# JWST UNCOVER: The Overabundance of Ultraviolet-luminous Galaxies at $z>9$

Iryna Chemerynska1 , Hakim Atek1, Lukas J. Furtak2, Adi Zitrin2, Jenny E.
Greene3, Pratika Dayal4, Andrea Weibel5, Vasily Kokorev4, Andy D. Goulding6,
Christina C. Williams7,8, Themiya Nanayakkara9,10, Rachel Bezanson11, Gabriel
Brammer12, Sam E. Cutler13, Ivo Labbe9, Joel Leja14,15,16, Richard Pan17,
Sedona H. Price11, Bingjie Wang14,15,16, John R. Weaver13, Katherine E.
Whitaker12,13
1Institut d’Astrophysique de Paris, CNRS, Sorbonne Université, 98bis Boulevard
Arago, 75014, Paris, France
2Physics Department, Ben-Gurion University of the Negev, PO Box 653, Be’er-
Sheva 8410501, Israel
3Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane,
Princeton, NJ 08544
4Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, 9700
AV Groningen, The Netherlands
5Department of Astronomy, University of Geneva, Chemin Pegasi 51, 1290
Versoix, Switzerland
6Department of Astrophysical Sciences, Princeton University, Princeton, NJ
08544, USA
7NSF’s National Optical-Infrared Astronomy Research Laboratory, Tucson, AZ
85719, USA
8Steward Observatory, University of Arizona, Tucson, AZ 85721, USA
9Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Melbourne, VIC 3122, Australia
10ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions
(ASTRO-3D), Australia
11Department of Physics and Astronomy and PITT PACC, University of Pittsburgh,
Pittsburgh, PA 15260, USA
12Cosmic Dawn Center (DAWN), Niels Bohr Institute, University of Copenhagen,
Jagtvej 128, København N, DK-2200, Denmark
13Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA
14Department of Astronomy & Astrophysics, The Pennsylvania State University,
University Park, PA 16802, USA
15Institute for Computational & Data Sciences, The Pennsylvania State
University, University Park, PA 16802, USA
16Institute for Gravitation and the Cosmos, The Pennsylvania State University,
University Park, PA 16802, USA
17Department of Physics & Astronomy, Tufts University, MA 02155, USA E-mail:
<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Over the past year, JWST has uncovered galaxies at record-breaking distances
up to $z\sim 13$. The JWST UNCOVER (ultra-deep NIRSpec and NIRcam observations
before the epoch of reionization) program has obtained ultra-deep
multiwavelength NIRCam imaging of the massive galaxy cluster Abell 2744 over
$\sim 45$ arcmin2 down to $\sim 29.5$ AB mag. Here, we present a robust
ultraviolet (UV) luminosity function derived through lensing clusters at
$9<z<12$. Using comprehensive end-to-end simulations, we account for all
lensing effects and systematic uncertainties in deriving both the
amplification factors and the effective survey volume. Our results confirm the
intriguing excess of UV-bright galaxies ($M_{\rm UV}$ $<-20$ AB mag)
previously reported at $z>9$ in recent JWST studies. In particular, a double
power-law (DPL) describes better the bright-end of the luminosity function
compared to the classical Schechter form. The number density of these bright
galaxies is 10-100 times larger than theoretical predictions and previous
findings based on Hubble Space Telescope (HST) observations. Additionally, we
measure a star formation rate density of $\rho_{\rm SFR}=10^{-2.64}$ M⊙ yr-1
Mpc-3 at these redshifts, which is 4 to 10 times higher than galaxy formation
models that assume a constant star formation efficiency. Future wide-area
surveys and accurate modeling of lensing-assisted observations will reliably
constrain both the bright and the dim end of the UV luminosity function at
$z>9$, which will provide key benchmarks for galaxy formation models.

###### keywords:

galaxies:high-redshift – galaxies: evolution – gravitational lensing: strong

††pubyear: 2023††pagerange: JWST UNCOVER: The Overabundance of Ultraviolet-
luminous Galaxies at $z>9$–JWST UNCOVER: The Overabundance of Ultraviolet-
luminous Galaxies at $z>9$

##  1 Introduction

The advent of the James Webb Space Telescope (JWST) has opened a new era in
our exploration of the distant universe. While the Hubble Space Telescope
(HST) helped identify more than 2,000 dropout galaxy candidates at $z>6$, its
restricted near-infrared coverage, and the limited capabilities of the Spitzer
Space Telescope hampered the identification of galaxies at $z>9$ and the
characterization of their stellar populations. The unprecedented capabilities
of JWST’s Near Infrared Camera (NIRCam; Rieke et al., 2023), which uniformly
covers the $0.8-5\mu m$ spectral range with exquisite spatial resolution,
provides the opportunity to routinely identify $z>9$ galaxies.

The first JWST observing programs, which included the Early Release
Observations (ERO) and the Early Release Science Programs (ERS) (e.g.,
Pontoppidan et al., 2022; Treu et al., 2022; Finkelstein et al., 2022b), have
unveiled a large sample of galaxies at redshifts higher than $z=9$ (Atek et
al., 2023a; Castellano et al., 2022; Donnan et al., 2023; Finkelstein et al.,
2022a; Morishita et al., 2023; Naidu et al., 2022b; Robertson et al., 2023;
Bunker et al., 2023a; Adams et al., 2023; Austin et al., 2023). These sources
have been photometrically identified via their Lyman-break signature,
photometric redshifts derived from model fitting to their spectral energy
distribution (SED), or a combination thereof. Furthermore, spectroscopic
follow-up campaigns with the Near-infrared Spectrograph (NIRSpec; Jakobsen et
al., 2022) instrument has allowed us to confirm the high-redshift nature of
these candidates at an unprecedented rate (e.g. Curtis-Lake et al., 2022;
Arrabal Haro et al., 2023a; Hainline et al., 2023; Roberts-Borsani et al.,
2022, 2023; Hsiao et al., 2023; Bunker et al., 2023a; Wang et al., 2023a;
Fujimoto et al., 2023)

One of the most prominent results is the surprising over-abundant population
of UV-bright galaxies at $z\sim 9-12$ when compared to theoretical predictions
of the UV luminosity function at those redshifts (e.g. Naidu et al., 2022b;
Harikane et al., 2023b; Bouwens et al., 2023; Mauerhofer & Dayal, 2023).
Indeed, most models suggest that galaxy evolution should extend beyond $z>10$
(e.g.; Hutter et al., 2021; Dayal et al., 2022), including a rapid decline in
the star formation efficiency. However, strong observational constraints have
been lacking until the recent JWST results. Given the small area probed by
these surveys, the expected rapid evolution predicts more than an order of
magnitude fewer galaxies than observed. This small survey area could also
result in a significant cosmic variance (e.g.; Ucci et al., 2021). From the
theoretical point of view, several physical explanations have been
investigated, which are mostly based on the star formation histories and the
stellar population properties of these galaxies. Some suggest that the
expected decline in the number density of galaxies with redshift is balanced
by the decrease of dust content (Ferrara et al., 2022), while others suggest
the inefficient star-formation feedback (Dekel et al., 2023) or a weaker pre-
reionization background (Harikane et al., 2023b) result in a larger population
of bright galaxies at $z>10$. Stochastic star formation histories (SFH) have
also been invoked to explain this excess, resulting in notable disagreements
across the literature. Some show that bursty SFHs cause UV luminosity
deviations large enough to explain these observations (Shen et al., 2023; Sun
et al., 2023; Muñoz et al., 2023; Whitler et al., 2023) while others find it
to be insufficient (Pallottini & Ferrara, 2023; Ciesla et al., 2023; Mason et
al., 2023). An evolution in the initial mass function (IMF) or UV contribution
from active galactic nuclei (AGNs Ono et al., 2018; Fujimoto et al., 2023) can
also explain such UV excess (Pacucci et al., 2022). Indeed, the past year of
JWST observations has revealed an astonishing number of optically red AGNs at
$z>6$ that have been entirely missed by previous UV-based selections (Matthee
et al., 2023; Furtak et al., 2023c, a; Labbe et al., 2023; Greene et al.,
2023; Maiolino et al., 2023). A few galaxy candidates have shown signs of
black hole activity via their emission lines or their X-ray emission (Kokorev
et al., 2023; Goulding et al., 2023; Fujimoto et al., 2023; Larson et al.,
2023), potentially proving a non-negligible contribution to the bright-end of
the UV luminosity function. While their number density is still an order of
magnitude lower than that of galaxies, it appears to be larger than previous
UV-based determinations at $z=6$. Another potential source of contamination is
the low-redshift dusty galaxies that can mimic the broadband colors of high-
redshift galaxies (e.g.; Naidu et al., 2022a; Zavala et al., 2023; Arrabal
Haro et al., 2023a).

In this work, we present the galaxy UV luminosity function (UV LF) over the
redshift range $z=9-12$ based on the lensing-assisted observations from the
JWST UNCOVER program. The observations consist of deep NIRCam imaging of the
Abell 2744 cluster (A2744), which is at the redshift $z=0.31$. This work
builds on a comprehensive assessment of the lensing effects impacting the UV
LF using end-to-end simulations from the source plane to the final UV LF. The
paper is organized as follows: in Section 2 we describe the imaging data-set
used in the study and the lensing model is covered in Section 3. We present
the high-redshift galaxies catalog at $z>9$ and mock galaxies at the same
redshift in Section 4. Our forward modeling procedure and the final UV LF with
the associated uncertainties are presented in Section 5 while the star
formation rate density in the early Universe is detailed in Section 6. The
conclusion is given in Section 7.

Throughout this work, we assume a flat $\Lambda$CDM cosmology with $H_{0}$ =
70 km s-1 Mpc-1, $\Omega_{M}$ = 0.3 and $\Omega_{\Lambda}$ = 0.7.

##  2 Observations

The first part of UNCOVER consisted of multi-wavelength NIRCam imaging of the
lensing cluster Abell 2744 in 6 broadband filters (F115W, F150W, F200W, F277W,
F356W, and F444W) and one medium-band filter (F410M), reaching a limiting
magnitude of $\sim 29.5$ AB over $\sim 45$ arcmin2 (Bezanson et al., 2022).
Observations were obtained across multiple days, between November 2nd and 15th
2022. The JWST imaging data also include parallel observations with the Near
Infrared Imager and Slitless Spectrograph (NIRISS), using five broadband
filters — F115W, F150W, F200W, F356W, and F444W. We also incorporate imaging
data obtained by the ERS program GLASS (Treu et al., 2022) and the DDT
(Director Discretionary Time) program ID 2756, which cover the outer regions
of the UNCOVER field and which use a nearly identical filter set, except for
the addition of F090W for the former, and the absence of F444W for the latter,
respectively.

Table 1: UNCOVER Imaging: Limiting AB magnitudes at 5$\sigma$, measured in 0.32" diameter apertures. Filter | Exposure | Depth
---|---|---
F115W | 6.0h | 28.85
F150W | 6.0h | 28.27
F200W | 3.7h | 28.92
F277W | 3.7h | 29.34
F356W | 3.7h | 29.45
F410M | 3.7h | 28.85
F444W | 4.6h | 29.10

The reduction of the imaging data was performed using the grizli (Brammer et
al., 2022) software and presented in Weaver et al. (2023). The data were
drizzled into mosaics with a pixel scale of 0.400 pix-1 (Atek et al., 2023b).
The exposure times with the resulting magnitude limits in all filters are
listed in Table 1.

The galaxy cluster A2744 was part of the Hubble Frontier Fields (HFF)
clusters. As such, it has deep Hubble Space Telescope (HST) imaging data
across the optical and near-infrared range, including ancillary data from
multiple programs (Lotz et al., 2017). These data include deep Advanced Camera
for Surveys (ACS) imaging in the cluster core (F435W, F606W, and F814W) and
Wide-Field Camera Three (WFC3) observations in 4 filters (F105W, F125W, F140W,
and F160W). In addition, A2744 was observed as part of the HST program BUFFALO
(Steinhardt et al., 2020). The ACS observations included three broadband
filters (F435W, F606W, F814W) while the WFC3 used four filters (F105W, F125W,
F140W, F160W). The JWST and HST observations were drizzled to the same pixel
scale and aligned. Weaver et al. (2023) contains a thorough discussion of the
data reduction procedure.

##  3 Gravitational lensing

To compute the UV LF at $z$ = 9 - 12, we need to have a good understanding of
the lensing power of the galaxy cluster A2744. Lensing models are crucial not
only for estimating the magnification of the sources but also for estimating
the effective survey volume. In this work, we adopt the v1.1 UNCOVER strong
lensing (SL) model of A2744, presented in Furtak et al. (2023b), which is
publicly available on the UNCOVER website111https://jwst-
uncover.github.io/DR2.html#LensingMaps. This model was constructed using a new
version of the parametric code by Zitrin et al. (2015), updated to be fully
analytic and thus not dependent on a fixed grid, which allows for faster
computation and with a higher resolution (Pascale et al., 2022; Furtak et al.,
2023b). The model for A2744 comprises five smooth cluster-scale dark matter
halos, centered on the five brightest cluster galaxies (BCGs), and 421 cluster
member galaxies, as detailed in (Furtak et al., 2023b). More than half of the
cluster galaxies are spectroscopically confirmed (Bergamini et al., 2023a).
The v1.1 of the model used here is constrained by a total of 141 multiple
images (belonging to 48 sources), of which 96 have spectroscopic redshifts
(Bergamini et al., 2023a, b; Roberts-Borsani et al., 2023) and the remaining
ones are photometric systems discovered with the UNCOVER imaging (Furtak et
al., 2023b, c). With these constraints, the model achieves a lens plane image
reproduction RMS of $\Delta_{\mathrm{RMS}}=0.51\arcsec$. We compute analytic
magnifications and their uncertainties for our sample at each object’s
position and spectroscopic redshift.

Figure 1: This schematic illustrates the process of computing the UV LF. The
first part is the detection of lensed galaxies in the observed image and
estimates of their lensing amplification and multiplicity to determine the
observed number counts. The second step is the survey completeness, which
consists of simulating galaxies directly in the source plane before projecting
them back to the image plane using the same lensing model used for
observations. The completeness function, informed by simulated sources, is
combined with survey area reduction as a function of magnification to
determine the effective survey volume.

##  4 High-redshift galaxy sample

###  4.1 Observed galaxies

The first step is to select a sample of dropout galaxies in the imaging data
of A2744, before proceeding to compute their number density. In this work, we
rely on the sample selection and the derived high-redshift galaxy catalog
presented in Atek et al. (2023b). The general UNCOVER catalog is presented in
Weaver et al. (2023). However, our high-redshift selection is based on a
second photometric catalog, which is tailored towards high-redshift sources,
and presented in Atek et al. (2023b). The full description of this catalog
will be given in Weibel et al. (in prep). Briefly, this catalog was produced
by using the SExtractor tool (Bertin & Arnouts, 1996) in its dual mode, using
the F444W as the detection image. Fluxes in each filter are measured in 0.24″
apertures, whereas total fluxes are derived by applying a scaling factor
calculated from the ratio of aperture flux and F444W SExtractor AUTO FLUX. We
adopted the Lyman break selection criteria defined in Atek et al. (2023a) to
define the selection window. This color selection was done to minimize the
contamination rate. The most important sources of contamination consist of
dust-obscured and evolved galaxies at lower redshift with extremely red
colors, and low-mass stars. In addition to selection criteria, we require non-
detection in the bands blueward of the Lyman break. All details are described
in Atek et al. (2023b).

Table 2: The photometric and physical characteristics of the sample of high-redshift candidates identified through the Abell 2744 cluster. The object presented with an asterisk indicates the potential AGN source in our sample. Source IDs correspond to those used in Atek et al. (2023b). For the spectroscopically-confirmed sources, we also provide ID numbers quoted in Fujimoto et al. (2023) ID | RA | Dec | $z_{\mathrm{phot}}$ | $z_{\mathrm{spec}}$ | $M_{\mathrm{UV}}$ | $\mu$
---|---|---|---|---|---|---
1870 | 3.648010 | -30.426616 | $9.32_{-6.95}^{+0.96}$ |  | -19.78 $\pm$ 0.18 | $1.30_{-0.01}^{+0.01}$
3148 | 3.646481 | -30.421615 | $9.40_{-7.14}^{+0.88}$ |  | -20.51 $\pm$ 0.18 | $1.31_{-0.01}^{+0.02}$
17987 | 3.641572 | -30.382825 | $9.41_{-7.12}^{+0.60}$ |  | -19.39 $\pm$ 0.18 | $1.31_{-0.01}^{+0.01}$
26928 | 3.511925 | -30.371861 | $9.47_{-0.07}^{+0.44}$ |  | -20.36 $\pm$ 0.12 | $1.67_{-0.09}^{+0.07}$
2065 (3686) | 3.617194 | -30.425536 | $9.50_{-0.08}^{+0.34}$ | $9.325_{-0.001}^{+0.000}$ | -21.67 $\pm$ 0.12 | $1.65_{-0.03}^{+0.02}$
83338 | 3.454706 | -30.316898 | $9.55_{-0.57}^{+0.91}$ |  | -19.24 $\pm$ 0.18 | $1.17_{-0.01}^{+0.01}$
10619 | 3.594996 | -30.400738 | $9.69_{-0.12}^{+0.33}$ |  | -17.57 $\pm$ 0.13 | $11.50_{-0.50}^{+0.40}$
21623* (26185) | 3.567067 | -30.377869 | $10.01_{-0.26}^{+0.36}$ | $10.071_{-0.001}^{+0.000}$ | -19.01 $\pm$ 0.14 | $3.72_{-0.18}^{+0.14}$
52008 | 3.478739 | -30.345535 | $10.37_{-1.09}^{+0.32}$ |  | -19.90 $\pm$ 0.14 | $1.26_{-0.02}^{+0.02}$
81198 | 3.451367 | -30.320717 | $10.50_{-0.66}^{+0.23}$ |  | -19.90 $\pm$ 0.14 | $1.17_{-0.01}^{+0.01}$
39074 (37126) | 3.590115 | -30.359743 | $10.60_{-0.31}^{+0.21}$ | $10.255_{-0.001}^{+0.001}$ | -20.03 $\pm$ 0.14 | $1.89_{-0.06}^{+0.05}$
73667 | 3.451412 | -30.321807 | $10.68_{-0.31}^{+0.21}$ |  | -20.55 $\pm$ 0.13 | $1.17_{-0.01}^{+0.01}$
22360 | 3.637111 | -30.376780 | $10.73_{-1.19}^{+0.44}$ |  | -19.85 $\pm$ 0.18 | $1.33_{-0.01}^{+0.01}$
3160 | 3.591436 | -30.421663 | $10.74_{-1.45}^{+0.37}$ |  | -19.06 $\pm$ 0.15 | $2.49_{-0.08}^{+0.09}$
46026 | 3.605690 | -30.352664 | $10.86_{-8.30}^{+0.32}$ |  | -19.92 $\pm$ 0.16 | $1.47_{-0.03}^{+0.04}$
31763 | 3.519867 | -30.366428 | $11.31_{-8.63}^{+0.20}$ |  | -18.89 $\pm$ 0.17 | $1.92_{-0.11}^{+0.11}$
42329 (38766) | 3.513568 | -30.356804 | $11.83_{-7.93}^{+1.05}$ | $12.393_{-0.001}^{+0.004}$ | -19.13 $\pm$ 0.18 | $1.57_{-0.05}^{+0.06}$
46075 | 3.546722 | -30.352425 | $12.23_{-0.50}^{+1.38}$ |  | -19.10 $\pm$ 0.19 | $1.82_{-0.05}^{+0.11}$
70846 | 3.498983 | -30.324758 | $12.50_{-0.15}^{+0.46}$ |  | -20.79 $\pm$ 0.12 | $1.27_{-0.02}^{+0.02}$

The final sample consists of 19 galaxies in the redshift range $9<z<12$. Among
these four sources were included in the NIRSpec MSA (Micro Shutter Assembly)
design of the UNCOVER spectroscopic follow-up Fujimoto et al. (2023); Wang et
al. (2023a). The physical parameters of the galaxy candidates are listed in
Table 2 together with their spectroscopic confirmation $z_{\mathrm{spec}}$.
Remarkably, we report a 100% success rate in our spectroscopic confirmation,
demonstrating the robustness of the photometric selection. Other studies
(e.g.. Bunker et al., 2023b; Hainline et al., 2023; Arrabal Haro et al.,
2023b) also show high confirmation rate, 80% or more.

###  4.2 Simulated galaxies

The second step consists of computing the survey completeness function through
the lensing cluster alongside its uncertainties. Following the procedure
adopted in Atek et al. (2018), we generated a set of 50,000 mock galaxies,
which were randomly distributed directly in the source plane, which was
constructed using the latest lensing model (see Section 3). The properties of
these simulated objects were randomly allocated: the redshift in the range
$z=8.5-12.5$, with intrinsic absolute magnitudes $M_{\rm UV}$ from -23 to -15
mag. The input galaxy sizes follow a log-normal distribution and the size-
luminosity relation derived for high-redshift galaxies, adopting the Yang et
al. (2022) determination for faint objects ($M_{\rm UV}$$>-17.2$) and Shibuya
et al. (2015) for the bright sources.

A uniform distribution in the source plane, i.e. the physical plane, will
undersample the regions of higher magnification in the image plane, leading to
smaller statistics for the completeness function. For this reason, we decided
to add a second layer of mock galaxies in the higher magnification area
($\mu>2$) within the source plane.

Overall, this forward modeling naturally accounts for the galaxy shape
distortion following the lensing shear, which directly affects the
completeness function. Most importantly, the completeness function depends on
several parameters, some of which are interdependent, such as the
magnification and the source position, and need to be simultaneously accounted
for.

In order to compute the synthetic fluxes of the mock galaxies, we first
generate SEDs models with BEAGLE (Chevallard & Charlot, 2016) according to
their simulated physical properties. These templates, characterized by delayed
star-formation histories $\psi(t)\propto t\exp(-t/\tau)$, and an SMC
extinction law (Pei, 1992), and a constant metallicity Z = 0.1Z⊙. Templates
were redshifted and normalized to the observed magnitude within the F150W
filter, corresponding to the rest-frame UV. In the end, we used GalSim (Rowe
et al., 2015) to simulate the galaxies, which were in turn injected into the
source plane of A2744, mapped into the image plane, and then inserted into the
UNCOVER mosaics of A2744, placing 100 galaxies at a time. Then we follow the
same procedure used for the observations to extract the sources and select
dropout galaxies in the redshift range of $z=$ 9 - 12.

##  5 The UV luminosity function at $z>9$

The observed galaxy number counts are computed in the uniform magnitude bins
within the range of -22.5 $\leqslant$ M${}_{UV}\leqslant$ -17.5 mag, with the
size bin of $\Delta$mag = 1.0, except for the faintest bin which has a size of
$\Delta$mag = 1.5 .In our attempt to compute the UV LF, we also need to
estimate the effective survey volume probed at each intrinsic magnitude (see
Figure 1).

To compute the survey volume, we first determine the survey area as a function
of magnification and the redshift selection function. The effective volume
consists of the co-moving maximal volume, which is distorted by gravitational
lensing multiplied by the completeness function. As a result, the effective
survey volume for each galaxy is expressed as:

$V_{eff,M_{UV,int}}=\int_{z=9}^{z=12}\int_{\mu=1}^{\mu=\mu_{max}}C(M_{UV,int},z)\frac{dV(\mu,z)}{dz}d\mu
dz$ (1)

where, $C$ represents the completeness function, which is computed by
comparing the output catalog with the original input one as a function of the
intrinsic magnitude ($M_{UV,int}$), $\mu$ – the magnification factor at the
given redshift and $\mu_{max}$ is the magnification value at which a galaxy
with a magnitude $M_{UV}$ can be detected, and $dV(\mu,z)$ represents the
volume element available for the selection of a galaxy at a given redshift and
amplification factor. The maximum volume depends mainly on the total surface
area probed by the cluster, which is estimated to be $\sim 35$ arcmin2. The
completeness function values vary between 85% on the bright-end and 10% on the
faint-end. Using this effective survey volume, the intrinsic UV LF can be
calculated as follows:

$\centering\phi(M_{i})dM_{i}=\frac{N_{obj,i}}{V_{eff}(M_{i})}\@add@centering$
(2)

where $N_{obj,i}$ is the number of galaxies within each magnitude bin, and
$V_{eff}(M_{i})$ represents the effective survey volume corresponding to the
$i$th bin of absolute magnitude $M_{i}$. The effective survey volume of the
Abell 2744 cluster is presented in Figure 2. We can see that the curve drops
quickly at the bright-end, where the maximum volume depends mainly on the
surface area with no magnification.

Figure 2: The effective volume as a function of the intrinsic absolute
magnitude. The volume is computed from the completeness function and the
surface area of the UNCOVER field. The 1$\sigma$ uncertainties are represented
by the colored area around the curve.

Figure 3: The galaxy UV luminosity function at $9<z<12$ from the UNCOVER
survey. Left: The red circles, and associated error bars, represent our UV LF
determination. The other points represent binned LF results from the
literature: Recent results by Castellano et al. (2022, gold stars), Harikane
et al. (2023b, green squares), Leung et al. (2023, blue triangles),
Finkelstein et al. (2022a, purple triangles), and Donnan et al. (2023, brown
octagons). Our best-fit DPL function is shown with a red solid line. Right:
Our UV LF results (red points and solid line) together with theoretical
predictions. The light- and dark-grey solid lines represent the Delphi model
estimates at z $\sim$ 10 - 12 (Mauerhofer & Dayal, 2023), and the dark grey
region corresponds to CoDaII constraints at $z=10$ (Ocvirk et al., 2020).
Also, recent results from FIRE-2 (Sun et al., 2023) at different redshifts are
illustrated by solid light- and dark-purple lines. The red shaded area on both
figures indicates uncertainties of the fitting.

To estimate the uncertainties of the UV LF, we considered several sources such
as small-number Poisson statistics (Gehrels, 1986)and cosmic variance, which
was calculated following Trapp & Furlanetto (2020). More importantly, we took
into account statistical uncertainties in the lensing model, which impact both
the amplification factor, the survey area, and to some extent the
completeness. To estimate the systematic uncertainties of the lensing models,
we compared two independent models constructed by Furtak et al. (2023b) and
Bergamini et al. (2023b). Overall, we did not find a significant difference
between the two models, as the intrinsic uncertainties were in good agreement.
Magnification uncertainties from the first lensing model were incorporated
into the observed magnitude uncertainties in addition to the photometric
errors. Then we used the Markov chain Monte Carlo (MCMC) simulations to
explore the full error space for each galaxy, encompassing both photometric
scatter and magnification factor uncertainties. For each of these iterations,
we construct a luminosity function, which allows a galaxy to switch magnitude
bins, hence changing the observed number counts. Regarding the effective
survey volume, we include for each galaxy the $2-\sigma$ survey area
uncertainty as a function of magnification. All these uncertainties were
included in the final UV LF, incorporating the completeness errors in the
process.

Table 3: Binned ultraviolet luminosity function at 9 $<z<$ 12\.  MUV |  Nobj | $\log(\phi)$
---|---|---
|  |  [mag-1Mpc-3]
-22 | 1 |  -5.19 ${}^{+0.63}_{-0.31}$
-21 | 3 |  -4.68 ${}^{+0.36}_{-0.17}$
-20 | 7 |  -4.21 ${}^{+0.42}_{-0.21}$
-19 | 7 |  -4.02 ${}^{+0.47}_{-0.23}$
-17.5 | 1 |  -3.89 ${}^{+1.70}_{-0.86}$

Our determination of the UV LF is shown in Figure 3, together with the recent
results from other surveys in the same redshift range. The tabulated values of
UV LF are presented in Table 3. In general, our sample consists of relatively
bright galaxies ($M_{\rm UV}$< -19), except for one faint galaxy at ($M_{\rm
UV}$< -17.5). The most important result of our study is the apparent
overabundance of bright galaxies compared to theoretical expectations (Mason
et al., 2015; Tacchella et al., 2018; Harikane et al., 2022; Mauerhofer &
Dayal, 2023) or extrapolations from lower-redshift determinations. This excess
is in broad agreement with the most recent JWST results that show a similar
trend (Harikane et al., 2023b; Bouwens et al., 2023; Finkelstein et al.,
2022b; McLeod et al., 2023; Adams et al., 2023).

We fit our LF data points with a double power-law function (e.g., Bowler et
al., 2020; Finkelstein & Bagley, 2022; Donnan et al., 2023), which better
describes the overall functional form of the LF at high redshifts compared to
a classical Schechter (Schechter, 1976) function.

$\phi(M)=\dfrac{\phi^{*}}{10^{0.4(M-M^{*})(\alpha+1)}+10^{0.4(M-M^{*})(\beta+1)}}$
(3)

where $\phi^{*}$ is a normalization, $M^{*}$ represents characteristic
magnitude, $\alpha$ and $\beta$ are the faint-end slope and the bright-end
slope, respectively. Because we mainly probe the bright-end of the LF, we
chose to combine robust literature data points (Harikane et al., 2023b; Leung
et al., 2023; Donnan et al., 2023) and for the faint-end with our results on
the bright-end ($M_{\rm UV}$< -19 mag). To determine the best-fit function, we
applied the Levenberg-Marquardt (LM) approach using MCMC simulations. We fixed
the parameters $M^{*}$ = -20.67 and $\alpha$ = -2.1 in the fitting procedure,
which is similar to the value adopted by recent JWST studies at similar
redshift (Harikane et al., 2023b; Adams et al., 2023).

The results are presented in Table 4, together with the results of recent
studies. The best-fit DPL function is represented by the red curve in Figure
3. We can see that the DPL fits reasonably well the bright-end of the LF,
while our determinations at the faint-end (which are not included in the fit)
are lower, with larger uncertainties. We find a shallower bright-end slope
($\beta=-2.66\pm 1.09$) compared to other studies, albeit with large
uncertainties. Our results are in better agreement with (Castellano et al.,
2022), whose galaxy sample has a significant overlap with our study, although
they used a simple treatment of lensing effects. We also compare our results
with the UV LF predicted by galaxy formation models in a similar redshift
range. Our results are above most theoretical determinations from
hydrodynamical simulations (Ocvirk et al., 2020; Sun et al., 2023) and semi-
analytical models (Mauerhofer & Dayal, 2023). We note that the FIRE (Feedback
In Realistic Environments) simulations reproduce better our results at $z=10$.

##  6 The star formation rate density

We compute the UV luminosity density by integrating the best-fit DPL of
luminosity function down to a magnitude limit of $M_{\rm UV}$ = - 17 mag,
following recent literature results. Adopting a fixed faint-end slope $\alpha$
= -2.1, we obtain log($\rho_{UV}$/ergs s-1 Hz-1 Mpc-3) = 25.3, which is
slightly higher than recent JWST results. A full comparison with recent
literature results is presented in Table 4, alongside the best-fit luminosity
function parameters. Furthermore, we derive the star-formation rate density
($\rho_{SFR}$) using a canonical conversion factor $K_{UV}$ =
1.15$\times$10-28 M⊙ yr-1/erg s-1 Hz-1 (Madau & Dickinson, 2014). In Figure 4,
we show how our results compare with literature values and galaxy formation
models. At similar redshifts, our value is slightly higher than values derived
from the main JWST surveys (Adams et al., 2023; Harikane et al., 2023b).
Within the uncertainties, our result is closer to the results of McLeod et al.
(2023) and Bouwens et al. (2022b), when using their entire sample, including
“possible” high$-z$ candidates.

From the theoretical viewpoint, our results also appear at odds with galaxy
formation models. There has been a long-standing debate about the redshift-
evolution of the star formation efficiency (SFE) during the pre-JWST era. At
redshifts higher than $z=9$ several models argued for a constant SFE, which
were able to reproduce HST observations (e.g. Mason et al., 2015; Oesch et
al., 2018). In Figure 4 we compare our results with predictions of a few
examples of such models. Our derived SFRD value is 4 to 10 times higher than
values predicted by constant-SFE models (Mason et al., 2015; Tacchella et al.,
2018; Harikane et al., 2022). Together with literature results at other
redshifts, this shows a clear excess relative to predictions of constant-SFE
models. Given the reliability of our photometric selection, sample
contamination from low-redshift sources is highly unlikely to explain this
excess.

In a recent spectroscopic follow-up with NIRSpec, Fujimoto et al. (2023) has
explored the AGN nature of 4 confirmed candidates in our sample. One candidate
(ID 26185) is detected in the observed-frame 2–7 keV band in Chandra
observations at a $\sim 4\sigma$ level (Bogdan et al., 2023; Goulding et al.,
2023). Another candidate (ID 20466) shows a broad feature in the H$\beta$
emission line profile but it is not part of our sample. In order to assess the
contribution of these potential AGN sources to the UV LF, and to what extent
they can explain the overabundance of bright galaxies at $z>9$, we recompute
the SFRD without the AGN source. The result is shown with the red empty circle
in Figure 3. The main results remain unchanged. The slightly lower value at
the $M_{\rm UV}$ = -19 mag bin does not affect the best-fit DPL solution.
Therefore, the estimated SFRD in Figure 4 remains virtually the same.

Many recent studies hint at the existence of a substantial population of AGNs
at $5<z<8$ (Matthee et al., 2023; Larson et al., 2023; Kokorev et al., 2023),
with a redder rest-frame optical than UV emission, and which appear more
numerous than UV-selected AGNs. (Labbe et al., 2023; Furtak et al., 2023a;
Greene et al., 2023). Other AGNs have also been identified at $5<z<7$, based
on their broad H$\alpha$ emission line (Harikane et al., 2023a; Maiolino et
al., 2023). The exact contribution of AGNs to the UV luminosity function
remains unclear at this point, as their UV emission could originate from star
formation as well as dust-scatted AGN light. Further SED modeling,
observations in the infrared, and spectroscopic line diagnostics will be
needed to obtain stronger constraints on the AGN contribution.

Figure 4: The star formation rate density (SFRD) at $z\sim 10.5$. Our SFRD
result, integrated down to -17 mag, is shown by a red circle. We also show a
selection of literature results covering a similar redshift range: Bouwens et
al. (2022a, blue points), Harikane et al. (2023b, green points), and Adams et
al. (2023, pink points). The SFR densities derived by Bouwens et al. (2022a)
at $z\sim 10-17$ are shown in light grey, dark pink, and blue shaded regions,
which correspond in their definition to “robust”, “solid”, and “possible”,
candidates, respectively. The gold lines represent theoretical predictions for
the cosmic SFR density as a function of redshift based on the models of Mason
et al. (2015, solid line), Tacchella et al. (2018, dashed line). The yellow
dot-dashed line is the best-fit result of Harikane et al. (2022) at $z<7$,
which was extrapolated to higher redshifts ($z>10$) assuming a constant star
formation efficiency.

Other explanations for the UV LF enhancement at high redshift involve an
evolution of the physical properties of galaxies and the star formation
processes. A decrease in the dust attenuation at higher redshift as a result
of strong outflows expelling gas and dust out of these early galaxies has been
suggested in Ferrara et al. (2022). However, this strong redshift-evolution of
the dust attenuation is currently not supported by the UV colors of galaxies
across $6<z<12$ (Finkelstein et al., 2023). Alternatively, a modification of
the stellar mass-to-light ratio can also explain the UV enhancement while the
underlying mass function remains unchanged. One of the physical processes that
can cause such variation is a stochastic star formation history. Rapid SFR
variations can lead to significant deviations in the M/L ratio, making the UV
luminosity an unreliable tracer of the stellar mass function. However, recent
theoretical efforts have shown significant disagreements regarding the level
of this UV luminosity variation. A model including variability in the physical
processes (SFR, dust, metallicity) predicts the scatter of lower mass galaxies
to brighter luminosity bins due to the steep slope of the LF. A UV luminosity
scatter of $\sigma_{\rm UV}=1.75$ is sufficient to reproduce the observed UV
excess (Shen et al., 2023; Sun et al., 2023). On the other hand,
hydrodynamical simulations that include stochasticity result in significantly
lower values around $\sigma_{\rm UV}=0.6$, which remain below the levels
required to match observations (Pallottini & Ferrara, 2023). Using SED
modeling that includes stochastic SFHs, Ciesla et al. (2023) reach similar
conclusions. Pacucci et al. (2022) show that AGN at high redshifts can also
contribute to such UV excess. Finally, another possible cause for the M/L
deviations is a different initial mass function (IMF) at early epochs. A
different IMF, with a characteristic mass of $M_{c}=10$ M⊙, would decrease the
M/L ratio by a factor of several (Raiter et al., 2010). Although changes in
the IMF are expected at early epochs (e.g.; Steinhardt et al., 2023; Woodrum
et al., 2023; Wang et al., 2023b), no observational evidence of such an
evolution has been reported yet.

Table 4: The best-fit parameters for the double power-law function of recent studies together alongside luminosity consistency and star formation density. Values presented with an asterisk indicate the parameter is fixed to this value in the fitting procedure. Study | z | $\log(\phi)$ | $M^{*}$ | $\alpha$ | $\beta$ | $\log(\rho_{UV})$ | $\log(\rho_{SFR})$ | KUV
---|---|---|---|---|---|---|---|---
|  | [mag-1Mpc-3] | [mag] |  |  | [ergs s-1 Hz-1 Mpc-3 ] | [M⊙yr-1Mpc-3] | [M⊙ yr-1erg-1 s Hz]
Harikane+23 | 9 | -3.50${}^{+1.53}_{-0.65}$ | -19.33${}^{+2.24}_{-0.96}$ | -2.1∗ | -3.27${}^{+0.34}_{-0.37}$ | 25.28${}^{+0.19}_{-0.16}$ | -2.61${}^{+0.19}_{-0.16}$ | 1.15$\times$10-28
Bouwens+23 | 10 | -3.55 $\pm$ 0.14 | -19.67∗ | -2.35∗ | -3.75∗ | 24.69 $\pm$ 0.14 | -3.46 $\pm$ 0.14 | 0.7$\times$10-29
Adams+23 | 10.5 | -4.47 $\pm$ 0.65 | -20.72 $\pm$ 0.97 | -2.1∗ | -4.06 $\pm$ 0.94 | 24.95 $\pm$ 0.41 | -3.01 $\pm$ 0.41 | 1.15$\times$10-28
Leung+23 | 11 | -4.75${}^{+0.15}_{-0.16}$ | -20.99∗ | -2.22${}^{+0.23}_{-0.23}$ | -4.19∗ |  |  |
McLeod+23 | 11 | -4.70 $\pm$ 0.45 | -20.87 $\pm$ 0.62 | -2.35∗ | -4.18 $\pm$ 0.71 | 25.14${}^{+0.10}_{-0.12}$ | 2.80${}^{+0.10}_{-0.12}$ | 1.15$\times$10-28
This work | 10.5 | -4.22 $\pm$ 0.71 | -20.67∗ | -2.1∗ | -2.66 $\pm$ 1.09 | 25.30 $\pm$ 0.36 | -2.64 $\pm$ 0.36 | 1.15$\times$10-28

##  7 Conclusions

In the present paper, we used a sample of $z>9$ galaxies discovered in the
UNCOVER survey to construct a robust UV luminosity function across $9<z<12$.
This high-redshift catalog consists of 16 galaxies observed behind the lensing
cluster A2744 with intrinsic magnitudes between M${}_{UV}\sim$ -22 and -17
mag. Sources were selected using a combination of color-color dropout criteria
and photometric redshift estimates derived from SED fitting (Atek et al.,
2023a). Among these sources, four were followed-up with NIRSpec Prism
observations as part of the UNCOVER survey. All four sources were confirmed
around their photometric redshift (Fujimoto et al., 2023), achieving a 100%
confirmation rate, which underscores the reliability of the present
photometric sample.

To compute the most accurate UV luminosity function at $z>9$ through lensing
clusters, we first conducted a forward modeling procedure to derive the
effective survey volume. By operating directly in the source plane, we
naturally take into account all lensing effects. Furthermore, in order to
assess systematic uncertainties related to lensing, we compared two
independent models derived by Furtak et al. (2023b) and Bergamini et al.
(2023b). The most important result is the overabundance of UV-bright galaxies,
which reach a factor of 10-100 higher than theoretical expectations, or
previous HST observations. Our results confirm the emerging picture describing
a strong redshift-evolution of the physical properties or the physical
processes governing star formation in early galaxies (Harikane et al., 2023b;
Finkelstein et al., 2023; Bouwens et al., 2023). At the same time, given the
depth of these lensing-assisted observations and the supposedly steep faint-
end slope of the LF at these redshifts, the lack of faint galaxies ($M_{\rm
UV}$>-17 mag) in our survey is surprising. It may lead to the dearth of the
low luminosity objects and requires further investigation.

Our determination of the star formation rate density at $z\sim 10.5$ lies
above most theoretical models of galaxy formation (Mason et al., 2015; Ocvirk
et al., 2020; Mauerhofer & Dayal, 2023). Among the variety of scenarios
proposed to explain this excess, star formation stochasticity has been widely
explored. For instance, by including variability in the conversion from dark
matter halo mass to UV luminosity, a dispersion in the UV luminosity of
$\sigma_{\rm UV}$ = 1.5 to 2 is required to match the observations at these
redshifts (e.g. Shen et al., 2023). At the same time, other theoretical
efforts based on hydrodynamical simulations or stellar population modeling
have measured an insufficient variability to explain such excess (Pallottini &
Ferrara, 2023; Ciesla et al., 2023). While early studies indicate that
high$-z$ galaxies experience bursty star formation (Endsley et al., 2023;
Looser et al., 2023), spectroscopic observations of a large sample of these
sources will help constrain the stochastic SFH and the inferred UV luminosity
dispersion. A combination of SED modeling associated with observational
constraints of SFR indicators on different timescales is key to addressing
this question. Such efforts will be largely complemented by wide-area surveys,
such as Euclid, which will uncover thousands of galaxies brighter than $M_{\rm
UV}$ = -21 mag at redshifts higher than $z=8$. Large ground-based
spectroscopic follow-up campaigns will be essential for their redshift
confirmation.

Stellar feedback, which causes large variations in star formation history,
predominantly affects low-mass galaxies. They are therefore the best sites to
study the strength and the effects of stochasticity on the observed physical
properties in general. Ultra-deep JWST imaging surveys such as GLIMPSE (PID
3293) are set to measure the prevalence of ultra-faint galaxies at $z>6$ and
infer the constraints on the implementation of feedback in galaxy formation
models. Such surveys will also probe the so far elusive, yet supposedly
common, population of faint galaxies during the Dark Ages, to test whether
this surprising redshift-evolution of bright galaxies also applies to low-mass
galaxies, which are expected to be the dominant population at early epochs.

## Acknowledgments

This work is based on observations obtained with the NASA/ESA/CSA JWST and the
NASA/ESA Hubble Space Telescope (HST), retrieved from the Mikulski Archive for
Space Telescopes (MAST) at the Space Telescope Science Institute (STScI).
STScI is operated by the Association of Universities for Research in
Astronomy, Inc. under NASA contract NAS 5-26555. This work was supported by
CNES, focused on the JWST mission. This work was supported by the Programme
National Cosmology and Galaxies (PNCG) of CNRS/INSU with INP and IN2P3, co-
funded by CEA and CNES. This work has made use of the CANDIDE Cluster at the
Institut d’Astrophysique de Paris (IAP), made possible by grants from the PNCG
and the region of Île de France through the program DIM-ACAV+, and the Cosmic
Dawn Center and maintained by S. Rouberol. AZ acknowledges support by grant
No. 2020750 from the United States-Israel Binational Science Foundation (BSF)
and grant No. 2109066 from the United States National Science Foundation
(NSF); by the Israel Science Foundation grant No. 864/23; and by the Ministry
of Science & Technology, Israel. PD acknowledges support from the NWO grant
016.VIDI.189.162 (“ODIN") and from the European Commission’s and University of
Groningen’s CO-FUND Rosalind Franklin program.

## Data Availability

The data underlying this article are publicly available on the Mikulski
Archive for Space Telescopes222https://archive.stsci.edu/ (MAST), under
program ID 2561. Reduced and calibrated mosaics, as well as lensing products,
are available on the UNCOVER webpage: https://jwst-uncover.github.io/

## References

  * Adams et al. (2023) Adams N. J., et al., 2023, MNRAS, 518, 4755
  * 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, ApJ, 951, L22
  * Atek et al. (2018) Atek H., Richard J., Kneib J.-P., Schaerer D., 2018, MNRAS, 479, 5184
  * Atek et al. (2023a) Atek H., et al., 2023a, MNRAS, 519, 1201
  * Atek et al. (2023b) Atek H., et al., 2023b, MNRAS, 524, 5486
  * Austin et al. (2023) Austin D., et al., 2023, arXiv e-prints, p. arXiv:2302.04270
  * Bergamini et al. (2023a) Bergamini P., et al., 2023a, A&A, 670, A60
  * Bergamini et al. (2023b) Bergamini P., et al., 2023b, ApJ, 952, 84
  * 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
  * Bogdan et al. (2023) Bogdan A., et al., 2023, arXiv e-prints, p. arXiv:2305.15458
  * Bouwens et al. (2022a) Bouwens R. J., et al., 2022a, arXiv e-prints, p. arXiv:2211.02607
  * Bouwens et al. (2022b) Bouwens R. J., et al., 2022b, ApJ, 931, 160
  * Bouwens et al. (2023) Bouwens R., Illingworth G., Oesch P., Stefanon M., Naidu R., van Leeuwen I., Magee D., 2023, MNRAS, 523, 1009
  * 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
  * Brammer et al. (2022) Brammer G., Strait V., Matharu J., Momcheva I., 2022, grizli, Zenodo, doi:10.5281/zenodo.6672538
  * Bunker et al. (2023a) Bunker A. J., et al., 2023a, arXiv e-prints, p. arXiv:2302.07256
  * Bunker et al. (2023b) Bunker A. J., et al., 2023b, arXiv e-prints, p. arXiv:2306.02467
  * Castellano et al. (2022) Castellano M., et al., 2022, arXiv e-prints, p. arXiv:2212.06666
  * Chevallard & Charlot (2016) Chevallard J., Charlot S., 2016, MNRAS, 462, 1415
  * Ciesla et al. (2023) Ciesla L., et al., 2023, arXiv e-prints, p. arXiv:2309.15720
  * Curtis-Lake et al. (2022) Curtis-Lake E., et al., 2022, arXiv e-prints, p. arXiv:2212.04568
  * Dayal et al. (2022) Dayal P., et al., 2022, MNRAS, 512, 989
  * Dekel et al. (2023) Dekel A., Sarkar K. S., Birnboim Y., Mandelker N., Li Z., 2023, arXiv e-prints, p. arXiv:2303.04827
  * Donnan et al. (2023) Donnan C. T., et al., 2023, MNRAS, 518, 6011
  * Endsley et al. (2023) Endsley R., et al., 2023, arXiv e-prints, p. arXiv:2306.05295
  * Ferrara et al. (2022) Ferrara A., Pallottini A., Dayal P., 2022, arXiv e-prints, p. arXiv:2208.00720
  * Finkelstein & Bagley (2022) Finkelstein S. L., Bagley M. B., 2022, ApJ, 938, 25
  * Finkelstein et al. (2022a) Finkelstein S. L., et al., 2022a, arXiv e-prints, p. arXiv:2211.05792
  * Finkelstein et al. (2022b) Finkelstein S. L., et al., 2022b, ApJ, 940, L55
  * Finkelstein et al. (2023) Finkelstein S. L., et al., 2023, arXiv e-prints, p. arXiv:2311.04279
  * Fujimoto et al. (2023) Fujimoto S., et al., 2023, arXiv e-prints, p. arXiv:2308.11609
  * Furtak et al. (2023a) Furtak L. J., et al., 2023a, arXiv e-prints, p. arXiv:2308.05735
  * Furtak et al. (2023b) Furtak L. J., et al., 2023b, MNRAS, 523, 4568
  * Furtak et al. (2023c) Furtak L. J., et al., 2023c, ApJ, 952, 142
  * Gehrels (1986) Gehrels N., 1986, ApJ, 303, 336
  * Goulding et al. (2023) Goulding A. D., et al., 2023, ApJ, 955, L24
  * Greene et al. (2023) Greene J. E., et al., 2023, arXiv e-prints, p. arXiv:2309.05714
  * Hainline et al. (2023) Hainline K. N., et al., 2023, arXiv e-prints, p. arXiv:2306.02468
  * Harikane et al. (2022) Harikane Y., et al., 2022, ApJS, 259, 20
  * Harikane et al. (2023a) Harikane Y., et al., 2023a, arXiv e-prints, p. arXiv:2303.11946
  * Harikane et al. (2023b) Harikane Y., et al., 2023b, ApJS, 265, 5
  * Hsiao et al. (2023) Hsiao T. Y.-Y., et al., 2023, arXiv e-prints, p. arXiv:2305.03042
  * Hutter et al. (2021) Hutter A., Dayal P., Yepes G., Gottlöber S., Legrand L., Ucci G., 2021, MNRAS, 503, 3698
  * Jakobsen et al. (2022) Jakobsen P., et al., 2022, A&A, 661, A80
  * Kokorev et al. (2023) Kokorev V., et al., 2023, arXiv e-prints, p. arXiv:2308.11610
  * Labbe et al. (2023) Labbe I., et al., 2023, arXiv e-prints, p. arXiv:2306.07320
  * Larson et al. (2023) Larson R. L., et al., 2023, ApJ, 953, L29
  * Leung et al. (2023) Leung G. C. K., et al., 2023, ApJ, 954, L46
  * Looser et al. (2023) Looser T. J., et al., 2023, arXiv e-prints, p. arXiv:2306.02470
  * Lotz et al. (2017) Lotz J. M., et al., 2017, ApJ, 837, 97
  * Madau & Dickinson (2014) Madau P., Dickinson M., 2014, ARA&A, 52, 415
  * Maiolino et al. (2023) Maiolino R., et al., 2023, arXiv e-prints, p. arXiv:2308.01230
  * Mason et al. (2015) Mason C., Trenti M., Treu T., 2015, preprint,  (arXiv:1508.01204)
  * Mason et al. (2023) Mason C. A., Trenti M., Treu T., 2023, MNRAS, 521, 497
  * Matthee et al. (2023) Matthee J., et al., 2023, arXiv e-prints, p. arXiv:2306.05448
  * Mauerhofer & Dayal (2023) Mauerhofer V., Dayal P., 2023, MNRAS, 526, 2196
  * McLeod et al. (2023) McLeod D. J., et al., 2023, arXiv e-prints, p. arXiv:2304.14469
  * Morishita et al. (2023) Morishita T., et al., 2023, ApJ, 947, L24
  * Muñoz et al. (2023) Muñoz J. B., Mirocha J., Furlanetto S., Sabti N., 2023, MNRAS, 526, L47
  * Naidu et al. (2022a) Naidu R. P., et al., 2022a, arXiv e-prints, p. arXiv:2208.02794
  * Naidu et al. (2022b) Naidu R. P., et al., 2022b, ApJ, 940, L14
  * Ocvirk et al. (2020) Ocvirk P., et al., 2020, MNRAS, 496, 4087
  * Oesch et al. (2018) Oesch P. A., Bouwens R. J., Illingworth G. D., Labbé I., Stefanon M., 2018, ApJ, 855, 105
  * Ono et al. (2018) Ono Y., et al., 2018, PASJ, 70, S10
  * Pacucci et al. (2022) Pacucci F., Dayal P., Harikane Y., Inoue A. K., Loeb A., 2022, MNRAS, 514, L6
  * Pallottini & Ferrara (2023) Pallottini A., Ferrara A., 2023, A&A, 677, L4
  * Pascale et al. (2022) Pascale M., et al., 2022, ApJ, 938, L6
  * Pei (1992) Pei Y. C., 1992, ApJ, 395, 130
  * Pontoppidan et al. (2022) Pontoppidan K. M., et al., 2022, ApJ, 936, L14
  * Raiter et al. (2010) Raiter A., Schaerer D., Fosbury R. A. E., 2010, A&A, 523, A64
  * Rieke et al. (2023) Rieke M. J., et al., 2023, PASP, 135, 028001
  * Roberts-Borsani et al. (2022) Roberts-Borsani G., et al., 2022, ApJ, 938, L13
  * Roberts-Borsani et al. (2023) Roberts-Borsani G., et al., 2023, Nature, 618, 480
  * Robertson et al. (2023) Robertson B. E., et al., 2023, Nature Astronomy, 7, 611
  * Rowe et al. (2015) Rowe B. T. P., et al., 2015, Astronomy and Computing, 10, 121
  * Schechter (1976) Schechter P., 1976, ApJ, 203, 297
  * Shen et al. (2023) Shen X., Vogelsberger M., Boylan-Kolchin M., Tacchella S., Kannan R., 2023, MNRAS, 525, 3254
  * Shibuya et al. (2015) Shibuya T., Ouchi M., Harikane Y., 2015, ApJS, 219, 15
  * Steinhardt et al. (2020) Steinhardt C. L., et al., 2020, ApJS, 247, 64
  * Steinhardt et al. (2023) Steinhardt C. L., Kokorev V., Rusakov V., Garcia E., Sneppen A., 2023, ApJ, 951, L40
  * Sun et al. (2023) Sun G., Faucher-Giguère C.-A., Hayward C. C., Shen X., Wetzel A., Cochrane R. K., 2023, ApJ, 955, L35
  * Tacchella et al. (2018) Tacchella S., Bose S., Conroy C., Eisenstein D. J., Johnson B. D., 2018, ApJ, 868, 92
  * Trapp & Furlanetto (2020) Trapp A. C., Furlanetto S. R., 2020, MNRAS, 499, 2401
  * Treu et al. (2022) Treu T., et al., 2022, ApJ, 935, 110
  * Ucci et al. (2021) Ucci G., et al., 2021, MNRAS, 506, 202
  * Wang et al. (2023a) Wang B., et al., 2023a, arXiv e-prints, p. arXiv:2308.03745
  * Wang et al. (2023b) Wang B., et al., 2023b, arXiv e-prints, p. arXiv:2310.06781
  * Weaver et al. (2023) Weaver J. R., et al., 2023, arXiv e-prints, p. arXiv:2301.02671
  * Whitler et al. (2023) Whitler L., Endsley R., Stark D. P., Topping M., Chen Z., Charlot S., 2023, MNRAS, 519, 157
  * Woodrum et al. (2023) Woodrum C., et al., 2023, arXiv e-prints, p. arXiv:2310.18464
  * Yang et al. (2022) Yang L., et al., 2022, AJL, 938, L17
  * Zavala et al. (2023) Zavala J. A., et al., 2023, ApJ, 943, L9
  * Zitrin et al. (2015) Zitrin A., et al., 2015, ApJ, 801, 44