black. Redshift distributions of the 3 sub-samples of ultra-blue candidate
galaxies are shown in the lower left plot inset.

To analyze the possible scenarios that could give rise to these extreme blue
average $\beta$ values, we compare our results to the Pop. I, II, and III
instantaneous burst SED models produced by the Yggdrasil SPS code (Zackrisson
et al., 2011). The Pop. I and Pop. II models are plotted with metallicities
$Z_{\star}=\\{0.02,0.2,1\\}~{}\mathrm{Z}_{\odot}$, a Starburst99 single
stellar population (SSP) based on Padova-AGB tracks (Leitherer et al., 1999;
Vázquez & Leitherer, 2005), a gas density
$n_{\mathrm{H}}=100~{}\mathrm{cm}^{-2}$, and a universal Kroupa (2001) IMF in
the range $0.1-100~{}\mathrm{M}_{\odot}$. The “PopIII” model uses the same
Kroupa (2001) IMF as the Pop. I and Pop. II models, although with a rescaled
SSP from Schaerer (2002). The “PopIII.2” model uses a moderately top-heavy IMF
(lognormal with $10~{}\mathrm{M}_{\odot}$ characteristic mass, dispersion
$\sigma=1.0$, and $1-500~{}\mathrm{M}_{\odot}$ wings) from Raiter et al.
(2010b), while the “PopIII.1” model uses the most top-heavy IMF
($50-500~{}\mathrm{M}_{\odot}$ with Salpeter (1955) IMF slope) from Schaerer
(2002). All Pop. III models assume zero metallicity by definition.

In Figure 17, we calculate $\beta$ in the 10 C94 filters for a range of ages,
$10^{6}-10^{9}$ yr, and plot against our average $\beta$ results at
$M_{\mathrm{UV}}=-19$ given in Table 7 from our best-fitting power law to the
$\beta-M_{\mathrm{UV}}$ relation in our 3 redshift bins. First of all, we
conclude that since none of these dust-free models can reproduce our results
at $6.5<z<8.5$, there must have been dust built up in the majority of these
galaxies already at this epoch. We now focus our attention towards our highest
redshift bin, where the bluest and most extreme $\langle\beta\rangle$ are
observed. At these redshifts, we cannot rule out the possibility that there
are Pop. III sources within our sample and propose 2 plausible scenarios which
could explain our observational results:

  1. 1.

We are dominated by low-metallicity, $Z_{\star}<\mathrm{Z}_{\odot}$, stellar
populations with moderate to extreme Lyman continuum leakage,
$f_{\mathrm{esc,LyC}}>0.5$, in dust-free environments. It has been shown,
however, that both FSPS (Conroy et al., 2009; Conroy & Gunn, 2010; Byler et
al., 2017) and $\alpha$-enhanced BPASS (Byrne et al., 2022) models reduce the
dependence of $\beta$ of $f_{\mathrm{esc,LyC}}$ and hence allow for lower
values of $f_{\mathrm{esc,LyC}}$ to coincide with our observations (see Cullen
et al., 2023b, Fig. 9).

  2. 2.

There exists a non-negligible number of galaxies in the sample with a more
top-heavy (potentially Pop. III) IMF which either must have
$f_{\mathrm{esc,LyC}}\simeq 1$, if enshrouded in dust, or moderate
$f_{\mathrm{esc,LyC}}\gtrsim 0.5$ if dust-free. We note that we have already
seen evidence of strong metal lines in spectra at $z>11$ (e.g. GN-z11), making
it unlikely that many of our high redshift galaxy sample host entirely metal-
free Pop. III stellar populations. There remains the possibility, however,
that Pop. III stars contribute a non-negligible amount to the stellar SED due
to the co-existence and incomplete mixing of these with more metal-enriched
stars (Sarmento et al., 2018, 2019).

Aside from these two scenarios that would explain these blue $\beta$ mentioned
above, there still remains the possibility that our subsample is biased blue
by Ly$\alpha$ emission at (as much as $\Delta\beta=-0.6$ for
$\mathrm{EW}_{\mathrm{Ly}\alpha}=300~{}\mathrm{\AA}$ at $z\sim 7$), is
dominated by contamination from Balmer break galaxies, or is simply produced
as a result of photometric scatter in our wide-band photometric NIRCam
surveys.

Figure 17: Power law measured UV $\beta$ slopes as a function of galaxy age
for the instantaneous burst Yggdrasil population I, II, and III SEDs
(Zackrisson et al., 2011) measured in the 10 C94 filters to avoid bias from
nebular rest-UV line emission prevalent at young ages. Bias corrected power
law $\beta$ constraints for our three redshift bins are highlighted in light
orange showing the most notable new $11<z<13$ ultra-blue $\langle\beta\rangle$
measurements.

##  7 Conclusions

In this paper, we have calculated the UV continuum slopes, $\beta$, absolute
UV magnitudes, $M_{\mathrm{UV}}$, and stellar masses, $M_{\star}$, for 1011
high redshift galaxies at $6.5<z<13$ taken from the EPOCHS v1 sample across
$178.9~{}\mathrm{arcmin}^{2}$ of unmasked blank sky area. The main aims of
this study are to both trace the build up of dust from the average $\beta$
values as well as search for extremely blue $\beta<-3$ in individual galaxies
in the EoR. We favor the power law method to measure $\beta$ as it is not
biased red by the Bayesian prior on $\beta$ and it better matches 41 cross-
matched NIRSpec PRISM derived $\beta_{\mathrm{spec}}$ collated from the DJA.
We summarize the main results of this paper below:

  1. 1.

We quantify the potential impact of rest-frame UV line emission, Lyman alpha
emitters (LAEs) and damped Lyman alpha systems (DLAs) on the measured $\beta$
as a function of redshift in the range $6.5<z<13$. Biases can be seen as large
as $\lvert\Delta\beta\rvert\simeq 0.1$ for UV-line emitters per
$10~{}\mathrm{\AA}$ EW, $\Delta\beta=-0.6$ for the strongest LAEs with
EW=$300~{}\mathrm{\AA}$, and $\Delta\beta=0.5$ for proximate DLAs with
$N_{\mathrm{HI}}=10^{23.5}~{}\mathrm{cm}^{-2}$. Though some JWST/NIRCam medium
band filters are present in several wide-field surveys, expanding the number
of filters used in deep fields can help in reducing these biases, for instance
in the JADES Origin Field (PID: 3215).

  2. 2.

Our $\beta$ bias simulations show that the faintest galaxies in our sample are
biased blue, with maximum $\Delta\beta\simeq-0.55$. This bias is larger for
redder galaxies due to the increased selectability of blue objects, and is
especially poor ($\Delta\beta\sim-0.3$ even in the brightest sources) for red
objects at $6.5<z<7.5$ in fields where blue supplementary HST/ACS data is not
included and at $7.5<z<9.5$ in CEERS and NGDEEP where there is no F090W filter
even when including F814W data from HST/ACS.

  3. 3.

We measure a decreasing trend of $\beta$ with redshift, $\beta=-1.51\pm
0.08-(0.097\pm 0.010)\times z$. This is corroborated by our
$\beta(M_{\mathrm{UV}}=-19)$ decreasing from to
$\beta(M_{\mathrm{UV}}=-19)=-2.19\pm 0.06$ at $z\simeq 7$ to
$\beta(M_{\mathrm{UV}}=-19)=-2.73\pm 0.06$ at $z\simeq 11.6$, implying minimal
average dust attenuation at the highest redshifts and deviating from the
FLARES, DELPHI, SC SAM GUREFT, and DREaM simulations. Our $\beta-z$ relation
is also discrepant with recent JWST observations by Topping et al. (2023) and
falls between those by Cullen et al. (2023b) and Roberts-Borsani et al. (2024)
due to differing sample $M_{\mathrm{UV}}$ distributions and selection
procedures.

  4. 4.

We measure a flatter $\mathrm{d}\beta/\mathrm{d}M_{\mathrm{UV}}=0.03\pm 0.02$,
leading an $M_{\mathrm{UV}}$ independent $\beta-z$ relation, and a shallower
$\mathrm{d}\beta/\mathrm{d}\log_{10}(M_{\star}/\mathrm{M}_{\odot})=0.24\pm
0.01$ at $z\simeq 7$ than seen in previous HST studies (e.g. Finkelstein et
al., 2012; Bhatawdekar & Conselice, 2021), revealing a large population of low
mass, faint, red galaxies. These could be DLAs or nebular dominated galaxies,
but if indeed reddened by dust this would imply either early dust production
in the stellar winds of asymptotic giant branch (AGB) or carbon-rich Wolf-
Rayet binaries coupled with reduced dust destruction in subsequent SNe reverse
shocks.

  5. 5.

The observed steepening of
$\mathrm{d}\beta/\mathrm{d}\log_{10}(M_{\star}/\mathrm{M}_{\odot})$ towards
high redshift implies that dust produced by core-collapse SNe at the earliest
times is ejected by SNe-induced outflows and retained by the large
gravitational potential wells of high mass galaxies.

  6. 6.

We identify 68 $\beta+\sigma_{\beta}<-2.8$ ultra-blue galaxy candidates that
are potential LyC leakers and may host Pop. III or top-heavy IMFs, although
comparison to spectroscopy shows the $\beta$ of individual objects is
difficult to accurately constrain.

We have collated one of the largest samples of high-redshift galaxies at
$z>6.5$ and performed a comprehensive analysis of the $\beta$ biases
associated with this sample. Whilst we speculate on the implications of our
results regarding the dust content and production channels, we note that many
scenarios here are degenerate and indistinguishable with photometric data
alone. Our candidate ultra-blue ($\beta+\sigma_{\beta}<-2.8$) galaxies may
provide evidence for Pop. III stellar populations and/or significant Lyman
continuum leakage, although high UV continuum SNR spectra from NIRSpec remain
crucial to confirm these theories.

##  8 Acknowledgments

We acknowledge support from the ERC Advanced Investigator Grant EPOCHS
(788113), as well as two studentships from STFC for DA and TH. LW acknowledges
funding from the Faculty of Science & Engineering at the University of
Manchester. LF acknowledges financial support from Coordenação de
Aperfeiçoamento de Pessoal de Nível Superior - Brazil (CAPES) in the form of a
PhD studentship. RW, SHC, and RAJ acknowledge support from NASA JWST
Interdisciplinary Scientist grants NAG5 12460, NNX14AN10G and 80NSSC18K0200
from GSFC. CC is supported by the National Natural Science Foundation of
China, No. 11803044, 11933003, 12173045. This work is sponsored (in part) by
the Chinese Academy of Sciences (CAS), through a grant to the CAS South
America Center for Astronomy (CASSACA). We acknowledge the science research
grants from the China Manned Space Project with No. CMS-CSST-2021-A05. MAM
acknowledges the support of a National Research Council of Canada Plaskett
Fellowship, and the Australian Research Council Centre of Excellence for All
Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number
CE17010001. MN acknowledges INAF-Mainstreams 1.05.01.86.20. CNAW acknowledges
support from the NIRCam Science Team contract to the University of Arizona,
NAS5-02015.

This work is based on observations made with the NASA/ESA Hubble Space
Telescope (HST) and NASA/ESA/CSA James Webb Space Telescope (JWST) 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, Inc., under NASA contract NAS 5-03127
for JWST, and NAS 5–26555 for HST. The PEARLS observations used in this work
are associated with JWST programs 1176 and 2738. In addition, public datasets
from JWST programs 1180, 1210, 1895, 1963 (JADES), 1324 (GLASS), 1345 (CEERS)
and 2079 (NGDEEP) are also used within the work presented. Some of the data
products presented herein were retrieved from the Dawn JWST Archive (DJA). DJA
is an initiative of the Cosmic Dawn Center, which is funded by the Danish
National Research Foundation under grant No. 140. The authors thank all
involved in the construction and operations of the telescope as well as those
who designed and executed these observations, their number are too large to
list here and without each of their continued efforts such work would not be
possible. The authors also thank Adam Carnall for their prompt help with
Bagpipes via email, as well as helpful discussions with Rebecca Bowler, Fergus
Cullen, and Albert Zijlstra which significantly improved the discussion of
results. This work is dedicated to the memory of our dedicated colleague and
co-author Mario Nonino, who sadly passed during the completion of this work.

The authors thank Anthony Holloway and Sotirios Sanidas for their providing
their expertise in high performance computing and other IT support throughout
this work. Data used in this publication (including catalogues and imaging)
will be made publicly available once initial works are completed with students
involved in its reduction and analysis. The anticipated timescale is early
Summer 2024. Products using GTO data will be made available as and when
exclusive access periods lapse. This work makes use of astropy (Astropy
Collaboration et al., 2013, 2018, 2022), matplotlib (Hunter, 2007), reproject,
DrizzlePac (Hoffmann et al., 2021), SciPy (Virtanen et al., 2020), photutils
(Bradley et al., 2022), and the currently private galfind. v1 of the galfind
code is expected to be released to the public within the next year.

##  Appendix A The impact of little red dots

Inital JWST images have uncovered a large sample of “little red dots” (LRDs)
that have been catalogued from photometric (e.g. Labbe et al., 2023; Kokorev
et al., 2024) and spectroscopic (e.g. Matthee et al., 2023; Kocevski et al.,
2024) data, some of which have been confirmed to be partially dust obscured
AGN via their broadened H$\alpha$ lines. We identify 34 LRDs when applying the
‘red2’ color selection criteria, compactness criterion, and SNR requirements
from Kokorev et al. (2024) to our EPOCHS-III sample, representing the same
sub-sample as in EPOCHS-IV. The location of these systems in the
$(\beta,M_{\mathrm{UV}})$ and $(\beta,M_{\star})$ parameter spaces is plotted
in Figure 18.

These LRDs in general fall within the lowest redshift $6.5<z<8.5$ bin and are
mainly intermediate to bright in the rest-frame UV compared with the rest of
our EPOCHS-III sample. They are also known to exhibit high stellar masses due
to the confusion of the red AGN SED component with an aged stellar population.
The $\beta$ slopes of these LRDs exhibit a wide range of values, but on
average are redder than the general SFG population, most likely due to dust
production in enriched quasar-driven winds (e.g. Valiante et al., 2014;
Sarangi et al., 2019). While we do not re-compute our $\beta-M_{\mathrm{UV}}$
and $\beta-M_{\star}$ fits excluding these sources, we note that this would
likely have minimal impact due to the small relative sample size compared to
our full EPOCHS-III sample($34/1011$).

Figure 18: The location of the 34 “little red dots” identified in our EPOCHS-
III sample using the Kokorev et al. (2024) selection criteria. The majority
host high observed stellar masses, many of which are likely overestimated, and
red rest-frame UV colours, although we note the large scatter in the $\beta$
distribution of these sources.

##  Appendix B NIRSpec PRISM cross-matches from the DJA

A total of 24 of the 41 spectroscopically confirmed galaxies in our sample
have been found by previous studies (Arrabal Haro et al., 2023a; Bunker et
al., 2023; Curtis-Lake et al., 2023; Hainline et al., 2023b; Heintz et al.,
2023b, a; Nakajima et al., 2023; Tang et al., 2023; Sanders et al., 2024),
with 3 found in photometric surveys by Donnan et al. (2023) and Hainline et
al. (2023b). We provide results of these cross-matches in Table 8, where we
calculate $\beta$ both from the NIRSpec PRISM data as well as the NIRCam
photometry using the two techniques discussed in this work. The spectroscopic
$\beta$ are measured in the C94 filters and the
$1250<\lambda_{\mathrm{rest}}~{}/~{}\mathrm{\AA}<3000$ wavelength range
showing the wavelength dependence of these $\beta$ measurements especially in
low cases of low UV continuum signal-to-noise ratio (SNR).

Table 8: Spectroscopically confirmed galaxies from a cross match of our EPOCHS-III sample with the DJA. We provide spectroscopic $\beta$ measurements in the C94 filters and the $1250-3000~{}\mathrm{\AA}$ rest-frame wavelength range as well as photometric $\beta$ from beta bias corrected power law fits to the photometry and Bagpipes SED fitting. $\mathrm{SNR}_{\mathrm{UV}}$ indicates the SNR obtained from the PRISM spectrum averaged over $1250<\lambda_{\mathrm{rest}}~{}/~{}\mathrm{\AA}<3000$. We reference works that have previously reported these galaxies following the numbering system: 1) Donnan et al. (2023), 2) Heintz et al. (2023b), 3) Curtis-Lake et al. (2023), 4) Bunker et al. (2023), 5) Hainline et al. (2023b), 6) Arrabal Haro et al. (2023a), 7) Heintz et al. (2023a), 8) Nakajima et al. (2023), 9) Sanders et al. (2024), 10) Tang et al. (2023). PID | RA | Dec | $z_{\mathrm{spec}}$ | $\beta_{\mathrm{spec}}$ | $\beta_{\mathrm{spec}}$ | SNRUV | $z_{\mathrm{phot}}$ | $\beta_{\mathrm{phot,PL}}$ | $\beta_{\mathrm{phot,SED}}$ | Ref.
---|---|---|---|---|---|---|---|---|---|---
(C94) | (1250-3000Å)
1180 | $53.155144$ | $-27.760742$ | $6.3139$ | $-2.26\pm 0.03$ | $-2.27\pm 0.08$ | $9.51$ | $6.52_{-0.07}^{+0.05}$ | $-2.53_{-0.32}^{+0.34}$ | $-2.44_{-0.05}^{+0.07}$ | -
1180 | $53.127316$ | $-27.788040$ | $6.3845$ | $-3.00\pm 0.05$ | $-2.58\pm 0.16$ | $3.81$ | $6.57_{-0.07}^{+0.04}$ | $-2.62_{-0.33}^{+0.35}$ | $-2.52_{-0.04}^{+0.05}$ | -
1180 | $53.137429$ | $-27.765207$ | $6.6223$ | $-2.30\pm 0.04$ | $-2.40\pm 0.15$ | $3.53$ | $6.59_{-0.06}^{+0.03}$ | $-2.32_{-0.34}^{+0.30}$ | $-2.46_{-0.04}^{+0.09}$ | -
1180 | $53.169516$ | $-27.753317$ | $6.6284$ | $-2.53\pm 0.07$ | $-2.68\pm 0.15$ | $4.66$ | $6.60_{-0.02}^{+0.02}$ | $-2.58_{-0.32}^{+0.32}$ | $-2.27_{-0.09}^{+0.10}$ | -
1180 | $53.118187$ | $-27.793008$ | $6.7895$ | $-1.96\pm 0.06$ | $-2.38\pm 0.18$ | $3.12$ | $6.89_{-0.04}^{+0.03}$ | $-2.31_{-0.32}^{+0.32}$ | $-2.13_{-0.16}^{+0.12}$ | -
1180 | $53.138054$ | $-27.781863$ | $7.1391$ | $-2.66\pm 0.06$ | $-2.24\pm 0.25$ | $2.12$ | $7.40_{-0.24}^{+0.05}$ | $-2.73_{-0.51}^{+0.48}$ | $-2.40_{-0.06}^{+0.10}$ | -
1180 | $53.161709$ | $-27.785391$ | $7.2349$ | $-1.45\pm 0.04$ | $-1.96\pm 0.13$ | $4.05$ | $7.45_{-0.11}^{+0.07}$ | $-2.27_{-0.48}^{+0.52}$ | $-1.73_{-0.14}^{+0.14}$ | -
1180 | $53.164824$ | $-27.788258$ | $7.2406$ | $-1.87\pm 0.06$ | $-1.86\pm 0.13$ | $3.47$ | $7.39_{-0.08}^{+0.09}$ | $-2.31_{-0.48}^{+0.50}$ | $-1.94_{-0.11}^{+0.12}$ | -
1210 | $53.162377$ | $-27.803300$ | $6.2942$ | $1.88\pm 0.25$ | $-2.27\pm 0.88$ | $0.88$ | $6.51_{-0.28}^{+0.04}$ | $-1.92_{-0.40}^{+0.46}$ | $-2.32_{-0.07}^{+0.07}$ | 4
1210 | $53.175819$ | $-27.774465$ | $6.3351$ | $-1.70\pm 0.03$ | $-1.66\pm 0.10$ | $8.22$ | $6.58_{-0.11}^{+0.04}$ | $-2.08_{-0.28}^{+0.32}$ | $-2.37_{-0.05}^{+0.07}$ | 4
1210 | $53.169041$ | $-27.778842$ | $6.6322$ | $-2.68\pm 0.02$ | $-2.59\pm 0.06$ | $13.86$ | $6.59_{-0.02}^{+0.03}$ | $-2.70_{-0.36}^{+0.34}$ | $-2.45_{-0.04}^{+0.06}$ | 4
1210 | $53.151385$ | $-27.819159$ | $6.7074$ | $-2.03\pm 0.05$ | $-1.87\pm 0.17$ | $4.58$ | $6.63_{-0.04}^{+0.04}$ | $-2.17_{-0.34}^{+0.28}$ | $-2.39_{-0.07}^{+0.15}$ | 4
1210 | $53.155794$ | $-27.815199$ | $6.7186$ | $-2.33\pm 0.05$ | $-2.30\pm 0.13$ | $6.18$ | $6.65_{-0.03}^{+0.03}$ | $-2.50_{-0.33}^{+0.33}$ | $-2.30_{-0.12}^{+0.08}$ | 4
1210 | $53.152839$ | $-27.801940$ | $7.2621$ | $-2.26\pm 0.03$ | $-2.35\pm 0.10$ | $5.59$ | $7.56_{-0.29}^{+0.11}$ | $-2.36_{-0.49}^{+0.49}$ | $-2.48_{-0.03}^{+0.04}$ | 4
1210 | $53.155083$ | $-27.801769$ | $7.2697$ | $-2.31\pm 0.02$ | $-2.34\pm 0.04$ | $17.63$ | $7.69_{-0.39}^{+0.14}$ | $-2.42_{-0.49}^{+0.51}$ | $-2.48_{-0.03}^{+0.03}$ | 4
1210 | $53.156825$ | $-27.767159$ | $7.9807$ | $-2.17\pm 0.02$ | $-2.21\pm 0.06$ | $10.22$ | $7.95_{-0.08}^{+0.14}$ | $-2.71_{-0.50}^{+0.53}$ | $-2.15_{-0.22}^{+0.13}$ | 4
1210 | $53.164468$ | $-27.802181$ | $8.4790$ | $-2.08\pm 0.07$ | $-1.93\pm 0.15$ | $3.15$ | $8.89_{-0.20}^{+0.07}$ | $-2.10_{-0.53}^{+0.51}$ | $-2.29_{-0.13}^{+0.13}$ | 4,5
1210 | $53.167357$ | $-27.807502$ | $9.6886$ | $-2.71\pm 0.03$ | $-2.75\pm 0.07$ | $7.19$ | $9.44_{-0.04}^{+0.72}$ | $-2.23_{-0.32}^{+0.30}$ | $-2.36_{-0.13}^{+0.10}$ | -
1210 | $53.164763$ | $-27.774625$ | $11.5922$ | $-2.48\pm 0.03$ | $-2.52\pm 0.06$ | $8.25$ | $11.94_{-0.21}^{+0.19}$ | $-1.92_{-0.29}^{+0.27}$ | $-2.40_{-0.11}^{+0.10}$ | 3,4,5
1345 | $214.731462$ | $52.736427$ | $5.3535$ | $-1.73\pm 0.16$ | $-3.70\pm 0.96$ | $0.69$ | $7.08_{-1.16}^{+0.23}$ | $-2.72_{-0.48}^{+0.42}$ | $-2.37_{-0.15}^{+0.11}$ | -
1345 | $214.806478$ | $52.878827$ | $6.1086$ | $-2.25\pm 0.04$ | $-2.08\pm 0.12$ | $6.36$ | $6.51_{-0.30}^{+0.04}$ | $-2.06_{-0.33}^{+0.33}$ | $-2.06_{-0.10}^{+0.11}$ | 8
1345 | $214.832181$ | $52.885089$ | $6.6203$ | $-2.30\pm 0.06$ | $-2.60\pm 0.23$ | $2.42$ | $6.61_{-0.17}^{+0.04}$ | $-1.58_{-0.37}^{+0.35}$ | $-2.13_{-0.19}^{+0.15}$ | 8
1345 | $215.128019$ | $52.984951$ | $6.6815$ | $-3.74\pm 0.20$ | $-2.39\pm 0.28$ | $6.40$ | $6.69_{-0.03}^{+0.02}$ | $-2.34_{-0.35}^{+0.33}$ | $-1.64_{-0.07}^{+0.06}$ | -
1345 | $214.789828$ | $52.730794$ | $6.7370$ | $-2.25\pm 0.04$ | $-2.19\pm 0.09$ | $7.17$ | $6.67_{-0.04}^{+0.03}$ | $-2.67_{-0.33}^{+0.35}$ | $-2.39_{-0.05}^{+0.05}$ | 8
1345 | $214.948681$ | $52.853273$ | $6.7501$ | $0.56\pm 0.30$ | $-1.00\pm 0.55$ | $1.32$ | $6.77_{-0.04}^{+0.03}$ | $-2.18_{-0.32}^{+0.28}$ | $-2.41_{-0.05}^{+0.09}$ | -
1345 | $215.001120$ | $53.011273$ | $7.1028$ | $-2.17\pm 0.04$ | $-2.44\pm 0.16$ | $3.33$ | $7.12_{-0.06}^{+0.23}$ | $-2.67_{-0.38}^{+0.35}$ | $-2.42_{-0.07}^{+0.12}$ | 2,8,10
1345 | $214.859185$ | $52.853595$ | $7.1135$ | $-1.38\pm 0.05$ | $-2.23\pm 0.15$ | $4.08$ | $7.03_{-0.03}^{+0.33}$ | $-2.34_{-0.32}^{+0.31}$ | $-2.43_{-0.06}^{+0.10}$ | 8
1345 | $214.813057$ | $52.834241$ | $7.1785$ | $-2.54\pm 0.05$ | $-2.48\pm 0.14$ | $3.98$ | $7.37_{-0.19}^{+0.08}$ | $-3.11_{-0.51}^{+0.49}$ | $-2.46_{-0.05}^{+0.06}$ | 8,10
1345 | $214.812062$ | $52.746747$ | $7.4757$ | $-2.74\pm 0.04$ | $-2.43\pm 0.12$ | $4.34$ | $7.38_{-0.24}^{+0.06}$ | $-2.38_{-0.48}^{+0.52}$ | $-2.32_{-0.12}^{+0.14}$ | 8
1345 | $214.806079$ | $52.750868$ | $7.6487$ | $-2.16\pm 0.05$ | $-2.15\pm 0.14$ | $3.86$ | $8.20_{-0.38}^{+0.15}$ | $-2.70_{-0.47}^{+0.54}$ | $-2.40_{-0.05}^{+0.06}$ | 6
1345 | $214.882999$ | $52.840419$ | $7.8314$ | $-1.55\pm 0.04$ | $-1.66\pm 0.12$ | $4.34$ | $8.06_{-0.12}^{+0.12}$ | $-2.54_{-0.52}^{+0.48}$ | $-2.29_{-0.13}^{+0.11}$ | 2,8,9,10
1345 | $214.961271$ | $52.842360$ | $8.6351$ | $-2.96\pm 0.16$ | $-1.73\pm 0.30$ | $1.74$ | $8.64_{-0.27}^{+0.25}$ | $-2.82_{-0.66}^{+0.63}$ | $-2.02_{-0.16}^{+0.16}$ | 6,8
1345 | $214.811853$ | $52.737113$ | $9.5635$ | $-2.64\pm 0.05$ | $-2.58\pm 0.13$ | $3.86$ | $10.42_{-0.65}^{+0.20}$ | $-1.98_{-0.42}^{+0.40}$ | $-2.18_{-0.08}^{+0.13}$ | 6
1345 | $214.732527$ | $52.758097$ | $9.8505$ | $-3.07\pm 0.07$ | $-2.90\pm 0.17$ | $2.95$ | $9.61_{-0.04}^{+0.79}$ | $-2.18_{-0.30}^{+0.28}$ | $-2.30_{-0.13}^{+0.10}$ | 6
2750 | $214.878972$ | $52.896751$ | $6.5357$ | $-2.57\pm 0.03$ | $-2.59\pm 0.07$ | $10.34$ | $6.58_{-0.13}^{+0.03}$ | $-2.38_{-0.33}^{+0.33}$ | $-2.48_{-0.04}^{+0.07}$ | -
2750 | $214.877890$ | $52.897677$ | $6.5361$ | $-2.63\pm 0.05$ | $-2.56\pm 0.12$ | $5.22$ | $6.54_{-0.32}^{+0.03}$ | $-2.08_{-0.31}^{+0.29}$ | $-2.47_{-0.05}^{+0.09}$ | -
2750 | $214.941618$ | $52.929132$ | $6.9806$ | $-1.99\pm 0.03$ | $-2.06\pm 0.08$ | $6.43$ | $7.04_{-0.01}^{+0.38}$ | $-2.05_{-0.37}^{+0.34}$ | $-2.21_{-0.06}^{+0.08}$ | -
2750 | $214.940489$ | $52.932559$ | $7.5524$ | $-2.48\pm 0.04$ | $-2.44\pm 0.13$ | $4.41$ | $7.47_{-0.45}^{+0.53}$ | $-2.62_{-0.75}^{+0.73}$ | $-2.46_{-0.05}^{+0.07}$ | -
2750 | $214.906639$ | $52.945504$ | $11.0419$ | $-1.82\pm 0.05$ | $-1.85\pm 0.13$ | $5.48$ | $11.54_{-0.34}^{+0.23}$ | $-1.88_{-0.41}^{+0.44}$ | $-2.17_{-0.11}^{+0.11}$ | -
2750 | $214.922777$ | $52.911524$ | $11.1168$ | $-1.65\pm 0.06$ | $-2.08\pm 0.21$ | $3.62$ | $11.22_{-0.85}^{+0.37}$ | $-2.61_{-0.50}^{+0.45}$ | $-2.40_{-0.09}^{+0.12}$ | 1,6
2750 | $214.943146$ | $52.942446$ | $11.4111$ | $-1.88\pm 0.04$ | $-2.10\pm 0.11$ | $5.14$ | $11.90_{-0.32}^{+0.17}$ | $-3.13_{-0.42}^{+0.43}$ | $-2.53_{-0.03}^{+0.06}$ | 6,7
|  |  |  |  |  |  |  |  |  |

## References

  * Adams et al. (2023a) Adams, N. J., Conselice, C. J., Ferreira, L., et al. 2023a, MNRAS, 518, 4755, doi: 10.1093/mnras/stac3347
  * Adams et al. (2023b) Adams, N. J., Conselice, C. J., Austin, D., et al. 2023b, arXiv e-prints, arXiv:2304.13721, doi: 10.48550/arXiv.2304.13721
  * Arrabal Haro et al. (2023a) Arrabal Haro, P., Dickinson, M., Finkelstein, S. L., et al. 2023a, ApJ, 951, L22, doi: 10.3847/2041-8213/acdd54
  * Arrabal Haro et al. (2023b) —. 2023b, Nature, 622, 707, doi: 10.1038/s41586-023-06521-7
  * 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. (2023) Atek, H., Shuntov, M., Furtak, L. J., et al. 2023, MNRAS, 519, 1201, doi: 10.1093/mnras/stac3144
  * Austin et al. (2023) Austin, D., Adams, N., Conselice, C. J., et al. 2023, ApJ, 952, L7, doi: 10.3847/2041-8213/ace18d
  * Bagley et al. (2023a) Bagley, M. B., Finkelstein, S. L., Koekemoer, A. M., et al. 2023a, ApJ, 946, L12, doi: 10.3847/2041-8213/acbb08
  * Bagley et al. (2023b) Bagley, M. B., Pirzkal, N., Finkelstein, S. L., et al. 2023b, arXiv e-prints, arXiv:2302.05466, doi: 10.48550/arXiv.2302.05466
  * Barbary (2016) Barbary, K. 2016, Journal of Open Source Software, 1, 58, doi: 10.21105/joss.00058
  * Bertin & Arnouts (1996) Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393, doi: 10.1051/aas:1996164
  * Bezanson et al. (2022) Bezanson, R., Labbe, I., Whitaker, K. E., et al. 2022, arXiv e-prints, arXiv:2212.04026, doi: 10.48550/arXiv.2212.04026
  * Bhatawdekar & Conselice (2021) Bhatawdekar, R., & Conselice, C. J. 2021, ApJ, 909, 144, doi: 10.3847/1538-4357/abdd3f
  * Bianchi et al. (2009) Bianchi, S., Schneider, R., & Valiante, R. 2009, in Astronomical Society of the Pacific Conference Series, Vol. 414, Cosmic Dust - Near and Far, ed. T. Henning, E. Grün, & J. Steinacker, 65
  * Blaizot et al. (2023) Blaizot, J., Garel, T., Verhamme, A., et al. 2023, MNRAS, 523, 3749, doi: 10.1093/mnras/stad1523
  * Bocchio et al. (2016) Bocchio, M., Marassi, S., Schneider, R., et al. 2016, A&A, 587, A157, doi: 10.1051/0004-6361/201527432
  * Bohlin (2016) Bohlin, R. C. 2016, AJ, 152, 60, doi: 10.3847/0004-6256/152/3/60
  * Böker et al. (2023) Böker, T., Beck, T. L., Birkmann, S. M., et al. 2023, PASP, 135, 038001, doi: 10.1088/1538-3873/acb846
  * Bouwens et al. (2023a) Bouwens, R., Illingworth, G., Oesch, P., et al. 2023a, MNRAS, 523, 1009, doi: 10.1093/mnras/stad1014
  * Bouwens et al. (2023b) —. 2023b, MNRAS, 523, 1009, doi: 10.1093/mnras/stad1014
  * Bouwens et al. (2015a) Bouwens, R. J., Illingworth, G. D., Oesch, P. A., et al. 2015a, ApJ, 811, 140, doi: 10.1088/0004-637X/811/2/140
  * Bouwens et al. (2009) Bouwens, R. J., Illingworth, G. D., Franx, M., et al. 2009, ApJ, 705, 936, doi: 10.1088/0004-637X/705/1/936
  * Bouwens et al. (2010) Bouwens, R. J., Illingworth, G. D., Oesch, P. A., et al. 2010, ApJ, 708, L69, doi: 10.1088/2041-8205/708/2/L69
  * Bouwens et al. (2011) —. 2011, ApJ, 737, 90, doi: 10.1088/0004-637X/737/2/90
  * Bouwens et al. (2012) —. 2012, ApJ, 754, 83, doi: 10.1088/0004-637X/754/2/83
  * Bouwens et al. (2014) —. 2014, ApJ, 793, 115, doi: 10.1088/0004-637X/793/2/115
  * Bouwens et al. (2015b) —. 2015b, ApJ, 803, 34, doi: 10.1088/0004-637X/803/1/34
  * Bouwens et al. (2016) Bouwens, R. J., Oesch, P. A., Labbé, I., et al. 2016, ApJ, 830, 67, doi: 10.3847/0004-637X/830/2/67
  * 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. (2024) Bowler, R. A. A., Inami, H., Sommovigo, L., et al. 2024, MNRAS, 527, 5808, doi: 10.1093/mnras/stad3578
  * Bradley et al. (2022) Bradley, L., Sipőcz, B., Robitaille, T., et al. 2022, Zenodo, doi: 10.5281/zenodo.6825092
  * Brammer et al. (2008) Brammer, G. B., van Dokkum, P. G., & Coppi, P. 2008, ApJ, 686, 1503, doi: 10.1086/591786
  * Bruzual & Charlot (2003) Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000, doi: 10.1046/j.1365-8711.2003.06897.x
  * Bunker et al. (2023) Bunker, A. J., Cameron, A. J., Curtis-Lake, E., et al. 2023, arXiv e-prints, arXiv:2306.02467, doi: 10.48550/arXiv.2306.02467
  * Bushouse et al. (2022) Bushouse, H., Eisenhamer, J., Dencheva, N., et al. 2022, JWST Calibration Pipeline, 1.8.2, Zenodo, doi: 10.5281/zenodo.7325378
  * Byler et al. (2017) Byler, N., Dalcanton, J. J., Conroy, C., & Johnson, B. D. 2017, ApJ, 840, 44, doi: 10.3847/1538-4357/aa6c66
  * Byrne et al. (2022) Byrne, C. M., Stanway, E. R., Eldridge, J. J., McSwiney, L., & Townsend, O. T. 2022, MNRAS, 512, 5329, doi: 10.1093/mnras/stac807
  * Calvi et al. (2016) Calvi, V., Trenti, M., Stiavelli, M., et al. 2016, ApJ, 817, 120, doi: 10.3847/0004-637X/817/2/120
  * Calzetti et al. (2000) Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682, doi: 10.1086/308692
  * Calzetti et al. (1994) Calzetti, D., Kinney, A. L., & Storchi-Bergmann, T. 1994, ApJ, 429, 582, doi: 10.1086/174346
  * Cameron et al. (2023a) Cameron, A. J., Katz, H., Rey, M. P., & Saxena, A. 2023a, MNRAS, 523, 3516, doi: 10.1093/mnras/stad1579
  * Cameron et al. (2023b) Cameron, A. J., Katz, H., Witten, C., et al. 2023b, arXiv e-prints, arXiv:2311.02051, doi: 10.48550/arXiv.2311.02051
  * 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
  * Castellano et al. (2023) —. 2023, ApJ, 948, L14, doi: 10.3847/2041-8213/accea5
  * Castellano et al. (2024) Castellano, M., Napolitano, L., Fontana, A., et al. 2024, arXiv e-prints, arXiv:2403.10238, doi: 10.48550/arXiv.2403.10238
  * Chabrier (2003) Chabrier, G. 2003, PASP, 115, 763, doi: 10.1086/376392
  * Charbonnel et al. (2023) Charbonnel, C., Schaerer, D., Prantzos, N., et al. 2023, A&A, 673, L7, doi: 10.1051/0004-6361/202346410
  * Charlot & Fall (2000) Charlot, S., & Fall, S. M. 2000, ApJ, 539, 718, doi: 10.1086/309250
  * Chen et al. (2024) Chen, Z., Stark, D. P., Mason, C., et al. 2024, MNRAS, doi: 10.1093/mnras/stae455
  * Chevallard & Charlot (2016) Chevallard, J., & Charlot, S. 2016, MNRAS, 462, 1415, doi: 10.1093/mnras/stw1756
  * Chisholm et al. (2020) Chisholm, J., Prochaska, J. X., Schaerer, D., Gazagnes, S., & Henry, A. 2020, MNRAS, 498, 2554, doi: 10.1093/mnras/staa2470
  * Chisholm et al. (2022) Chisholm, J., Saldana-Lopez, A., Flury, S., et al. 2022, MNRAS, 517, 5104, doi: 10.1093/mnras/stac2874
  * Choustikov et al. (2023) Choustikov, N., Katz, H., Saxena, A., et al. 2023, arXiv e-prints, arXiv:2304.08526, doi: 10.48550/arXiv.2304.08526
  * Conroy & Gunn (2010) Conroy, C., & Gunn, J. E. 2010, FSPS: Flexible Stellar Population Synthesis, Astrophysics Source Code Library, record ascl:1010.043
  * Conroy et al. (2009) Conroy, C., Gunn, J. E., & White, M. 2009, ApJ, 699, 486, doi: 10.1088/0004-637X/699/1/486
  * Cullen et al. (2023a) Cullen, F., McLure, R. J., McLeod, D. J., et al. 2023a, MNRAS, 520, 14, doi: 10.1093/mnras/stad073
  * Cullen et al. (2023b) Cullen, F., McLeod, D. J., McLure, R. J., et al. 2023b, arXiv e-prints, arXiv:2311.06209, doi: 10.48550/arXiv.2311.06209
  * Curtis-Lake et al. (2023) Curtis-Lake, E., Carniani, S., Cameron, A., et al. 2023, Nature Astronomy, 7, 622, doi: 10.1038/s41550-023-01918-w
  * Davé et al. (2019) Davé, R., Anglés-Alcázar, D., Narayanan, D., et al. 2019, MNRAS, 486, 2827, doi: 10.1093/mnras/stz937
  * De Barros et al. (2019) De Barros, S., Oesch, P. A., Labbé, I., et al. 2019, MNRAS, 489, 2355, doi: 10.1093/mnras/stz940
  * D’Eugenio et al. (2023) D’Eugenio, F., Maiolino, R., Carniani, S., et al. 2023, arXiv e-prints, arXiv:2311.09908, doi: 10.48550/arXiv.2311.09908
  * Donnan et al. (2023) Donnan, C. T., McLeod, D. J., Dunlop, J. S., et al. 2023, MNRAS, 518, 6011, doi: 10.1093/mnras/stac3472
  * Donnan et al. (2024) Donnan, C. T., McLure, R. J., Dunlop, J. S., et al. 2024, arXiv e-prints, arXiv:2403.03171, doi: 10.48550/arXiv.2403.03171
  * Draine (2009) Draine, B. T. 2009, in Astronomical Society of the Pacific Conference Series, Vol. 414, Cosmic Dust - Near and Far, ed. T. Henning, E. Grün, & J. Steinacker, 453, doi: 10.48550/arXiv.0903.1658
  * Draine (2011) Draine, B. T. 2011, Physics of the Interstellar and Intergalactic Medium
  * Draine & Salpeter (1979) Draine, B. T., & Salpeter, E. E. 1979, ApJ, 231, 77, doi: 10.1086/157165
  * Drakos et al. (2022) Drakos, N. E., Villasenor, B., Robertson, B. E., et al. 2022, ApJ, 926, 194, doi: 10.3847/1538-4357/ac46fb
  * Driver et al. (2011) Driver, S. P., Hill, D. T., Kelvin, L. S., et al. 2011, MNRAS, 413, 971, doi: 10.1111/j.1365-2966.2010.18188.x
  * Dunlop et al. (2012) Dunlop, J. S., McLure, R. J., Robertson, B. E., et al. 2012, MNRAS, 420, 901, doi: 10.1111/j.1365-2966.2011.20102.x
  * Dunlop et al. (2013) Dunlop, J. S., Rogers, A. B., McLure, R. J., et al. 2013, MNRAS, 432, 3520, doi: 10.1093/mnras/stt702
  * Eisenstein et al. (2023) Eisenstein, D. J., Willott, C., Alberts, S., et al. 2023, arXiv e-prints, arXiv:2306.02465, doi: 10.48550/arXiv.2306.02465
  * Eldridge et al. (2017) Eldridge, J. J., Stanway, E. R., Xiao, L., et al. 2017, PASA, 34, e058, doi: 10.1017/pasa.2017.51
  * Ellis et al. (2013) Ellis, R. S., McLure, R. J., Dunlop, J. S., et al. 2013, ApJ, 763, L7, doi: 10.1088/2041-8205/763/1/L7
  * Endsley et al. (2023) Endsley, R., Stark, D. P., Whitler, L., et al. 2023, MNRAS, 524, 2312, doi: 10.1093/mnras/stad1919
  * Feltre et al. (2016) Feltre, A., Charlot, S., & Gutkin, J. 2016, MNRAS, 456, 3354, doi: 10.1093/mnras/stv2794
  * Ferland et al. (2017) Ferland, G. J., Chatzikos, M., Guzmán, F., et al. 2017, Rev. Mexicana Astron. Astrofis., 53, 385, doi: 10.48550/arXiv.1705.10877
  * Ferrara et al. (2023) Ferrara, A., Pallottini, A., & Dayal, P. 2023, MNRAS, 522, 3986, doi: 10.1093/mnras/stad1095
  * Ferreira et al. (2022) Ferreira, L., Adams, N., Conselice, C. J., et al. 2022, ApJ, 938, L2, doi: 10.3847/2041-8213/ac947c
  * Ferruit et al. (2022) Ferruit, P., Jakobsen, P., Giardino, G., et al. 2022, A&A, 661, A81, doi: 10.1051/0004-6361/202142673
  * Finkelstein et al. (2010) Finkelstein, S. L., Papovich, C., Giavalisco, M., et al. 2010, ApJ, 719, 1250, doi: 10.1088/0004-637X/719/2/1250
  * Finkelstein et al. (2012) Finkelstein, S. L., Papovich, C., Salmon, B., et al. 2012, ApJ, 756, 164, doi: 10.1088/0004-637X/756/2/164
  * 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
  * Finkelstein et al. (2023a) Finkelstein, S. L., Bagley, M. B., Ferguson, H. C., et al. 2023a, ApJ, 946, L13, doi: 10.3847/2041-8213/acade4
  * Finkelstein et al. (2023b) Finkelstein, S. L., Leung, G. C. K., Bagley, M. B., et al. 2023b, arXiv e-prints, arXiv:2311.04279, doi: 10.48550/arXiv.2311.04279
  * Fujimoto et al. (2023) Fujimoto, S., Arrabal Haro, P., Dickinson, M., et al. 2023, ApJ, 949, L25, doi: 10.3847/2041-8213/acd2d9
  * Furtak et al. (2023) Furtak, L. J., Shuntov, M., Atek, H., et al. 2023, MNRAS, 519, 3064, doi: 10.1093/mnras/stac3717
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1, doi: 10.1051/0004-6361/201833051
  * Gail et al. (2009) Gail, H. P., Zhukovska, S. V., Hoppe, P., & Trieloff, M. 2009, ApJ, 698, 1136, doi: 10.1088/0004-637X/698/2/1136
  * Gardner et al. (2023) Gardner, J. P., Mather, J. C., Abbott, R., et al. 2023, PASP, 135, 068001, doi: 10.1088/1538-3873/acd1b5
  * Gonzalez-Perez et al. (2013) Gonzalez-Perez, V., Lacey, C. G., Baugh, C. M., Frenk, C. S., & Wilkins, S. M. 2013, MNRAS, 429, 1609, doi: 10.1093/mnras/sts446
  * Gordon et al. (2003) Gordon, K. D., Clayton, G. C., Misselt, K. A., Landolt, A. U., & Wolff, M. J. 2003, ApJ, 594, 279, doi: 10.1086/376774
  * Grogin et al. (2011) Grogin, N. A., Kocevski, D. D., Faber, S. M., et al. 2011, ApJS, 197, 35, doi: 10.1088/0067-0049/197/2/35
  * Groth et al. (1994) Groth, E. J., Kristian, J. A., Lynds, R., et al. 1994, in American Astronomical Society Meeting Abstracts, Vol. 185, American Astronomical Society Meeting Abstracts, 53.09
  * Gunn & Peterson (1965) Gunn, J. E., & Peterson, B. A. 1965, ApJ, 142, 1633, doi: 10.1086/148444
  * Gutkin et al. (2016) Gutkin, J., Charlot, S., & Bruzual, G. 2016, MNRAS, 462, 1757, doi: 10.1093/mnras/stw1716
  * Haiman (2002) Haiman, Z. 2002, ApJ, 576, L1, doi: 10.1086/343101
  * Hainline et al. (2023a) Hainline, K., Robertson, B., Tacchella, S., et al. 2023a, in American Astronomical Society Meeting Abstracts, Vol. 55, American Astronomical Society Meeting Abstracts, 212.02
  * Hainline et al. (2023b) Hainline, K. N., Johnson, B. D., Robertson, B., et al. 2023b, arXiv e-prints, arXiv:2306.02468, doi: 10.48550/arXiv.2306.02468
  * 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
  * Harvey et al. (2024) Harvey, T., Conselice, C., Adams, N. J., et al. 2024, arXiv e-prints, arXiv:2403.03908, doi: 10.48550/arXiv.2403.03908
  * Hathi et al. (2008) Hathi, N. P., Malhotra, S., & Rhoads, J. E. 2008, ApJ, 673, 686, doi: 10.1086/524836
  * Hathi et al. (2013) Hathi, N. P., Cohen, S. H., Ryan, R. E., J., et al. 2013, ApJ, 765, 88, doi: 10.1088/0004-637X/765/2/88
  * Heintz et al. (2023a) Heintz, K. E., Watson, D., Brammer, G., et al. 2023a, arXiv e-prints, arXiv:2306.00647, doi: 10.48550/arXiv.2306.00647
  * Heintz et al. (2023b) Heintz, K. E., Brammer, G. B., Giménez-Arteaga, C., et al. 2023b, Nature Astronomy, 7, 1517, doi: 10.1038/s41550-023-02078-7
  * Heintz et al. (2024) Heintz, K. E., Brammer, G. B., Watson, D., et al. 2024, arXiv e-prints, arXiv:2404.02211, doi: 10.48550/arXiv.2404.02211
  * Hensley & Draine (2023) Hensley, B. S., & Draine, B. T. 2023, ApJ, 948, 55, doi: 10.3847/1538-4357/acc4c2
  * Hodges (1958) Hodges, J. L. 1958, Arkiv for Matematik, 3, 469, doi: 10.1007/BF02589501
  * 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
  * Höfner & Olofsson (2018) Höfner, S., & Olofsson, H. 2018, A&A Rev., 26, 1, doi: 10.1007/s00159-017-0106-5
  * Hsiao et al. (2023) Hsiao, T. Y.-Y., Abdurro’uf, Coe, D., et al. 2023, arXiv e-prints, arXiv:2305.03042, doi: 10.48550/arXiv.2305.03042
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55
  * Inayoshi et al. (2022) Inayoshi, K., Harikane, Y., Inoue, A. K., Li, W., & Ho, L. C. 2022, ApJ, 938, L10, doi: 10.3847/2041-8213/ac9310
  * Inoue et al. (2014) Inoue, A. K., Shimizu, I., Iwata, I., & Tanaka, M. 2014, MNRAS, 442, 1805, doi: 10.1093/mnras/stu936
  * Jaacks et al. (2018) Jaacks, J., Finkelstein, S. L., & Bromm, V. 2018, MNRAS, 475, 3883, doi: 10.1093/mnras/sty049
  * Jakobsen et al. (2022) Jakobsen, P., Ferruit, P., Alves de Oliveira, C., et al. 2022, A&A, 661, A80, doi: 10.1051/0004-6361/202142663
  * Jansen & Windhorst (2018) Jansen, R. A., & Windhorst, R. A. 2018, PASP, 130, 124001, doi: 10.1088/1538-3873/aae476
  * Jaskot & Ravindranath (2016) Jaskot, A. E., & Ravindranath, S. 2016, ApJ, 833, 136, doi: 10.3847/1538-4357/833/2/136
  * Johnson et al. (2021) Johnson, B. D., Leja, J., Conroy, C., & Speagle, J. S. 2021, ApJS, 254, 22, doi: 10.3847/1538-4365/abef67
  * Kannan et al. (2022) Kannan, R., Smith, A., Garaldi, E., et al. 2022, MNRAS, 514, 3857, doi: 10.1093/mnras/stac1557
  * Katz et al. (2022) Katz, H., Garel, T., Rosdahl, J., et al. 2022, MNRAS, 515, 4265, doi: 10.1093/mnras/stac1437
  * Keating et al. (2023) Keating, L. C., Bolton, J. S., Cullen, F., et al. 2023, arXiv e-prints, arXiv:2308.05800, doi: 10.48550/arXiv.2308.05800
  * Kirchschlager et al. (2024) Kirchschlager, F., Mattsson, L., & Gent, F. A. 2024, arXiv e-prints, arXiv:2402.06543, doi: 10.48550/arXiv.2402.06543
  * Kirchschlager et al. (2019) Kirchschlager, F., Schmidt, F. D., Barlow, M. J., et al. 2019, MNRAS, 489, 4465, doi: 10.1093/mnras/stz2399
  * Kocevski et al. (2024) Kocevski, D. D., Finkelstein, S. L., Barro, G., et al. 2024, arXiv e-prints, arXiv:2404.03576, doi: 10.48550/arXiv.2404.03576
  * Koekemoer et al. (2011) Koekemoer, A. M., Faber, S. M., Ferguson, H. C., et al. 2011, ApJS, 197, 36, doi: 10.1088/0067-0049/197/2/36
  * Koekemoer et al. (2013) Koekemoer, A. M., Ellis, R. S., McLure, R. J., et al. 2013, ApJS, 209, 3, doi: 10.1088/0067-0049/209/1/3
  * Kokorev et al. (2024) Kokorev, V., Caputi, K. I., Greene, J. E., et al. 2024, arXiv e-prints, arXiv:2401.09981, doi: 10.48550/arXiv.2401.09981
  * Kron (1980) Kron, R. G. 1980, ApJS, 43, 305, doi: 10.1086/190669
  * Kroupa (2001) Kroupa, P. 2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x
  * Labbe et al. (2023) Labbe, I., Greene, J. E., Bezanson, R., et al. 2023, arXiv e-prints, arXiv:2306.07320, doi: 10.48550/arXiv.2306.07320
  * Lanzetta (2000) Lanzetta, K. 2000, in Encyclopedia of Astronomy and Astrophysics, ed. P. Murdin, 2141, doi: 10.1888/0333750888/2141
  * Larson et al. (2023) Larson, R. L., Hutchison, T. A., Bagley, M., et al. 2023, ApJ, 958, 141, doi: 10.3847/1538-4357/acfed4
  * Lau et al. (2020) Lau, R. M., Eldridge, J. J., Hankins, M. J., et al. 2020, ApJ, 898, 74, doi: 10.3847/1538-4357/ab9cb5
  * Lau et al. (2022) Lau, R. M., Hankins, M. J., Han, Y., et al. 2022, Nature Astronomy, 6, 1308, doi: 10.1038/s41550-022-01812-x
  * Leitherer et al. (1999) Leitherer, C., Schaerer, D., Goldader, J. D., et al. 1999, ApJS, 123, 3, doi: 10.1086/313233
  * 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
  * Leung et al. (2023) Leung, G. C. K., Bagley, M. B., Finkelstein, S. L., et al. 2023, ApJ, 954, L46, doi: 10.3847/2041-8213/acf365
  * Levesque et al. (2006) Levesque, E. M., Massey, P., Olsen, K. A. G., et al. 2006, ApJ, 645, 1102, doi: 10.1086/504417
  * Liske et al. (2015) Liske, J., Baldry, I. K., Driver, S. P., et al. 2015, MNRAS, 452, 2087, doi: 10.1093/mnras/stv1436
  * Looser et al. (2023) Looser, T. J., D’Eugenio, F., Maiolino, R., et al. 2023, arXiv e-prints, arXiv:2302.14155, doi: 10.48550/arXiv.2302.14155
  * 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
  * Lovell et al. (2021) Lovell, C. C., Vijayan, A. P., Thomas, P. A., et al. 2021, MNRAS, 500, 2127, doi: 10.1093/mnras/staa3360
  * Lu et al. (2024) Lu, T.-Y., Mason, C. A., Hutter, A., et al. 2024, MNRAS, 528, 4872, doi: 10.1093/mnras/stae266
  * Madau & Dickinson (2014) Madau, P., & Dickinson, M. 2014, ARA&A, 52, 415, doi: 10.1146/annurev-astro-081811-125615
  * Mainali et al. (2017) Mainali, R., Kollmeier, J. A., Stark, D. P., et al. 2017, ApJ, 836, L14, doi: 10.3847/2041-8213/836/1/L14
  * Malhotra & Rhoads (2006) Malhotra, S., & Rhoads, J. E. 2006, ApJ, 647, L95, doi: 10.1086/506983
  * Marassi et al. (2019) Marassi, S., Schneider, R., Limongi, M., et al. 2019, MNRAS, 484, 2587, doi: 10.1093/mnras/sty3323
  * Marley et al. (2021) Marley, M., Saumon, D., Morley, C., et al. 2021, Zenodo, doi: 10.5281/zenodo.5063476
  * Mascia et al. (2023) Mascia, S., Pentericci, L., Calabrò, A., et al. 2023, A&A, 672, A155, doi: 10.1051/0004-6361/202345866
  * Mason et al. (2023) Mason, C. A., Trenti, M., & Treu, T. 2023, MNRAS, 521, 497, doi: 10.1093/mnras/stad035
  * Matthee et al. (2023) Matthee, J., Naidu, R. P., Brammer, G., et al. 2023, arXiv e-prints, arXiv:2306.05448, doi: 10.48550/arXiv.2306.05448
  * Mauerhofer & Dayal (2023) Mauerhofer, V., & Dayal, P. 2023, MNRAS, 526, 2196, doi: 10.1093/mnras/stad2734
  * McLeod et al. (2023) McLeod, D. J., Donnan, C. T., McLure, R. J., et al. 2023, MNRAS, doi: 10.1093/mnras/stad3471
  * McLure et al. (2011) McLure, R. J., Dunlop, J. S., de Ravel, L., et al. 2011, MNRAS, 418, 2074, doi: 10.1111/j.1365-2966.2011.19626.x
  * McQuinn (2016) McQuinn, M. 2016, ARA&A, 54, 313, doi: 10.1146/annurev-astro-082214-122355
  * Menanteau et al. (2012) Menanteau, F., Hughes, J. P., Sifón, C., et al. 2012, ApJ, 748, 7, doi: 10.1088/0004-637X/748/1/7
  * Meurer et al. (1999) Meurer, G. R., Heckman, T. M., & Calzetti, D. 1999, ApJ, 521, 64, doi: 10.1086/307523
  * Micelotta et al. (2018) Micelotta, E. R., Matsuura, M., & Sarangi, A. 2018, Space Sci. Rev., 214, 53, doi: 10.1007/s11214-018-0484-7
  * Miralda-Escudé (1998) Miralda-Escudé, J. 1998, ApJ, 501, 15, doi: 10.1086/305799
  * Mirocha & Furlanetto (2023) Mirocha, J., & Furlanetto, S. R. 2023, MNRAS, 519, 843, doi: 10.1093/mnras/stac3578
  * Momcheva et al. (2016) Momcheva, I. G., Brammer, G. B., van Dokkum, P. G., et al. 2016, ApJS, 225, 27, doi: 10.3847/0067-0049/225/2/27
  * Morales et al. (2023) Morales, A. M., Finkelstein, S. L., Leung, G. C. K., et al. 2023, arXiv e-prints, arXiv:2311.04294, doi: 10.48550/arXiv.2311.04294
  * 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
  * Nakajima et al. (2023) Nakajima, K., Ouchi, M., Isobe, Y., et al. 2023, ApJS, 269, 33, doi: 10.3847/1538-4365/acd556
  * Nakane et al. (2023) Nakane, M., Ouchi, M., Nakajima, K., et al. 2023, arXiv e-prints, arXiv:2312.06804, doi: 10.48550/arXiv.2312.06804
  * Nanayakkara et al. (2019) Nanayakkara, T., Brinchmann, J., Boogaard, L., et al. 2019, A&A, 624, A89, doi: 10.1051/0004-6361/201834565
  * Nanayakkara et al. (2023) Nanayakkara, T., Glazebrook, K., Jacobs, C., et al. 2023, ApJ, 947, L26, doi: 10.3847/2041-8213/acbfb9
  * Napolitano et al. (2024) Napolitano, L., Pentericci, L., Santini, P., et al. 2024, arXiv e-prints, arXiv:2402.11220, doi: 10.48550/arXiv.2402.11220
  * O’Brien et al. (2024) O’Brien, R., Jansen, R. A., Grogin, N. A., et al. 2024, arXiv e-prints, arXiv:2401.04944, doi: 10.48550/arXiv.2401.04944
  * Oesch et al. (2018) Oesch, P. A., Bouwens, R. J., Illingworth, G. D., Labbé, I., & Stefanon, M. 2018, ApJ, 855, 105, doi: 10.3847/1538-4357/aab03f
  * Oesch et al. (2013) Oesch, P. A., Bouwens, R. J., Illingworth, G. D., et al. 2013, ApJ, 773, 75, doi: 10.1088/0004-637X/773/1/75
  * 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
  * 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
  * Pei (1992) Pei, Y. C. 1992, ApJ, 395, 130, doi: 10.1086/171637
  * Pérez-González et al. (2023) Pérez-González, P. G., Costantin, L., Langeroodi, D., et al. 2023, ApJ, 951, L1, doi: 10.3847/2041-8213/acd9d0
  * Perrin et al. (2014) Perrin, M. D., Sivaramakrishnan, A., Lajoie, C.-P., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9143, Space Telescopes and Instrumentation 2014: Optical, Infrared, and Millimeter Wave, ed. J. Oschmann, Jacobus M., M. Clampin, G. G. Fazio, & H. A. MacEwen, 91433X, doi: 10.1117/12.2056689
  * Perrin et al. (2012) Perrin, M. D., Soummer, R., Elliott, E. M., Lallo, M. D., & Sivaramakrishnan, A. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8442, Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave, ed. M. C. Clampin, G. G. Fazio, H. A. MacEwen, & J. Oschmann, Jacobus M., 84423D, doi: 10.1117/12.925230
  * Planck Collaboration et al. (2016) Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016, A&A, 594, A13, doi: 10.1051/0004-6361/201525830
  * Planck Collaboration et al. (2020) Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6, doi: 10.1051/0004-6361/201833910
  * Raiter et al. (2010a) Raiter, A., Schaerer, D., & Fosbury, R. A. E. 2010a, A&A, 523, A64, doi: 10.1051/0004-6361/201015236
  * Raiter et al. (2010b) —. 2010b, A&A, 523, A64, doi: 10.1051/0004-6361/201015236
  * Rasmussen Cueto et al. (2023) Rasmussen Cueto, E., Hutter, A., Dayal, P., et al. 2023, arXiv e-prints, arXiv:2312.12109, doi: 10.48550/arXiv.2312.12109
  * Rawle et al. (2022) Rawle, T. D., Giardino, G., Franz, D. E., et al. 2022, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 12180, Space Telescopes and Instrumentation 2022: Optical, Infrared, and Millimeter Wave, ed. L. E. Coyle, S. Matsuura, & M. D. Perrin, 121803R, doi: 10.1117/12.2629231
  * Rieke et al. (2005) Rieke, M. J., Kelly, D., & Horner, S. 2005, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 5904, Cryogenic Optical Systems and Instruments XI, ed. J. B. Heaney & L. G. Burriesci, 1–8, doi: 10.1117/12.615554
  * Rieke et al. (2023) Rieke, M. J., Kelly, D. M., Misselt, K., et al. 2023, PASP, 135, 028001, doi: 10.1088/1538-3873/acac53
  * Rigby et al. (2015) Rigby, J. R., Bayliss, M. B., Gladders, M. D., et al. 2015, ApJ, 814, L6, doi: 10.1088/2041-8205/814/1/L6
  * Roberts-Borsani et al. (2024) Roberts-Borsani, G., Treu, T., Shapley, A., et al. 2024, arXiv e-prints, arXiv:2403.07103, doi: 10.48550/arXiv.2403.07103
  * Rodrigo & Solano (2020) Rodrigo, C., & Solano, E. 2020, in XIV.0 Scientific Meeting (virtual) of the Spanish Astronomical Society, 182
  * Rogers et al. (2013) Rogers, A. B., McLure, R. J., & Dunlop, J. S. 2013, MNRAS, 429, 2456, doi: 10.1093/mnras/sts515
  * Rogers et al. (2014) Rogers, A. B., McLure, R. J., Dunlop, J. S., et al. 2014, MNRAS, 440, 3714, doi: 10.1093/mnras/stu558
  * Salim & Narayanan (2020) Salim, S., & Narayanan, D. 2020, ARA&A, 58, 529, doi: 10.1146/annurev-astro-032620-021933
  * Salpeter (1955) Salpeter, E. E. 1955, ApJ, 121, 161, doi: 10.1086/145971
  * Sanders et al. (2024) Sanders, R. L., Shapley, A. E., Topping, M. W., Reddy, N. A., & Brammer, G. B. 2024, ApJ, 962, 24, doi: 10.3847/1538-4357/ad15fc
  * Sarangi et al. (2019) Sarangi, A., Dwek, E., & Kazanas, D. 2019, ApJ, 885, 126, doi: 10.3847/1538-4357/ab46a9
  * Sarmento et al. (2018) Sarmento, R., Scannapieco, E., & Cohen, S. 2018, ApJ, 854, 75, doi: 10.3847/1538-4357/aa989a
  * Sarmento et al. (2019) Sarmento, R., Scannapieco, E., & Côté, B. 2019, ApJ, 871, 206, doi: 10.3847/1538-4357/aafa1a
  * Saxena et al. (2020) Saxena, A., Pentericci, L., Schaerer, D., et al. 2020, MNRAS, 496, 3796, doi: 10.1093/mnras/staa1805
  * Saxena et al. (2023a) Saxena, A., Bunker, A. J., Jones, G. C., et al. 2023a, arXiv e-prints, arXiv:2306.04536, doi: 10.48550/arXiv.2306.04536
  * Saxena et al. (2023b) Saxena, A., Robertson, B. E., Bunker, A. J., et al. 2023b, A&A, 678, A68, doi: 10.1051/0004-6361/202346245
  * Schaerer (2002) Schaerer, D. 2002, A&A, 382, 28, doi: 10.1051/0004-6361:20011619
  * Schaerer (2003) —. 2003, A&A, 397, 527, doi: 10.1051/0004-6361:20021525
  * Schmidt et al. (2017) Schmidt, K. B., Huang, K. H., Treu, T., et al. 2017, ApJ, 839, 17, doi: 10.3847/1538-4357/aa68a3
  * Schneider & Maiolino (2023) Schneider, R., & Maiolino, R. 2023, arXiv e-prints, arXiv:2310.00053, doi: 10.48550/arXiv.2310.00053
  * Senchyna et al. (2023) Senchyna, P., Plat, A., Stark, D. P., & Rudie, G. C. 2023, arXiv e-prints, arXiv:2303.04179, doi: 10.48550/arXiv.2303.04179
  * Skelton et al. (2014) Skelton, R. E., Whitaker, K. E., Momcheva, I. G., et al. 2014, ApJS, 214, 24, doi: 10.1088/0067-0049/214/2/24
  * Stanway & Eldridge (2018) Stanway, E. R., & Eldridge, J. J. 2018, MNRAS, 479, 75, doi: 10.1093/mnras/sty1353
  * Stark et al. (2017) Stark, D. P., Ellis, R. S., Charlot, S., et al. 2017, MNRAS, 464, 469, doi: 10.1093/mnras/stw2233
  * Stecher & Donn (1965) Stecher, T. P., & Donn, B. 1965, ApJ, 142, 1681, doi: 10.1086/148461
  * Stefanon et al. (2017) Stefanon, M., Labbé, I., Bouwens, R. J., et al. 2017, ApJ, 851, 43, doi: 10.3847/1538-4357/aa9a40
  * Steinhardt et al. (2023) Steinhardt, C. L., Kokorev, V., Rusakov, V., Garcia, E., & Sneppen, A. 2023, ApJ, 951, L40, doi: 10.3847/2041-8213/acdef6
  * Tacchella et al. (2022) Tacchella, S., Finkelstein, S. L., Bagley, M., et al. 2022, ApJ, 927, 170, doi: 10.3847/1538-4357/ac4cad
  * Tang et al. (2023) Tang, M., Stark, D. P., Chen, Z., et al. 2023, MNRAS, 526, 1657, doi: 10.1093/mnras/stad2763
  * Tang et al. (2024) Tang, M., Stark, D. P., Ellis, R. S., et al. 2024, arXiv e-prints, arXiv:2402.06070, doi: 10.48550/arXiv.2402.06070
  * Tepper-García (2006) Tepper-García, T. 2006, MNRAS, 369, 2025, doi: 10.1111/j.1365-2966.2006.10450.x
  * Todini & Ferrara (2001) Todini, P., & Ferrara, A. 2001, MNRAS, 325, 726, doi: 10.1046/j.1365-8711.2001.04486.x
  * Tomczak et al. (2014) Tomczak, A. R., Quadri, R. F., Tran, K.-V. H., et al. 2014, ApJ, 783, 85, doi: 10.1088/0004-637X/783/2/85
  * Topping et al. (2022) Topping, M. W., Stark, D. P., Endsley, R., et al. 2022, arXiv e-prints, arXiv:2208.01610.  https://arxiv.org/abs/2208.01610
  * Topping et al. (2023) —. 2023, arXiv e-prints, arXiv:2307.08835, doi: 10.48550/arXiv.2307.08835
  * Topping et al. (2024) Topping, M. W., Stark, D. P., Senchyna, P., et al. 2024, arXiv e-prints, arXiv:2401.08764, doi: 10.48550/arXiv.2401.08764
  * Totani et al. (2006) Totani, T., Kawai, N., Kosugi, G., et al. 2006, PASJ, 58, 485, doi: 10.1093/pasj/58.3.485
  * Treu et al. (2022) Treu, T., Roberts-Borsani, G., Bradac, M., et al. 2022, ApJ, 935, 110, doi: 10.3847/1538-4357/ac8158
  * Umeda et al. (2023) Umeda, H., Ouchi, M., Nakajima, K., et al. 2023, arXiv e-prints, arXiv:2306.00487, doi: 10.48550/arXiv.2306.00487
  * Valiante et al. (2014) Valiante, R., Schneider, R., Salvadori, S., & Gallerani, S. 2014, MNRAS, 444, 2442, doi: 10.1093/mnras/stu1613
  * Vallenari et al. (2022) Vallenari, A., Brown, A., & Prusti, T. 2022, Astronomy & Astrophysics
  * Vázquez & Leitherer (2005) Vázquez, G. A., & Leitherer, C. 2005, ApJ, 621, 695, doi: 10.1086/427866
  * Vijayan et al. (2019) Vijayan, A. P., Clay, S. J., Thomas, P. A., et al. 2019, MNRAS, 489, 4072, doi: 10.1093/mnras/stz1948
  * Vijayan et al. (2021) Vijayan, A. P., Lovell, C. C., Wilkins, S. M., et al. 2021, MNRAS, 501, 3289, doi: 10.1093/mnras/staa3715
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2
  * Wang et al. (2023) Wang, B., Fujimoto, S., Labbé, I., et al. 2023, ApJ, 957, L34, doi: 10.3847/2041-8213/acfe07
  * Whitaker et al. (2019) Whitaker, K. E., Ashas, M., Illingworth, G., et al. 2019, ApJS, 244, 16, doi: 10.3847/1538-4365/ab3853
  * Whitler et al. (2023) Whitler, L., Stark, D. P., Endsley, R., et al. 2023, arXiv e-prints, arXiv:2305.16670, doi: 10.48550/arXiv.2305.16670
  * Wilkins et al. (2016) Wilkins, S. M., Bouwens, R. J., Oesch, P. A., et al. 2016, MNRAS, 455, 659, doi: 10.1093/mnras/stv2263
  * Wilkins et al. (2013) Wilkins, S. M., Bunker, A., Coulton, W., et al. 2013, MNRAS, 430, 2885, doi: 10.1093/mnras/stt096
  * Wilkins et al. (2012) Wilkins, S. M., Gonzalez-Perez, V., Lacey, C. G., & Baugh, C. M. 2012, MNRAS, 424, 1522, doi: 10.1111/j.1365-2966.2012.21344.x
  * Wilkins et al. (2023a) Wilkins, S. M., Vijayan, A. P., Lovell, C. C., et al. 2023a, MNRAS, 519, 3118, doi: 10.1093/mnras/stac3280
  * Wilkins et al. (2023b) Wilkins, S. M., Turner, J. C., Bagley, M. B., et al. 2023b, arXiv e-prints, arXiv:2311.08065, doi: 10.48550/arXiv.2311.08065
  * Williams et al. (2018) Williams, C. C., Curtis-Lake, E., Hainline, K. N., et al. 2018, ApJS, 236, 33, doi: 10.3847/1538-4365/aabcbb
  * Windhorst et al. (2023) Windhorst, R. A., Cohen, S. H., Jansen, R. A., et al. 2023, AJ, 165, 13, doi: 10.3847/1538-3881/aca163
  * Witstok et al. (2023a) Witstok, J., Shivaei, I., Smit, R., et al. 2023a, Nature, 621, 267, doi: 10.1038/s41586-023-06413-w
  * Witstok et al. (2023b) Witstok, J., Smit, R., Saxena, A., et al. 2023b, arXiv e-prints, arXiv:2306.04627, doi: 10.48550/arXiv.2306.04627
  * Wu et al. (2020) Wu, X., Davé, R., Tacchella, S., & Lotz, J. 2020, MNRAS, 494, 5636, doi: 10.1093/mnras/staa1044
  * Xiao et al. (2018) Xiao, L., Stanway, E. R., & Eldridge, J. J. 2018, MNRAS, 477, 904, doi: 10.1093/mnras/sty646
  * 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. (2024) Yung, L. Y. A., Somerville, R. S., Finkelstein, S. L., Wilkins, S. M., & Gardner, J. P. 2024, MNRAS, 527, 5929, doi: 10.1093/mnras/stad3484
  * Yung et al. (2023) Yung, L. Y. A., Somerville, R. S., Nguyen, T., et al. 2023, arXiv e-prints, arXiv:2309.14408, doi: 10.48550/arXiv.2309.14408
  * Zackrisson et al. (2013) Zackrisson, E., Inoue, A. K., & Jensen, H. 2013, ApJ, 777, 39, doi: 10.1088/0004-637X/777/1/39
  * Zackrisson et al. (2011) Zackrisson, E., Rydberg, C.-E., Schaerer, D., Östlin, G., & Tuli, M. 2011, ApJ, 740, 13, doi: 10.1088/0004-637X/740/1/13
  * Zhukovska et al. (2008) Zhukovska, S., Gail, H. P., & Trieloff, M. 2008, A&A, 479, 453, doi: 10.1051/0004-6361:20077789
  * Ziparo et al. (2023) Ziparo, F., Ferrara, A., Sommovigo, L., & Kohandel, M. 2023, MNRAS, 520, 2445, doi: 10.1093/mnras/stad125


# Studying [CII] Emission in Low-mass Galaxies at $z\sim 7$

Kelsey Glazer1, Maru$\breve{\textrm{s}}$a Brada$\breve{\textrm{c}}$ 1,2, Ryan
L. Sanders 1,8, Seiji Fujimoto 3, Patricia Bolan 1, Andrea Ferrara4, Victoria
Strait 5,6, Tucker Jones 1, Brian C. Lemaux 1,7, Livia Vallini9, Russell
Ryan10
1Department of Physics and Astronomy, University of California, Davis, 1
Shields Ave, Davis, CA 95616, USA
2University of Ljubljana, Department of Mathematics and Physics, Jadranska
ulica 19, SI-1000 Ljubljana, Slovenia
3Department of Astronomy, The University of Texas at Austin, Austin, TX 78712,
USA
4Scuola Normale Superiore, Piazza dei Cavalieri 7, 50126 Pisa, Italy
5Cosmic Dawn Center (DAWN), Denmark
6Niels Bohr Institute, University of Copenhagen, Jagtvej 128, DK-2200
Copenhagen N, Denmark
7Gemini Observatory, NSF’s NOIRLab, 670 N. A’ohoku Place, Hilo, Hawai’i,
96720, USA
8Department of Physics and Astronomy, University of Kentucky, Lexington, KY
40506, USA
9INAF-Osservatorio di Astrofisica e Scienza dello Spazio, via Gobetti 93/3,
I-40129, Bologna, Italy
10Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218, USA  0000-0002-4453-5870 0000-0001-5984-0395 0000-0003-4792-9119
0000-0001-7201-5066 0000-0002-7365-4131 0000-0002-9400-7312
0000-0002-6338-7295 0000-0001-5860-3419 0000-0002-1428-7036
0000-0002-3258-3672 0000-0003-0894-1588

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We report on a $\rm{[CII]}_{158\mu\rm{m}}$ search using the Atacama Large
Millimeter/submillimeter Array (ALMA) on three lensed, confirmed Ly$\alpha$
emitting galaxies at $z\sim 7$. Our targets are ultra-violet (UV) faint
systems with stellar masses on the order of $M_{*}\sim 10^{9}M_{\sun}$. We
detect a single [CII] line emission ($4\sigma$) from the brightest ($L\sim
2.4\times 10^{10}L_{\odot}$) galaxy in our sample, MACS0454-1251. We determine
a systemic redshift ($z_{\rm{[CII]}}=6.3151\pm 0.0005$) for MACS0454-1251 and
measure a Ly$\alpha$ velocity offset of $\Delta v\approx 300\pm
70\rm{km\,s}^{-1}$. The remaining two galaxies we detect no [CII] but provide
$3\sigma$ upper limits on their [CII] line luminosities which we use to
investigate the $L_{\textrm{[CII]}}-\rm{SFR}$ relation. Overall our single
[CII] detection shows agreement with the relation for dwarf and local
starburst galaxies. Our [CII] deficient galaxies could potentially be
exhibiting low metallicities ($Z<Z_{\odot}$). Another possible explanation for
weaker [CII] emission could be strong feedback from star formation disrupting
molecular clouds. We do not detect continuum emission in any of the sources,
placing upper limits on their dust masses. Assuming a single dust temperature
of $T_{d}=35\rm{K}$ dust masses ($M_{\rm{dust}}$) range from $<4.8\times
10^{7}M_{\odot}$ to $2.3\times 10^{8}M_{\odot}$. Collectively, our results
suggest faint reionization era sources could be metal poor and/or could have
strong feedback suppressing [CII] emission.

###### keywords:

galaxies:high-redshift – gravitational lensing:strong

††pubyear: 2023††pagerange: Studying [CII] Emission in Low-mass Galaxies at
$z\sim 7$–Studying [CII] Emission in Low-mass Galaxies at $z\sim 7$

##  1 Introduction

In the past decade, the Atacama Large Millimeter/submillimeter Array (ALMA)
observations of metal fine structure lines such as the
$\rm{[CII]}_{158\mu\rm{m}}$ line have opened up studies into the epoch of
reionization (EoR; $z>6$) by providing an unobscured view of galaxies. With
the advent of the James Webb Space Telescope (JWST), which can also provide a
similar a view of non-resonant optical lines (e.g., H$\alpha$), ALMA
observations still provide a complementary view for far infrared (FIR)
emission lines. FIR lines hold immense value for EoR studies because they are
not affected by dust extinction, in contrast to rest-optical lines accessible
with JWST. There have been numerous [CII] detections in UV-bright, high-$z$
($z>6$) galaxies (e.g., Willott et al., 2015; Carniani et al., 2017; Laporte
et al., 2017; Smit et al., 2018a; Matthee et al., 2019; Harikane et al., 2019;
Bakx et al., 2020). However, there are considerably fewer recorded [CII]
detections for characteristically faint, $L<L^{*}_{z\sim 7}$ (where $L^{*}$ is
the characteristic luminosity) EoR galaxies (e.g., Schaerer et al., 2015;
Watson et al., 2015; Knudsen et al., 2016; Bradač et al., 2017; Fujimoto et
al., 2021; Laporte et al., 2021). Faint galaxies are much more numerous than
bright ($L<L^{*}_{z\sim 7}$) galaxies (e.g. Bouwens et al., 2022; Bolan et
al., 2022) and, as such, can be a key driver of reionization. However, this
connection has been heavily debated (e.g. Finkelstein et al., 2019; Naidu et
al., 2020; Robertson, 2022; Endsley et al., 2023). In order to resolve this
question, we need to study the physical properties of these fainter primordial
systems; this step is key to understanding their role in cosmic reionization.

Here we use [CII] observations to study $z\sim 7$ galaxies. The [CII] line is
of particular interest because it predominantly traces the dense neutral gas
in photodissociation regions (PDRs, Wolfire et al., 2022) associated with
molecular clouds, and the diffuse neutral gas (Wolfire et al., 2003;
Hollenbach & Tielens, 1999). It is the most luminous line in the FIR band
($\sim 0.1-1\%$ of the FIR luminosity, Baier-Soto et al., 2022) and one the
strongest emission lines of star-forming galaxies at FIR/radio wavelengths
(Carilli & Walter, 2013; Stacey et al., 1991, 2010). Additionally, the [CII]
line can be used to trace the systemic redshift, and therefore velocity, of
the host galaxy because it is optically thin and not affected by dust
extinction. When paired with detected Ly$\alpha$ emission, we can estimate
interstellar medium (ISM) properties of the galaxy under some assumptions. For
instance, we can estimate the amount of neutral gas assuming the offset stems
from Ly$\alpha$ resonant scattering in ISM gas (Mason et al., 2018).111We
remind that outflows might also generate comparable velocity offsets.
Ly$\alpha$ photons travelling through neutral ISM scatter more frequently and
emerge with a larger $\Delta v$ compared to photons traveling through less
neutral ISM (Yang et al., 2016; Yang et al., 2017; Guaita et al., 2017).
Previous observations of $z>5$ galaxies have typically measured $\Delta
v\lesssim 500\rm{kms}^{-1}$ (Cassata et al., 2020; Carniani et al., 2018a;
Pentericci et al., 2016; Bunker et al., 2023; Prieto-Lyon et al., 2023) with
the largest $\Delta v\approx 1000\rm{kms}^{-1}$ recorded by Baier-Soto et al.
(2022). Cassata et al. (2020) find that galaxies ($4.4<z<6$) with smaller
$\Delta v$ have larger Ly$\alpha$ rest-frame equivalent widths and
$f_{\rm{esc}}(\textrm{Ly$\alpha$})$. However, for intrinsically faint systems
($M_{\rm{UV}}\gtrsim-20.5$) at $z>6$, a limited sample size restricts our
ability to make robust conclusions (see Endsley et al., 2022 and references
therein).

In addition to velocity offsets, we can also measure [CII] line luminosities
($L_{\rm{[CII]}}$) and evaluate the empirical [CII] line luminosity to star
formation rate ($\rm{L}_{[CII]}-\rm{SFR}$) relation. This tight relation is
well established for a wide range of local galaxy types (e.g., Boselli et al.,
2002; De Looze et al., 2011; De Looze et al., 2014; Sargsyan et al., 2012;
Pineda et al., 2014; Herrera-Camus et al., 2015), but initial [CII] searches
in $z>5$ galaxies revealed lower than expected or missing [CII] emission from
"normal" ($\rm{SFR}<100\rm{M}_{\odot}\rm{yr}^{-1}$) star-forming galaxies (see
Carniani et al., 2020 and references therein). The coined "[CII] deficit"
problem brought into question whether or not [CII] could remain a good tracer
of SFR at higher-$z$ systems as well as the applicability of the low-$z$
$\rm{L}_{[CII]}-\rm{SFR}$ relation. Observational studies (e.g., Maiolino et
al., 2015; Capak et al., 2015; Knudsen et al., 2016; Matthee et al., 2017;
Carniani et al., 2018b; Matthee et al., 2019; Schaerer et al., 2020; Romano et
al., 2022) have focused on understanding the $\rm{L}_{[CII]}-\rm{SFR}$
relation and if there indeed is missing [CII] emission for $z\sim 7$.

Theoretical studies have also extensively modeled the under/undetected [CII]
emission (e.g., Vallini et al., 2013, 2015; Olsen et al., 2017; Katz et al.,
2017; Katz et al., 2019; Pallottini et al., 2017, 2022; Lupi & Bovino, 2020).
The analytical approach by Ferrara et al. (2019) concluded that under-luminous
[CII] systems can result from a combination of factors: (a) large upward
deviations from the Kennicutt-Schmidt relation (corresponding to bursty
phases); (b) low metallicity; (c) low gas density, at least for the most
extreme sources. These results have been supported by cosmological numerical
simulations (Vallini et al., 2015; Pallottini et al., 2019).

As mentioned previously, majority of EoR studies investigating [CII] have
targeted UV-bright galaxies, which traditionally have higher SFRs. This,
however, gives a biased view especially when fainter galaxies with lower SFRs
outnumber the larger and brighter galaxies. In this paper we report on a [CII]
study carried out with ALMA that targeted a rare set of lensed, sub-$L_{*}$
galaxies with SFRs<$20M_{\odot}\rm{yr}^{-1}$, confirmed to be in the EoR via
spectroscopically detected Ly$\alpha$ emission. The paper is organized as
follows. Section 2 explains various observations used to compile our sample
and the specific ALMA data reduction performed on our data. In Section 3 we
discuss the measurements and derived properties from the ALMA data as well as
the spectral energy density (SED) fitting performed for galaxy property
estimates. In Section 4 we analyze and discuss our results with literature
findings. In Section 5 we summarize our conclusions. Throughout this paper we
assume a $\Lambda$CDM concordance cosmology with $\Omega_{m}=0.27$,
$\Omega_{\Lambda}=0.73$ and Hubble constant
$H_{0}=73\rm{km\,s}^{-1}\;\rm{Mpc}^{-1}$. Coordinates are given for the epoch
J2000.0, magnitudes are in the AB system, and we use the Chabrier (2003)
initial mass function (IMF).

##  2 Observations and Data Reduction

Table 1: Properties of observed galaxies. Target ID | $z_{\rm{Ly}\alpha}$ | $\mu_{\rm{best}}^{a}$ | Refb |  $M_{\rm stellar}$ $\times f_{\mu}^{c,d}$ |  $\rm{SFR}_{\rm{SED}}$ $\times f_{\mu}^{c,d}$ |  $\rm{SFR}_{\rm{UV}}$ $\times f_{\mu}^{c,e}$ | Aged | $M_{\rm{UV}}-2.5\log(f_{\mu})^{c}$ | Lf
---|---|---|---|---|---|---|---|---|---
– | – | – | – | $10^{9}M_{\odot}$ | $M_{\odot}yr^{-1}$ | $M_{\odot}yr^{-1}$ | Myr | mag | $L^{*}$
MACS0454-1251 | $6.323\pm 0.002^{g}$ | $4.4\pm 0.4$ | $[1]$ | $5.52_{-1.5}^{+1.6}$ | $13.5_{-3.9}^{+4.1}$ | $8.82\pm 0.15$ | $55.0_{-29}^{+58}$ | $-20.9\pm 0.1$ | $0.7\pm 0.09$
MACS2129-1412 | $6.846\pm 0.001$ | $11_{-0.7}^{+0.1}$ | $[2]$ | $1.73_{-0.61}^{+4.2}$ | $6.93_{-2.4}^{+5.9}$ | $1.06\pm 0.04$ | $216_{-80}^{+330}$ | $-18.6\pm 0.2$ | $0.1\pm 0.02$
RXJ1347-018 | $7.161\pm 0.001$ | $21.4_{-1.3}^{+1.7}$ | $[3]$ | $2.49_{-2.0}^{+3.0}$ | $7.48_{-5.7}^{+11.8}$ | $0.292\pm 0.01$ | $249_{-147}^{+335}$ | $-17.2\pm+0.2$ | $0.03\pm 0.01$

Figure 1: MACS0454-1251 velocity-integrated [CII] line intensity overlaid on a
_HST_ /WFC3 F160W image. The contours are shown in red and are spaced linearly
by intervals of $1\sigma$ which range from $2-4\sigma$. The beam is given in
the bottom right with a $3"\times 3"$ zoom-in shown in the bottom left. Blue
cross hairs mark the target in the center.

The lesning galaxy clusters of our sample have been extensively studied in
past works. All three clusters have imaging from the _Hubble Space Telescope
(HST)_. The Cluster Lensing and Supernova Survey with Hubble (CLASH, Postman
et al., 2012) program observed MACS2129 and RXJ1347. The two CLASH clusters
were also spectroscopically observed with The Grism Lens-Amplified Survey from
Space (GLASS Treu et al., 2015) program. MACS0454 was imaged with the _HST_
-GO-11591(PI: Kneib)/GO-9836(PI:Ellis)/GO-9722(PI: Ebeling) programs.
Additionally, the three clusters were imaged with the _Spitzer_ UltRa Faint
SUrvey Program (SURFSUP Bradač et al., 2014) which observed a total of ten
lesning clusters. Spectroscopic follow ups using the DEep Imaging Multi-Object
Spectrograph (DEIMOS, Faber et al., 2003) and Multi-Object Spectrometer for
InfraRed Exploration (MOSFIRE, McLean et al., 2010) instruments on _Keck_
confirmed Ly$\alpha$ emission in the galaxies that make up our sample for this
work (Huang et al., 2016a, b; Hoag et al., 2019b).

ALMA observations (Proposal ID: 2019.1.00003.S) were carried out between March
of 2020 and April 2021 using ALMA Band $6$ with 43 12-m antennae in array
configurations C$43-4$ and C$43-5$. The precipitable water vapor (PWV) ranged
from $0.5$mm to $2.1$mm. The spectral setup consisted of one spectral window
centered on the expected observed frequency of $\rm{[CII]}_{158\mu\rm{m}}$
estimated from the Ly$\alpha$ redshift. The remaining two spectral windows
were used for continuum measurements. The on-source time varied from $20$ to
$35$ min. per target.

The data was reduced and calibrated with the Common Astronomy Software
Applications (CASA) package, version 6.1.1.15 following standard procedures.
We reimaged the data with the CASA task TCLEAN, setting ROBUST=$2.0$,
UVTAPER$=0".6$, and adopting Briggs weighting. The angular resolution for each
object is equal to beam size which differed slightly from object to object.
All three targets were unresolved in their final data products and were
spectrally binned into $25$-km s-1 velocity channels. To ensure positional
accuracy, we astrometrically calibrated _HST_ reference images to GAIA DR2
when comparing [CII] to UV emission. Continuum maps were made with all
spectral windows.

Figure 2: Extracted spectrum showing the detected [CII] emission. Flux (left axis) shown as a function of frequency (bottom axis) and velocity (top axis). Red dashed line represents the best fit Gaussian and grey dashed line represents Lyman-$\alpha$ redshift with boxed $1\sigma$ uncertainty. Table 2: Results from ALMA. Target ID | $z_{\rm{[CII]}}$ | $S_{\rm{line}}$ | $\rm{FWHM}$ | $S_{\rm{line}}\Delta v$ | $L_{\rm{[CII]}}\times f_{\mu}$ | Continuuma | $L_{\rm{FIR}}\times f_{\mu}^{a,b}$ | $\rm{SFR}_{\rm{FIR}}^{a,b,c}$ | $M_{\rm{dust}}^{a,c}$
---|---|---|---|---|---|---|---|---|---
– | – | $(\rm{mJy})$ | (km$\rm{s}^{-1}$) | ($\rm{Jykm\,s}^{-1}$) | $(\times 10^{8}L_{\odot})$ | $(\mu\rm{Jy})$ | $(\times 10^{10}L_{\odot})$ | $M_{\odot}\rm{yr}^{-1}$ | $\times 10^{8}M_{\odot}$
MACS0454-1251 | $6.3151\pm 0.0005$ | $3.7_{-0.9}^{+0.9}$ | $163\pm 46$ | $0.64\pm+0.15$ | $1.5_{-0.4}^{+0.5}$ | $<1380$ | $<32$ | $<35$ | $<2.3$
MACS2129-1412 | $-$ | $-$ | $-$ | $-$ | $<0.043$ | $<18.3$ | $<0.19$ | $<0.21$ | $<0.93$
RXJ1347-018 | $-$ | $-$ | $-$ | $-$ | $<0.062$ | $<47.0$ | $<1.1$ | $<1.2$ | $<0.48$

##  3 Measurements and Derived Properties

We observed three highly magnified ($\mu\sim 4-20$) Lyman alpha emitting
(LAEs) galaxies with ALMA at $z_{\rm{Ly}\alpha}=6.323\pm 0.003$
(MACS0454-1251), $6.846\pm 0.001$ (MACS2129-1412), and $7.161\pm 0.001$
(RXJ1347-018). We report a single [CII] detection (4$\sigma$, Fig 1) from
MACS0454-1251. We extracted the spectrum over an extended elliptical aperture
(semi-axes: $\sim 1.\arcsec 5\times 0.\arcsec 5$, pitch angle: $\sim
35^{\circ}$) to account of the slightly oblong shape in the [CII] contours of
the moment0 map (see Fig 1). We fit a Gaussian (see Fig 2) to estimate the
peak line flux $S_{\textrm{line}}=3.7\pm 0.9\textrm{mJy}$. We calculate the
integrated line flux ($S_{\rm{line,g}}\Delta v$) as $0.64\pm
0.15\rm{Jykm\,s}^{-1}$ with a FWHM of $163\pm 46\rm{km\,s}^{-1}$. We determine
the systemic redshift $z_{\textrm{[CII]}}=6.315\pm 0.001$ which is in close
agreement with the redshift found via Ly$\alpha$ ($z_{\rm{spec}}=6.323$). The
calculated [CII] line luminosity (eq.18, Casey et al., 2014) is
$L_{\rm{[CII]}}=1.5^{+0.5}_{-0.4}\times 10^{8}L_{\odot}$ and find a velocity
offset (the difference between Ly$\alpha$ and [CII]:
$v_{\rm{Ly}\alpha}-v_{\rm{[CII]}}$) $\Delta v=320\pm 70\,\textrm{km\,s}^{-1}$.

The remaining two galaxies, MACS2129-1412 and RXJ1347-018, yielded non-
detections for [CII] emission (see Fig 3). Because their intrinsic [CII] line
widths are unknown, we estimate their $L_{\rm{[CII]}}$ ($3\sigma$) upper
limits by integrating over the same width of channels ( $9$ channels,
$225\rm{km\,s}^{-1}$) as was done in MACS0454-1251. In the absence of known
systemic redshifts, we use Ly$\alpha$ redshifts to predict expected [CII]
emitting frequency of each object 222This assumes there is no velocity offset
between Ly$\alpha$ and [CII] emission for these two galaxies. The RMS
uncertainty was calculated using the $1\sigma$ intensity value extracted from
a $0.\arcsec 5$ aperture centered to the HST imaging centroid of the target.
We list the calculated $L_{\rm{[CII]}}(3\sigma)$ upper limits in Table
LABEL:tab:ALMA_results.

We constructed a continuum map for MACS0454-1251 from all four spectral
windows (SPWs), masking out the channels expected to contain [CII] emission.
As seen in Fig 2, the [CII] line of MACS0454-1254 appears to be extended over
roughly nine channels which corresponds to a width of $225\rm{km\,s}^{-1}$.
All nine channels were masked when producing the final continuum map from
which we derived an upper limit on $L_{\rm{FIR}}$. We assume a wavelength
range of $8-1000\mu$m for $L_{\rm{FIR}}$ calculation. For the remaining non-
detection galaxies, we constructed continuum maps in the same manner excluding
nine channels centered on the central frequency. To estimate $L_{\rm{FIR}}$,
we used a grey-body spectral energy distribution model (Casey, 2012), assuming
a spectral index of $\beta=1.5$ . In the absence of multi-band observations,
we assumed a dust temperature ($T_{\rm{d}}=35\rm{K}$) across all three objects
and estimated $3\sigma L_{\rm{FIR}}$ which is recorded in table
LABEL:tab:ALMA_results. Alternative literature values for assumed $T_{\rm{d}}$
can range from $38-90\rm{K}$ (Fujimoto et al., 2021, 2022; Fudamoto et al.,
2023). A recent study by Sommovigo et al. (2022) showed $z\sim 7$ galaxies
having an average dust temperature of $\langle T_{d}\rangle=47\pm 6\rm{K}$.
Because $\rm{SFR}_{\rm{FIR}}$ and $M_{\rm{dust}}$ are extremely sensitive to
the assumed $T_{d}$, assuming a lower $T_{\rm{d}}$ than the average found by
Sommovigo et al. (2022) provides conservative upper limit on $M_{\rm{dust}}$.

Assuming conservatively $T_{d}=35\rm{K}$ for all three galaxies, we estimated
$\rm{SFR}_{\rm{FIR}}$ using eq.3 from Kennicutt (1998b) converted from
Salpeter IMF to Chabrier IMF and calculated $3\sigma$ dust mass
($M_{\rm{dust}}$) estimates for each object. We assumed a dust mass absorption
coefficient of $\kappa=\kappa_{0}(\nu/\nu_{0})^{\beta_{\rm{d}}}$, where
$\kappa_{0}=0.232\rm{m}^{2}\rm{kg}^{-1}$ at $\nu_{0}=250\mu\rm{m}$ (Draine,
2003; Bianchi, 2013). Resulting ${SFR}_{\rm FIR}$ and $M_{\rm{dust}}$ limits
are listed in Table LABEL:tab:ALMA_results.

To estimate age and stellar mass ($M_{\rm stellar}$) of the sample, we use
Bayesian Analysis of Galaxies for Physical Inference and Parameter EStimation
(BAGPIPES, Carnall et al., 2018). BAGPIPES fits physical parameters using the
MultiNest sampling algorithm (Feroz & Hobson, 2008; Feroz et al., 2009). We
use the default set of stellar population templates from Bruzal and Charlot
(Bruzual & Charlot, 2003, BC03). The SED fitting is done assuming the Kroupa
(2001) IMF which we convert to Chabrier (2003), a metallicity of
0.02$Z_{\odot}$, the Calzetti dust law (Calzetti et al., 2000), and a constant
star formation history. We allow dust extinction to range from $A_{v}=0-3$
magnitudes. The $M_{\rm stellar}$ values reflected in Table
LABEL:tab:Spec_table have been converted to Chabrier IMF via conversion factor
$0.923$. We take the general prescription for the fitting from Strait et al.
(2020). See Bolan et al. in prep. for more information on the SED fitting.

Figure 3: MACS2129-1412 (left) and RXJ1347 -018 (right) velocity-integrated
[CII] line intensity overlaid on _HST_ /WFC3 F160W image. The contours are
shown in red and linearly spaced at $1\sigma$ intervals from $1-4\sigma$. The
beam is given in the bottom right with a $3\arcsec\times 3\arcsec$ zoom-in
shown in the bottom left. The galaxies are out lined by the blue cross hairs
on the _HST_ images.

##  4 Results

###  4.1 Velocity and Spatial Offset

Observational studies have used [CII] emission as a tracer of systemic
velocities (e.g Pentericci et al., 2016; Matthee et al., 2019). Using the peak
[CII] emission from the extracted spectrum of MACS0454-1251, we find $\Delta
v_{\rm{Ly}\alpha-\rm{[CII]}}\approx 320\pm 70\rm{km\,s}^{-1}$. This is shown
in Fig 2 where the velocity axis is centered on the [CII] emission and the
grey dashed line represents Ly$\alpha$. The magnitude of the offset falls
within literature ranges quoted for $z=2\sim 3$ (Erb et al., 2014) and
high-$z$ galaxies (e.g., Cassata et al., 2020; Endsley et al., 2022).

The spectrum shows a clear redshift of Ly$\alpha$ emission. Given the resonant
nature of Ly$\alpha$, revealing the direct cause of the offset is both a
complex and active place of research. Redshifted Ly$\alpha$ could indicate
scattered emission from outflowing (or expanding) gas from the galaxy.
Outflows may originate from strong star formation feedback which could reduce
the covering fraction of neutral gas in the ISM and boost Ly$\alpha$ escape
(Jones et al., 2013; Trainor et al., 2015; Leethochawalit et al., 2016).
Ly$\alpha$ could also be redshifted by neutral hydrogen inside a galaxy’s ISM,
where the emerging $\Delta v$ would be a proxy for the column density of
neutral hydrogen (Yang et al., 2016; Yang et al., 2017; Guaita et al., 2017).
Additionally, the model put forth by Mason et al. (2018) used $\Delta v$ as a
way to measure the intergalactic medium (IGM) neutral fraction. A more neutral
IGM will scatter Ly$\alpha$ photons more causing Ly$\alpha$ to emerge at a
higher $\Delta v$ relative to systemic.

It is not uncommon for $z>5$ galaxies to have [CII] emission tracing the
systemic redshift of the galaxy but spatially offset from the UV component
(Maiolino et al., 2015; Willott et al., 2015; Capak et al., 2015; Carniani et
al., 2017; Carniani et al., 2018b; Carniani et al., 2018a; Jones et al., 2017;
Matthee et al., 2019; Fujimoto et al., 2022). In fact, spatial offsets between
Ly$\alpha$ and UV have also been found at $z>5$ (Hoag et al., 2019a; Lemaux et
al., 2021). Carniani et al. (2018a) shows that most of the [CII] spatial
offsets are indeed physically motivated but further observations are needed to
understand the mechanisms causing the offsets. Recently, Fujimoto et al.
(2022) was able to determine the necessity of past outflow activity in a
galaxy at $z\sim 8.5$ based on dual observations with ALMA and JWST.

We roughly estimate the [CII]-UV spatial offset in MACS0454-1251 using the
brightest pixels found in the [CII] moment0 map and the centroid of the _HST_
rest-UV image. The lensed spatial offset is $\sim 0.\arcsec 5$ which is
greater than the ALMA astrometric accuracy of $\sim 0.\arcsec 08$
333Calculated from ALMA technical handbook
https://almascience.nrao.edu/documents-and-tools/cycle10/alma-technical-
handbook.. Taking into account the magnification, we estimate the lens-
corrected offset to be $\sim 1.4\mbox{kpc}$ 444For isotropic lensing
distortion, we spatially scale with $/\sqrt{\mu}$. The offset could be
physically associated with intrinsic ISM properties (e.g. different
distribution in the ionized vs neutral gas phase). A possible explanation for
the spatial offset could also be the ejection of material by galactic outflows
or galaxy mergers (e.g., Maiolino et al., 2015; Vallini et al., 2015;
Pallottini et al., 2017; Katz et al., 2017; Gallerani et al., 2018; Kohandel
et al., 2019).

###  4.2 $L_{\rm{[CII]}}-\rm{SFR}$ Relation

Figure 4: A plot of $L_{\textrm{[CII]}}$ vs. $\rm{SFR_{\rm{UV}}}$ relation for
our study (red stars) and literature. The blue ($z>6$) and purple ($z>7$)
circles show previous studies Willott et al. (2015); Maiolino et al. (2015);
Knudsen et al. (2016); Pentericci et al. (2016); Matthee et al. (2017); Bradač
et al. (2017); Carniani et al. (2018a); Smit et al. (2018b); Hashimoto et al.
(2018); Matthee et al. (2019); Schouws et al. (2022); Harikane et al. (2020);
Fujimoto et al. (2021); Molyneux et al. (2022); Schaerer et al. (2015); Inoue
et al. (2016); Carniani et al. (2020); Watson et al. (2015); Wong et al.
(2022); Katz et al. (2017); Bakx et al. (2020); Bowler et al. (2018);
Hashimoto et al. (2019); Fujimoto et al. (2022); Heintz et al. (2023); Ferrara
et al. (2022); Sommovigo et al. (2022). Upper limits are denoted by open
markers. The lines represent the results from Vallini et al. (2015) with black
$Z=Z_{\odot}$ (C1), orange $Z=0.2Z_{\odot}$ (CO2), and blue $Z=0.05Z_{\odot}$
(C005) representing a constant metallicity. The magenta dashed line (P005)
represents a density-dependent metallicity of $Z=0.05Z_{\odot}$. The dark and
light grey represents the $1\sigma$ scatter around the best-fit relations for
dwarf and local starburst galaxies from De Looze et al. (2014).

In Fig 4 we show the $L_{\rm{[CII]}}-\rm{SFR}_{\rm{UV}}$ relation for our
galaxies (stars) alongside available $z>6$ observations from the literature.
The reported $\rm{SFR}_{\rm{UV}}$ values for our objects can be found in Table
LABEL:tab:Spec_table along with $\rm{SFR}_{\rm{SED}}$ values that were derived
through SED fitting described in Section 3. $\rm{SFR_{\rm{UV}}}$ is calculated
assuming no dust attenuation and therefore should be considered a lower limit
as it does not include obscured star formation. We also recognize that in the
event of a more top heavy IMF (i.e., the median of the mass-to-light ratio of
stars being born decreases), $\rm{SFR}_{\rm{UV}}$ would be an overestimate
assuming constant dust properties.

Our single [CII] detection, MACS0454-1251, falls within the $1\sigma$ scatter
of the De Looze et al. (2014) relation for dwarf($\sim 0.2$ dex below) and
local starburst galaxies($\sim 0.2$ dex above). We note, however,
MACS0454-1251 is the most UV luminous galaxy ($L=0.74L^{*}$) in our sample.
The detection is also consistent with the C1 model put forth by the Vallini et
al. (2015) simulations which corresponds to a galaxy with constant solar
metallicity. If we compare this to our non-detections, the upper limit set by
RXJ1347-018 also is consistent with the. De Looze et al. (2014) relation;
having a scatter of $\sim 0.3$ dex from the average dwarf and local starburst
relations. The upper limit set by MACS2129-1412 is not consistent with the De
Looze et al. (2014) relations, falling $\sim 0.5$ dex from starburst galaxies
and $\sim 0.6$ dex from the dwarf galaxies. The one displayed Vallini et al.
(2015) model it could possibly support is the C005 model which represents a
galaxy with a constant metallicity of $Z=0.05Z_{\odot}$.

The possibility of a sub-solar metallicities is not surprising for these two
low-mass galaxies and aligns with recent work (Curti et al., 2023). Probing a
wide stellar mass range, ($M_{\rm{stellar}}/M_{\odot}\simeq
10^{6.5}-10^{8.5}$), Curti et al. (2023) shows their $z>6$ galaxies exhibit
sub-solar metallicities ($Z<Z_{\odot}$), with a scaling relation drawn near
$\sim~{}0.1Z_{\odot}$. While we do not have the observations to determine the
true metallicities of our sample, a low metallicity could explain the absence
of [CII] in our non-detections and would not contradict their respective upper
limits. Another possible reason for the lack of detected [CII] emission could
be negative feedback disrupting molecular clouds (MCs, Vallini et al., 2015).
For example, [CII] emission predominately originates from PDRs. Negative
feedback disrupting MCs would reduce the PDR layer at the edge of the MC where
most of the [CII] emission comes from. Additionally, we know stellar feedback
is efficient in galaxy centers, places where there is very active star
formation. In fact, studies done at lower-$z$ have supported a connection
between feedback efficiency and SFR surface density (e.g., Hayward & Hopkins,
2016; Heckman et al., 2011). Since high-$z$ galaxies are more compact than
local analogs, this would also support negative feedback suppressing [CII]
emission at the systemic redshift of the galaxy.

##  5 Conclusions

We present new ALMA observations investigating [CII] $158\mu\rm{m}$ line
emission in three lensed galaxies at $z>6$. We find a $4\sigma$ [CII]
detection in our most luminous galaxy ($L\sim 0.7L^{*}$) MACS0454-1251 and
calculate the systemic redshift to be $z_{\rm{[CII]}}=6.3151\pm 0.0005$. We
measure a $\Delta v=320\pm 20\rm{km\,s}^{-1}$ and calculate
$L_{\textrm{[CII]}}=1.5_{-0.4}^{+0.5}\times 10^{8}L_{\odot}$. For the
remaining two galaxies we do not detect [CII] emission but provide $3\sigma$
upper limits for their $L_{\textrm{[CII]}}$. Our main findings are:

(i) MACS0454-1251 exhibits both a velocity and a spatial offset between
between ALMA [CII] and rest-frame HST UV emission. The spatial offset is
larger than the the ALMA astrometric uncertainty which could mean the offset
is physically motivated by intrinsic ISM properties.

(ii) Feedback is a very important process in both the emission of [CII] and
Ly$\alpha$. On one hand, strong feedback can suppress [CII] emission by
disrupting MCs (Vallini et al., 2015). On the other hand strong feedback from
star formation can drive outflows which redshifts the Ly$\alpha$ line. A
possibility that puts together the spatial offset and the [CII] deficit is
that feedback destroys the emitting MCs at the center, allowing only displaced
MCs to contribute to the [CII] emission.

(iii) Our single [CII] detection in MACS0454-1251 falls within the $1\sigma$
scatter of the De Looze et al. (2014) $L_{\rm{[CII]}}-\rm{SFR}$ relations. As
such, it would support with the applicability of the $L_{\rm{[CII]}}-\rm{SFR}$
relation put forth by De Looze et al. (2014) for $z>6$ galaxies. That being
said, the upper limits set by our RXJ1347-018 and MACS2129-1412, would argue
an inconclusive result, especially with the $3\sigma$ upper limit of
MACS2129-1412 still falling well below De Looze et al. (2014). In general,
more observations of low-mass, UV faint galaxies are needed in order to break
this degeneracy.

(iv) Low metallicity is a possible justification for fainter galaxies falling
below the De Looze et al. (2014) $L_{\textrm{[CII]}}-\textrm{SFR}$ relation
(Vallini et al., 2013; Ferrara et al., 2019). Based on recent work (Curti et
al., 2023), we would expect lower mass, ($M_{\rm{stellar}}\lessapprox
10^{9.5}$) galaxies at $z>6$ to exhibit sub-solar metallicites. A possible
scenario for [CII] deficient systems with very low metalicity is powerful
feedback; involving the destruction of star forming sites occurring during
bursty evolutionary phases in relatively chemically unevolved systems (Vallini
et al., 2015; Ferrara et al., 2019).

(v) While we lack the proper observations to determine the true metallicity of
MACS0454-1251, based on the Vallini et al. (2015) models, MACS0454-1251 could
be experiencing a solar metallicity.

The work shown in this paper aims to shed light on faint EoR galaxy properties
which in the past was significantly been undersampled.

## Acknowledgements

We acknowledge support from the program HST-GO-16667, provided through a grant
from the STScI under NASA contract NAS5-26555. MB also acknowledges support
from the ERC Advanced Grant FIRSTLIGHT and Slovenian national research agency
ARRS through grants N1-0238 and P1-0188. RLS acknowledges support provided by
NASA through the NASA Hubble Fellowship grant #HST-HF2-51469.001-A awarded by
the Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Incorporated, under NASA contract
NAS5-26555. AF acknowledges support from the ERC Advanced Grant INTERSTELLAR
H2020/740120.

## Data Availability

The original data used in the work can be found and downloaded from the ALMA
archive https://almascience.nrao.edu using the science project ID:
2019.1.00003.S. The reduced data generated in this research will be shared on
reasonable request to the corresponding author.

## References

  * Baier-Soto et al. (2022) Baier-Soto R., Herrera-Camus R., Förster Schreiber N. M., Contursi A., Genzel R., Lutz D., Tacconi L., 2022, A&A, 664, L5
  * Bakx et al. (2020) Bakx T. J. L. C., et al., 2020, MNRAS, 493, 4294
  * Bianchi (2013) Bianchi S., 2013, A&A, 552, A89
  * Bolan et al. (2022) Bolan P., et al., 2022, MNRAS, 517, 3263
  * Boselli et al. (2002) Boselli A., Gavazzi G., Lequeux J., Pierini D., 2002, A&A, 385, 454
  * Bouwens et al. (2022) Bouwens R. J., Illingworth G., Ellis R. S., Oesch P., Stefanon M., 2022, ApJ, 940, 55
  * Bowler et al. (2018) Bowler R. A. A., Bourne N., Dunlop J. S., McLure R. J., McLeod D. J., 2018, MNRAS, 481, 1631
  * Bradač et al. (2014) Bradač M., et al., 2014, ApJ, 785, 108
  * Bradač et al. (2017) Bradač M., et al., 2017, The Astrophysical Journal, 836, L2
  * Bruzual & Charlot (2003) Bruzual G., Charlot S., 2003, MNRAS, 344, 1000
  * Bunker et al. (2023) Bunker A. J., et al., 2023, arXiv e-prints, p. arXiv:2302.07256
  * Calzetti et al. (2000) Calzetti D., Armus L., Bohlin R. C., Kinney A. L., Koornneef J., Storchi-Bergmann T., 2000, ApJ, 533, 682
  * Capak et al. (2015) Capak P. L., et al., 2015, Nature, 522, 455
  * Carilli & Walter (2013) Carilli C., Walter F., 2013, Annual Review of Astronomy and Astrophysics, 51, 105
  * Carnall et al. (2018) Carnall A. C., McLure R. J., Dunlop J. S., Davé R., 2018, MNRAS, 480, 4379
  * Carniani et al. (2017) Carniani S., et al., 2017, A&A, 605, A42
  * Carniani et al. (2018a) Carniani S., et al., 2018a, MNRAS, 478, 1170
  * Carniani et al. (2018b) Carniani S., Maiolino R., Smit R., Amorín R., 2018b, ApJ, 854, L7
  * Carniani et al. (2020) Carniani S., et al., 2020, MNRAS, 499, 5136
  * Casey (2012) Casey C. M., 2012, MNRAS, 425, 3094
  * Casey et al. (2014) Casey C. M., Narayanan D., Cooray A., 2014, Phys. Rep., 541, 45
  * Cassata et al. (2020) Cassata P., et al., 2020, A&A, 643, A6
  * Chabrier (2003) Chabrier G., 2003, PASP, 115, 763
  * Curti et al. (2023) Curti M., et al., 2023, arXiv e-prints, p. arXiv:2304.08516
  * De Looze et al. (2011) De Looze I., Baes M., Bendo G. J., Cortese L., Fritz J., 2011, MNRAS, 416, 2712
  * De Looze et al. (2014) De Looze I., et al., 2014, A&A, 568, A62
  * Draine (2003) Draine B. T., 2003, ARA&A, 41, 241
  * Endsley et al. (2022) Endsley R., et al., 2022, MNRAS, 517, 5642
  * Endsley et al. (2023) Endsley R., Stark D. P., Whitler L., Topping M. W., Chen Z., Plat A., Chisholm J., Charlot S., 2023, MNRAS, 524, 2312
  * Erb et al. (2014) Erb D. K., et al., 2014, ApJ, 795, 33
  * Faber et al. (2003) Faber S. M., et al., 2003, in Iye M., Moorwood A. F. M., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 4841, Instrument Design and Performance for Optical/Infrared Ground-based Telescopes. pp 1657–1669, doi:10.1117/12.460346
  * Feroz & Hobson (2008) Feroz F., Hobson M. P., 2008, MNRAS, 384, 449
  * Feroz et al. (2009) Feroz F., Hobson M. P., Bridges M., 2009, MNRAS, 398, 1601
  * Ferrara et al. (2019) Ferrara A., Vallini L., Pallottini A., Gallerani S., Carniani S., Kohandel M., Decataldo D., Behrens C., 2019, MNRAS, 489, 1
  * Ferrara et al. (2022) Ferrara A., et al., 2022, MNRAS, 512, 58
  * Finkelstein et al. (2019) Finkelstein S. L., et al., 2019, ApJ, 879, 36
  * Fudamoto et al. (2023) Fudamoto Y., et al., 2023, arXiv e-prints, p. arXiv:2303.07513
  * Fujimoto et al. (2021) Fujimoto S., et al., 2021, The Astrophysical Journal, 911, 99
  * Fujimoto et al. (2022) Fujimoto S., et al., 2022, arXiv e-prints, p. arXiv:2212.06863
  * Gallerani et al. (2018) Gallerani S., Pallottini A., Feruglio C., Ferrara A., Maiolino R., Vallini L., Riechers D. A., Pavesi R., 2018, MNRAS, 473, 1909
  * Guaita et al. (2017) Guaita L., et al., 2017, A&A, 606, A19
  * Harikane et al. (2019) Harikane Y., et al., 2019, ApJ, 883, 142
  * Harikane et al. (2020) Harikane Y., et al., 2020, The Astrophysical Journal, 896, 93
  * Hashimoto et al. (2018) Hashimoto T., et al., 2018, Nature, 557, 392
  * Hashimoto et al. (2019) Hashimoto T., et al., 2019, PASJ, 71, 71
  * Hayward & Hopkins (2016) Hayward C. C., Hopkins P. F., 2016, Monthly Notices of the Royal Astronomical Society, 465, 1682
  * Heckman et al. (2011) Heckman T. M., et al., 2011, ApJ, 730, 5
  * Heintz et al. (2023) Heintz K. E., et al., 2023, ApJ, 944, L30
  * Herrera-Camus et al. (2015) Herrera-Camus R., et al., 2015, ApJ, 800, 1
  * Hoag et al. (2019a) Hoag A., et al., 2019a, MNRAS, 488, 706
  * Hoag et al. (2019b) Hoag A., et al., 2019b, ApJ, 878, 12
  * Hollenbach & Tielens (1999) Hollenbach D. J., Tielens A. G. G. M., 1999, Reviews of Modern Physics, 71, 173
  * Huang et al. (2016a) Huang K.-H., et al., 2016a, ApJ, 817, 11
  * Huang et al. (2016b) Huang K.-H., et al., 2016b, ApJ, 823, L14
  * Inoue et al. (2016) Inoue A. K., et al., 2016, Science, 352, 1559
  * Jones et al. (2013) Jones T. A., Ellis R. S., Schenker M. A., Stark D. P., 2013, ApJ, 779, 52
  * Jones et al. (2017) Jones G. C., Willott C. J., Carilli C. L., Ferrara A., Wang R., Wagg J., 2017, The Astrophysical Journal, 845, 175
  * Katz et al. (2017) Katz H., Kimm T., Sijacki D., Haehnelt M. G., 2017, MNRAS, 468, 4831
  * Katz et al. (2019) Katz H., et al., 2019, MNRAS, 487, 5902
  * Kennicutt (1998a) Kennicutt J., 1998a, Annual Review of Astronomy and Astrophysics, 36, 189
  * Kennicutt (1998b) Kennicutt Robert C. J., 1998b, ApJ, 498, 541
  * Knudsen et al. (2016) Knudsen K. K., Richard J., Kneib J.-P., Jauzac M., Clément B., Drouart G., Egami E., Lindroos L., 2016, MNRAS, 462, L6
  * Kohandel et al. (2019) Kohandel M., Pallottini A., Ferrara A., Zanella A., Behrens C., Carniani S., Gallerani S., Vallini L., 2019, MNRAS, 487, 3007
  * Kroupa (2001) Kroupa P., 2001, MNRAS, 322, 231
  * Laporte et al. (2017) Laporte N., Nakajima K., Ellis R. S., Zitrin A., Stark D. P., Mainali R., Roberts-Borsani G. W., 2017, ApJ, 851, 40
  * Laporte et al. (2021) Laporte N., et al., 2021, MNRAS, 505, 4838
  * Leethochawalit et al. (2016) Leethochawalit N., Jones T. A., Ellis R. S., Stark D. P., Zitrin A., 2016, ApJ, 831, 152
  * Lemaux et al. (2021) Lemaux B. C., et al., 2021, MNRAS, 504, 3662
  * Lupi & Bovino (2020) Lupi A., Bovino S., 2020, MNRAS, 492, 2818
  * Maiolino et al. (2015) Maiolino R., et al., 2015, MNRAS, 452, 54
  * Mason et al. (2018) Mason C. A., Treu T., Dijkstra M., Mesinger A., Trenti M., Pentericci L., de Barros S., Vanzella E., 2018, ApJ, 856, 2
  * Matthee et al. (2017) Matthee J., et al., 2017, The Astrophysical Journal, 851, 145
  * Matthee et al. (2019) Matthee J., et al., 2019, ApJ, 881, 124
  * McLean et al. (2010) McLean I. S., et al., 2010, in McLean I. S., Ramsay S. K., Takami H., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III. p. 77351E, doi:10.1117/12.856715
  * Molyneux et al. (2022) Molyneux S. J., et al., 2022, MNRAS, 512, 535
  * Naidu et al. (2020) Naidu R. P., Tacchella S., Mason C. A., Bose S., Oesch P. A., Conroy C., 2020, ApJ, 892, 109
  * Olsen et al. (2017) Olsen K., Greve T. R., Narayanan D., Thompson R., Davé R., Niebla Rios L., Stawinski S., 2017, ApJ, 846, 105
  * Pallottini et al. (2017) Pallottini A., Ferrara A., Gallerani S., Vallini L., Maiolino R., Salvadori S., 2017, MNRAS, 465, 2540
  * Pallottini et al. (2019) Pallottini A., et al., 2019, MNRAS, 487, 1689
  * Pallottini et al. (2022) Pallottini A., et al., 2022, MNRAS, 513, 5621
  * Pentericci et al. (2016) Pentericci L., et al., 2016, The Astrophysical Journal, 829, L11
  * Pineda et al. (2014) Pineda J. L., Langer W. D., Goldsmith P. F., 2014, A&A, 570, A121
  * Postman et al. (2012) Postman M., et al., 2012, ApJS, 199, 25
  * Prieto-Lyon et al. (2023) Prieto-Lyon G., et al., 2023, arXiv e-prints, p. arXiv:2304.02666
  * Robertson (2022) Robertson B. E., 2022, ARA&A, 60, 121
  * Romano et al. (2022) Romano M., et al., 2022, A&A, 660, A14
  * Sargsyan et al. (2012) Sargsyan L., et al., 2012, ApJ, 755, 171
  * Schaerer et al. (2015) Schaerer D., Boone F., Zamojski M., Staguhn J., Dessauges-Zavadsky M., Finkelstein S., Combes F., 2015, A&A, 574, A19
  * Schaerer et al. (2020) Schaerer D., et al., 2020, A&A, 643, A3
  * Schouws et al. (2022) Schouws S., et al., 2022, arXiv e-prints, p. arXiv:2202.04080
  * Smit et al. (2018b) Smit R., et al., 2018b, Nature, 553, 178
  * Smit et al. (2018a) Smit R., et al., 2018a, Nature, 553, 178
  * Sommovigo et al. (2022) Sommovigo L., et al., 2022, MNRAS, 513, 3122
  * Stacey et al. (1991) Stacey G. J., Geis N., Genzel R., Lugten J. B., Poglitsch A., Sternberg A., Townes C. H., 1991, The Astrophysical Journal, 373, 423
  * Stacey et al. (2010) Stacey G. J., Hailey-Dunsheath S., Ferkinhoff C., Nikola T., Parshley S. C., Benford D. J., Staguhn J. G., Fiolet N., 2010, The Astrophysical Journal, 724, 957
  * Strait et al. (2020) Strait V., et al., 2020, ApJ, 888, 124
  * Trainor et al. (2015) Trainor R. F., Steidel C. C., Strom A. L., Rudie G. C., 2015, ApJ, 809, 89
  * Treu et al. (2015) Treu T., et al., 2015, ApJ, 812, 114
  * Vallini et al. (2013) Vallini L., Gallerani S., Ferrara A., Baek S., 2013, MNRAS, 433, 1567
  * Vallini et al. (2015) Vallini L., Gallerani S., Ferrara A., Pallottini A., Yue B., 2015, ApJ, 813, 36
  * Watson et al. (2015) Watson D., Christensen L., Knudsen K. K., Richard J., Gallazzi A., Michałowski M. J., 2015, Nature, 519, 327
  * Willott et al. (2015) Willott C. J., Carilli C. L., Wagg J., Wang R., 2015, ApJ, 807, 180
  * Wolfire et al. (2003) Wolfire M. G., McKee C. F., Hollenbach D., Tielens A. G. G. M., 2003, ApJ, 587, 278
  * Wolfire et al. (2022) Wolfire M. G., Vallini L., Chevance M., 2022, ARA&A, 60, 247
  * Wong et al. (2022) Wong Y. H. V., et al., 2022, arXiv e-prints, p. arXiv:2202.13613
  * Yang et al. (2016) Yang H., Malhotra S., Gronke M., Rhoads J. E., Dijkstra M., Jaskot A., Zheng Z., Wang J., 2016, ApJ, 820, 130
  * Yang et al. (2017) Yang H., et al., 2017, ApJ, 844, 171