 1000Å,
assuming the continuum flux at rest-frame $\sim$5000Å is similar to what we
measure out to $\sim$4500Å.

We do not detect the higher ionization species C iv $\lambda$1549\. This
combined with the strong C iii] emission suggests that an AGN is likely not
the driving ionizing source in this galaxy. Detections of strong C iv are
often associated with AGN activity (e.g., Baskin & Laor, 2005; Le Fèvre et
al., 2019). However, young stellar populations can also drive stronger C iv
emission as well (e.g., Mainali et al., 2017).

If anything, we see a hint of C iv absorption, as also predicted by our
piXedfit best-fit model. Such C iv absorption is observed (and modeled) for
young stellar populations with ages $<$ 10 Myr (e.g., Leitherer et al., 1999;
Chisholm et al., 2019) and can constrain stellar age and metallicity when
detected at high signal-to-noise and resolution. The ISM can also absorb C iv
due to internal gas kinematics and/or higher column density (Steidel et al.,
2016; Jaskot & Ravindranath, 2016).

###  3.5 Ionization $\log(U)$ and log($\xi_{\rm ion}$)

The line ratio O32 $=$ [O iii] $\lambda$5007 $/$ [O ii] $\lambda$3727 has long
been used (e.g., Hicks et al., 2002) as a diagnostic for the ionization
parameter $\log(U)$. At high redshifts, when [O iii] $\lambda$5007 is
unavailable, the line ratio Ne3O2 $=$ [Ne iii] $\lambda$3869 $/$ [O ii]
$\lambda$3727 has been proposed as an alternative diagnostic (Pérez-Montero et
al., 2007; Levesque & Richardson, 2014; Maiolino & Mannucci, 2019; Witstok et
al., 2021). Strong correlations are observed between Ne3O2 and O32 in nearby
galaxies when all lines are detected with strong significance (Jaskot & Oey,
2013; Izotov et al., 2018; Flury et al., 2022), especially the case for higher
ionization (i.e., similar to properties of galaxies expected and found at
$z>6$). More distant galaxies at $z\sim 2$ – 7 exhibit similar trends
(Christensen et al., 2012; Tang et al., 2019; Vanzella et al., 2020b; Tang et
al., 2023).

In MACS0647$-$JD, we measure a high value for Ne3O2 $=1.8\pm 0.2$. According
to Witstok et al. (2021, Equations 1–3), this Ne3O2 ratio corresponds to O32
$=30\pm 6$ and ionization parameter $\log(U)$ $=-1.84\pm 0.06$, using
$\log(U)$ = 0.80 $\times$ log(O32) $-$ 3.02 from (Díaz et al., 2000).

We also used hii-chi-mistry version 5.22141414
https://home.iaa.csic.es/$\sim$epm/HII-CHI-mistry-opt.html (Pérez-Montero,
2014) to estimate $\log(U)$ using the observed and extrapolated line flux
ratios discussed in §3.6 and listed in Table 6. Our inputs were measured line
fluxes for [O ii] $\lambda$3727, [Ne iii] $\lambda$3869, and [O iii]
$\lambda$4363, all normalized to our extrapolated H$\beta$ flux based on
H$\gamma$. Here we did not use the extrapolated [O iii] $\lambda$5007 flux. We
obtain an ionization parameter of $\log(U)$ $=-2.09\pm 0.02$, similar to but
slightly lower than the value estimated above from Ne3O2.

Kewley et al. (2019) noted the line ratio C iii] $\lambda\lambda$1907,1909 $/$
[C ii] $\lambda$2325 (blend) is an excellent diagnostic for ionization
parameter $\log(U)$ at low metallicities 12+log(O/H) $<8.5$ (see their Figure
7). Our non-detection of [C ii] with flux $<0.55$ $\times 10^{-18}$ erg
s${}^{-1}\,$cm-2 (1 $\sigma$ limit), yielding a line ratio C iii] $/$ [C ii]
$>5.7$ corresponds to $\log(U)$ $>-2.8$ for 12+log(O/H) $\sim$ 7.6.

We conclude $\log(U)$ $=-1.9\pm 0.2$ based on the three estimates (see also
Table 7). This is comparable to the value $\log(U)$ $\sim$ $-2$ obtained for
GN-z11 (Bunker et al., 2023).

Our H$\alpha$ luminosity measurement (delensed and assuming no dust) yields an
estimate for the production rate of hydrogen-ionizing photons: $\dot{N}_{\rm
ion}$ = (3.3$\pm 0.1$)$\times 10^{53}$ s-1(${\rm log}(L_{\rm H\alpha})={\rm
log}(N_{\rm ion}/{\rm s})-11.87$). Combined with our measured and demagnified
UV luminosity for clump A (corresponding to $M_{UV}=-19.5\pm 0.2$), we
estimate an ionizing photon production efficiency $\xi_{\rm ion}=\dot{N}_{\rm
ion}/L_{\nu}^{\rm UV}=1.6\pm 0.3$ $\times 10^{25}$ erg-1 Hz, or log($\xi_{\rm
ion})=25.2\pm 0.2$. This is consistent with predictions for high-redshift
galaxies, with higher values expected for younger, lower-metallicity galaxies
(e.g., Schaerer, 2003; Robertson et al., 2013; Wilkins et al., 2016).
Observationally, recent studies reported higher values ${\rm log}(\xi_{\rm
ion})\sim 25.7-26.0\,$erg-1 Hz for high-redshift ($7<z<11$) galaxies (e.g.,
Tang et al., 2023; Bunker et al., 2023; Fujimoto et al., 2023). Our
$\dot{N}_{\rm ion}$ estimate should be treated as a lower limit that could
increase due to dust and/or escape fraction $f_{\rm esc}$ (see Topping et al.
in preparation).

Table 6: Metallicity Estimates

Method | Emission Lines | 12+log(O/H) | $Z$
---|---|---|---
pyneb | [O ii], [O iii] $\lambda$4363; extrapolateda H$\beta$, [O iii] $\lambda$5007 | $8.0\pm 0.2$ |  $0.20^{+0.12}_{-0.07}$ $Z_{\odot}$
hii-chi-mistry | [O ii], [Ne iii] $\lambda$3869, [O iii] $\lambda$4363; extrapolateda H$\beta$ | $7.5\pm 0.2$ |  $0.06^{+0.04}_{-0.02}$ $Z_{\odot}$
Ne3O2 | [O ii], [Ne iii] $\lambda$3869 | $7.6\pm 0.3$ |  $0.08^{+0.08}_{-0.04}$ $Z_{\odot}$
R23 | [O ii]; extrapolateda H$\beta$, [O iii] $\lambda$5007 | $8.0\pm 0.3$ |  $0.20^{+0.20}_{-0.10}$ $Z_{\odot}$
R23 and O32 | [O ii]; extrapolateda H$\beta$, [O iii] $\lambda$5007 | $7.7\pm 0.2$ |  $0.10^{+0.06}_{-0.04}$ $Z_{\odot}$
EW(C iii]) | C iii] | $7.8\pm 0.2$ |  $0.13^{+0.07}_{-0.05}$ $Z_{\odot}$

aafootnotetext: Extrapolated line fluxes correspond to those derived from
either the theoretical line ratios (e.g., H$\beta$/H$\gamma$) or empirical
calibrations (e.g., Ne3O2 vs O3O2).

Table 7: Physical properties of MACS0647$-$JD (entire galaxy) and individual
clumps A and B, estimated based on observed and estimated line fluxes and SED
fitting to the photometry. Star formation rate (average within the past 10
Myr) and stellar mass are corrected for lensing magnification.

Parameter | Variable | MACS0647-JD | clump A | clump B
---|---|---|---|---
Emission lines
Metallicity (gas phase) | 12+log(O/H) |  | 7.5 – 8.0 |
$Z_{\rm gas}/Z_{\odot}$ |  | 0.06 – 0.2 |
Ionization parameter | $\log(U)$ |  | $-1.9\pm 0.2$ |
Ionizing photon production efficiency | log($\xi_{\rm ion}/$erg-1 Hz) |  | $25.2\pm 0.2$ |
Star formation rate | SFR (${\rm M_{\odot}/yr}$) |  | $1.4\pm 0.2$ |
SED fitting
Absolute UV magnitude |  $M_{UV}$ (AB mag) | $-20.3\pm 0.2$ | $-19.5\pm 0.2$ | $-17.9\pm 0.2$
Star formation rate | SFR (${\rm M_{\odot}/yr}$) | $8\pm 3$ | $2\pm 1$ | $0.9\pm 0.3$
Stellar mass | log($M_{*}/M_{\odot}$) | $8.1\pm 0.3$ | $7.8\pm 0.3$ | $7.5\pm 0.3$
Specific star formation rate | log(sSFR/Gyr-1) | $-7.1\pm 0.3$ | $-7.2\pm 0.3$ | $-7.5\pm 0.3$
Mass-weighted age |  ${\rm age}_{\rm M}\,$(Myr) | $20\pm 20$ | $10^{+30}_{-9}$ | $40\pm 30$
Dust |  $A_{V}$ (mag) | $0.07\pm 0.06$ |  $<$ 0.06 | $0.10\pm 0.05$

††footnotetext:  Note. BAGPIPES assumes Kroupa et al. (1993); to renormalize
those results, we multiplied the stellar masses by 0.94 (Madau & Dickinson,
2014).

###  3.6 Metallicity

We use various methods and line ratio diagnostics to estimate MACS0647$-$JD’s
gas-phase metallicity 12+log(O/H) = 7.5 – 8.0, or (0.06 – 0.2) $Z_{\odot}$,
where we adopt a solar metallicity 12+log(O/H) = 8.7 (Asplund et al., 2021).
Table 6 summarizes our results, and we describe our methods below.

The auroral line [O iii] $\lambda$4363 can provide a “direct” metallicity
measurement via electron temperature when detected and measured along with
other lines including [O iii] $\lambda$4959,$\lambda$5007 (e.g., Peimbert,
1967; Osterbrock, 1989; Sanders et al., 2023). Given our estimate O32 $=30\pm
6$ (§3.5) and observed line flux for [O ii], we can estimate the expected [O
iii] $\lambda$5007 line flux as $(1.3\pm 0.3)\times 10^{-17}\,$erg
s${}^{-1}\,$cm-2, assuming no dust, or $\sim$50 times stronger than [O iii]
$\lambda$4363\. Note the [O iii] $\lambda$5007 line is 2.98 times stronger
than [O iii] $\lambda$4959 (Storey & Zeippen, 2000), so our extrapolated
combined [O iii] $\lambda$4959,$\lambda$5007 flux is 1.34 times the [O iii]
$\lambda$5007 flux.

We use pyneb151515http://research.iac.es/proyecto/PyNeb (Luridiana et al.,
2015) to analyze the observed and extrapolated emission line ratios. For the
entire procedure, we assumed no dust and an electron density $n_{\rm e}=100$
cm-3. First, we use the task getCrossTemDen, taking into account the [O iii]
$\lambda$5007 $/$ 4363 $\sim$ 50 with a 20% uncertainty. In this way, we
obtain the electron temperature of the high-ionization zone $T_{\rm e}$([O
iii]) $=15000\pm 1400$ K. The $T_{\rm e}$ uncertainty is estimated by running
the task 1000 times and taking the standard deviation of all the values. Then,
we use the Garnett (1989) relation to estimate the low-ionization gas
temperature $T_{\rm e}$([N ii]) $=13600\pm 1000$ K. Finally, we calculated the
O++ and O+ ionic abundances with the task getCrossTemDen, using as input [O
iii] $\lambda$5007 $/$ H$\beta$ $\sim$ 8 and $T_{\rm e}$([O iii]), and [O ii]
$\lambda$3727 $/$ H$\beta$ $\sim$ 0.26 and $T_{\rm e}$([N ii]), respectively,
with the same method to estimate the uncertainties. The total of both species
yields 12+log(O/H) $=8.0\pm 0.2$, or $\sim$20% $Z_{\odot}$ (0.13 – 0.32
$Z_{\odot}$).

We also utilize hii-chi-mistry version 5.22 to analyze our observed line
ratios, as described in §3.5. We obtain 12+log(O/H) $\sim$ $7.5\pm 0.2$,
corresponding to $\sim$$0.06^{+0.04}_{-0.02}$$Z_{\odot}$.

Next, we turn to line ratio diagnostics, beginning with Ne3O2. Previous
reviews find no strong correlation between Ne3O2 and metallicity, as seen, for
example, in local metal-poor galaxies analyzed by Nakajima et al. (2022,
Figure 9 therein). But the few galaxies with high Ne3O2 $\sim$ 2 in that study
were clustered between roughly 12+log(O/H) $=7.6\pm 0.2$, or 0.05 – 0.13
$Z_{\odot}$. It is unclear if that low-redshift result can be extended to
high-redshift galaxies.

Another metallicity diagnostic is the line ratio R23 = ([O iii]
$\lambda$4959,$\lambda$5007+ [O ii] $\lambda$3727) $/$ H$\beta$ (e.g.,
Nakajima et al., 2022; Sanders et al., 2023). Based on our observed [O ii],
extrapolated [O iii], and H$\beta$ inferred from H$\gamma$, we extrapolate R23
$=11\pm 3$. This is among the highest values measured for local metal-poor
galaxies by Nakajima et al. (2022). That puts R23 $\sim$ 11 in the zone of
confusion in the bimodal R23–metallicity relation, severely limiting its
usefulness as a metallicity diagnostic, though it can still provide a rough
estimate. We note in Nakajima et al. (2022, Figure 3), that galaxies with R23
$=11\pm 3$ have metallicities 12+log(O/H) $=8.0\pm 0.3$, or between $\sim$0.1
and 0.4 $Z_{\odot}$. We note some of the scatter in the R23 vs. $Z$ is due to
ionization, with higher ionization yielding higher R23 values for a fixed
metallicity (e.g., Pérez-Montero, 2014, Figure 5).

Izotov et al. (2021) propose a metallicity indicator combining R23 and O32
(their Equation 5) for improved accuracy at low metallicities $<$ 6%
$Z_{\odot}$, or 12+log(O/H) $<7.5$. Nakajima et al. (2023) show this relation
works up to 12+log(O/H) $\sim$ 7.8 for $z=4$ – 8.5 galaxies with direct
metallicity measurements from NIRSpec. For MACS0647-JD, this relation yields
12 + log(O/H) $\sim$ $7.7\pm 0.2$, or 0.06 – 0.16 $Z_{\odot}$.

Finally, we use the rest-frame UV line C iii] $\lambda\lambda$1907,1909 as a
metallicity diagnostic. Mingozzi et al. (2022) analyzed 45 local high-redshift
analogs observed by the CLASSY survey (Berg et al., 2022), measuring a
relation between C iii] EW and metallicity with 0.18 dex intrinsic scatter for
galaxies with EW $>$ 5Å. Using their equation 7 and our observed C iii] EW
14.2$\pm 2.5\,$Å (discussed in §3.4), we estimate 12+log(O/H) $=7.84\pm 0.18$,
or 0.09 – 0.21 $Z_{\odot}$.

We find broad general agreement among our 6 metallicity indicators with best-
fit estimates ranging between 12+log(O/H) = 7.5 – 8.0, or (0.06 – 0.2)
$Z_{\odot}$, as summarized in Table 6, which is also consistent with the
metallicity of 12+log(O/H) = 7–7.8 expected from Astraeus simulations for
galaxies at z$\sim$10 with a stellar mass of $10^{8.1}\,M_{\odot}$ (Ucci et
al., 2023). This is promising for future studies that only have one or more of
these diagnostics available either in the rest-frame optical or rest-frame UV.
On the other hand, greater precision will be achieved by generally improving
these diagnostics and in our specific case by obtaining additional spectra of
MACS0647$-$JD covering longer wavelengths including [O iii]
$\lambda$4959,$\lambda$5007, H$\beta$, and H$\alpha$.

Figure 4:  Left: A Lyman damping wing is required to more closely fit the
observed Lyman break (black). The piXedfit SED model (blue) is convolved with
the IGM transmission (orange) and NIRSpec prism spectral resolution yielding
the transmitted model spectrum (red). The vertical dotted line denotes the
systemic wavelength of Ly$\alpha$ at $z=10.17$. Right: Black lines represent
1$\sigma$, 2$\sigma$, and 3$\sigma$ contours of the probability distribution
of $X_{\rm HI}$ and $R_{\rm HII}$. A highly neutral IGM ($X_{\rm HI}>0.9$ at a
1$\sigma$ lower limit) with a small ($R_{\rm HII}<0.2$ pMpc) ionized bubble
around MACS0647$-$JD yields the best fit to the data. Additional model
complexity will be required to properly reproduce the observed damping wing.

###  3.7 Lyman-$\alpha$ damping wing

The Ly$\alpha$ photon scattering cross section as a function of wavelength is
given by the Voigt profile, which combines a Gaussian core and Lorentzian
wings (Tasitsiomi, 2006). Resonant scattering of Ly$\alpha$ photons by the
neutral IGM suppresses line and continuum fluxes at wavelengths bluer than the
rest-frame Ly$\alpha$ at 1216Å. Additionally, the Lorentzian wing cross
section accumulates the attenuation to the redward continuum, softening the
shape of Ly$\alpha$ break. This is known as Ly$\alpha$ damping wing
attenuation (Miralda-Escude & Babul, 1995). Recently, this effect has been
observed in NIRSpec prism observations of high-redshift galaxies (Bunker et
al., 2023; Boyett et al., 2023; Arrabal Haro et al., 2023a, b; Curtis-Lake et
al., 2023).

We model the Ly$\alpha$ damping wing optical depth following Equation (30) in
Dijkstra (2014), as done in Arrabal Haro et al. (2023a, b). The damping wing
description has two free parameters (with redshift held fixed at our measured
$z=10.17$): (1) the neutral hydrogen fraction in the IGM ($X_{\text{HI}}$) and
(2) the size of the ionized bubble ($R_{\text{HII}}$), or Stromgren sphere. In
short, a higher neutral fraction in the IGM makes the break cutoff become
smoother, and a larger ionized bubble size shifts the break blueward allowing
the escape of photons at shorter wavelengths than the rest frame Ly$\alpha$.
To reproduce the observed continuum spectrum, the galaxy model SEDs are
convolved with the IGM transmission ($T_{\text{IGM}}\propto e^{-\tau}$, where
$\tau$ is damping wing optical depth). We then smooth the model spectra with
prism spectral resolution and apply an additional 5% of systemic errors in the
$\chi^{2}$ estimation.

We perform fitting using an MCMC sampler package described in Jung et al.
(2017). We use flat linear priors for the free parameters $X_{\rm HI}$ and
$R_{\rm HII}$. In each MCMC chain step, we take a random model spectrum from
the range of models generated by piXedfit (see §3.2) to accommodate the
uncertainties in galaxy SED modeling.

Figure 4 shows our results suggesting a small size of an ionized bubble
($R_{\rm HII}$ $\ll 1$ pMpc) with a highly neutral IGM ($X_{\rm HI}$ $>$ 0.9
at a 1$\sigma$ lower limit). The $R_{\text{HII}}$ measurement appears reliable
in the sense that the observed spectra show no positive signals blueward of
the systemic wavelength of Ly$\alpha$. However, the interpretation of the
$X_{\text{HI}}$ measurement is rather complicated. The modeled spectra present
a Ly$\alpha$ break still considerably steeper than the observed spectrum. As
the modeled spectra already include Ly$\alpha$ damping wing opacity with
almost fully-neutral IGM, such discrepancies cannot be explained with the IGM
attenuation alone. In fact, the total Ly$\alpha$ optical depth combines the
IGM damping wing optical depth ($\tau_{\rm IGM}$) and the optical depth due to
resonant scattering within the circumgalactic (CGM; Dijkstra, 2014). However,
the latter part is missed in our simple description of damping wing opacity.
To mitigate the differences between the modeled spectra and the observed, it
is necessary to carefully model the CGM contribution (Sadoun et al., 2017;
Weinberger et al., 2018; Mason & Gronke, 2020). Including the CGM contribution
would result in additional softening on Ly$\alpha$ break closer to the
observed spectrum, which possibly requires less contribution from IGM
attenuation and could allow for a slightly more ionized IGM. Detailed modeling
of Ly$\alpha$ attenuation of the CGM requires knowledge of density profiles of
HI gas and radiation field from a host galaxy (Weinberger et al., 2018; Mason
& Gronke, 2020), which is beyond the scope of this study. Also, the relation
between IGM attenuation and bubble size can deviate from the theoretical model
of Dijkstra (2014) due to the stochasticity of individual sightlines, such as
fluctuations in density/velocity and random encounters of self-shielded
systems (Hutter et al., 2014; Park et al., 2021; Smith et al., 2022). Ideally,
one needs to average over a large number of observations to suppress such
uncertainties. Additionally, the uncertainties in modeling intrinsic rest-UV
spectra make the interpretation more complicated.

###  3.8 Ionized bubble size

We also estimate the radius of the ionized bubble around MACS0647$-$JD by
integrating the total ionizing photon production over the galaxy’s lifetime as
in Shapiro & Giroux (1987):

$\frac{4}{3}\pi R_{\rm HII}^{3}\sim\frac{\dot{N}_{\rm ion}\,f_{\rm
esc}\,t_{*}}{\chi_{\rm HI}\,n_{\rm H}}.$ (1)

We estimate $\dot{N}_{\rm ion}$ $\sim$ 3.3$\times 10^{53}$ s-1 based on SFR
$\sim$ 1.4 $M_{\odot}$ yr-1 for clump A (§3.5) with stars having formed
continuously for perhaps $t_{*}$ $\sim$ 20 Myr (§3.2). Based on the Ly$\alpha$
damping wing, we find that the IGM is completely neutral, or nearly so
$\chi_{\rm HI}\approx 1$ (§3.7). The average density of hydrogen particles in
the universe at $z=10.17$ is $n_{\rm H}$ $\sim$ 7$\times 10^{69}$ Mpc-3, where
$n_{\rm H}=(1-Y_{\rm He})\,\rho_{\rm crit}\,\Omega_{\rm b}\,(1+z)^{3}\,m_{\rm
H}^{-1}$.

Estimates of $f_{\rm esc}$ for MACS0647$-$JD will be presented by Topping et
al. (in preparation). Here, it suffices to explore possible values. For
example, $f_{\rm esc}=10$% yields $R_{\rm HII}$ $\sim$ 0.09 pMpc. A more
extreme $f_{\rm esc}=50$% would only increase that to $R_{\rm HII}$ $\sim$
0.15 pMpc. These are likely too small to allow for the transmission of
Lyman-$\alpha$ photons since to a first approximation, the spatial scale
imposed by the Gunn-Peterson damping wing corresponds to $\sim$0.2 pMpc at
$z\sim 10$ (Miralda-Escudé, 1998).

Above, we use the SFR for clump A. The entire galaxy has SFR $\sim$ 10
$M_{\odot}$ yr-1, or $\sim$ 7$\times$ higher. We might expect that most of the
ionizing radiation comes from the blue clump A. But even generously assuming
the same ionizing photon production efficiency $\xi_{\rm ion}$ for the entire
galaxy and increasing $\dot{N}_{\rm ion}$ by 4$\times$, $R_{\rm HII}$ only
increases by a factor of $\sim$1.6 to $R_{\rm HII}$ $\sim$ 0.24 pMpc, again
assuming a very high $f_{\rm esc}=50$%.

Figure 5: NIRSpec prism spectra of two lensed images of the candidate
companion galaxy C. Figures show slitlet coverages, 2D spectra, and 1D
extractions, similar to Figure 1 for MACS0647$-$JD. Redshift is fixed to the
same value $z=10.17$.  Figure 6: Stack of the spectra shown in Figure 5 for
two lensed images of the candidate companion galaxy C. No emission lines are
confidently detected; their expected wavelengths are labeled assuming a
redshift $z=10.17$ as derived for MACS0647$-$JD.

###  3.9 Candidate companion galaxy C

As discovered in Hsiao et al. (2022), a nearby triply-lensed J-band dropout
galaxy is suspected to be a companion of MACS0647$-$JD $\sim$3 kpc away. The
photometric redshift and geometric lens model redshift of this companion “C”
are consistent with MACS0647$-$JD; the observed lensed positions require a
similar or identical redshift. Here we show the NIRSpec spectra of the
candidate companion C in Figure 5 and the 1D stack in Figure 6. The Obs 21
spectrum shows a clear Lyman break consistent with $z=10.17$. The Obs 23
spectrum is noisier but also consistent with the redshift of MACS0647–JD
($z=10.17$). This supports our conclusion from Hsiao et al. (2022) that
MACS0647$-$JD is likely the most distant galaxy merger known at $z=10.17$,
including two merging components A and B plus a third component C nearby,
where component C may indeed be a companion of A and B components.

Given the lower SNR spectrum of the companion C, we do not detect emission
lines, nor do we detect the Ly$\alpha$ damping wing expected due to the
proximity to A.

##  4 Conclusions

In this study, we report NIRSpec prism observations of MACS0647$–$JD,
primarily targeting its small component A with delensed radius $r\sim 70\,$pc.
We measure a spectroscopic redshift $z=10.17$ based on detections of 7
emission lines: C iii] $\lambda\lambda$1907,1909, [O ii] $\lambda$3727, [Ne
iii] $\lambda$3869, [Ne iii] $\lambda$3968, H$\delta$, H$\gamma$, and [O iii]
$\lambda$4363.

This redshift is slightly lower than the photometric redshifts $z\sim 10.6$
estimated previously based on HST and +HST imaging. This may be explained by a
Lyman-$\alpha$ damping wing revealed by NIRSpec that suppresses the photometry
at $\sim$1.5 $\mu$m more than expected for a sharp Lyman break. Our analysis
of the Lyman damping wing suggests a completely neutral IGM with MACS0647$-$JD
not having ionized any significant volume beyond its immediate surroundings
($R_{\text{HII}}\ll 1$ pMpc). Based on observed and extrapolated line ratios
of JDA, we estimate an ionization parameter $\log(U)$ $=-1.9\pm 0.2$, and
ionizing photon production efficiency log($\xi_{\rm ion})=25.2\pm 0.2$ for
clump A. This log($\xi_{\rm ion}$) value is similar to values measured in
sub-$L^{*}$ $z\sim 4$ – 5 galaxies (Bouwens et al., 2016) but lower than
measured in $z\sim 7$ – 8 galaxies: log($\xi_{\rm ion}$) = 25.7 – 26.0 (Tang
et al., 2023).

Based on the observed and extrapolated line ratios of JDA, we also estimate a
gas phase metallicity 12+log(O/H) = 7.5 – 8.0, or (0.06 – 0.2) $Z_{\odot}$
derived using 6 different methods, including optical line diagnostics as well
as one diagnostic based on the rest-UV line C iii] (Mingozzi et al., 2022).
Derived metallicities are consistent across different methods. The overall
agreement is encouraging, supporting the use of each individual method in
galaxies with fewer detected emission lines. Additional MIRI spectroscopy
covering [O iii] $\lambda$4959,$\lambda$5007, H$\beta$, and H$\alpha$ would
enable a more precise “direct” metallicity measurement when combined with the
other lines presented here, including the auroral line [O iii] $\lambda$4363.

The total stellar mass of MACS0647$-$JD is log($M/M_{*}$) $=8.1\pm 0.3$ based
on SED fitting to the photometry of the entire galaxy including both clumps A
and B. This is towards the low end of stellar masses for $z=4$ – 10 galaxies
with direct metallicity estimates from JWST NIRSpec spectroscopy (Nakajima et
al., 2023). The metallicity of MACS0647$-$JD at $z=10.17$ (if we assume the
metallicity of clump A is representative of the whole galaxy) is consistent
with the metallicities measured for $4<z<10$ galaxies of similar stellar mass.

MACS0647$-$JD has a delensed absolute UV magnitude $M_{UV}=-20.3\pm 0.2$,
including $M_{UV}=-19.5\pm 0.2$ for clump A and $M_{UV}=-17.9\pm 0.2$ for
clump B. SED fitting to the observed photometry of clump A yields a stellar
mass log($M/M_{*}$) $=7.8\pm 0.3$, likely all produced within the most recent
20 Myr. This young age estimate is supported by the observed strong C iii]
$\lambda\lambda$1907,1909 with rest-frame equivalent width $14\pm 2$ Å. The
star formation rate of clump A based on H$\gamma$ and assuming no dust is
$1.4\pm 0.2\,M_{\odot}/{\rm yr}$ over the past 10 Myr. This is similar to the
estimate $2\pm 1\,M_{\odot}/{\rm yr}$ based on SED fitting to clump A’s
photometry.

Clump B is likely older with a rising star formation history over $\sim$50 Myr
or more, stellar mass log($M/M_{*}$) = $7.8\pm 0.3$, and $0.13\pm 0.07$ mag
dust. The older age of clump B suggests it may have merged with clump A rather
than the two clumps forming together in the same galaxy (Hsiao et al., 2022).
Spectroscopy of a nearby galaxy C $\sim$3 kpc away (delensed) reveals a Lyman
break consistent with MACS0647$-$JD’s redshift $z=10.17$. This companion C may
be destined to merge with A and B. MACS0647$-$JD is likely the most distant
galaxy merger yet known.

Emission line spectroscopy is possible for the triply-lensed galaxy
MACS0647$-$JD thanks to its 3 images magnified by factors $\sim$8, 5, and 2.
The brightest lensed image JD1 is F200W AB mag 25.0, including AB mag 25.8 for
clump A. Of all known $z>10$ galaxies, only GN-z11 at $z=10.603$ (Bunker et
al., 2023) is similarly bright (AB mag 26.0; Tacchella et al. 2023), while
most others are AB mag 28 – 29 (Curtis-Lake et al., 2023; Arrabal Haro et al.,
2023a). MACS0647$-$JD and GN-z11 offer unique opportunities for detailed
studies of galaxies within the first 500 Myr.

Many of the physical properties presented in this work rely on extrapolations
for [O iii] $\lambda$5007, H$\beta$ and/or H$\alpha$ line fluxes. MIRI
spectroscopy covering these lines would improve measurements of all physical
parameters, including a “direct” metallicity measurement for MACS0647$-$JD at
$z=10.17$.

## Acknowledgments

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

This work is based on observations made with the NASA/ESA/CSA James Webb Space
Telescope () 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 .

These observations are associated with programs 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. 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. The Cosmic Dawn
Center is funded by the Danish National Research Foundation (DNRF) under grant
#140. EZ and AV acknowledge support from the Swedish National Space Agency. EZ
also acknowledges grant 2022-03804 from the Swedish Research Council. MB
acknowledges support from the Slovenian national research agency ARRS through
grant N1-0238. TAH is supported by an appointment to the NASA Postdoctoral
Program (NPP) at NASA Goddard Space Flight Center, administered by Oak Ridge
Associated Universities under contract with NASA. AZ 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
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. EV acknowledges
support from the INAF GO Grant 2022 “The revolution is around the corner: JWST
will probe globular cluster precursors and Population III stellar clusters at
cosmic dawn”. ACC thanks the Leverhulme Trust for their support via a
Leverhulme Early Career Fellowship.

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