# The galaxy UV luminosity function at $\mathbf{z\simeq 11}$ from a suite of
public JWST ERS, ERO and Cycle-1 programs

D. J. McLeod1, C. T. Donnan1, R. J. McLure1, J. S. Dunlop1, D. Magee2, R.
Begley1 Email<EMAIL_ADDRESS>A. C. Carnall1, F. Cullen1, R. S. Ellis3, M.
L. Hamadouche1, T. M. Stanton1

1 Institute for Astronomy, University of Edinburgh, Royal Observatory,
Edinburgh EH9 3HJ, UK
2 Department of Astronomy and Astrophysics, UCO/Lick Observatory, University
of California, Santa Cruz, CA 95064, USA
3 Department of Physics and Astronomy, University College London, Gower
Street, London, WC1E 6BT, UK

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

###### Abstract

We present a new determination of the evolving galaxy UV luminosity function
(LF) over the redshift range $9.5<z<12.5$ based on a wide-area ($>250$
arcmin2) data set of JWST NIRCam near-infrared imaging assembled from thirteen
public JWST surveys. Our relatively large-area search allows us to uncover a
sample of 61 robust $z>9.5$ candidates detected at $\geq 8\sigma$, and hence
place new constraints on the intermediate-to-bright end of the UV LF. When
combined with our previous JWST+UltraVISTA results, this allows us to measure
the form of the LF over a luminosity range corresponding to four magnitudes
($M_{1500}$). At these early times we find that the galaxy UV LF is best
described by a double power-law function, consistent with results obtained
from recent ground-based and early JWST studies at similar redshifts. Our
measurements provide further evidence for a relative lack of evolution at the
bright-end of the UV LF at $z=9-11$, but do favour a steep faint-end slope
($\alpha\leq-2$). The luminosity-weighted integral of our evolving UV LF
provides further evidence for a gradual, smooth (exponential) decline in co-
moving star-formation rate density ($\rho_{\mathrm{SFR}}$) at least out to
$z\simeq 12$, with our determination of $\rho_{\mathrm{SFR}}(z=11)$ lying
significantly above the predictions of many theoretical models of galaxy
evolution.

###### keywords:

galaxies: high-redshift – galaxies: evolution – galaxies: formation

††pubyear: 2023††pagerange: The galaxy UV luminosity function at
$\mathbf{z\simeq 11}$ from a suite of public JWST ERS, ERO and Cycle-1
programs–A.12

##  1 INTRODUCTION

Although JWST has not yet completed its first year of science operations, it
is already transforming our view of the young Universe. Despite its many
achievements, the Hubble Space Telescope (HST) was unable to advance the
search for early galaxies significantly beyond redshifts $z\simeq 10$, due to
its limited near-infrared wavelength coverage ($\lambda<1.6$ $\mu$m) (e.g.,
Ellis et al. 2013; Coe et al. 2013; Oesch et al. 2016). By contrast, the
exquisite near/mid-infrared imaging now being provided by the NIRCam
instrument on-board the larger and colder JWST has already pushed the redshift
frontier out to $z\simeq 13$ (Naidu et al., 2022; Finkelstein et al., 2022b;
Robertson et al., 2023), with candidate high-redshift galaxies already being
uncovered at redshifts as extreme as $z=16-17$ (Harikane et al., 2023b).

The photometric selection of high-redshift galaxy candidates from deep imaging
not only supplies targets for spectroscopic follow-up to determine their
astrophysical properties, but also enables the statistical study of the
evolution of the galaxy population provided sufficiently large and robust
samples can be assembled. In particular, a key goal is to chart the evolution
of the galaxy luminosity function (LF) back to early times for comparison with
theoretical predictions. At very high redshifts, near/mid-infrared imaging
enables the evolving rest-frame ultraviolet (UV) galaxy LF to be determined,
the luminosity-weighted integral of which gives the evolution of (co-moving)
UV luminosity density, which can then be converted into the evolution of
cosmic star-formation rate density, $\rho_{\mathrm{SFR}}$. In large part due
to the impact of HST, there is now a general consensus over the evolution of
$\rho_{\mathrm{SFR}}$ out to $z\simeq 8$. However, before the advent of JWST,
the lack of significant galaxy samples at higher redshifts resulted in
considerable disagreement over the evolution of star-formation rate density at
earlier times. Specifically, some studies concluded in favour of a rapidly
steepening decline in $\rho_{\mathrm{SFR}}$ with increasing look-back time
beyond $z\simeq 8$ (e.g., Oesch et al. 2013; Oesch et al. 2018), while others
presented evidence for a continued smooth, more gradual evolution implying the
existence of substantial star-formation activity at still earlier times
(McLeod et al., 2015; McLeod et al., 2016).

This debate/disagreement over the very high-redshift evolution of the UV LF,
and hence $\rho_{\mathrm{SFR}}$, was largely a consequence of the limitations
of pre-JWST facilities mentioned above. Specifically, at redshifts $z\geq 9$
the WFC3/IR camera on HST rapidly runs out of filters capable of sampling
continuum emission beyond the Lyman break at $\lambda_{\mathrm{rest}}=1216$ Å.
For most of the deep extragalactic imaging surveys performed with HST only
F125W and F160W imaging are available for this purpose, at least for the
majority of the CANDELS (Grogin et al., 2011) area. The addition of the F140W
filter for such surveys as the HUDF (Beckwith et al., 2006; Ellis et al.,
2013), CLASH (Postman et al., 2012) and the Frontier Fields (Lotz et al.,
2017) was key for selecting $z=9$ galaxies in McLeod et al. (2015); McLeod et
al. (2016) as it provided a third filter with high-resolution imaging that
probes beyond the Lyman break. The Spitzer space telescope (e.g., S-CANDELS;
Ashby et al. 2015) and the deepest ground-based $K_{s}-$band imaging (e.g.
Very Large Telescope (VLT)’s HUGS; Fontana et al. 2014) helped to extend the
wavelength baseline beyond $\lambda=1.6$ $\mu$m and provided constraints on
the rest-frame optical continuum of some brighter high-redshift galaxies, but
this redder non-HST imaging lacked the resolution and the depth to benefit
searches for more typical galaxies at $z>8$.

JWST has effectively unlocked the longer wavelength near/mid-infrared coverage
previously only provided by ground-based facilities and Spitzer, but now with
enormous improvements in both angular resolution and depth. Several early,
public JWST NIRCam surveys have reached $5\sigma$ limiting depths of
$28.5-29.0$ mag in filters spanning the wavelength range $\lambda\simeq 1-5$
$\mu$m, already probing several magnitudes deeper than typical Spitzer
surveys, and with diffraction-limited imaging down to $\lambda\simeq 1$ $\mu$m
delivering near-infrared imaging of much improved resolution compared to HST’s
WFC3/IR. This combination of depth and resolution has already been
transformative in the selection of ultra-high redshift galaxies.
Encouragingly, many of the $z>10$ candidates photometrically selected from the
early NIRCam imaging are already being confirmed spectroscopically with JWST
NIRSpec (Arrabal Haro et al., 2023a, b; Harikane et al., 2023a).

While several theoretical models of galaxy evolution appear to predict a rapid
decline in $\rho_{\mathrm{SFR}}$ at $z>8$ (e.g., Mason et al. 2015; Yung et
al. 2019), early JWST studies have provided evidence to the contrary. Donnan
et al. (2023a) conducted a wide-area, ground-based search for bright $z=8-10$
galaxy candidates using COSMOS/UltraVISTA DR5 (McCracken et al., 2012), in
combination with a search for fainter galaxies at these redshifts with the
JWST CEERS (Finkelstein et al., 2023), GLASS-parallel (Treu et al., 2022) and
SMACS0723-73 (Pontoppidan et al., 2022) public surveys. The resulting UV LF
determination was found to be consistent with the earlier HST-based works of
McLeod et al. (2015); McLeod et al. (2016), with $\rho_{\mathrm{SFR}}$
displaying an extended smooth decline at $z>8$ and indeed continuing to
display a log-linear relation with redshift until at least $z\sim 12$. At the
bright-end, the number densities of $z=8-10$ galaxy candidates found using the
latest COSMOS/UltraVISTA ground-based data suggested that the UV LF follows a
double power-law functional form, as previously found by Bowler et al. (2020).
Although the exceptionally bright $z=16$ candidate CEERS-93316 first reported
in Donnan et al. (2023a) has now been spectroscopically confirmed to be a
lower redshift interloper at $z=4.9$ (Arrabal Haro et al., 2023a), this is a
particularly pathological case in which a peculiar combination of very strong
emission lines conspired to masquerade as the blue continuum above the Lyman-
break. Another potential $z=16$ candidate behind Stephan’s Quintet may yet
suggest that significant star-formation activity is still taking place at
$z\geq 14$ (Harikane et al., 2023b).

As well as the discovery of extremely high-redshift galaxies at $z>12$ (Naidu
et al., 2022; Atek et al., 2023; Donnan et al., 2023a; Harikane et al.,
2023b), JWST has been yielding surprisingly large numbers of bright $z\simeq
10$ galaxies, with a particularly high number density reported by Castellano
et al. (2022a) in the area around the Abell 2744 cluster. Such densities are
potentially up to a factor ten times greater than expectations based on
previous observations and theoretical models of galaxy evolution. This would
challenge our existing understanding, with many existing theoretical models of
galaxy evolution having to invoke more efficient star formation or less dust
attenuation at the highest redshifts to match these observational results.
Alternatively, these early observations may be biased to a particular
population of young and rapidly star-forming galaxies (Mason et al., 2023).
There is thus an open question as to how accurately the early JWST-selected
galaxy samples represent the true number densities of bright ${z=10}$
galaxies, with existing high-redshift galaxy searches typically restricted to
small areas.

The address this issue, the study presented here aims to exploit all relevant
available JWST NIRCam Early Release Observations (ERO), Early Release Science
(ERS) and public Cycle-1 programs to conduct a systematic wide-area search for
extreme-redshift galaxy candidates with high signal-to-noise ($\geq 8\sigma$).
The resulting combined survey, covering a raw area of $\simeq 260$ arcmin2,
provides a new opportunity to uncover statistically significant samples of
galaxies in the redshift range $9.5<z<12.5$, and hence yield improved
constraints on the number densities of bright to intermediate $M_{1500}$
galaxies over this redshift range. By combining the new results with our
previously-derived constraints on the number densities of fainter galaxies
(Donnan et al., 2023a), we are hence able to determine the evolving UV LF and
$\rho_{\mathrm{SFR}}$ at $z=10-12$, deep into the redshift range where the
results derived using HST had diverged. Moreover, our wide-area search may
also uncover other examples of extremely high-redshift ($z>12$) galaxy
candidates, such as those found in the ERO surveys (e.g. Atek et al. 2023;
Harikane et al. 2023b).

The structure of this paper is as follows. In Section 2 we describe each of
the data sets included in our high-redshift galaxy search. Section 3 describes
the construction of our multi-wavelength catalogues and candidate selection.
We discuss our candidates and draw comparisons with other recent JWST searches
in the literature in Section 4. In Section 5, we use our high-redshift galaxy
sample to determine the form of the UV LF over the redshift range $9.5<z<12.5$
and how it evolves from $z\simeq 8$ to $z\simeq 12$. In Section 6 we integrate
the UV LF in order to determine the star-formation rate density and how it
evolves with cosmic time. Finally, in Section 7 we summarise our conclusions.
Throughout the paper, we adopt a cosmology with
$\Omega_{0}=0.3,\Omega_{\Lambda}=0.7$ and $H_{0}=70$ kms-1Mpc-1, and use the
AB magnitude system (Oke, 1974; Oke & Gunn, 1983).

##  2 DATA

###  2.1 Imaging data

We begin with a description of the various data sets employed in this study.
Each of the data sets were downloaded as “rate” products, either from the CADC
or STScI MAST database, and processed through the Primer Enhanced NIRCam Image
Processing Library (PENCIL; Magee in prep) software, which is a customised
version of the JWST pipeline version 1.6.2. This version of the pipeline
includes additional routines for the removal of snowballs and wisps, as well
as background subtraction and correcting for 1/f noise striping. Given the
different timeframes in which the various data sets were taken, released,
reduced and analysed, there are very slight differences in the CRDS context
depending on when the data set was released, although the pmap is always at
least pmap 0989, which included the most recent zero-point corrections at the
time of writing. Where applicable, HST data sets were downloaded as their
high-level science products from the STScI MAST, aligned to the JWST imaging
and registered using SWARP (Bertin, 2010). The exception is for CEERS, where
HST EGS imaging in F606W and F814W was provided in a data release by the CEERS
team (see Koekemoer et al. 2011).

The global 5$\sigma$ limiting magnitudes for each of the different surveys and
in each filter can be found in Table 1. These global depths were measured in
$0.35^{\prime\prime}-$diameter apertures and corrected to total assuming a
point-source correction. Note that the global depth in a given survey is
subject to potentially significant spatial variations in local depth, owing to
differences in exposure time, source-crowding (particularly for the Quintet,
Cartwheel and cluster fields) or sensitivities of the NIRCam modules. We also
include the effective survey area for each of the fields, accounting for de-
lensing where applicable.

Filter | SM0723 | Quintet | C’wheel | W0137 | NEP-TDF | J1235 | M0647 | R2129 | GLASS | DDT | UNCOVER | CEERS
---|---|---|---|---|---|---|---|---|---|---|---|---
F435W | 26.7 | - | - | 26.6 | - | - | 26.7 | 26.8 | - | - | 28.2 | 27.8
F606W | 27.7 | - | - | 27.4 | - | - | 27.2 | 27.2 | - | - | 28.6 | 28.4
F814W | 26.8 | - | - | 26.8 | - | - | 27.2 | 26.7 | - | - | 28.4 | 28.0
F070W | - | - | - | - | - | 27.9 | - | - | - | - | - | -
F090W | 28.5 | 26.9 | 27.3 | 27.7 | 28.1 | 28.4 | - | - | 28.8 | - | - | -
F115W | - | - | - | 27.9 | 28.2 | 28.5 | 27.7 | 27.2 | 28.9 | 28.5 | 28.6 | 28.5
F150W | 28.6 | 27.0 | 27.3 | 28.0 | 28.0 | 28.4 | 27.8 | 27.8 | 28.5 | 28.6 | 28.6 | 28.4
F200W | 28.7 | 27.3 | 27.6 | 28.1 | 28.3 | 28.8 | 28.2 | 27.6 | 28.7 | 28.8 | 28.8 | 28.6
F277W | 28.7 | 27.7 | 27.9 | 28.3 | 28.7 | 28.9 | 28.3 | 27.9 | 28.9 | 28.7 | 28.8 | 28.6
F300M | - | - | - | - | - | 28.6 | - | - | - | - | - | -
F356W | 28.7 | 27.8 | 27.9 | 28.2 | 28.5 | 28.9 | 28.3 | 28.3 | 28.9 | 28.9 | 28.9 | 28.5
F410M | - | - | - | 27.9 | 28.1 | - | - | - | - | - | 28.5 | 28.0
F444W | 28.4 | 27.4 | 27.8 | 27.9 | 28.3 | 28.3 | 28.0 | 27.7 | 28.8 | 28.3 | 28.5 | 28.2
Area (arcmin2) |  o7.0 | 40.9 |  o4.2 |  o5.9 | 10.5 |  o9.9 |  o5.1 |  o3.1 | 10.1 |  o6.6 | 12.2 | 95.0
Table 1: The $5\sigma$ global limiting magnitudes for each of the fields
analysed in this study. These have been measured in
$0.35^{\prime\prime}-$diameter apertures on the PSF-homogenized imaging, and
corrected to total assuming a point-source correction. Note that for some
fields e.g. the clusters and Quintet, these global values are subject to
significant variations (as high as $>0.5$ mag) across the field of view owing
to crowding and enhanced background, as illustrated in Fig. 5. We also provide
the effective areas in each field, accounting for cluster subtraction and de-
lensing where applicable.

We illustrate the distribution in depths across the various surveys in Fig. 1.
Assuming a flat UV spectral slope (fν), we derive a rest-frame $M_{1500}$
limiting magnitude for each survey, corresponding to a $z=11$ galaxy at the
8$\sigma$ apparent magnitude limit in the F200W filter. Using the UV
luminosity function determined in Donnan et al. (2023a), we also show the
predicted average number of $z\sim 11$ galaxies found per NIRCam pointing
($\simeq 9.6$ sq. arcmin).

Figure 1: An illustration of the distribution of F200W $8\sigma$ global depths
across the various surveys utilised in our search for $z\geq 9.5$ galaxies.
Although we do not perform a new search over JEMS for this study, we utilise
the sample as found in Donnan et al. (2023b), and so we include the F182M
depth here. The solid teal line shows the predicted number of galaxies at
$z\geq 9.5$ in the area of one NIRCam pointing assuming the luminosity
functions from Donnan et al. (2023a). The top $x-$axis shows the absolute UV
magnitude for a $z=11$ galaxy with an apparent magnitude given by bottom
$x-$axis at $z=11$.

####  2.1.1 SMACS 0723

In this study, we cover three Early Release Observations (Pontoppidan et al.,
2022) surveys: the SMACS 0723 cluster, Stephan’s Quintet and the Cartwheel
galaxy. All three of these surveys are comprised of imaging in six NIRCam
filters spanning $0.9-4.4\,\mu$m: F090W, F150W, F200W, F277W, F356W and F444W.

The first ERO field we will discuss is the SMACS 0723 cluster field (PID 2736,
PI Pontoppidan; Pontoppidan et al. 2022). This field has already seen
extensive study by various groups in search of high-redshift candidates since
the July 2022 data release (e.g. Atek et al. 2023; Adams et al. 2023; Donnan
et al. 2023a; Harikane et al. 2023b; Bouwens et al. 2023). This survey is
covered by two NIRCam modules, with one module centred on the cluster field
and the other on a “blank” parallel field. Due to lensing by the foreground
galaxy cluster, which serves to magnify objects in the background, there is
also a reduction in the effective area of the search.

To avoid uncertain lensing volume corrections and areas with significantly
shallower depths than the global depth, we remove the portion of the image
worst affected by intracluster light and enhanced crowding. We then determine
the magnification of sources and the remaining effective survey area by
utilising the recent light-traces-mass (LTM) model from Golubchik et al.
(2022). Although the raw survey area of the SMACS 0723 field is 11.5 sq.
arcmin, after excluding the cluster and accounting for lensing this is reduced
to an effective area of 7.0 sq. arcmin. This area is calculated with the
assumption that any part of the field-of-view that is not covered by a
gravitational lensing map has a magnification $\mu$=1.2, which is what we
adopt for all cluster+parallel pair surveys to take into account that the
“blank” field is still subject to magnification (see Section 5).

Over the cluster portion of the field there is ancillary HST data from the
RELICS survey (PI Coe; Coe et al. 2019), with ACS imaging in F435W, F606W and
F814W as well as WFC3/IR imaging in F105W, F125W, F140W and F160W. We include
the HST ACS data in order to provide wavelength coverage in the optical
portion of the spectrum. Although the $5\sigma$ limiting magnitudes of the HST
ACS data are significantly shallower than the JWST data, the data still serves
to verify any non-detections short-ward of the Lyman break. The $5\sigma$
depths ($0.35^{\prime\prime}-$diameter apertures corrected to total) of the
ACS F435W and F814W imaging are approximately 26.8 mag, with the F606W deeper
at 27.7 mag.

####  2.1.2 Stephan’s Quintet

The Stephan’s Quintet field was also imaged as part of the Early Release
Observations (PID 2732, PI Pontoppidan; Pontoppidan et al. 2022). To date,
this field has had one published search for high-redshift galaxies by Harikane
et al. (2023b), which yielded one galaxy candidate at $z\simeq 12$ and another
candidate at $z\simeq 16$. This field has the same NIRCam filter set as SMACS
0723, but lacks sufficiently deep ancillary HST data. The Quintet field has
significant variations in depth across the imaging owing to crowding and
enhanced background light. The overall area of the field is approximately 46.7
sq. arcmin, which reduces to an effective area of 40.9 sq. arcmin after
removing the Quintet.

####  2.1.3 Cartwheel galaxy

The Cartwheel galaxy, or PGC 2248, was imaged as part of the Early Release
Observations (ERO PID 2727, PI Pontoppidan). Once again, the complement of
NIRCam filters for this field is the same as for SMACS 0723 and Stephan’s
Quintet, and there is no useful ancillary HST ACS imaging. Similarly to the
Quintet field, the depth across the imaging varies significantly, even when
masking out the Cartwheel galaxy itself. The field spans $\sim 5.7$ sq.
arcmin, which reduces to 4.2 sq. arcmin after masking out the Cartwheel galaxy
and the two large foreground galaxies to the north east.

####  2.1.4 WHL 0137

The WHL0137 cluster, known for the lensed “sunrise arc” galaxy and the $z=6.2$
star candidate “Earendel”, was imaged as part of Cycle 1 GO PID 2282 (PI Coe;
see Welch et al. 2022; Bradley et al. 2022). Imaging was taken over a single
NIRCam pointing, with one module on the cluster and the other on a parallel
blank field. The filter set includes the SW channel F090W, F115W, F150W and
F200W bands, as well as the LW channel F277W, F356W, F410M and F444W bands.
The raw survey area of this field is approximately 10.5 sq. arcmin, which
reduces to an effective area of 5.9 sq. arcmin when accounting for the
gravitational lensing. This data set has been the subject of a previous search
for high-redshift galaxies by Bradley et al. (2022), which yielded a sample of
twelve $z=9-13$ candidates. Our current study covers the first epoch of
observations from July 2022.

As with SMACS 0723, this field has ancillary HST RELICS (Coe et al., 2019)
data over the cluster region, which we use both in SED fitting and to check
against any potential low-redshift interlopers in our final sample. The
$5\sigma$ depths ($0.35^{\prime\prime}-$diameter apertures, corrected to
total) of the ACS F435W and F814W imaging are approximately 26.7 mag, with the
F606W imaging significantly deeper at 27.4 mag.

The lensing maps we utilise for WHL 0137 were those prepared for the RELICS
survey: Zitrin-LTM (see Broadhurst et al. 2005; Zitrin et al. 2015, Glafic
(Oguri, 2010) and LENSTOOL (Jullo & Kneib, 2009; Kneib et al., 2011).

####  2.1.5 MACS 0647

The MACS 0647 galaxy cluster was previously one of the HST CLASH clusters
(Postman et al., 2012). The field in which MACS 0647 resides is known to
contain a triply-lensed $z=11$ galaxy candidate, MACS0647-JD1 (Coe et al.,
2013), which was one of the highest-redshift galaxy candidates in the pre-JWST
era. MACS 0647 was imaged as part of JWST GO proposal 1433 (PI Coe) in order
to follow-up this object, with a cluster+parallel pair of NIRCam modules
imaged in F115W, F150W, F200W, F277W, F356W and F444W. With this imaging,
taken in September 2022, the object was re-analysed and found to be a
potential merger system at $z\sim 10$ (Hsiao et al., 2022). Most recently, the
object was spectroscopically confirmed to lie at $z=10.17$ (Harikane et al.,
2023a).

To complement the JWST photometry, we also employ the HST ACS optical imaging
from the CLASH survey, which covers the cluster module and has a $5\sigma$
depth of $\simeq$27.0 mag. The raw area of the MACS 0647 field was found to be
10.5 sq. arcmin, which reduces to 5.1 sq. arcmin after de-lensing, and the
removal of un-useable regions due to the presence of particularly bright
stars.

We use the lensing maps that were produced as part of CLASH, i.e the Zitrin-
NFW and Zitrin-LTM-Gauss models (Zitrin et al., 2015).

####  2.1.6 RXJ 2129

Another HST CLASH cluster, the RXJ 2129 field was imaged in October 2022 as
part of Director’s Discretionary Time (DDT, PID 2767; PI Kelly). One NIRCam
module was imaged in F115W, F150W, F200W, F277W, F356W and F444W, although the
exposure times vary significantly between filters, with the F356W imaging
being particularly deep. The complement of HST imaging matches that of MACS
0647. The lensing maps also include Zitrin-LTM-Gauss and Zitrin-NFW but with
an additional model from Caminha et al. (2019). This field was initially
selected as a DDT proposal to follow up a supernova at $z=1.5$, but has also
yielded a very faint, yet highly magnified ($\mu\sim 20$) galaxy confirmed
with spectroscopy to be at $z=9.51$ (Williams et al., 2022). The raw area of
this field is 5.3 sq. arcmin, with a de-lensed effective area of 3.1 sq.
arcmin.

####  2.1.7 GLASS

As part of JWST PID 1324 (PI Treu; Treu et al. 2022; see also Paris et al.
2023), a pair of NIRCam pointings were taken in parallel to NIRISS
observations of the Abell 2744 cluster field. The first epoch of observations
was taken in July 2022, and has been the subject of numerous searches for
high-redshift galaxies, including the discovery of an exceptionally bright
$z=12$ galaxy candidate GLASS-z12 (Castellano et al., 2022b; Naidu et al.,
2022). The second epoch of observations was taken in November 2022, and has
yielded yet further exciting results, including the discovery of an over-
density of bright $z=10$ galaxy candidates (Castellano et al., 2022a).

We include both epochs of observations in our present study. The NIRCam filter
set comprises F090W, F115W, F150W, F200W, F277W, F356W and F444W. One NIRCam
module benefits from increased exposure time from repeated observation, and
there is an additional two NIRCam modules with significant overlap, producing
a total raw search area of 13.3 sq. arcmin.

Some of the GLASS parallel field is covered by the Furtak et al. (2022)
lensing model of the Abell 2744 cluster, which was released as part of UNCOVER
Data Release 1. Where there is coverage we adopt this lensing map, and set a
floor of $\mu$=1.2 for the rest of the area that is not covered. This gives us
an effective de-lensed area of 10.1 sq. arcmin.

####  2.1.8 North Ecliptic Pole Time Domain Field (NEP TDF)

The NEP TDF field was imaged in September 2022 as part of the PEARLS survey
(PID 2738, PI Windhorst; see Windhorst et al. 2023). NIRCam imaging was taken
in F090W, F115W, F150W, F200W, F277W, F356W, F410M and F444W. The majority of
this data set is proprietary, however one of the pointings in the NEP TDF was
made publicly available immediately for use by the community. Although the
footprint of the F150W and F356W imaging is larger, we focus on the $\simeq
10.5$ sq. arcmin overlap between all of the available NIRCam filters.

####  2.1.9 CEERS

The Cosmic Evolution Early Release Science Survey (CEERS, ERS 1345, PI
Finkelstein; see Bagley et al. 2023b for imaging release) is an early release
science program covering approximately 100 sq. arcmin of the CANDELS Extended
Groth Strip (EGS) field. This field has been studied extensively since the
first epoch of observations was taken in July 2022 (e.g. Finkelstein et al.
2022b, 2023; Donnan et al. 2023a; Bouwens et al. 2023. This study has also
already seen the spectroscopic confirmation of several high-redshift galaxies
at $z=8-11$, including “Maisie’s galaxy” (Finkelstein et al., 2022b; Arrabal
Haro et al., 2023a, b).

In this study, we include an analysis of both the first and second epochs of
observations, taken in July and December 2022, respectively. JWST imaging is
available in seven NIRCam bands: F115W, F150W, F200W, F277W, F356W, F410M and
F444W. We also employ HST ACS imaging to provide additional wavelength
coverage in the optical. As noted earlier, a reduction of the HST imaging in
ACS F606W and F814W has been made publicly available by the CEERS team (HDR1;
see Koekemoer et al. 2011). Additional F435W imaging was available from the
UVCANDELS survey (GO 15647, PI Teplitz; DOI: 10.17909/8s31-f778).

####  2.1.10 UNCOVER

The UNCOVER survey (Cycle 1 2561, PI Labbe; Bezanson et al. 2022) is an ultra-
deep survey of the Abell 2744 cluster field covering a raw area of $\simeq 29$
sq. arcmin ($\simeq 12$ sq. arcmin after delensing and masking) to a depth in
excess of 29 mag (0.35${}^{\prime\prime}-$diameter apertures). The NIRCam
filter set is F115W, F150W, F200W, F277W, F356W, F410M and F444W. The lensing
map used for this data set was the Furtak et al. (2022) model that was
publicly released as part of UNCOVER’s Data Release 1. We also employ this
lensing map for the regions of GLASS and DDT 2756 where there is coverage.

Abell 2744 was imaged with HST as one of the Hubble Frontier Fields (Lotz et
al., 2017). This survey includes among the deepest HST observations in the ACS
and WFC3/IR filters, with depths of $28.2-28.6$ mag. Although the ACS
observations cover less than half of the UNCOVER survey area, we include the
ACS F435W, F606W and F814W data in order to extend our wavelength coverage
into the optical.

####  2.1.11 DDT 2756: Abell2744

The Abell 2744 cluster was imaged with NIRCam as part of DDT program 2756 (PI
Chen), a program designed to follow-up a $z=3.47$ supernova. Two epochs of
observations in six NIRCam bands (F115W, F150W, F200W, F277W, F356W and F444W)
were taken in October 2022 and December 2022. Although the Abell 2744 module
imaging was included in the UNCOVER reduction, each epoch includes an
additional parallel NIRCam module. These two partially overlap, but together
provide another 6.6 sq. arcmin of effective search area. This field was also
found by Castellano et al. (2022a) to contain a very bright $z\simeq 10$
galaxy candidate, with reported $M_{UV}\simeq-21.60$. Ultimately, the object
has been spectroscopically confirmed to lie at $z=9.31$, and is likely an
interacting system (Boyett et al., 2023). That being said, an independent
search over both epochs of data for this survey is clearly desirable to
discover if there are other exceptionally bright candidates at similarly
extreme redshifts.

####  2.1.12 PID 1063 Nircam Flats: J1235

As part of NIRCam commissioning (PID 1063, PI Sunnquist), exceptionally deep
imaging was taken of a field centred at RA=12:35:48, Dec$=+$04:55:45. The
filter set included is also more extensive than the other JWST surveys: F070W,
F090W, F115W, F150W, F200W, F277W, F300M, F356W and F444W. The coverage across
this rich filter set is not homogeneous, and so we restrict our analysis to an
area of $\simeq 9.9$ sq. arcmin covered by all of the available filters. This
field was recently studied as part of a search for quiescent galaxies by
Valentino et al. (2023).

####  2.1.13 JEMS

Deep medium band observations of the HUDF were taken as part of the JEMS
survey (ID 1963; PI Williams; see Williams et al. 2023). This included SW
F182M and F210M imaging along with LW imaging in F430M, F460M and F480M. The
total $5\sigma$ global depths are $\simeq 29$ mag for the SW channel filters
and $\simeq 28.5$ mag for the LW channel filters.

Using this data set, Donnan et al. (2023b) uncovered a sample of six high-
redshift candidates, including three spectroscopically confirmed $z>10$
galaxies (Curtis-Lake et al., 2023; Robertson et al., 2023). Among these is
UDFj-39546284, a $z\simeq 12$ galaxy first discovered a decade previously with
HST imaging (Bouwens et al., 2011; Ellis et al., 2013). Although we do not
search the JEMS data set in this study, we include the six candidates found in
Donnan et al. (2023b) in our LF analysis in Section 5.

##  3 Sample Selection

###  3.1 Catalogue Construction

For each of the fields, we construct multi-wavelength catalogues using Source-
Extractor (Bertin & Arnouts, 1996) in dual-image mode. As our study is focused
on selecting $9.5<z<12.5$ galaxies, the position of the Lyman break will move
through the F150W filter as we probe to higher redshift, with the IGM
absorption having attenuated half of the flux in the F150W band by $z=11$.
Hence, in order to facilitate the detection of galaxies beyond a Lyman break
of 1.5 $\mu$m, we use the F200W imaging as our primary detection band. We
create additional catalogues using each of the broadband LW filters (F277W,
F356W, F444W) as detection images, in order to supplement this first catalogue
with any sources that may have been missed. For the three fields lacking F115W
coverage (SMACS 0723, Cartwheel, Quintet), we cannot search as effectively for
$z<11$ galaxies and a F150W detection image would not add significant value.
Hence for consistency across all of the fields, we do not include F150W
detection images in this study. We also adjust our selection criteria in these
three fields to account for the reduced filter coverage (see Section 3.3).

Prior to any aperture photometry, we homogenized the PSF of all of the NIRCam
images to match that of the F444W image, in order to minimize any colour
systematics in subsequent analyses. Aperture photometry was performed on these
PSF-homogenized images with fluxes measured in $0.35^{\prime\prime}-$diameter
apertures. Photometric uncertainties were calculated object-by-object by
taking the median absolute deviation of the nearest 150-200 blank-sky
0.35${}^{\prime\prime}-$diameter apertures, and scaling to $\sigma$ by
multiplying by 1.4826, following the method by McLeod et al. (2021).

For each of our initial catalogues, we required a $5\sigma$ detection in the
detection image, as well as an additional $3\sigma$ detection in at least one
other band to reduce the number of spurious detections.

###  3.2 SED-fitting and photometric redshifts

We performed SED fitting on all of the sources within our initial catalogues
using the SED fitting code LePhare (Arnouts & Ilbert, 2011). The SED library
that we used was Bruzual & Charlot (2003) (BC03), using a Chabrier (2003)
initial mass function, a Calzetti et al. (2000) dust attenuation law and the
IGM absorption prescription from Madau (1995). These SED templates included
declining star-formation histories with various $\tau$ values from 0.1 to 15
Gyr, and metallicities of 0.2 Z⊙ and Z⊙. We included emission lines, and the
$A_{V}$ was allowed to range from 0 to as high as 6 to clean the sample of any
extremely reddened low-redshift interlopers masquerading as high-redshift
galaxies. We measured rest-frame $M_{1500}$ magnitudes using a 100 Å-wide
tophat filter on the best-fitting SED.

###  3.3 Selection of high-redshift candidates

We initially selected candidates with a photometric redshift solution
$z_{\mathrm{phot}}\geq 8.5$ and a goodness of fit $\chi^{2}_{\nu}\leq 10$.
Only candidates considered “robust”, with $\Delta\chi^{2}\geq 4$ between the
primary and secondary photo-z solutions, were retained for the final sample.
We also further refined our sample selection to require a $\geq 8\sigma$
detection in at least one of the F150W, F200W and F277W images, to ensure that
we were only analysing high signal-to-noise objects. Due to the IGM absorption
of any flux short-ward of the Lyman break at $z\leq 9.5$, we further required
a non-detection ($\leq 2\sigma$) in the F090W band, as well as in F115W and
the HST ACS imaging if available. The condition of F115W$<$2$\sigma$ precludes
any complete statistical investigation of the $8.5<z<9.5$ population, given
than a $z\simeq 9.0$ galaxy can still be detectable in F115W. Consequently, we
confine our later LF analysis to $z>9.5$, but include any $8.5<z<9.5$
candidates in our tabulated sample.

We double-checked any high-redshift candidates by also performing SED fitting
using the code EAZY (Brammer et al., 2008), including the Pegase (Fioc &
Rocca-Volmerange, 1999) templates. The primary solution is determined allowing
the templates to vary over the redshift range $0<z<25$ with a secondary lower-
redshift solution by restricting to the range $0<z<6$.

As well as performing the flux cuts to remove any significant detections
shortward of the break, we inspected the F090W, F115W and ACS imaging, in
order to verify that our candidates do not have any marginal detections.

The Cartwheel, SMACS 0723 and Quintet fields lack the F115W filter, and this
creates additional challenges in determining the redshift of any candidates in
those fields. As the F090W transmission ends at 1.0 $\mu$m, any F090W-dropout
followed by a significant F150W detection can essentially lie anywhere between
$z\sim 7.2$ and $z\sim 12.0$, assuming it is not a low-redshift interloper.
This issue is mitigated where there is a F115W non-detection, which helps
narrow down the redshift solution to $z\gtrsim 9$. We therefore included an
extra criterion for these fields, whereby we required either a non-detection
($\leq 2\sigma$) in F150W, or a red F150W-F200W$\geq 0.75$ colour. Although
this shifts our selection window for these three fields to above
z$\simeq$11.5, these criteria prevent the final sample from being contaminated
by z$\simeq 7-8$ interlopers.

##  4 High-redshift candidates

In Tables 2-3 we list basic properties for the candidates uncovered across the
various fields. We also provide a colour-coded illustration of the
distribution of intrinsic $M_{1500}$ with redshift, and the distribution of
F200W 0.35${}^{\prime\prime}-$diameter aperture magnitude with redshift for
our final sample in Fig. 2. In Fig. 3 and Fig. 4 we present some example SEDs
and postage stamps for a sub-set of the final candidates.

|
---|---
Figure 2: The left-hand panel shows the distribution of apparent F200W
magnitude (0.35${}^{\prime\prime}-$diameter aperture) with photometric
redshift for our selected sample of high-redshift candidates. The right-hand
panel shows the corresponding de-lensed rest-frame $M_{1500}$ magnitude
(corrected to total) distribution with photometric redshift, including the
additional candidates from the Donnan et al. (2023b) study of JEMS.

Given the remarkably high resolution of JWST’s NIRCam imaging, even the
highest-redshift galaxies are often not well approximated by point-sources.
Hence, we apply an additional correction to total fluxes, which we also apply
to the $M_{1500}$. We measure the total fluxes by scaling to the FLUX_AUTO
value measured by Source-Extractor and add a further 10% correction.

ID | RA | Dec | $\rm z_{phot}$ | $M_{1500}$ | $\rm\mu$ | References
---|---|---|---|---|---|---
CEERS-NE-z10-3069854 | 14:20:03.35 |  $+$53:00:24.37 | $10.4^{+0.2}_{-1.0}$ |  $-$19.83 | - | -
CEERS-2-2-z10-22229 | 14:20:03.68 |  $+$52:54:49.37 | $\phantom{o}9.8^{+0.4}_{-0.3}$ |  $-$19.11 | - | -
CEERS-2-3-z10-6303 | 14:19:38.56 |  $+$52:52:33.11 | $10.4^{+0.3}_{-1.1}$ |  $-$20.38 | - | -
CEERS-2-5-z10-9617 | 14:18:55.80 |  $+$52:45:29.06 | $10.3^{+0.3}_{-0.8}$ |  $-$20.20 | - | Ha23
CEERS-2-5-z10-17402 | 14:19:10.56 |  $+$52:46:45.07 | $10.4^{+0.7}_{-0.6}$ |  $-$19.19 | - | -
CEERS-2-6-z10-3530 | 14:19:14.85 |  $+$52:44:13.63 | $10.4^{+0.1}_{-0.2}$ |  $-$20.49 | - | Ha23
CEERS-2-6-z10-17416 | 14:19:31.50 |  $+$52:46:22.66 | $10.1^{+0.4}_{-0.4}$ |  $-$19.22 | - | -
CEERS-2-6-z10-7927 | 14:19:16.11 |  $+$52:44:54.05 | $10.0^{+0.3}_{-0.5}$ |  $-$19.97 | - | -
DDT2756-z10-1010177 | 00:14:35.54 |  $-$30:25:35.80 | $10.0^{+0.5}_{-0.4}$ |  $-$19.08 | 1.30 | -
DDT2756-z10-1010612† | 00:14:28.17 |  $-$30:25:31.69 | $\phantom{o}9.5^{+0.5}_{-0.3}$ |  $-$19.47 | 1.65 | C22
GLASS-z10-3283 | 00:14:02.87 |  $-$30:22:18.71 | $10.3^{+0.4}_{-0.7}$ |  $-$20.15 |  $\phantom{o}1.68$o | C22, N22, D23, H23, B23
GLASS-z10-15864 | 00:13:54.90 |  $-$30:20:43.95 | $\phantom{o}9.6^{+0.1}_{-0.1}$ |  $-$19.52 |  o1.20⋆ | C22
GLASS-z9-32411 | 00:13:49.13 |  $-$30:19:00.85 | $\phantom{o}9.3^{+0.2}_{-0.2}$ |  $-$19.15 |  o1.20⋆ | -
GLASS-z9-9023 | 00:14:03.99 |  $-$30:21:33.00 | $\phantom{o}9.3^{+1.5}_{-0.3}$ |  $-$17.94 |  $\phantom{o}1.65$o | -
J1235-z10-1046989 | 12:35:52.06 |  $+$04:55:03.82 | $\phantom{o}9.7^{+0.7}_{-0.2}$ |  $-$18.69 | - | -
MACS0647-z9-20158 | 06:47:36.95 |  $+$70:14:34.69 | $\phantom{o}9.5^{+0.6}_{-0.2}$ |  $-$19.21 |  $\phantom{o}2.75$o | -
NEPTDF-z10-1042051 | 17:23:00.91 |  $+$65:49:25.20 | $\phantom{o}9.6^{+0.8}_{-0.1}$ |  $-$20.17 | - | -
RXJ2129-z9-16261 | 21:29:38.97 |  $+$00:06:50.84 | $\phantom{o}9.1^{+0.3}_{-0.3}$ |  $-$20.21 |  $\phantom{o}1.24$o | -
RXJ2129-z9-3021681 | 21:29:40.45 |  $+$00:06:43.45 | $\phantom{o}8.8^{+0.4}_{-0.4}$ |  $-$19.91 |  $\phantom{o}1.29$o | -
UNCOVER-z9-3658 | 00:14:20.82 |  $-$30:25:23.25 | $\phantom{o}9.3^{+0.7}_{-0.2}$ |  $-$18.51 |  $\phantom{o}2.10$o | -
UNCOVER-z10-3892 | 00:14:24.69 |  $-$30:25:20.55 | $\phantom{o}9.7^{+0.7}_{-0.3}$ |  $-$18.01 |  $\phantom{o}2.21$o | -
UNCOVER-z10-23585 | 00:14:29.82 |  $-$30:23:20.69 | $10.4^{+0.3}_{-1.4}$ |  $-$18.43 |  $\phantom{o}1.47$o | -
UNCOVER-z10-15452 | 00:14:22.79 |  $-$30:24:02.56 | $10.4^{+0.6}_{-0.2}$ |  $-$18.29 | 10.74o | Z14
UNCOVER-z10-32757 | 00:14:16.09 |  $-$30:22:40.16 | $10.4^{+0.1}_{-0.2}$ |  $-$19.17 |  $\phantom{o}3.72$o | C22
UNCOVER-z10-47904 | 00:14:23.90 |  $-$30:21:37.14 | $\phantom{o}9.6^{+1.0}_{-0.3}$ |  $-$18.18 |  $\phantom{o}1.62$o | -
UNCOVER-z9-3061884 | 00:14:05.50 |  $-$30:21:40.34 | $\phantom{o}9.3^{+1.5}_{-0.3}$ |  $-$19.02 |  $\phantom{o}1.87$o | -
WHL0137-10187 | 01:37:25.74 |  $-$08:26:38.21 | $\phantom{o}9.3^{+0.2}_{-0.2}$ |  $-$17.60 |  $\phantom{o}7.95$o | Br22
WHL0137-2004877 | 01:37:22.12 |  $-$08:28:00.71 | $\phantom{o}9.4^{+0.6}_{-0.6}$ |  $-$18.54 |  $\phantom{o}2.86$o | -
WHL0137-21722 | 01:37:19.28 |  $-$08:25:25.64 | $\phantom{o}9.3^{+1.0}_{-0.3}$ |  $-$19.18 |  o1.20⋆ | -
Table 2: Our final sample of $8.5<z<10.5$ galaxies across all of the fields
studied. We include the photometric redshift and intrinsic rest-frame UV
magnitude $M_{1500}$, as well as the magnification $\mu$ if applicable. We
also include a references column if the candidate has appeared elsewhere
(Z14=Zitrin et al. 2014, C22=Castellano et al. 2022b, a, Br22=Bradley et al.
2022, N22=Naidu et al. 2022, B23=Bouwens et al. 2023, D23=Donnan et al. 2023a,
F23=Finkelstein et al. 2023, H23=Harikane et al. 2023b, Ha23=Arrabal Haro et
al. 2023a).
⋆ Magnification is fixed to a floor of 1.2 due to a lack of lensing map
coverage.
† DDT2756-z10-1010612 is the north-east component of what is believed to be a merging system, first found by Castellano et al. (2022a) and confirmed with spectroscopy to be at $z=9.31$ (Boyett et al., 2023). ID | RA | Dec | $\rm z_{phot}$ | $M_{1500}$ | $\rm\mu$ | References
---|---|---|---|---|---|---
CEERS-NE-z11-17070 | 14:19:37.59 |  $+$52:56:43.83 | $11.0^{+0.5}_{-0.4}$ |  $-$19.61 | - | F23, D23
CEERS-NE-z11-39491 | 14:20:10.56 |  $+$52:59:39.52 | $10.6^{+0.5}_{-1.3}$ |  $-$19.19 | - | F23, D23
CEERS-NE-z11-2543 | 14:19:41.47 |  $+$52:54:41.51 | $11.0^{+0.7}_{-0.3}$ |  $-$19.56 | - | F23, D23
CEERS-NE-z12-15760 | 14:19:46.35 |  $+$52:56:32.82 | $11.6^{+0.3}_{-0.2}$ |  $-$20.42 | - | F23, D23, B23, H23
CEERS-SW-z11-26592 | 14:19:28.72 |  $+$52:50:37.15 | $11.4^{+0.4}_{-0.3}$ |  $-$20.14 | - | F23
CEERS-SW-z11-3961 | 14:19:24.03 |  $+$52:48:29.00 | $11.2^{+0.3}_{-0.5}$ |  $-$19.54 | - | D23, F23, B23
CEERS-SW-z11-20687 | 14:19:00.64 |  $+$52:50:11.98 | $10.9^{+0.3}_{-0.7}$ |  $-$19.50 | - | B23
CEERS-SW-z11-51314 | 14:19:26.62 |  $+$52:52:52.18 | $10.8^{+0.5}_{-0.2}$ |  $-$19.80 | - | -
CEERS-SW-z11-1099004 | 14:19:30.20 |  $+$52:54:48.81 | $10.7^{+0.3}_{-0.2}$ |  $-$20.02 | - | -
CEERS-SW-z14-37967 | 14:19:27.31 |  $+$52:51:29.23 | $14.0^{+0.5}_{-1.7}$ |  $-$19.56 | - | D23
CEERS-2-1-z12-20465 | 14:20:36.36 |  $+$52:58:31.70 | $11.5^{+0.2}_{-0.2}$ |  $-$20.47 | - | -
CEERS-2-3-z12-8536 | 14:19:33.58 |  $+$52:52:53.37 | $12.1^{+0.3}_{-0.3}$ |  $-$20.37 | - | -
CEERS-2-4-z11-10389 | 14:19:32.62 |  $+$52:49:08.57 | $10.8^{+0.5}_{-0.3}$ |  $-$19.69 | - | -
CEERS-2-4-z11-1032400 | 14:19:43.67 |  $+$52:50:30.73 | $10.6^{+0.2}_{-0.3}$ |  $-$20.41 | - | -
CEERS-2-6-z11-570 | 14:19:12.14 |  $+$52:43:31.87 | $10.5^{+0.5}_{-0.5}$ |  $-$19.68 | - | -
DDT2756-z11-1001979 | 00:14:33.03 |  $-$30:26:56.99 | $10.6^{+0.2}_{-0.3}$ |  $-$20.53 | 1.20⋆ | -
DDT2756-z12-1004647 | 00:14:32.13 |  $-$30:26:25.87 | $11.5^{+0.2}_{-0.4}$ |  $-$19.67 | 1.35o | -
DDT2756-z12-1023292 | 00:14:34.98 |  $-$30:24:04.00 | $11.7^{+0.5}_{-0.4}$ |  $-$18.80 | 1.31o | -
GLASS-z11-1481 | 00:14:04.53 |  $-$30:22:43.10 | $11.1^{+0.4}_{-0.6}$ |  $-$18.49 | 1.84o | -
GLASS-z11-17225 | 00:14:01.76 |  $-$30:20:35.53 | $10.7^{+0.3}_{-0.6}$ |  $-$19.08 | 1.38o | -
GLASS-z11-29748 | 00:13:48.34 |  $-$30:19:18.50 | $10.7^{+0.2}_{-0.3}$ |  $-$20.08 | 1.20⋆ | C22
GLASS-z11-30367 | 00:13:48.33 |  $-$30:19:14.62 | $10.6^{+0.2}_{-0.3}$ |  $-$19.96 | 1.20⋆ | C22
GLASS-z11-12329 | 00:14:03.30 |  $-$30:21:05.64 | $10.6^{+0.4}_{-0.5}$ |  $-$19.00 | 1.50o | C22, H23
GLASS-z14-33570 | 00:13:57.62 |  $-$30:18:53.50 | $13.6^{+1.0}_{-1.1}$ |  $-$19.40 | 1.20⋆ | B23
GLASS-z12-28072 | 00:13:59.76 |  $-$30:19:29.15 | $12.2^{+0.2}_{-0.1}$ |  $-$20.62 | 1.20⋆ | C22, N22, D23, B23
GLASS-z12-9974 | 00:14:03.26 |  $-$30:21:24.54 | $12.1^{+0.6}_{-0.6}$ |  $-$19.04 | 1.57o | -
J1235-z11-2056758 | 12:35:48.19 |  $+$04:55:54.84 | $10.9^{+0.3}_{-0.6}$ |  $-$19.56 | - | -
J1235-z12-8807 | 12:35:44.96 |  $+$04:54:34.76 | $11.8^{+0.4}_{-0.3}$ |  $-$18.94 | - | -
MACS0647-z11-26400 | 06:47:55.47 |  $+$70:15:38.13 | $10.8^{+0.1}_{-0.2}$ |  $-$20.37 | 2.53o | C13
MACS0647-z11-20148 | 06:47:55.74 |  $+$70:14:35.81 | $10.6^{+0.2}_{-0.4}$ |  $-$20.10 | 5.69o | C13
NEPTDF-z11-12882 | 17:22:57.72 |  $+$65:46:24.54 | $11.3^{+0.3}_{-0.4}$ |  $-$19.84 | - | -
Quintet-z12-9091 | 22:35:51.43 |  $+$33:54:32.81 | $12.2^{+0.2}_{-0.3}$ |  $-$21.44 | - | -
SMACS0723-z12-7442 | 07:22:56.36 |  $-$73:29:00.52 | $11.7^{+0.3}_{-0.3}$ |  $-$19.47 | 1.20⋆ | D23
UNCOVER-z11-48395 | 00:14:21.62 |  $-$30:21:34.96 | $10.6^{+0.1}_{-0.1}$ |  $-$19.70 | 1.89o | -
UNCOVER-z11-53033 | 00:14:25.36 |  $-$30:21:09.45 | $10.8^{+0.4}_{-0.2}$ |  $-$19.94 | 1.47o | -
UNCOVER-z11-2037921 | 00:14:31.07 |  $-$30:23:02.76 | $11.0^{+0.2}_{-0.3}$ |  $-$19.43 | 1.40o | -
UNCOVER-z12-30657 | 00:14:09.79 |  $-$30:22:49.48 | $11.9^{+0.2}_{-0.2}$ |  $-$19.42 | 3.25o | -
UNCOVER-z12-12816 | 00:14:14.10 |  $-$30:24:16.27 | $12.0^{+0.3}_{-0.4}$ |  $-$18.83 | 1.73o | -
UNCOVER-z12-30621 | 00:14:09.80 |  $-$30:22:50.08 | $12.3^{+0.2}_{-0.3}$ |  $-$19.07 | 3.19o | -
UNCOVER-z12-6502 | 00:14:23.42 |  $-$30:24:54.47 | $11.6^{+0.3}_{-0.3}$ |  $-$18.07 | 5.00o | -
UNCOVER-z12-53293 | 00:14:11.21 |  $-$30:21:08.56 | $12.0^{+0.4}_{-0.4}$ |  $-$19.06 | 1.81o | -
UNCOVER-z14-2019859 | 00:14:17.00 |  $-$30:24:05.56 | $13.6^{+0.6}_{-1.2}$ |  $-$18.76 | 2.51o | -
WHL0137-22312 | 01:37:18.46 |  $-$08:24:26.34 | $11.1^{+0.3}_{-0.5}$ |  $-$20.00 | 1.20⋆ | Br22
Table 3: Our final sample of $z\geq 10.5$ galaxies across all of the fields
studied. We include the photometric redshift and intrinsic rest-frame UV
magnitude $M_{1500}$, as well as the magnification $\mu$ if applicable. We
also include a references column if the candidate has appeared elsewhere
(C13=Coe et al. 2013, C22=Castellano et al. 2022b, a, Br22=Bradley et al.
2022, N22=Naidu et al. 2022, B23=Bouwens et al. 2023, D23=Donnan et al. 2023a,
F23=Finkelstein et al. 2023, H23=Harikane et al. 2023b).
⋆ Magnification is fixed to a floor of 1.2 due to a lack of lensing map coverage. |
---|---
|
|
Figure 3: Examples of LePhare SED plots for high-redshift candidates selected
in this study. We include both the primary high-redshift solution (blue line),
as well as the competing lower-redshift secondary solution (red line). Each
plot includes an inset of the $\chi^{2}$ distribution with redshift for the
SED fitting. Downward arrows in the plot denote the 1$\sigma$ upper limit for
non-detections.

Figure 4: Postage stamps for each of the candidates shown in Fig. 3. The
shortest wavelength column is NIRCam F090W or HST F814W, depending on
availability, followed by each of the broadband NIRCam filters from F115W to
F444W. Note that in some surveys lacking ACS ancillary data, e.g. DDT-2756,
our shortest wavelength band is F115W. The greyscale has been set to the
median background flux $\pm$2$\sigma$, after excluding flux contributions from
sources defined by a segmentation map.

In the Appendix, we provide a field-by-field analysis of the high-redshift
candidates that we have selected, where we draw comparisons with other works
in the literature. Although we do not search the HUDF for candidates in this
particular study, we performed a search for $z>9.5$ galaxies in Donnan et al.
(2023b) very recently using the JEMS (Williams et al., 2023) data. We include
the six robust F182M-selected candidates found over one NIRCam pointing in our
UV LF determination in Section 5.

##  5 UV Luminosity Function

In this section, we present our determination of the UV luminosity function at
$9.5\leq z\leq 12.5$. We first describe our methods for assigning survey
areas, effective volumes, completeness corrections and uncertainties in galaxy
number densities. We then calculate and fit the UV LF, before comparing our
new results with relevant determinations from the literature.

###  5.1 Survey Area Definition

As this study is conducted over many inhomogeneous fields, care must be taken
in order to define an accurate overall survey area. In particular, the fields
with clusters are subject to the effects of gravitational lensing. At the
faintest luminosities, the differences between lensing models has been shown
to have a potentially large impact on the faint end of the UV luminosity
function, with the high magnification regime ($\mu$ $>$10) more subject to
systematic uncertainties (see e.g. Bouwens et al. 2017). Moreover, the cluster
regions are typically significantly shallower than the survey global depth due
to enhanced background from intracluster light and source crowding. For each
of our cluster fields, we therefore mask out these shallow cluster regions.
Any candidates positioned on these masks are excluded from the UV LF
calculation.

For the cluster surveys, we subtract the clusters in a fairly simple way. We
first measure the global depth $\sigma_{g}$ across the whole field of view, as
well as local depths across the survey pixel by pixel, and produce a depth map
as shown in Fig. 5. We then mask out all pixels that have a local depth that
is shallower than $2\times\sigma_{g}$, removing the cluster and any regions
particularly impacted by large foreground galaxies or stars. We then re-
calculate $\sigma_{g}$ as our final global depth for the survey. We adopt the
same strategy for the fields that are hampered by large foreground objects,
e.g. the Cartwheel and Quintet fields.

Figure 5: Depth maps for the cluster fields and Stephan’s Quintet,
demonstrating the inhomogeneities in depth across the imaging. The top row is
MACS 0647 (left) and WHL 0137 (right), the middle row is SMACS 0723 and RXJ
2129, and the bottom row is UNCOVER and Stephan’s Quintet.

We de-lens each of the cluster surveys using the lensing models described in
Section 2.1. To measure effective survey areas, we calculate the magnification
map taking the mid-point of our redshift bin, $z=11$. However, for each
candidate, we calculate $\mu$ by generating a magnification map using its
$z_{\mathrm{phot}}$. Where there are multiple lensing models considered (i.e.
for WHL 0137, MACS 0647 and RXJ 2129), we perform this calculation for each
lensing model, and then take the median $\mu$ and de-lensed area. For SMACS
0723 and Abell2744 (UNCOVER, GLASS and DDT 2756) we simply use the
magnification and areas calculated using the single lensing model.

For RXJ 2129, we only have one module on the cluster; however for the three
surveys with cluster+parallel survey configurations, the lensing maps
typically do not to extend to the parallel module, and so we lose the ability
to measure the magnification $\mu$. For cluster+parallel pairs, and for the
GLASS and DDT-2756 parallels to Abell 2744, we adopt a constant value of
$\mu$=1.2 where we do not have any lensing map coverage. This value is
motivated by the typical $\mu$ values found around the edge of the lensing
maps of the various surveys. We note that adopting an alternative choice of
$\mu$=1.1 reduces the overall number densities at the 1-2% level, as the
parallel regions comprise $<$15% of the overall survey area.

###  5.2 Completeness

An accurate determination of the UV LF requires that the incompleteness of the
galaxy sample is accounted for. This becomes of particular importance close to
the detection limit of the data. Due to our adoption of a more stringent
8$\sigma$ detection limit throughout, this becomes less of an issue in this
survey. The completeness as a function of apparent magnitude in the F200W
imaging (F182M for the JEMS data) is determined using the method described in
Donnan et al. (2023a). Point sources were injected into the F200W imaging in 3
regions for each field from $m_{\rm{F200W}}=24-31$ in steps of 0.1 mag. At
each step 800 sources are injected and the rate of recovery is measured,
producing the completeness as a function of the apparent magnitude in F200W.
This process is repeated 10 times for each region and therefore a total of
1,680,000 sources are injected into each field. We correct the effective
volumes of our candidates by their completeness as determined in this
procedure.

In a study of the first Hubble Frontier Fields, Oesch et al. (2015) showed the
impact of including shear on completeness simulations, finding that large
$\mu$ can affect the relative completeness of sources close to the
completeness limit. Having removed much of the area around the cluster
regions, the effective area of the lensed fields with significant
magnification probed in our study presents a modest fraction of the total
search area ($<10$%). This, and the fact that we are conservative in only
selecting SNR$>$8 sources, allows us to be confident that the impact of shear
on our overall completeness and effective survey volumes is negligible.

###  5.3 The $\mathbf{z=11}$ UV luminosity function

To determine the UV luminosity function for our $9.5\leq z\leq 12.5$ sample we
use the $1/{V_{\rm max}}$ estimator (Schmidt, 1968). We only include objects
for which our F200W detection is greater significance than $8\sigma_{g}$,
where $\sigma_{g}$ is the global depth for a given survey. We split our sample
into four number density bins between $M_{1500}=-21.8$ and $M_{1500}=-19.3$.
At the bright-end, we scale the $M_{1500}=-22.57$ ground-based LF bin from
Donnan et al. (2023a) to match our redshift range, add in the area we
searched, and include it as a fifth bin. In Table 4 we present our number
densities $\phi$ in each $M_{1500}$ bin, along with their errors. To calculate
the uncertainty in our number densities, we sum in quadrature the uncertainty
found through a bootstrap analysis ($\sigma_{b}$) and cosmic variance
($\sigma_{CV}$) as estimated using the Trenti & Stiavelli (2008) cosmic
variance calculator. One of the key advantages of using many non-contiguous
fields for this study is that the relative uncertainties across all the bins
are significantly reduced.

$M_{1500}$ |  $\phi$ / $10^{-5}$ Mpc-3
---|---
$-$22.57* |  *0.012 $\pm$ 00.010
$-$21.80* |  *0.128 $\pm$ 00.128
$-$20.80* |  *1.251 $\pm$ 00.424
$-$20.05* |  *3.951 $\pm$ 01.319
$-$19.55* |  *9.713 $\pm$ 04.170
$-$18.85* | 23.490 $\pm$ 09.190
$-$18.23* | 63.080 $\pm$ 28.650
Table 4: Our number density measurements for the $z\simeq 11$ UV LF, including those from Donnan et al. (2023a) where the absolute magnitude bin has been marked with an asterisk. Note that the $M_{1500}=-22.57$ bin from Donnan et al. (2023a) is based on a search over the 1.8 deg2 area of COSMOS/UltraVISTA DR5. |
---|---
Figure 6: The UV luminosity function over $9.5<z<12.5$ as found by this study.
On the left panel, we include our five number density bins along with data-
points from a host of other studies: Donnan et al. (2023a, green), Harikane et
al. (2023b, purple $z=9$), Castellano et al. (2022a, orange), Finkelstein et
al. (2023, grey), Bouwens et al. (2023, red), Pérez-González et al. (2023,
navy). For the right panel, we have adopted the two fainter $M_{1500}$ bins
from Donnan et al. (2023a) in order to increase our dynamic range in
$M_{1500}$. We have hence fitted a double power law function (DPL) to our LF,
adopting as our fiducial DPL fit the fixed $\alpha=-2.35$ case shown in Table
5. We also plot the HST-based Schechter function fits from Oesch et al. (2018,
red) and McLeod et al. (2016, blue).

In the left-hand panel of Fig. 6 we present our determination of the UV LF at
$z=11$, along with determinations across a host of other studies in the
literature. There have been numerous LF measurements based on early CEERS
epoch 1 and GLASS data, including Harikane et al. (2023b), Bouwens et al.
(2023) and Finkelstein et al. (2023). In the range $M_{1500}=-21.5$ to
$-19.5$, we find good agreement with the general consensus in the literature,
although we note that they are all over slightly different selection windows:
the Bouwens et al. (2023) datapoint is based on $z\simeq 9-11$ galaxies,
Donnan et al. (2023a) is based on a $9.5<z<11.5$ sample and Finkelstein et al.
(2023) is over $9.5<z<12.0$. Although we recover all of the candidates in
GLASS from Castellano et al. (2022a), our number densities at
$M_{1500}\leq-20.5$ are significantly lower. This suggests that the GLASS
footprint does cover an overdensity, which is smoothed out by having a much
larger overall search area in this study. The faintest $M_{1500}$ bin is in
concordance with our earlier work in Donnan et al. (2023a) and indeed with
earlier HST $z=10$ results from McLeod et al. (2016). However, the excess in
the $M_{1500}<=-20.5$ bins presents a clear departure from HST-based
determinations of the UV LF (e.g. McLeod et al., 2016; Oesch et al., 2018).

In order to increase the overall dynamic range, we incorporate the faintest
two bins of the UV LF as determined in Donnan et al. (2023a), encouraged by
the excellent agreement between our faintest bin and their bin at a similar
$M_{1500}$. As well as sharing a similar set of reductions, SED fitting codes
and selection criteria, the median redshift of our $9.5\leq z\leq 12.5$ sample
is $z=10.7$, which is close to the mid-point of their bin at $z=10.5$. The
amalgamation of these two studies allows us to determine a UV LF spanning
approximately four magnitudes in seven bins, from which we can determine the
functional form.

We proceed to fit a double power law, found by Bowler et al. (2014, 2020) and
Donnan et al. (2023a) to be the preferred functional form at the highest
redshifts, rather than a Schechter (Schechter, 1976) function as found in
earlier HST studies (e.g. McLeod et al. 2015; McLeod et al. 2016; Bouwens et
al. 2021). We fit the seven number density bins both with a free fit and with
a fixed faint-end slope. The tabulated double power law fits are presented in
Table 5, and the combined LF and functional forms are shown in the right panel
of Fig. 6.

Function | $M^{\star}$ | $\phi^{\star}$ | $\alpha$ | $\beta$ | $\rho_{\mathrm{UV}}$
---|---|---|---|---|---
DPL free |  $-$21.64 $\pm$ 1.26 | (0.41$\pm$1.08)$\times 10^{-5}$ |  $-$2.59 $\pm$ 0.35 |  $-$5.01 $\pm$ 2.58 | 25.16${}^{+0.14}_{-0.20}$
DPL fixed $\alpha$ |  $-$20.87 $\pm$ 0.62 | (2.01$\pm$2.08)$\times 10^{-5}$ |  $-$2.35 (fixed) |  $-$4.18 $\pm$ 0.71 | 25.14${}^{+0.10}_{-0.12}$
Table 5: The parameters determined for our double power law fits to the $z=11$
UV luminosity function. We include both our free fit and the fit fixing
$\alpha=-2.35$. We also provide the integrated luminosity density
$\rho_{\mathrm{UV}}$ for each of the cases, integrated to a limit of
$M_{1500}=-17$ (see Section 6).

We find the free fit double power law is steep at $\alpha=-2.59\pm 0.35$,
however the errors attached to each of the parameters are large, particularly
for $M^{\star}$. For the fixed fit, we use $\alpha=-2.35$, which is the $z=10$
slope predicted by the prescription for the evolving double power law as
determined by Bowler et al. (2020). It is also the mid-point between the fixed
$\alpha=-2.10$ slope utilised by early JWST studies at similar redshifts such
as Donnan et al. (2023a); Donnan et al. (2023b) and Harikane et al. (2023b),
and the free-fit value determined in this study. The fit with fixed $\alpha$
mitigates the uncertainties of the free fit significantly, and so we adopt
this as our fiducial fit for the functional form of the UV LF at $z=11$ for
the rest of this paper. Encouragingly, our fiducial double power law fit
appears to be in good agreement with the faintest bin from Pérez-González et
al. (2023), who probe exceptionally deep imaging of HUDF-par2 as part of their
MIRI deep survey of the UDF (PID 1283, PI Oestlin).

It should be noted that alternative fits utilising a range of different fixed
faint-end slope are almost indistinguishable over the luminosity range spanned
by this study. At $z=8$, Donnan et al. (2023a) fitted a faint-end slope
$\alpha=-2.04\pm 0.29$, leveraged by the excellent HST-based constraints of
the faint-end which reach $M_{1500}=-17$ (McLure et al., 2013). Although our
free fit double power law suggests some steepening between the $z=8$ faint-end
slope and that of our $z=11$ LF, fitting our data with fixed $\alpha=-2.04$
also presents an acceptable fit over the magnitude range spanned by this
study. This does leave the evolution of the faint-end slope at $z>8$ an open
question, despite all of the recent advances brought with this first tranche
of JWST surveys. With deeper data sets such as NGdeep (ID 2079, PI
Finkelstein; Bagley et al. 2023a), studies will be able to constrain $\alpha$
at $z>10$ to the accuracy made possible at $z=8$ with HST.

As well as drawing comparisons to recent JWST-based determinations of the UV
LF, it is instructive to compare to studies probing the bright-end
($M_{1500}<M^{\star}$) of the UV LF at high-redshift. In the left panel of
Fig. 7 we plot our fiducial LF but also include a compendium of studies
probing the bright-end of the LF, including a suite of ground-based studies
(Stefanon et al., 2019; Bowler et al., 2020; Kauffmann et al., 2022; Donnan et
al., 2023a) and combined HST Legacy fields from Bouwens et al. (2023). We also
include a comparison of our double power law fit to those determined by Donnan
et al. (2023a) in the right-hand panel.

It is clear from Fig. 7 that our results suggest there is very little
evolution in the bright end of the UV LF between $z=9-11$, a feature
previously reported by Bowler et al. (2020) between $z=8-10$. In the left-hand
panel, it can be seen that the $z=9-10$ literature points at $M_{1500}<-21.50$
scatter symmetrically around our $z=11$ double power law fit. Moreover, in the
right-hand panel, it can be seen that at $M_{1500}<-20.50$ there is little to
distinguish our $z=11$ fit from the $z=8-10.5$ fits derived by Donnan et al.
(2023a).

A relatively un-evolving bright-end has also been reported by Finkelstein et
al. (2022a) over the CANDELS fields (see also Finkelstein & Bagley 2022).
Although there have been some surprisingly high number densities of bright
$z>10$ galaxies reported in early JWST studies (Castellano et al., 2022b, a),
reports of high number densities of bright $z>8$ galaxies had become
commonplace even pre-JWST, with studies reporting high number densities with
wide-area pure parallel HST studies (Rojas-Ruiz et al., 2020; Bagley et al.,
2022), albeit with a greater potential risk of contamination due to limited
filter sets.

The interpretation for greater numbers of bright $z>8$ galaxies has been
discussed previously in Bowler et al. (2020), who suggest that the double
power law shape reflects a reduction in dust attenuation and/or inefficient
mass quenching. Another explanation could lie in the star-formation
efficiency, which may be higher at the bright-end to produce the double power
law shape at high-redshift (e.g. Harikane et al. 2022). After the early JWST
studies reporting large number densities of bright $z>8$ galaxies, Mason et
al. (2023) presented predictions of $z>8$ LFs under the assumption of 100%
star-formation efficiency (SFE). They demonstrated that a 100% SFE scenario
yields LFs several orders of magnitude higher than current results, i.e.
observations thus far are fully consistent with current cosmological
frameworks. They conclude that our view may be biased in that we are
predominantly witnessing young galaxies that are undergoing bursts of star-
formation, rather than a representative population.

There is also the potential for significant field-to-field variation resulting
in skewed number densities at the bright-end, where number statistics are
generally low. For example, (Finkelstein et al., 2022a) found the CANDELS EGS
field to be over-dense, with 7/11 of their bright $8.5<z<10.5$ candidates
across the five CANDELS fields coming from that field alone. More recently,
the over-density found in GLASS by (Castellano et al., 2022a) causes their
number densities to lie $\sim 3\times$ higher than other JWST studies.

This study mitigates some of the field-to-field variation with numerous non-
contiguous pointings over a relatively large area, while also bridging some of
the disconnect between the ground-based and early JWST results at $z>9.5$. Yet
more progress at the bright-end of the UV LF can be gained through using wide-
area surveys such as PRIMER (ID 1837; PI Dunlop) and COSMOS-Web (ID 1727, PI
Casey; Casey et al. 2022).

|
---|---
Figure 7: A comparison between our fiducial $z=11$ UV LF and results from
other studies. In the left-hand panel we plot a compendium of data points from
literature studies at $z=9-10$, whereas the right-hand panel compares our LF
with functional fits from Donnan et al. (2023a). Overall, our $z=11$ results
appear to be consistent with a lack of evolution in the very bright-end of the
LF from $z=9-11$.

##  6 Star-formation Rate Density

We proceed to calculate the luminosity-weighted integral for our functional
fits to the UV luminosity function in order to determine the UV luminosity
density $\rho_{\mathrm{UV}}$. The integral limit that we choose is
$M_{1500}=-17$, as has been convention with previous HST-based studies. Our
$\rho_{\mathrm{UV}}$ values are tabulated along with the UV LF functions in
Table 5. To convert this to a star-formation rate density,
$\rho_{\mathrm{SFR}}$, we use the conversion factor $\cal{K}$${}_{\rm
UV}=1.15\times 10^{-28}$ M⊙ yr-1/erg s-1 Hz-1 (Madau & Dickinson, 2014). The
free-fit and fixed $\alpha=-2.35$ double power law cases yield very similar
values of $\rho_{\mathrm{UV}}$. We adopt
$\rho_{\mathrm{UV}}=25.15^{+0.12}_{-0.17}$ as our fiducial value.

We also include a tentative measurement of $\rho_{\mathrm{UV}}$ at $z=13.5$,
based on our $12.5<z<14.5$ sample. We fit a double power law fixing both
$\alpha$ and $\beta$ to the fiducial $z=11$ LF values and allowing $M^{\star}$
and $\phi^{\star}$ to float. Based on the lack of evolution in the bright-end
of the UV LF between $z=9-11$, we anchor our double power law fit at the
bright-end to the $M_{1500}=-22.57$ bin from our $z=11$ LF. Although the
resulting double power law is highly uncertain, integrating this yields
$\rho_{\mathrm{UV}}=24.56^{+0.16}_{-0.26}$ at $z=13.5$.

In the left-hand panel of Fig. 8 we present our determination of
$\rho_{\mathrm{UV}}$ along with those from other observations in the
literature. Overplotted is the previous HST-based results from Oesch et al.
(2018) and their rapidly declining $\rho_{\mathrm{SFR}}(\mathrm{z})$ relation,
following the evolution of the dark matter halo mass function. We also include
the constant star-formation efficiency model from Harikane et al. (2023b,
2022), which follows $\rho_{\mathrm{SFR}}\propto\mathrm{(}1+z)^{-0.5}$, and
the log-linear relation we previously determined in Donnan et al. (2023a)

$\mathrm{\log}_{10}{(\rho_{\mathrm{UV}})}=-0.231\,\rm z+27.5.$ (1)

As can be seen from the left-hand panel, our new determination of
$\rho_{\mathrm{UV}}$, and hence $\rho_{\mathrm{SFR}}$, at $z=11$ is found to
be slightly higher than, although still consistent with, our previous
estimates from Donnan et al. (2023a); Donnan et al. (2023b). With our
significantly larger area spread over numerous additional fields, we once
again find evidence in support of a smoothly declining $\rho_{\mathrm{SFR}}$
at least to $z=12$. Although tentative, our $z=13.5$ data point also appears
to be consistent with the results from Donnan et al. (2023a), Harikane et al.
(2023b) and Pérez-González et al. (2023), and suggests the smooth decline in
$\rho_{\mathrm{SFR}}$ may yet continue beyond $z=12$.

Given that the $\rho_{\mathrm{UV}}$ can be sensitive to the assumed faint-end
slope, we want to ensure that our result is robust against the assumed
$\alpha$ slope, particularly as the current JWST data are still unable to
robustly constrain this parameter to the same level seen at $z=8$ with HST.
Hence, we also explore the impact of adopting $\alpha=-2.04$, which was the
slope found at $z=8$ by Donnan et al. (2023a) and still presents an acceptable
fit to our UV LF at $z=11$. We find that
$\rho_{\mathrm{UV}}(\mathrm{z}=11)=25.08^{+0.12}_{-0.17}$, which is in
excellent agreement with the log-linear relation from Donnan et al. (2023a).
Our conclusion of a smoothly declining $\rho_{\mathrm{SFR}}(\mathrm{z})$
between $z=8-11$ is therefore robust against the assumed value of $\alpha$.

Pre-JWST, the rate that $\rho_{\mathrm{SFR}}$ declined at $z>8$ was a matter
of debate, with Oesch et al. (2018) advocating a rapid decline based on a lack
of $z=10$ galaxies found among HST Legacy fields. This was a conclusion shared
by Ishigaki et al. (2018) when integrating to a limit of $M_{1500}=-17$, the
limit of HST’s capabilities, although they noted that this depends on the
choice of $M_{1500}$ limit, and that a limit of $M_{1500}=-15$ resulted in a
smoothly declining $\rho_{\mathrm{SFR}}$. Many theoretical models of galaxy
evolution also follow such a trend of rapidly declining
$\rho_{\mathrm{SFR}}(\mathrm{z})$ beyond $z>8$. In the right-hand panel of
Fig. 8, we include a comparison between our results and those of theoretical
models of galaxy evolution, where $\rho_{\mathrm{UV}}$ has been determined by
integrating to the same $M_{1500}$ limit. Our new results lie above a number
of theoretical models that follow more closely the rapidly declining relation,
such as Yung et al. (2019), FiBy (Paardekooper et al., 2013), Millenium TNG
(Kannan et al., 2022) and Mason et al. (2015). However, the Behroozi & Silk
(2015) and FLARES (Wilkins et al., 2023) models appear to be entirely
consistent with our $z=11$ results.

As well as lying above the Oesch et al. (2018) rapidly declining
$\rho_{\mathrm{SFR}}$ relation we also lie above the constant star-formation
efficiency model from Harikane et al. (2022). Although the constant star-
formation efficiency model is in close agreement with Harikane et al. (2023b)
and Donnan et al. (2023a) up to $z=9$, the observations begin to diverge from
the model at higher redshifts. This is discussed in detail by Harikane et al.
(2023b), who show that increasing the star-formation efficiency at $z>10$, or
adjusting the initial mass function (IMF) to be more top-heavy, can account
for such discrepancies. Alternatively, as was mentioned earlier, Mason et al.
(2023) suggest that observations thus far with JWST may be biased towards
young galaxies with copious star-formation, drawn from the upper envelope of
the $M_{1500}-\mathcal{M}_{\mathrm{halo}}$ relation, and that a more
representative sample may be found when probing fainter apparent magnitudes,
e.g. $m_{200}>30$.

On the other hand, a study by Bouwens et al. (2023) suggests that perhaps the
star-formation rate density may yet lie higher than the results of Harikane et
al. (2023b), Donnan et al. (2023a) and this study. They compute
$\rho_{\mathrm{SFR}}$ when considering a more inclusive (but still referred to
as “solid”) sample of high-redshift candidates, rather than solely the most
“robust” candidates, and find a significantly higher $\rho_{\mathrm{SFR}}$.
Their study highlights the requirement for spectroscopy to confirm or refute
the high-redshift nature of candidates. That said, it is worth noting that
early JWST NIRSpec results from e.g. Curtis-Lake et al. (2023), Roberts-
Borsani et al. (2022), Bunker et al. (2023) and Arrabal Haro et al. (2023a)
suggest that $z=9-11$ candidate selection with photometric redshifts has been
largely successful.

|
---|---
Figure 8: Our determination of the luminosity density and star-formation rate
density at $z=11$, integrated to a limit of $M_{1500}=-17$. We also include a
tentative $z=13.5$ measurement based on our handful of $12.5<z<14.5$
candidates. In the left-hand panel, we include a compilation of early JWST
studies integrating to the same limit of $M_{1500}=-17$. Note that we have
corrected the quoted value from Pérez-González et al. (2023), who adopted a
$M_{1500}=-16.5$ limit in their study. We also include the HST-based
determination at $z=10$ from Oesch et al. (2018), based on the HST Legacy
Fields, and the rapidly declining $\rho_{\mathrm{SFR}}(z)$ relation based on
the evolution of the dark matter halo mass function (pink shading). Finally,
we also show the constant star-formation efficiency model (purple line) from
Harikane et al. (2023b). We find that our new results are slightly higher
than, but fully consistent with, the log-linear
$\rho_{\mathrm{UV}}(\mathrm{z})$ relation (blue line) from Donnan et al.
(2023a). In the right-hand panel, we compare our measurements with a suite of
theoretical models of galaxy evolution. Typically, the models under-predict
the $\rho_{\mathrm{SFR}}$ measurements found both in this study and Donnan et
al. (2023a); Donnan et al. (2023b), with the exception of the Behroozi & Silk
(2015) and FLARES Wilkins et al. (2023) models.

##  7 Conclusions

We have presented a search for high signal-to-noise $z\geq 9.5$ galaxy
candidates across a suite of twelve JWST surveys spanning a raw survey area of
$\sim$260 sq. arcmin. We uncover 61 $z\geq 9.5$ candidates detected at
8$\,\sigma$, of which eighteen are at $z\geq 11.5$. The exceptional brightness
of many of these candidates makes them ideal for follow-up spectroscopy with
NIRSpec.

With the inclusion of six additional candidates found in our earlier study,
Donnan et al. (2023b), we proceed to construct the UV LF over $9.5<z<12.5$.
When combined with faint-end constraints from Donnan et al. (2023a), and
UVISTA-based constraints at the bright-end, our $z=11$ LF spans four
magnitudes of dynamic range in $M_{1500}$. Our LF is consistent with previous
JWST-based number densities in the literature at similar redshifts, but with
tighter constraints owing to our wider search area. At the bright-end, our LF
is consistent with a lack of evolution between $z=9-11$, similar to results
from Bowler et al. (2020), who found such trends between $z=8-10$. This lack
of evolution suggests that we are entering a regime where mass quenching
efficiency is lower or that there is reduced dust attenuation (Bowler et al.,
2020).

At the faint-end, our $\alpha$ measurements suggest a steep $\alpha$, which we
fix to $\alpha=-2.35$ for our fiducial LF. With the present data, we are not
yet able to robustly determine how $\alpha$ evolves between $z=8-11$, given
that a fit with $\alpha=-2.04$ (as measured at $z=8$ by Donnan et al. 2023a)
still provides an acceptable fit.

By integrating our LF, we arrive at the luminosity density and hence star-
formation rate density. Our $\rho_{\mathrm{UV}}$ at $z=11$ lies slightly
above, but is still consistent with, our previous log-linear
$\rho_{\mathrm{UV}}(\mathrm{z})$ relationship from Donnan et al. (2023a). Our
$\rho_{\mathrm{SFR}}$ at $z=11$ suggests a continued smoothly declining
$\rho_{\mathrm{SFR}}$ to at least $z=12$, with tentative $z=13.5$ measurements
based on a handful of $z>12.5$ candidates further re-inforcing this. This
result lies above both the rapidly declining $\rho_{\mathrm{SFR}}$ suggested
in pre-JWST studies (e.g. Oesch et al. 2018; Ishigaki et al. 2018) and the
constant star-formation efficiency model from Harikane et al. (2022), as well
as numerous theoretical models of galaxy evolution.

There are numerous potential interpretations for the high number densities of
bright $z\simeq 10$ galaxies and the higher $\rho_{\mathrm{SFR}}$ than
predicted by models. At the highest redshifts, we may be seeing a rise in the
star-formation efficiency (Harikane et al., 2023a), or that we are potentially
viewing the upper envelope of the $M_{1500}-\mathcal{M}_{\mathrm{halo}}$
relation (Mason et al., 2023). Although there have been suggestions that the
early JWST studies may be subject to significant contamination by low-redshift
interlopers, particularly as the overlap in sources between studies has
hitherto been relatively low (see discussion by Bouwens et al. 2023), we can
be encouraged by the number of spectroscopic confirmations of many
photometrically selected $z>8$ candidates (e.g. Curtis-Lake et al. 2023;
Arrabal Haro et al. 2023a, b).

The prospects for building upon this LF determination with further JWST Cycle
1 surveys are excellent. In the bright-to-intermediate regime, PRIMER will be
instrumental in providing homogeneous coverage of COSMOS and UDS at even
greater areas than those probed in this study, and to comparable depths. At
the very brightest luminosities, COSMOS-Web (Casey et al., 2022) will provide
$>0.5$ sq. deg. of imaging, which will be crucial for uncovering the brightest
(and rarest) high-redshift galaxies. At the faint-end, exceptionally deep
surveys such as NGDeep (Bagley et al., 2023a) and JADES (Robertson et al.,
2023) will help to better constrain the evolution of the faint-end slope
$\alpha$.

## acknowledgements

We would like to express our appreciation to all of those who have worked
tremendously hard to make all of these JWST surveys happen. We are also
thankful that all of these data sets were made publicly available immediately.

We would also like to thank all those involved in the creation of the
ancillary HST data that was publicly available, and to all of those who have
provided gravitational lensing models publicly for the community.This work
utilizes gravitational lensing models produced by PIs Bradač, Natarajan &
Kneib (CATS), Merten & Zitrin, Sharon, Williams, Keeton, Bernstein and Diego,
and the GLAFIC group. This lens modeling was partially funded by the HST
Frontier Fields program conducted by STScI. STScI is operated by the
Association of Universities for Research in Astronomy, Inc. under NASA
contract NAS 5-26555. The lens models were obtained from the Mikulski Archive
for Space Telescopes (MAST).

This research has made use of the SVO Filter Profile Service
(http://svo2.cab.inta-csic.es/theory/fps/) supported from the Spanish MINECO
through grant AYA2017-84089 (Rodrigo et al., 2012) (Rodrigo & Solano, 2020)

This research used the facilities of the Canadian Astronomy Data Centre
operated by the National Research Council of Canada with the support of the
Canadian Space Agency.

This work is based on observations taken by the RELICS Treasury Program (GO
14096) with the NASA/ESA HST, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.

D. J. McLeod, C. Donnan, R. J. McLure, J. S. Dunlop, R. Begley and M. L.
Hamadouche acknowledge the support of the Science and Technology Facilities
Council. A. C. Carnall acknowledges the Leverhulme Trust for their support via
a Leverhulme Early Career Fellowship. F. Cullen and T. M. Stanton acknowledge
support from a UKRI Frontier Research Guarantee Grant [grant reference
EP/X021025/1]. R. S. Ellis acknowledges funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
program (grant agreement No. 669253).

## References

  * Adams et al. (2023) Adams N. J., et al., 2023, MNRAS, 518, 4755
  * Arnouts & Ilbert (2011) Arnouts S., Ilbert O., 2011, LePHARE: Photometric Analysis for Redshift Estimate (ascl:1108.009)
  * Arrabal Haro et al. (2023a) Arrabal Haro P., et al., 2023a, arXiv e-prints, p. arXiv:2303.15431
  * Arrabal Haro et al. (2023b) Arrabal Haro P., et al., 2023b, arXiv e-prints, p. arXiv:2304.05378
  * Ashby et al. (2015) Ashby M. L. N., et al., 2015, ApJS, 218, 33
  * Atek et al. (2023) Atek H., et al., 2023, MNRAS, 519, 1201
  * Bagley et al. (2022) Bagley M. B., et al., 2022, arXiv e-prints, p. arXiv:2205.12980
  * Bagley et al. (2023a) Bagley M. B., et al., 2023a, arXiv e-prints, p. arXiv:2302.05466
  * Bagley et al. (2023b) Bagley M. B., et al., 2023b, ApJ, 946, L12
  * Beckwith et al. (2006) Beckwith S. V. W., et al., 2006, AJ, 132, 1729
  * Behroozi & Silk (2015) Behroozi P. S., Silk J., 2015, ApJ, 799, 32
  * Bertin (2010) Bertin E., 2010, SWarp: Resampling and Co-adding FITS Images Together, Astrophysics Source Code Library, record ascl:1010.068 (ascl:1010.068)
  * Bertin & Arnouts (1996) Bertin E., Arnouts S., 1996, A&AS, 117, 393
  * Bezanson et al. (2022) Bezanson R., et al., 2022, arXiv e-prints, p. arXiv:2212.04026
  * Bouwens et al. (2011) Bouwens R. J., et al., 2011, Nature, 469, 504
  * Bouwens et al. (2017) Bouwens R. J., Oesch P. A., Illingworth G. D., Ellis R. S., Stefanon M., 2017, ApJ, 843, 129
  * Bouwens et al. (2021) Bouwens R. J., et al., 2021, AJ, 162, 47
  * Bouwens et al. (2023) Bouwens R., Illingworth G., Oesch P., Stefanon M., Naidu R., van Leeuwen I., Magee D., 2023, MNRAS,
  * Bowler et al. (2014) Bowler R. A. A., et al., 2014, MNRAS, 440, 2810
  * Bowler et al. (2020) Bowler R. A. A., Jarvis M. J., Dunlop J. S., McLure R. J., McLeod D. J., Adams N. J., Milvang-Jensen B., McCracken H. J., 2020, MNRAS, 493, 2059
  * Boyett et al. (2023) Boyett K., et al., 2023, arXiv e-prints, p. arXiv:2303.00306
  * Bradley et al. (2022) Bradley L. D., et al., 2022, arXiv e-prints, p. arXiv:2210.01777
  * Brammer et al. (2008) Brammer G. B., van Dokkum P. G., Coppi P., 2008, ApJ, 686, 1503
  * Broadhurst et al. (2005) Broadhurst T., et al., 2005, ApJ, 621, 53
  * 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
  * Caminha et al. (2019) Caminha G. B., et al., 2019, A&A, 632, A36
  * Casey et al. (2022) Casey C. M., et al., 2022, arXiv e-prints, p. arXiv:2211.07865
  * Castellano et al. (2022a) Castellano M., et al., 2022a, arXiv e-prints, p. arXiv:2212.06666
  * Castellano et al. (2022b) Castellano M., et al., 2022b, ApJ, 938, L15
  * Chabrier (2003) Chabrier G., 2003, PASP, 115, 763
  * Coe et al. (2013) Coe D., et al., 2013, ApJ, 762, 32
  * Coe et al. (2019) Coe D., et al., 2019, ApJ, 884, 85
  * Curtis-Lake et al. (2023) Curtis-Lake E., et al., 2023, Nature Astronomy,
  * Donnan et al. (2023a) Donnan C. T., et al., 2023a, MNRAS, 518, 6011
  * Donnan et al. (2023b) Donnan C. T., McLeod D. J., McLure R. J., Dunlop J. S., Carnall A. C., Cullen F., Magee D., 2023b, MNRAS, 520, 4554
  * Ellis et al. (2013) Ellis R. S., et al., 2013, ApJ, 763, L7
  * Finkelstein & Bagley (2022) Finkelstein S. L., Bagley M. B., 2022, ApJ, 938, 25
  * Finkelstein et al. (2022a) Finkelstein S. L., et al., 2022a, ApJ, 928, 52
  * Finkelstein et al. (2022b) Finkelstein S. L., et al., 2022b, ApJ, 940, L55
  * Finkelstein et al. (2023) Finkelstein S. L., et al., 2023, ApJ, 946, L13
  * Fioc & Rocca-Volmerange (1999) Fioc M., Rocca-Volmerange B., 1999, arXiv e-prints, pp astro–ph/9912179
  * Fontana et al. (2014) Fontana A., et al., 2014, The Messenger, 155, 42
  * Furtak et al. (2022) Furtak L. J., et al., 2022, arXiv e-prints, p. arXiv:2212.04381
  * Golubchik et al. (2022) Golubchik M., Furtak L. J., Meena A. K., Zitrin A., 2022, ApJ, 938, 14
  * Grogin et al. (2011) Grogin N. A., et al., 2011, ApJS, 197, 35
  * Harikane et al. (2022) Harikane Y., et al., 2022, ApJS, 259, 20
  * Harikane et al. (2023a) Harikane Y., Nakajima K., Ouchi M., Umeda H., Isobe Y., Ono Y., Xu Y., Zhang Y., 2023a, arXiv e-prints, p. arXiv:2304.06658
  * Harikane et al. (2023b) Harikane Y., et al., 2023b, ApJS, 265, 5
  * Hsiao et al. (2022) Hsiao T. Y.-Y., et al., 2022, arXiv e-prints, p. arXiv:2210.14123
  * Ishigaki et al. (2018) Ishigaki M., Kawamata R., Ouchi M., Oguri M., Shimasaku K., Ono Y., 2018, ApJ, 854, 73
  * Jullo & Kneib (2009) Jullo E., Kneib J. P., 2009, MNRAS, 395, 1319
  * Kannan et al. (2022) Kannan R., et al., 2022, arXiv e-prints, p. arXiv:2210.10066
  * Kauffmann et al. (2022) Kauffmann O. B., et al., 2022, A&A, 667, A65
  * Kneib et al. (2011) Kneib J.-P., Bonnet H., Golse G., Sand D., Jullo E., Marshall P., 2011, LENSTOOL: A Gravitational Lensing Software for Modeling Mass Distribution of Galaxies and Clusters (strong and weak regime), Astrophysics Source Code Library, record ascl:1102.004 (ascl:1102.004)
  * Koekemoer et al. (2011) Koekemoer A. M., et al., 2011, ApJS, 197, 36
  * Lotz et al. (2017) Lotz J. M., et al., 2017, ApJ, 837, 97
  * Madau (1995) Madau P., 1995, ApJ, 441, 18
  * Madau & Dickinson (2014) Madau P., Dickinson M., 2014, ARA&A, 52, 415
  * Mason et al. (2015) Mason C. A., Trenti M., Treu T., 2015, ApJ, 813, 21
  * Mason et al. (2023) Mason C. A., Trenti M., Treu T., 2023, MNRAS, 521, 497
  * McCracken et al. (2012) McCracken H. J., et al., 2012, A&A, 544, A156
  * McLeod et al. (2015) McLeod D. J., McLure R. J., Dunlop J. S., Robertson B. E., Ellis R. S., Targett T. A., 2015, MNRAS, 450, 3032
  * McLeod et al. (2016) McLeod D. J., McLure R. J., Dunlop J. S., 2016, MNRAS, 459, 3812
  * McLeod et al. (2021) McLeod D. J., McLure R. J., Dunlop J. S., Cullen F., Carnall A. C., Duncan K., 2021, MNRAS, 503, 4413
  * McLure et al. (2013) McLure R. J., et al., 2013, MNRAS, 432, 2696
  * Naidu et al. (2022) Naidu R. P., et al., 2022, ApJ, 940, L14
  * Oesch et al. (2013) Oesch P. A., et al., 2013, ApJ, 773, 75
  * Oesch et al. (2015) Oesch P. A., Bouwens R. J., Illingworth G. D., Franx M., Ammons S. M., van Dokkum P. G., Trenti M., Labbé I., 2015, The Astrophysical Journal, 808, 104
  * Oesch et al. (2016) Oesch P. A., et al., 2016, ApJ, 819, 129
  * Oesch et al. (2018) Oesch P. A., Bouwens R. J., Illingworth G. D., Labbé I., Stefanon M., 2018, ApJ, 855, 105
  * Oguri (2010) Oguri M., 2010, glafic: Software Package for Analyzing Gravitational Lensing, Astrophysics Source Code Library, record ascl:1010.012 (ascl:1010.012)
  * Oke (1974) Oke J. B., 1974, ApJS, 27, 21
  * Oke & Gunn (1983) Oke J. B., Gunn J. E., 1983, ApJ, 266, 713
  * Paardekooper et al. (2013) Paardekooper J. P., Khochfar S., Dalla C. V., 2013, MNRAS, 429, L94
  * Paris et al. (2023) Paris D., et al., 2023, arXiv e-prints, p. arXiv:2301.02179
  * Pérez-González et al. (2023) Pérez-González P. G., et al., 2023, arXiv e-prints, p. arXiv:2302.02429
  * Pontoppidan et al. (2022) Pontoppidan K. M., et al., 2022, ApJ, 936, L14
  * Postman et al. (2012) Postman M., et al., 2012, ApJS, 199, 25
  * Roberts-Borsani et al. (2022) Roberts-Borsani G., et al., 2022, arXiv e-prints, p. arXiv:2210.15639
  * Robertson et al. (2023) Robertson B. E., et al., 2023, Nature Astronomy,
  * Rodrigo & Solano (2020) Rodrigo C., Solano E., 2020, in XIV.0 Scientific Meeting (virtual) of the Spanish Astronomical Society. p. 182
  * Rodrigo et al. (2012) Rodrigo C., Solano E., Bayo A., 2012, SVO Filter Profile Service Version 1.0, IVOA Working Draft 15 October 2012, doi:10.5479/ADS/bib/2012ivoa.rept.1015R
  * Rojas-Ruiz et al. (2020) Rojas-Ruiz S., Finkelstein S. L., Bagley M. B., Stevans M., Finkelstein K. D., Larson R., Mechtley M., Diekmann J., 2020, ApJ, 891, 146
  * Schechter (1976) Schechter P., 1976, ApJ, 203, 297
  * Schmidt (1968) Schmidt M., 1968, ApJ, 151, 393
  * Stefanon et al. (2019) Stefanon M., et al., 2019, ApJ, 883, 99
  * Trenti & Stiavelli (2008) Trenti M., Stiavelli M., 2008, ApJ, 676, 767
  * Treu et al. (2022) Treu T., et al., 2022, ApJ, 935, 110
  * Valentino et al. (2023) Valentino F., et al., 2023, ApJ, 947, 20
  * Welch et al. (2022) Welch B., et al., 2022, ApJ, 940, L1
  * Wilkins et al. (2023) Wilkins S. M., et al., 2023, MNRAS, 519, 3118
  * Williams et al. (2022) Williams H., et al., 2022, arXiv e-prints, p. arXiv:2210.15699
  * Williams et al. (2023) Williams C. C., et al., 2023, arXiv e-prints, p. arXiv:2301.09780
  * Windhorst et al. (2023) Windhorst R. A., et al., 2023, AJ, 165, 13
  * Yung et al. (2019) Yung L. Y. A., Somerville R. S., Finkelstein S. L., Popping G., Davé R., 2019, MNRAS, 483, 2983
  * Zitrin et al. (2014) Zitrin A., et al., 2014, ApJ, 793, L12
  * Zitrin et al. (2015) Zitrin A., et al., 2015, ApJ, 801, 44

## data availability

At the time of writing, the data sets used in this manuscript were all
publicly available from the JWST archive on MAST and on the CADC.

##  Appendix A Discussion of High-redshift candidates

In the following sections, we discuss the results of our search for high-
redshift galaxies field-by-field, along with a (non-exhaustive) comparison to
some previous searches in the literature. The variation between JWST high-
redshift candidate samples has been a theme in the literature (see Bouwens et
al. 2023 for a comprehensive discussion). We stress that differences in the
candidate lists can result from a number of factors such as differing
reductions, photometry measurement and selection criteria such as non-
detection and $\Delta\chi^{2}$ thresholds.

The nomenclature adopted for our final candidate IDs is Field-redshift-
catalogueID (e.g. GLASS-z11-1481). When referring to candidates from other
studies we use their naming convention.

###  A.1 SMACS 0723

We select one high-redshift candidate from SMACS 0723 in our final sample,
SMACS0723-z12-7442.

There have been numerous studies of this cluster field to date, yielding
contrasting samples. We only compare candidates that have passed the
additional criteria of $F150W-F200W>0.75$ or $F150W<2\sigma$. Adams et al.
(2023) reported a sample of four $9<z<12$ galaxies, but only one of which can
be compared to our final sample. Their candidate with ID 10234 was initially
selected in our sample, where we found $z_{\mathrm{phot}}=11.8^{+0.2}_{-0.1}$.
However, there appeared to be a marginal F090W detection upon visual
inspection of the imaging, and so we discarded the candidate.

Atek et al. (2023) reported a sample of high-redshift candidates, including
two potential $z>15$ candidates and two potential $z=12$ candidates. We do not
include their ID z16a due to a $>3\sigma$ detection in F150W, which rules out
a potential $z>13$ solution. While we do find a
$z_{\mathrm{phot}}=15.6^{+0.5}_{-0.9}$ solution for their ID z16b, we exclude
it from our final sample as it has $\Delta\chi^{2}\simeq 2$. Both their
objects z12a and z12b have $\Delta\chi^{2}\simeq 1$ between the high-redshift
and low-redshift solutions, so are also excluded.

Most of the SMACS 0723 sample from Donnan et al. (2023a) was not included in
our final sample due to our more stringent selection and brightness criteria.
Their candidate with ID 8347 is in our final sample as SMACS0723-z12-7442.
While we find $z_{\mathrm{phot}}=12.2^{+0.5}_{-0.4}$ for their object with ID
1566, it just misses out on being in our final sample through having
$\Delta\chi^{2}=3.4$. Finally, their candidate with ID 10566 had been excluded
from our final sample due to a $>2\sigma$ detection in the HST ACS imaging in
our present analysis, potentially due to a noise spike that contaminated the
aperture.

###  A.2 GLASS

Using the maximum-depth combination of the epoch1+2 GLASS survey, we report a
sample of twelve $z\geq 9.3$ galaxy candidates, including five in the range
$10.5<z<11.5$ and three at $z>12$. The high density of bright $z\sim 10$
galaxies seen in Castellano et al. (2022a) is confirmed by this study, as we
re-select all five of their candidates at similar redshifts.

With the first epoch of GLASS imaging, Naidu et al. (2022) and Castellano et
al. (2022b) unveiled two particularly bright $z=10-12$ galaxies. We recover
both of these objects in our final sample as GLASS-z10-3283 (GLASS-z10/GHZ1)
and GLASS-z12-28072 (GLASS-z12/GHZ2).

A comprehensive study by Bouwens et al. (2023) also covered the GLASS data
set. Their final sample includes the two aforementioned candidates in common
with our study, Naidu et al. (2022) and Castellano et al. (2022b). We re-
select their $z=13.7$ candidate, GLASSP2H-3576218534 in our final sample as
GLASS-z14-33570. Although we also recover a high-redshift solution for their
candidate ID 4002721259, the $\Delta\chi^{2}$ was insufficient to include in
our final sample. Their alternative sample includes an additional $z=13.3$
candidate, GLASSP1H-4015021230, but we cannot confirm its redshift owing to a
flat p(z) distribution. Finally, GLASSP1YJ-4016420474 and GLASSP1YJ-4043920397
are $z=9.6$ and $z=9.7$ candidates that we do not include as they appear to
have a marginal detection in F115W. This is likely a result of the increased
depth when adding epoch 2, as the epoch 1-only version of the data appeared
consistent with non-detections for both objects.

###  A.3 CEERS

The first epoch of observations was split into two fields, north-east (NE) and
south-west (SW). In CEERS-NE we selected six candidates, among which are
CEERS-93316 (Donnan et al., 2023a) and Maisie’s galaxy (Finkelstein et al.,
2022b). While the former has recently been revealed by spectroscopy to be
lower redshift, Maisie’s galaxy has been spectroscopically confirmed to be at
high-redshift (DDT 2750, PI Arrabal Haro; Arrabal Haro et al. 2023a). We also
note that CEERS-NE-z11-2543 has also been recently spectroscopically confirmed
at high-redshift with the same program. Given its new spectroscopic redshift
$z_{\mathrm{spec}}=4.9$, we exclude CEERS-93316 from the subsequent analysis.
Four of the five remaining candidates were included in Finkelstein et al.
(2023).

There are five galaxies from Finkelstein et al. (2023) that we also find to be
$z>9.0$, but do not include in our final sample due to insufficient
$\Delta\chi^{2}$ and/or $<8\sigma$ detection. A further six candidates are not
included due to $>2\sigma$ detection in F115W, but five of those are
consistent with their $z_{\mathrm{phot}}=8-9$ solutions. The only higher
redshift candidate excluded by our study for a F115W detection is their
candidate ID CEERS-7227, for which we find the F115W to be marginally detected
at $2.6\sigma$. We note that Finkelstein et al. (2023) find a $2.2\sigma$ flux
for this object in F115W. Only CEERS-NE-z10-3069854 is unique to this study.

In CEERS-SW, we find six more high-redshift candidates, although only two of
the final sample are in common with Finkelstein et al. (2023) (our IDs CEERS-
SW-z11-26592 and CEERS-SW-z11-3961). Our candidates CEERS-SW-z11-20687 and
CEERS-SW-z14-37967 were also found in Bouwens et al. (2023) and Donnan et al.
(2023a) respectively.

Four objects in the Finkelstein et al. (2023) sample (their IDs 7603, 1748,
2324 and 4012) were also found to have preferred high-redshift solutions in
our catalogues, but were detected at $<8\sigma$ so were excluded. Finally,
four $z=8-9$ candidates were F115W$>2\sigma$ and so were excluded.

Epoch two of the CEERS observations were split into six NIRCam pointing pairs,
and we adopt this naming convention into our candidate IDs. We report twelve
high-redshift candidates across the $\sim 60$ sq. arcmin. Two of these objects
(CEERS-2-5-z10-9617 and CEERS-2-6-z10-3530) have very recently been
independently confirmed with spectroscopy to lie at $z\simeq 10$ (Arrabal Haro
et al., 2023b).

###  A.4 Stephan’s Quintet

Our search over the Quintet field yielded one high-redshift candidate over
$11.5<z<12.5$. Harikane et al. (2023b) also reported two candidates at $z>12$
from the Quintet field. Their $z\sim 12$ candidate was in our initial
catalogue, and with our photometry appears to be a robust candidate at
$z_{\mathrm{phot}}=11.7^{+0.4}_{-0.5}$ and $\Delta\chi^{2}=4.8$. It also
passes our additional F150W-F200W colour criteria, but we do not include it in
our final sample as it is only detected at $\sim 6\sigma$ in F200W and F277W.
For the $z=16$ candidate, we obtain a low-z preferred solution of $z=0.6$,
with other solutions at $z=16.4$ and $z=4.9$ being of similar probability
(within $1\sigma$). We cannot rule out that it is indeed a $z=16.4$ galaxy,
but based on the current fits we do not include it in our final sample.
Interestingly, the high and low-redshift solutions that we derive are very
similar to CEERS-93316. The low-redshift solution with emission lines was
ultimately the spectroscopic redshift, suggesting that candidates around
$z=16.4$ are vulnerable to this class of contaminant, especially in the
absence of photometric constraints from key medium bands such as F250M and
F300M.

###  A.5 UNCOVER

From our analysis of the UNCOVER field, we amass a sample of sixteen
candidates. We find UHZ1 from Castellano et al. (2022a) as UNCOVER-z10-32757
with a similar $z_{\mathrm{phot}}=10.4^{+0.1}_{-0.2}$ and
$\Delta\chi^{2}>100$. One additional candidate was a duplicate of
GLASS-z10-3283 and so was excluded.

We also find two components from the triply lensed $z\simeq 10$ galaxy from
Zitrin et al. (2014), which has now been spectroscopically confirmed to lie at
$z=9.8$ (Roberts-Borsani et al., 2022). We find JD1B as UNCOVER-z11-15452
which was observed to be exceptionally bright $M_{1500}=-20.9$, but is
magnified $\simeq 11\times$. JD1A was in our initial catalogue as
UNCOVER-z10-15137 with a robust $z_{\mathrm{phot}}=10.3^{+0.3}_{-0.9}$,
$\Delta\chi^{2}=17$ solution. This component had a magnification of 13.4 and
$M_{1500}=-17.3$. As it was only $7\sigma_{\rm{local}}$ in each of our
detection catalogues, it was not propagated to the final sample. The remaining
component, JD1C, was of insufficient signal-to-noise to make it into our
catalogues at $>5\sigma$, due to enhanced background and crowding.

###  A.6 DDT 2756

In the DDT 2756 parallel field to Abell2744, we found more examples of bright
and robust $z\sim 10$ candidates, providing more evidence that the region
around Abell2744 is over-dense with such galaxies. We report five $9.5<z<11.7$
candidates, including a particularly robust ($\Delta\chi^{2}\simeq 43$)
candidate with $z_{\mathrm{phot}}=10.6^{+0.1}_{-0.3}$, DDT2756-z11-1001979.

The DDT 2756 survey was also explored in Castellano et al. (2022a), who found
one remarkably bright $z\sim 10$ candidate, DHZ1. Due to the high-resolution
of the F200W imaging, our F200W-detected catalogue had de-blended DHZ1 into
two components. The north-east component was selected for our final sample as
DDT2756-z10-1010612, and yielded a robust high-redshift solution of
$z_{\mathrm{phot}}=9.5^{+0.6}_{-0.3}$. Although the south-west component was
excluded from our final sample due to a 2.2$\sigma$ detection in F115W, we
performed SED fitting and found an ultra robust $z_{\mathrm{phot}}=9.5\pm 0.1$
($\Delta\chi^{2}>150$) solution, consistent with the north-east component. The
system has since been spectroscopically confirmed to be $z=9.31$ (Boyett et
al., 2023).

###  A.7 WHL 0137

We report four high-redshift candidates in the WHL 0137 cluster+parallel data
set, three of which are $z\simeq 9$ candidates and the other with $z=11.1$.
There has been one reported search for $z>9$ galaxies over the WHL 0137 data
set to date, with Bradley et al. (2022) uncovering a sample of twelve galaxies
over $8.3<z<13.0$. We include in our final catalogue two of the twelve
candidates, WHL0137-z9-10187 (their WHL0137-2796) and WHL0137-z11-22312 (their
WHL0137-5330). Three candidates, while showing high-redshift solutions in
agreement with Bradley et al. (2022), had too low a $\Delta\chi^{2}$ to be
included in the final sample. Notably, our initial catalogue has a $z=13$
galaxy in common, their WHL0137-5021 was found by our study to have a robust
$z_{\rm{phot}}=12.8^{+0.8}_{-0.5}$ solution. The candidate was excluded due to
being detected at $\leq 8\sigma$. Six of the candidates are not in our initial
catalogue due to $>2\sigma$ detections in F115W, although a detection in F115W
is still consistent with the $8.3\leq z\leq 9.3$ solutions reported by Bradley
et al. (2022).

###  A.8 MACS 0647

We report three high-redshift candidates in the MACS 0647 cluster+parallel
data set. There has been a detailed analysis of MACS 0647 JD (Coe et al.,
2013) by Hsiao et al. (2022). We recover two of the three multiply imaged
components of JD: MACS0647-z11-20148 is JD1 and MACS0647-z11-26400 is JD3.
Both have extremely robust solutions $\Delta\chi^{2}>100$, and in excellent
agreement with the reported value of $z_{\mathrm{phot}}=10.6\pm 0.3$ in Hsiao
et al. (2022). This object has since been spectroscopically confirmed to lie
at $z=10.17$ by Harikane et al. (2023a).

We do not include JD2 in our final sample as it has a $2.8\sigma$ detection in
F435W, which aligns with Hsiao et al. (2022)’s F435W photometry also being
$>2\sigma$. For completeness, we note that we recover a $z=10.8\pm 0.2$
solution for JD2 using our photometry, with a $\Delta\chi^{2}=63$ showing it
is an extremely robust object despite the F435W SNR$>$2 measurement. For our
subsequent LF analysis in Section 5, we only propagate JD1 so as not to
double-count multiple images. In addition to MACS0647 JD, we find a notably
robust $z=9.5$ galaxy in the cluster module, MACS0647-z9-20158.

###  A.9 RXJ 2129

We report two $z\simeq 9$ galaxy candidates in this field, however we do not
uncover any $z\geq 9.5$ candidates. To date, there has been one reported
$z\geq 9.5$ galaxy in the RXJ 2129 field with the new JWST data (Williams et
al., 2022). This galaxy is reported to be intrinsically very faint with
$M_{1500}=-17.4$, but high magnification factor ($\mu\simeq 20$). We do not
recover this spectroscopically confirmed galaxy due to its position near the
RXJ 2129 cluster. The enhanced background in the region around the object had
caused the object to fail our signal-to-noise cuts in all of the catalogues.

###  A.10 NEP TDF

Our study of the NEP TDF data set uncovered one $z\sim 10$ candidate and one
$z\sim 11$ candidate. To date, there have been no published candidates in the
literature.

###  A.11 Cartwheel

Our final sample does not include any galaxy candidates at $z>9$ from the
Cartwheel galaxy field.

###  A.12 J1235

From our study of the J1235 field we report three high-redshift galaxy
candidates over $9.7\leq z\leq 11.8$. To date, there have been no other
published high-redshift candidates in the literature.