#  UNCOVER: A NIRSpec Census of Lensed Galaxies at $z=8.50$–13.08
Probing a High AGN Fraction and Ionized Bubbles in the Shadow

Seiji Fujimoto Hubble Fellow  Department of Astronomy, The University of Texas
at Austin, Austin, TX 78712, USA  Bingjie Wang Department of Astronomy &
Astrophysics, The Pennsylvania State University, University Park, PA 16802,
USA  Institute for Computational & Data Sciences, The Pennsylvania State
University, University Park, PA 16802, USA  Institute for Gravitation and the
Cosmos, The Pennsylvania State University, University Park, PA 16802, USA
John R. Weaver Department of Astronomy, University of Massachusetts, Amherst,
MA 01003, USA  Vasily Kokorev Kapteyn Astronomical Institute, University of
Groningen, 9700 AV Groningen, The Netherlands  Hakim Atek Institut
d’Astrophysique de Paris, CNRS, Sorbonne Université, 98bis Boulevard Arago,
75014, Paris, France  Rachel Bezanson Department of Physics and Astronomy and
PITT PACC, University of Pittsburgh, Pittsburgh, PA 15260, USA  Ivo Labbe
Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Melbourne, VIC 3122, Australia  Gabriel Brammer Cosmic Dawn Center
(DAWN), Niels Bohr Institute, University of Copenhagen, Jagtvej 128, København
N, DK-2200, Denmark  Jenny E. Greene Department of Astrophysical Sciences,
Princeton University, 4 Ivy Lane, Princeton, NJ 08544  Iryna Chemerynska
Institut d’Astrophysique de Paris, CNRS, Sorbonne Université, 98bis Boulevard
Arago, 75014, Paris, France  Pratika Dayal Kapteyn Astronomical Institute,
University of Groningen, 9700 AV Groningen, The Netherlands  Anna de Graaff
Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117, Heidelberg,
Germany  Lukas J. Furtak Physics Department, Ben-Gurion University of the
Negev, P.O. Box 653, Be’er-Sheva 84105, Israel  Pascal A. Oesch Department of
Astronomy, University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland
Cosmic Dawn Center (DAWN), Niels Bohr Institute, University of Copenhagen,
Jagtvej 128, København N, DK-2200, Denmark  David J. Setton Department of
Physics and Astronomy and PITT PACC, University of Pittsburgh, Pittsburgh, PA
15260, USA  Sedona H. Price Department of Physics and Astronomy and PITT PACC,
University of Pittsburgh, Pittsburgh, PA 15260, USA  Tim B. Miller Department
of Astronomy, Yale University, New Haven, CT 06511, USA  Center for
Interdisciplinary Exploration and Research in Astrophysics (CIERA) and
Department of Physics and Astronomy, Northwestern University, 1800 Sherman
Ave, Evanston IL 60201, USA  Christina C. Williams NSF’s National Optical-
Infrared Astronomy Research Laboratory, 950 N. Cherry Avenue, Tucson, AZ
85719, USA  Steward Observatory, University of Arizona, 933 North Cherry
Avenue, Tucson, AZ 85721, USA  Katherine E. Whitaker Department of Astronomy,
University of Massachusetts, Amherst, MA 01003, USA  Adi Zitrin Physics
Department, Ben-Gurion University of the Negev, P.O. Box 653, Be’er-Sheva
84105, Israel  Sam E. Cutler Department of Astronomy, University of
Massachusetts, Amherst, MA 01003, USA  Joel Leja Department of Astronomy &
Astrophysics, The Pennsylvania State University, University Park, PA 16802,
USA  Institute for Computational & Data Sciences, The Pennsylvania State
University, University Park, PA 16802, USA  Institute for Gravitation and the
Cosmos, The Pennsylvania State University, University Park, PA 16802, USA
Richard Pan Department of Physics and Astronomy, Tufts University, 574 Boston
Ave., Medford, MA 02155, USA  Dan Coe Space Telescope Science Institute
(STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA  Association of
Universities for Research in Astronomy (AURA), Inc. for the European Space
Agency (ESA)  Center for Astrophysical Sciences, Department of Physics and
Astronomy, The Johns Hopkins University, 3400 N Charles St. Baltimore, MD
21218, USA  Pieter van Dokkum Department of Astronomy, Yale University, New
Haven, CT 06511, USA  Robert Feldmann Institute for Computational Science,
University of Zurich, Zurich, CH-8057, Switzerland  Yoshinobu Fudamoto Waseda
Research Institute for Science and Engineering, Faculty of Science and
Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan
National Astronomical Observatory of Japan, 2-21-1, Osawa, Mitaka, Tokyo,
Japan  Andy D. Goulding Department of Astrophysical Sciences, Princeton
University, 4 Ivy Lane, Princeton, NJ 08544  Gourav Khullar Department of
Physics and Astronomy and PITT PACC, University of Pittsburgh, Pittsburgh, PA
15260, USA  Danilo Marchesini Physics and Astronomy Department, Tufts
University, 574 Boston Ave., Medford, MA 02155, USA  Michael Maseda Department
of Astronomy, University of Wisconsin-Madison, 475 N. Charter St., Madison, WI
53706 USA  Themiya Nanayakkara Centre for Astrophysics and Supercomputing,
Swinburne University of Technology, Melbourne, VIC 3122, Australia  Erica J.
Nelson Department for Astrophysical and Planetary Science, University of
Colorado, Boulder, CO 80309, USA  Renske Smit Astrophysics Research Institute,
Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK
Mauro Stefanon Departament d’Astronomia i Astrofìsica, Universitat de
València, C. Dr. Moliner 50, E-46100 Burjassot, València, Spain  Unidad
Asociada CSIC ”Grupo de Astrofísica Extragaláctica y Cosmología” (Instituto de
Física de Cantabria - Universitat de València)  Andrea Weibel Department of
Astronomy, University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland

###### Abstract

We present JWST NIRSpec prism spectroscopy of lensed galaxies at $z\gtrsim 9$
found behind the massive galaxy cluster Abell 2744 in the UNCOVER Cycle 1
Treasury Program. We confirm the redshift via emission lines and/or the
Ly$\alpha$ break for ten galaxies at $z=8.$50–13.08 down to
$M_{\rm\,UV}=-17.3$. We achieve a 100% confirmation rate for $z>9$ candidates
reported in Atek et al. (2023b). Using six sources with multiple line
detections, we find that offsets in redshift estimates between the lines and
the Ly$\alpha$ break alone can be $\pm 0.2$, raising caution in designing
future follow-up spectroscopy for the break-only sources. With spec-$z$
confirmed sources in UNCOVER and literature, we derive lower limits on the
rest-frame ultraviolet (UV) luminosity function (LF) at $z\simeq 9$–12 and
find that these lower limits agree with recent photometric measurements. We
identify at least two unambiguous and several possible active galactic nucleus
(AGN) systems based on X-ray, broad H$\beta$, high ionization lines (e.g., N
iv] $\lambda$1487, C iv $\lambda$1549), and excess in UVLF. This requires the
AGN LFs at $z\simeq$9–10 to be comparable or even higher than the X-ray AGN LF
estimated at $z\sim 6$ and suggests a plausible cause of the high abundance of
$z>9$ galaxies claimed in the recent photometric measurements is AGNs. One UV-
luminous source is confirmed at the same redshift as a broad-line AGN at
$z=8.50$ with a physical separation of 380 kpc in the source plane. These two
sources show the emission blueward of Ly$\alpha$, indicating a giant ionized
bubble enclosing them with a radius of $7.69\pm 0.18$ pMpc. Our results imply
that AGNs have a non-negligible contribution to cosmic reionization.

Early universe (435); Galaxy formation (595); Galaxy evolution (594); High-
redshift galaxies (734)

††journal: ApJ††software: msaexp (0.6.10; Brammer 2022), astropy (Astropy
Collaboration et al. 2013), eazy (Brammer et al. 2008), FSPS (Conroy & Gunn
2010), Prospector (Johnson et al. 2021).

##  1 Introduction

Studying early galaxies provides key clues to understanding fundamental
cosmological questions such as dark matter assembly, the development of large-
scale structure, the emergence of the first galaxies and black holes, and the
processes that govern cosmic reionization and early galaxy formation and
evolution (e.g., Dayal & Ferrara 2018; Inayoshi et al. 2020). In the last
decades, deep Hubble Space Telescope (HST) surveys have succeeded in
discovering thousands of galaxies in the Epoch of Reionization (EoR)
$6\lesssim z\lesssim 11$, providing valuable photometric insights for these
galaxies, including an initial characterization of the stellar component, in
terms of un-obscured star formation rates and sizes (e.g., Ellis et al. 2013;
Bouwens et al. 2015; Finkelstein et al. 2015; Oesch et al. 2016; Bhatawdekar
et al. 2019).

The advent of JWST (Gardner et al. 2023) has led to significant progress in
discovering and investigating galaxies at very early cosmic epochs. As
demonstrated in the Early Release Observations (ERO; Pontoppidan et al. 2022)
and the Early Release Science programs (ERS; e.g., Treu et al. 2022;
Finkelstein et al. 2023), dozens of high-redshift galaxy candidates have been
identified at $z\simeq$ 9–17 towards both lensing clusters and blank fields
(e.g., Adams et al. 2022; Atek et al. 2022, 2023b; Bouwens et al. 2022b;
Bradley et al. 2022; Castellano et al. 2022; Donnan et al. 2023; Finkelstein
et al. 2022b, 2023; Harikane et al. 2023b; Labbe et al. 2022; Morishita &
Stiavelli 2022; Naidu et al. 2022c; Yan et al. 2022; Williams et al. 2023;
Austin et al. 2023; Leung et al. 2023). Their abundance at the bright-end
($M_{\rm UV}\lesssim-20$) exceeds nearly all theoretical predictions so far
(e.g., Behroozi & Silk 2015; Dayal et al. 2017; Yung et al. 2019, 2020;
Behroozi et al. 2019, 2020; Davé et al. 2019; Wilkins et al. 2022b, a; Kannan
et al. 2022; Mason et al. 2022; Mauerhofer & Dayal 2023), suggesting several
possibilities, including that star formation in early systems is dominated by
a top-heavy initial mass function (IMF), complete lack of dust attenuation,
stochastic star-formation, and/or the emergence of the active galactic nucleus
(AGN) population (e.g., Harikane et al. 2023b; Finkelstein et al. 2023;
Pacucci et al. 2022; Ferrara et al. 2022; Boylan-Kolchin 2022; Lovell et al.
2022; Menci et al. 2022; Sun et al. 2023).

JWST NIRSpec follow-up spectroscopy has been performed for several bright
galaxy candidates at $z\simeq 10$–17, including Director’s Discretionary Time
(DDT). These follow-up observations confirm the source redshifts via emission
lines and/or the unambiguous Lyman-$\alpha$ break feature at $z=9.5$–13.2
(Williams et al. 2022; Roberts-Borsani et al. 2022; Bunker et al. 2023b;
Curtis-Lake et al. 2023; Arrabal Haro et al. 2023b, a; Hsiao et al. 2023;
Harikane et al. 2023a; Wang et al. 2023b). However, one remarkably UV-bright
($M_{\rm UV}\simeq-22$) galaxy candidate at $z\simeq 16$ turns out to be
$z=4.9$ with strong emission lines and red continuum that mimic the expected
colors of more distant objects (Naidu et al. 2022a; Zavala et al. 2023;
Fujimoto et al. 2022b; McKinney et al. 2023; Arrabal Haro et al. 2023b).
Recent JWST spectroscopic observations also find a numerous number of faint
AGN populations at $z\simeq 4$–7 (e.g., Kocevski et al. 2023; Harikane et al.
2023c; Matthee et al. 2023; Maiolino et al. 2023b), indicative of steeper
faint ends in the quasar/AGN LFs than suggested in previous studies, and some
studies suggest the identification of AGNs even at higher redshifts at $z\sim
9-11$ (Larson et al. 2023; Goulding et al. 2023; Maiolino et al. 2023c). These
results indicate the critical importance of spectroscopy in order to foremost
confirm the high-redshift nature of galaxy candidates and consequently verify
earlier (photometric) claims of a high abundance of $z\gtrsim 9$ galaxy
candidates in order to investigate its origins.

In this paper, we present JWST NIRSpec prism follow-up observations of
$z\gtrsim 9$ galaxy candidates, including an X-ray luminous supermassive black
hole (Goulding et al. 2023) and two $z>12$ galaxies (Wang et al. 2023b), all
identified in the Cycle 1 Treasury program of Ultradeep NIRSpec and NIRCam
Observations before the Epoch of Reionization survey (UNCOVER; #2561, PIs: I.
Labbe & R. Bezanson; Bezanson et al. 2022). This is the most extensive follow-
up program with NIRSpec prism in Cycle 1 for JWST-selected galaxy candidates
towards a massive lensing cluster, providing a unique opportunity for a
spectroscopic study for a large sample in the early universe over a wide UV
luminosity range. Following the recent successful spectroscopic confirmation
of the high redshift galaxies with JWST, this enlarges the spectroscopic
sample at $z\gtrsim 9$ for faint sources ($M_{\rm UV}>-19$) by a factor of
$\sim 3$ and further allows detailed investigations into the UV luminosity
function (LF) shape and the characterization of the high-redshift galaxy
population newly identified with JWST. In Section 2, we briefly describe
observations and data processing. Section 3 outlines our methods and results
for the redshift measurements. In Section 4, we present our UV LF measurements
at $z\simeq 9$–12 and a potential high abundance of AGN. In Section 5, we
report a discovery of a giant ionized bubble at $z=8.5$ and discuss the
contribution of AGN to forming it. We summarize this study in Section 6.
Throughout this paper, we assume a flat universe with $\Omega_{\rm m}=0.3$,
$\Omega_{\Lambda}=0.7$, $\sigma_{8}=0.8$, and $H_{0}=70$ km s-1 Mpc-1 (Hinshaw
et al. 2013). All magnitudes are expressed in the AB system (Oke & Gunn 1983).

##  2 Observations and Data processing

The JWST/NIRCam (Rieke et al. 2003, 2005; Beichman et al. 2012; Rieke et al.
2023) and NIRSpec (Jakobsen et al. 2022) data employed in this paper were
taken as a part of the UNCOVER survey (Bezanson et al. 2022). While the
complete descriptions of the NIRCam observations and NIRSpec observations are
presented in Weaver et al. (2023) and S. Price et al. in (prep.),
respectively, we briefly describe each part in the following subsection.

###  2.1 UNCOVER Survey

Abell 2744 (A2744) is among the most extensively studied massive galaxy
clusters at $z=0.308$ and serves as the focal point of the UNCOVER survey.
A2744 has been subjected to detailed observations using the Hubble Space
Telescope (HST) as one of the clusters observed in the Hubble Frontier Field
survey (HFF; Lotz et al. 2017). The sky area of A2744 has a low infrared
background, and its high magnification areas match well with the NIRCam field
of view. Multiple JWST Cycle 1 and 2 observations, including GTO, ERS, GO, and
DDT programs, have been conducted and further planned towards this cluster.
Specifically, a GO treasury program under the JWST Cycle 1 – UNCOVER (#2561;
PIs I. Labbe & R. Bezanson) is designed to acquire in-depth NIRCam and NIRSpec
observations over an extended $4^{\prime}\times 6^{\prime}$ area (Bezanson et
al. 2022), enveloping the area with magnifications of $\mu\geq 2$ encompassing
the primary cluster observed in HFF and two supplementary cluster cores in the
northern and north-west regions (Furtak et al. 2023c). UNCOVER consists of two
parts: 1) a deep NIRCam pre-imaging mosaic in 7 filters for $\sim 4-6$ hours
per band taken in November 2022, and 2) a $\sim 24$-hour NIRSpec prism low-
resolution follow-up of NIRCam-detected high-redshift galaxies in July-August
2023.

Figure 1:  NIRCam RGB (R: F444W, G: F356W, B: F277W) map of A2744 taken in
UNCOVER (Bezanson et al. 2022). The white-shaded region indicates the highly
magnified area with magnifications of $\geq 2$ (Furtak et al. 2023c). The
yellow squares show the positions of the 10 sources that are spectroscopically
confirmed at $z\geq 8.5$ in UNCOVER.  Figure 2:  Zoom-in $3\mbox{\kern
0.55974pt.\kern-4.09024pt\arcsec\kern-0.43057pt}6\times 3\mbox{\kern
0.55974pt.\kern-4.09024pt\arcsec\kern-0.43057pt}6$ NIRCam RGB (R: F444W, G:
F356W, B: F277W) cutouts of the 10 sources whose spec-$z$ are successfully
confirmed. The rectangles show the shutter configurations, where the standard
three-shutter slitlets and a three-point nodding were adopted, and thus the
five shutter positions are presented. The white, magenta, yellow, orange, red,
and cyan rectangles represent our MSA observations of MSA-2, 3, 4, 5, 6, and
7, respectively, where MSA-5, 6, and 7 overlap nearly entirely.

###  2.2 NIRCam data & Target selection

The galaxies discussed in this paper are selected from the UNCOVER NIRCam data
taken in November 2022 (Bezanson et al. 2022). The Weaver et al. (2023)
photometric catalog includes the measurements over the full NIRCam wavelength
range in the F115W, F150W, F200W, F277W, F356W, F410M, and F444W filters,
which have exposures of 3.7–6.0 hours per filter, as well as existing HST
Advanced Camera for Surveys (ACS) and WFC3 F606W, F814W, F105W, F125W, F140W,
and F160W filters. The galaxy candidates at $z\gtrsim 9$ are selected based on
photometric redshift $z_{\rm photo}$ estimates from several SED analyses led
by UNCOVER team members (e.g., Atek et al. 2023b; B. Wang et al. submitted),
while we also add several sources by visually checking the NIRCam SEDs and
image cutouts in a less conservative sample selected based on photometric
redshifts inferred from EAZY (Brammer et al. 2008) and Prospector (Johnson et
al. 2021; Wang et al. 2023a) in order not to miss possible candidates.
Together with other exciting high-redshift source candidates (e.g., faint
AGNs, quiescent galaxies, strongly magnified and multiply imaged sources), the
NIRSpec Multiobject Spectroscopy (MOS) configurations with the multi-shutter
array (MSA) were designed to maximize the number of observed exciting
candidates. We used seven MSA masks in our observations, referred to as MSA-1
through MSA-7. In this paper, we present ten sources whose redshifts are
successfully confirmed at $z\geq 8.5$ among a total of 680 MOS targets
(Section 3.1). In Figure 1, we show the distribution of the ten galaxies in
A2744, and Figure 2 presents their NIRCam RGB color images with their MSA
shutter configurations.

###  2.3 NIRSpec Data processing

The data were reduced using the STScI JWST pipeline for Level 1 data products
and processed with msaexp111https://github.com/gbrammer/msaexp that is built
on custom routines for further corrections in addition to the STScI pipeline
routines to generate Level 2 and 3 products. The full descriptions of the
NIRSpec data reduction will be presented in S. Price et al., in preparation
(see also Goulding et al. 2023; Wang et al. 2023b). Briefly, the data
reduction was processed from the raw data files by using the Detector1Pipeline
routine in combination with the latest batch of reference files
(jwst_1100.pmap) to correct detector-level artifacts and to convert the data
into count rate images. We then leverage custom pre-processing procedures from
msaexp to correct for 1/$f$ noise, remove “snowballs” and bias on a per
exposure basis before executing several STScI routines from the Spec2Pipeline
to generate the final 2D cutout images. The AssignWcs, Extract2dStep,
FlatFieldStep, and PhotomStep routines are utilized to perform WCS
registration, flat fielding, and flux calibration. The PathLossStep accounting
for the slitloss correction is turned off at this stage of the reduction
process. Instead, we perform slitloss corrections by applying a wavelength-
independent calibration to scale the normalization of the spectrum to the
photometry. We undertake background subtraction locally, employing a three-
shutter nod pattern before mapping the resultant images onto a uniform grid.
From that point, we extract the spectra optimally through an inverse-variance
weighted kernel derived by collapsing the 2D spectrum along the dispersion
axis and fitting the ensuing signal along the spatial axis with a Gaussian
profile. In some cases (ID31028, ID13151, ID13077), this Gaussian fitting is
challenging due to the low SNR of the trace or the contamination of nearby
sources in the shutters, and we manually set the Gaussian profile for the
extraction. In Figure 3, we show the 2$\sigma$ range of the Gaussian profile
used to extract the 2D spectrum.

##  3 Spectroscopic Redshift

###  3.1 Measurements & Results

Figure 3:  2D and 1D prism spectra for the ten sources whose spec-$z$ are
successfully confirmed $z\geq 8.5$ in this study. The red horizontal lines
indicate the 2$\sigma$ range of the Gaussian, which is used for extracting the
1D spectrum shown in the bottom panel. The orange and green vertical lines
denote wavelengths of the Ly$\alpha$ break and the faint emission lines
detected at SNR $\geq$ 2.5, respectively. The right panel shows the likelihood
of the source redshift $P(z)$ estimated from the eazy template fitting to the
prism spectrum, and the best-fit SED (forced at $z<6$) is presented with the
red (blue) curve overlaid on the 1D spectrum.

Figure 3 (continued)

Figure 4:  Redshift vs $M_{\rm UV}$. The magnification correction is applied
for the lensed sources. The red circles represent our spec-$z$ confirmed
sources in UNCOVER at $z\geq 8.5$, efficiently increasing the sample at a
faint ($M_{\rm UV}\gtrsim-19$) and high-redshift ($z\gtrsim 9.5$) regime. The
gold pentagons and the black squares show recent JWST spectroscopic results
from other field surveys of JADES (e.g., Bunker et al. 2023b) & FRESCO (e.g,
Oesch et al. 2023) and CEERS (e.g., Finkelstein et al. 2023), respectively,
where the values are taken from Hainline et al. (2023). The blue triangles
denote recent JWST/NIRSpec observation results for high-redshift lensed
galaxies (Hsiao et al. 2023; Williams et al. 2023). The grey crosses indicate
the photometric candidates with NIRCam publicly available in JADES v1.0
catalog (Hainline et al. 2023).  Table 1: Summary of Spectroscopically-
Confirmed Sources at $z\geq 8.5$ in UNCOVER

ID | R.A. | Dec | $z_{\rm spec}$ | F200W | F444W | $\mu$ | $M_{\rm UV}$ | Spec. feature | $T_{\rm exp.}$ | Photo Ref. | Spec Ref. | AGN$?$
---|---|---|---|---|---|---|---|---|---|---|---|---
| deg | deg |  | mag | mag |  |  |  | hours |  |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) |
20466 | 3.640408393 | $-30.38643761$ | $8.500^{+0.000}_{-0.001}$ | 28.47 | 26.20 | $1.3^{+0.0}_{-0.0}$ | $-18.11$ | Break, Line | 2.7 (2) | L23 | This | Y†
10646 | 3.636959984 | $-30.40636156$ | $8.511^{+0.000}_{-0.001}$ | 25.35 | 24.09 | $1.4^{+0.0}_{-0.0}$ | $-21.56$ | Break, Line | 2.7 (2) |  $\cdots$ | This | Y/N$\flat$
3686 | 3.617202003 | $-30.42553381$ | $9.325^{+0.000}_{-0.001}$ | 25.12 | 25.08 | $1.6^{+0.0}_{-0.0}$ | $-21.72$ | Break, Line | 2.7 (2) | A23 | B23, This | Y/N
22223 | 3.568114512 | $-30.38305164$ | $9.568^{+0.000}_{-0.001}$ | 28.68 | 28.74 | $3.9^{+0.3}_{-0.1}$ | $-17.28$ | Break, Line | 4.4 (4) |  $\cdots$ | This | N
31028 | 3.544169292 | $-30.37031863$ | $9.740^{+0.000}_{-0.001}$ | 27.46 | 27.48 | $6.7^{+0.1}_{-1.5}$ | $-17.85$ | Break | 6.9 (3,6) |  $\cdots$ | This | N
13151 | 3.592501339 | $-30.40146429$ | $9.880^{+0.012}_{-0.001}$ | 27.05 | 27.38 | $12.8^{+0.6}_{-0.8}$ | $-17.63$ | Break, Line | 11.8 (5,6,7) | Z14 | RB23, This | N
26185 | 3.567070796 | $-30.37786065$ | $10.071^{+0.000}_{-0.001}$ | 27.09 | 27.17 | $3.9^{+0.5}_{-0.1}$ | $-18.93$ | Break, Line | 7.1 (1,4) | A23, C23 | G23, This | Y♮
37126 | 3.590110772 | $-30.35974219$ | $10.255^{+0.001}_{-0.001}$ | 26.85 | 27.41 | $1.8^{+0.0}_{-0.1}$ | $-20.01$ | Break | 6.9 (3,4) | A23 | This | N
38766 | 3.513563316 | $-30.35679963$ | $12.393^{+0.004}_{-0.001}$ | 28.17 | 28.46 | $1.5^{+0.0}_{-0.0}$ | $-19.17$ | Break | 4.4 (4) | A23 | W23, This | N
13077 | 3.570869325 | $-30.40158533$ | $13.079^{+0.014}_{-0.001}$ | 27.73 | 28.82 | $2.3^{+0.0}_{-0.1}$ | $-19.24$ | Break | 7.4 (5,7) |  $\cdots$ | W23, This | N

Note. — (1): Source ID used in MSA. We also describe the ID used in the
photometric catalog (Weaver et al. 2023) in Appendix A. (2–3): Source
coordinate. (4): Spectroscopic redshift ($z_{\rm spec}$) determined by our SED
template fitting method (see text). (5–6): Total magnitude in NIRCam F200W and
F444W filters measured in Weaver et al. (2023). (7): Magnification factor
based on $z_{\rm spec}$ and the latest lens model, including eight more
multiple image systems spectroscopically confirmed in the UNCOVER NIRSpec
observations (Furtak et al. 2023c). (8): Absolute UV magnitude, calculated
with the total flux in the NIRCam F150W and F200W filter for the sources at
$z_{\rm spec}=8.5$–10 and $z_{\rm spec}>10$, respectively. (9): Key
spectroscopic features observed in the prism that critically determine the
source redshift in our method. “Line” denotes the sources with multiple line
detections. (10): Exposure time in hours. The MSA IDs are also denoted in
parentheses. (11–12): Reference for photometric and/or spectroscopic results
(L23; Labbe et al. 2023, A23; Atek et al. 2023b, B23; Boyett et al. 2023, C23;
Castellano et al. 2023, RB23; Roberts-Borsani et al. 2023, G23; Goulding et
al. 2023, W23; Wang et al. 2023b, Z14; Zitrin et al. 2014). (13): AGN or not.
“Y” indicates the AGN, while “N” indicates no evidence of AGN has been
observed in the current data. “Y/N” represents the potential AGN sources
implied from the emission line properties in prism (Section 3.1) and UVLF
measurements (Section 4).

$\dagger$ From the broad-line identification in H$\beta$ (see more details in
Kokorev et al. 2023). ID13556 in Labbe et al. (2023).

$\flat$ See more details in J. Weaver et al. in (prep.) for line diagnostics
and contributions from AGN and star-forming activities.

$\natural$ Recent deep 1.25 Ms Chandra observations show the 4.2$\sigma$
detection from ID26185 (Bogdan et al. 2023; see also Goulding et al. 2023).

We perform a template fitting to the NIRSpec prism 1D spectra to measure the
source redshift using eazy (Brammer et al. 2008) implemented in msaexp. The
eazy code adopts a set of templates added in a non-negative linear
combination, allowing us to securely measure the source redshift via any faint
emission lines as well as the Lyman-$\alpha$ break feature at $z\gtrsim 10$.
We use the corr_sfhz_13 subset models222https://github.com/gbrammer/eazy-
photoz/tree/master/templates/sfhz which include redshift-dependent star-
formation history (SFH), and dust attenuation. We additionally include the
best-fit SED template of the JWST-observed extreme objects of the strong
emission line galaxy at $z=8.5$ (ID4590) from Carnall et al. (2023) and an
obscured AGN at $z=4.50$ in the MACJ0647 lensing cluster (M. Killi in prep.)
to adequately model the potential strong emission lines and obscured AGNs that
have been frequently reported in recent NIRSpec studies (e.g., Kocevski et al.
2023; Harikane et al. 2023c; Furtak et al. 2023a). We include the absorption
of the intergalactic medium in the fitting to include the damping Ly$\alpha$
wing effect, especially towards high redshifts (e.g., Curtis-Lake et al. 2023;
Umeda et al. 2023; Heintz et al. 2023). We search for the best solution from
$\chi^{2}$ minimization over the redshift range of $z=$0.1–20 for all the MOS
targets. Fixing the best-fit redshift estimate, we also conduct a spline
fitting with msaexp to the continuum combined with the single Gaussian for
each emission line to evaluate the significance level for each faint emission
line at the corresponding wavelength.

Figure 3 summarizes the 2D and 1D spectra and the likelihood of the redshift
$P(z)$ for ten sources whose redshifts are estimated at $z\geq 8.5$ in our
analysis. All these ten sources show that the likelihood of $z$ below $z=8.0$
$P(z<8)$ is $\ll$ 3e-7. This suggests the significance of our spectroscopic
redshift confirmation being well beyond the $5\sigma$ level, and we regard
these ten sources as the successful spec-$z$ confirmed sources in this paper.
In Figure 3, we also present vertical lines highlighting the wavelengths of
the Ly$\alpha$ break and any faint emission lines detected with a signal-to-
noise ratio (SNR) $\geq 2.5$ via the spline+Gaussian fit to the prism spectrum
with the source redshift fixed at the one obtained from the template fitting.
From 7 out of 10 sources, we detect faint emission lines at secure SNRs ($\geq
5$), while the redshift is also constrained for the other three sources via
the Ly$\alpha$ break feature.

Among these ten prism spectra, we detect an unambiguous broad line (BL)
H$\beta$ component in ID20466 spectroscopically confirmed at $z=8.50$. The
line width of the BL H$\beta$ is estimated to be FWHM $=3439\pm 413$ km s-1.
The Balmer decrement measurement via H$\gamma$/H$\beta$ suggests a heavily
dust-obscured nature of $A_{\rm V}=2.1^{+1.1}_{-1.0}$ with the Small
Magellanic Cloud (SMC) dust attenuation law. Moreover, it shows a remarkably
bright [O iii] $\lambda$4363 line, resulting in the dust-corrected [O iii]
$\lambda$4363/[O iii] $\lambda$5008 ratio being 0.32. Such a high ratio cannot
be reproduced by typical electron temperatures and electron densities (e.g.,
Nicholls et al. 2020), while the high ratio is generally observed in local
Seyfart galaxies (e.g., Osterbrock 1978; Dopita & Sutherland 1995; Nagao et
al. 2001; Baskin & Laor 2005). From the BL line detection and the extremely
high ionization state, we conclude that ID20466 is the AGN, and we refer the
reader to the separate paper of Kokorev et al. (2023) for more
characterizations and discussions of this source.

Interestingly, we detect uniquely high ionization emission lines from several
other sources. For example, ID10646 shows a remarkable number of emission
lines with the secure SNRs, including N iv] $\lambda$1487, C iv $\lambda$1549,
and He ii $\lambda$1640\. Such high ionization emission lines may also be
caused by an AGN, although our current line flux measurements cannot rule out
the possibility that the galaxy emission is driven by star-forming activity
rather than AGN (J. Weaver et al. in prep.) based on rest-frame UV-optical
line diagnostics alone (e.g., Feltre et al. 2016). ID3686 also shows uniquely
high ionization emission lines such as N iv] $\lambda$1487\. Besides, the
ratio of [O iii] $\lambda$5008/H$\beta$ is observed to be
$16.3^{+21.8}_{-5.9}$, which exceeds the maximum value of $\sim 10$ observed
in recent NIRSpec studies for galaxies at $z\sim 2$–9 and falls in the AGN
regime in the [N ii], [S ii], and [O i] BPT diagrams (e.g., Sanders et al.
2023). Given the potential self-subtraction due to its extended morphology and
the three-shutter nod method (see Figure 2), we also perform a global
background subtraction by using a nearby empty shutter and confirm a similarly
high ratio of $11.2^{+4.2}_{-2.4}$ in the central shutter. While the high [O
iii] $\lambda$5008/H$\beta$ ratio is also induced by the shock excitation
(e.g., Kewley et al. 2013; Hirschmann et al. 2022), we also confirm a high
ratio reaching out to $17.5^{+17.5}_{-5.8}$ in the spectrum of the Southern
East shutter with the global subtraction method, where the emission is more
dominated by the compact component in the NIRCam map. These results may also
suggest that the uniquely high [O iii] $\lambda$5008/H$\beta$ ratio in ID3686
is the strong radiation from an AGN. Note that both ID10646 and ID3686 are
spatially resolved in the NIRCam filters. However, the BL AGNs have also been
identified in spatially-resolved sources at $z\simeq 4-7$ (e.g., Harikane et
al. 2023c), and the presence of the AGN does not always require a point source
morphology, depending on the contrast between the host galaxy and AGN. In
Table 1, we summarize our spectroscopic redshift estimates $z_{\rm spec}$ for
our ten spec-$z$ confirmed sources, together with basic source properties and
the implications of the AGN. We further discuss the potential AGN
interpretation of ID10646 and ID3686 in Section 4. In Figure 4, we summarize
$M_{\rm UV}$ as a function of redshift for our spec- $z$ confirmed sources,
together with the photometric and spectroscopic sample in the literature at
$z\gtrsim 8$. Owing to the deep survey layer efficiently explored by the
gravitationally lensing effect, our UNCOVER sources increase the sample in a
high-redshift ($z\gtrsim 9$) and faint ($M_{\rm UV}\lesssim-19$) regime by a
factor of 3.

Figure 5:  Left: Comparison between $z_{\rm phot}$ and $z_{\rm spec}$ for our
spec-$z$ confirmed sources. The red-filled and open circles represent the
sources selected from Atek et al. (2023b) (hereafter A23) and other
selections, respectively (see Section 3.1). The error bars show the $1\sigma$
error range for the A23 sample, while the other sources show the 2$\sigma$
error range given non-homogeneous selection criteria adopted in the MSA target
selection process (Section 2.2). Right: Comparison between the redshift
estimates based on lines ($z_{\rm line}$) and the Ly$\alpha$ break ($z_{\rm
break}$) for six sources whose multiple emission lines are successfully
detected in the prism spectrum. Two sources (ID20466, ID10646) show $z_{\rm
break}-z_{\rm line}<-0.1$, indicating the presence of the non-zero fluxes at
the blueward of the Ly$\alpha$ emission in the prism spectra and the ionized
bubbles around these two sources (Section 5).

###  3.2 $z_{\rm phot}$ vs $z_{\rm spec}$

In the left panel of Figure 5, we compare the $z_{\rm phot}$ and $z_{\rm
spec}$ estimates for the spec-$z$ confirmed sources. For the four sources
presented in A23 (red filled circles), we adopt the $z_{\rm phot}$ estimates
from A23 with the 1$\sigma$ error range. For the other six sources (red open
circles), we use the $z_{\rm phot}$ estimates from the eazy fitting with the
default corr_sfhz_13 template set (B. Wang et al. submitted). For the latter
six sources, we show the 2$\sigma$ error range, given the non-homogeneous
selection criteria adopted in the MSA target selection process (Section 2.2).
We find that all $z_{\rm phot}$ estimates agree with $z_{\rm spec}$ within the
$\sim 1$-2$\sigma$ error ranges. Among the sources presented in A23, there are
no other sources included in our MSA design apart from the four sources,
resulting in the success ratio of the spec-$z$ confirmation being 100%
($=4/4$) for the A23 sample. This high confirmation rate is consistent with
previous systematic NIRSpec follow-up studies for NIRCam-selected high-
redshift candidates at $z\gtrsim 9$ in the CEERS survey ($\simeq 90$%;
Fujimoto et al. 2023b; Arrabal Haro et al. 2023a), validating the classical
high-redshift galaxy selections based on the $z_{\rm photo}$ estimates and/or
the dropout technique. Interestingly, the A23 sample shows the offset of the
redshift $\Delta z(\equiv z_{\rm phot}-z_{\rm spec})\in[-0.4:+0.4]$, which is
in contrast to the previous NIRSpec follow-up studies showing a trend of the
overestimate in $z_{\rm phot}$ typically $\Delta z\simeq+0.5$ and maximally
$\sim+1$–2, regardless of the choice of the $z_{\rm phot}$ estimates from
different literature (Fujimoto et al. 2023b; Arrabal Haro et al. 2023a;
Hainline et al. 2023). The overestimate of $z_{\rm phot}$ is likely because of
the softened Ly$\alpha$-break shape routinely identified in the NIRSpec
spectra for high-redshift galaxies with possible causes of the IGM Ly$\alpha$
absorption, the intrinsic SED shape, and/or the additional Damping Ly$\alpha$
Absorbing systems (DLAs) (e.g., Curtis-Lake et al. 2023; Arrabal Haro et al.
2023a; Hsiao et al. 2023; Umeda et al. 2023; Heintz et al. 2023). In addition
to the deep NIRCam blue (F115W, F150W) filters taken in UNCOVER
($5\sigma\simeq 30$ mag) that are deeper than those taken in CEERS by $\simeq
1$ mag (Finkelstein et al. 2023), one of the most strict selection criteria is
adopted in the A23 selection, including the sharp Ly$\alpha$-break color of
$>1.5$ mag and the consistent redshift solutions from different SED fitting
codes. The presence of the deep blue filters and the strict sample selection
may be plausible reasons that mitigate the overestimation of $z_{\rm phot}$ in
the A23 sample.

###  3.3 $z_{\rm line}$ vs $z_{break}$

Figure 6:  Constraints on the UV luminosity function at $z\sim 9$, $z\sim 10$,
and $z\sim 12$. The magenta pentagons represent the AGN sources from the BL
(ID20466) and X-ray (ID26185) detection, and the red circles present the other
eight sources in our spec-$z$ confirmed sample in UNCOVER. The red squares
denote the spec-$z$ confirmed non-obvious AGN sources from UNCOVER, CEERS, and
JADES GOODS-S, where we do not include several sources in the $z=8.7$
overdensity reported in the CEERS field (see text). The grey shaded region and
grey squares show the previous photometric measurements, and the black solid
curve denotes the best-fit Schechter function estimated in Pérez-González et
al. (2023). The orange squares show the recent spectroscopic measurements
(Harikane et al. 2023c). The green squares denote the recent JWST-observed
bright objects of GNz11 (Maiolino et al. 2023c) and CEERS1019 (Larson et al.
2023) reported as AGNs. The magenta dashed curve presents the best-fit Double
power law (DPL) function for $z\sim 6$ AGNs Giallongo et al. (2019). The open
magenta pentagon remarks the two possible AGN sources at different redshifts
that show uniquely high ionization emission lines such as N iv] $\lambda$1749,
C iv $\lambda$1549, and He ii $\lambda$1640 (ID10646 at $z=8.51$) and high [O
iii] $\lambda$5008/H$\beta$ ratio of $>10$ (ID3686 at $z=9.33$), where the
excess is not caused by an overdensity but by their uniquely UV-bright
properties.

Among our spec-$z$ confirmed sources, some are detected with multiple emission
lines, making their $z_{\rm spec}$ estimates very secure. On the other hand,
others without the multiple emission line detection mainly rely on the
Ly$\alpha$ break feature, which may still have uncertainty in their $z_{\rm
spec}$ estimates. Motivated by this, we compare the line-based redshift
estimate ($z_{\rm line}$) and the Ly$\alpha$-break-based redshift estimate
($z_{\rm break}$). We use ID20466, ID10646, ID3686, ID22223, ID26185, and
ID13151, which show multiple emission line detection (Figure 3) and are
suitable for this experiment. For $z_{\rm line}$, we mask the $\pm 0.1\mu$m
range from the observed Ly$\alpha$ wavelength in the 1D spectra. For $z_{\rm
break}$, we mask all wavelengths with $\lambda\geq 3.0\mu$m and the $\pm
0.05\mu$m ranges from the observed wavelengths of detected emission lines in
the 1D spectra. We then rerun the same template fitting to the masked spectra
as Section 3.1 and derive $z_{\rm line}$ and $z_{\rm break}$.

In the right panel of Figure 5, we compare our $z_{\rm line}$ and $z_{\rm
break}$ estimates. We find that the offset between the line and Ly$\alpha$
break-based redshifts $\Delta z^{\prime}(\equiv z_{\rm line}-z_{\rm
break})\in[-0.2:+0.2]$. This indicates that the redshift estimate based on the
Ly$\alpha$ break feature alone may still have the uncertainty of $\pm 0.2$.
Given that we perform this experiment only with the sources with multiple
significant emission line detections, which are mostly equal to the best SNR
spectra, the offset could be even worse than $\pm 0.2$ with lower SNR data.
This is important for the design of future follow-up spectroscopy based on the
redshift estimates with NIRSpec/prism, especially when using instruments whose
redshift coverage of targeting emission lines can be narrower than this
potential redshift uncertainty (e.g., ALMA).

Individually, ID22223 shows $z_{\rm break}$ overestimated by $\sim$0.2. The 1D
spectrum clearly shows the softened shape of the Ly$\alpha$ break, which is
the natural cause of the overestimate of $z_{\rm break}$. ID3686, ID26185, and
ID13151 also show slight overestimates in $z_{\rm break}$ ($\Delta
z^{\prime}<0.05$). In the 1D spectra of these three sources, we identify the
softened shape in the Ly$\alpha$ break more or less similar to that of
ID22223. These results indicate that the slight overestimate of $z_{\rm
break}$ in these three sources is also caused by the similar softened shape of
the Ly$\alpha$ break, while the clear cut-off of the Ly$\alpha$ break
mitigates the effect. Therefore, an overestimation of $z_{\rm break}$ does not
always result from a softened Ly$\alpha$ break, depending on the SNR of the
spectrum.

In ID20466 and ID10646, on the other hand, the $z_{\rm break}$ values are
underestimated by $\sim$0.1–0.2. Their 1D spectra show that the Ly$\alpha$
line and continuum continue down to shorter wavelengths than the rest-frame
1216${\rm\AA}$, indicative of an enhanced transmission of the Ly$\alpha$ line
and continuum due to the presence of the so-called proximity zone, which has
been often observed around high-redshift luminous quasars (e.g., Eilers et al.
2017). We further discuss the proximity zone around ID20466 and ID10646 in
Section 5.

##  4 UVLF at $z\gtrsim 9$ and implications of AGN contributions

###  4.1 UVLF from UNCOVER

We calculate the UV LFs at $z\gtrsim 9$ using our spec-$z$ confirmed sources.
Note that we could not assign all the $z\gtrsim 9$ photometric candidates
slits in the MSA design, and thus our measurements provide only the lower
limits. In the same manner as Harikane et al. (2023a), we divide our sample
into three redshift bins at $z_{\rm spec}=8.5-9.5$, $9.5-11.0$, and
$11.0-13.5$. To simplify the calculation, we adopt a top-hat function for the
volume calculation according to the redshift bin. For the survey area, since
the MSA footprints are adjusted to the high-priority targets originally
identified from the NIRCam observation around the primary and two sub-cluster
regions in A2744, we use the NIRCam mosaic for the primary UNCOVER area ($\sim
28$ arcmin2; Bezanson et al. 2022) and obtain the effective survey area by
applying the magnification correction in the same manner as Atek et al.
(2023b). The uncertainty is calculated from Poisson errors with the values
presented in Gehrels (1986), where we take the cosmic variance into account,
following Trapp & Furlanetto (2020). No completeness correction is applied,
which makes our lower limit estimates conservative. Our full UVLF measurements
using the photometric sample leveraged by the success ratio of the spec-$z$
confirmation will be presented in I. Chemerynska et al. in (prep.).

The left panel of Figure 6 shows our UVLF measurements for galaxies (red
circles; $N=8$) and AGNs (magenta pentagons; $N=2$). For comparison, we also
present the previous photometric UVLF measurements (grey squares) taken from
the literature (Harikane et al. 2023b; Donnan et al. 2023; Bouwens et al.
2022a; Leethochawalit et al. 2023; Bouwens et al. 2021; Stefanon et al. 2019;
Bowler et al. 2020; McLeod et al. 2016; Oesch et al. 2018; Bagley et al. 2022;
Morishita et al. 2018; Morishita & Stiavelli 2022; Castellano et al. 2022;
Naidu et al. 2022b; Finkelstein et al. 2022a, b; Leung et al. 2023; Pérez-
González et al. 2023; Franco et al. 2023) and the best-fit Schechter function
(black curve) presented in Pérez-González et al. (2023). We also show two
bright JWST-observed sources, GNz11 and CEERS1019, that are argued to be AGNs
in the literature (e.g., Larson et al. 2023; Maiolino et al. 2023a). For
GNz11, we calculate the survey area with the entire CANDELS field (736
arcmin2; Bouwens et al. 2021). For CEERS1019, we calculate the survey area
from the CANDLES fields of GOODS-N, EGS, UDS, and COSMOS, where the original
spectroscopic sample was selected (Larson et al. 2022). For volume
calculations, we assume $\Delta z=1.0$ in the same manner as Oesch et al.
(2018) for both sources. The uncertainty is estimated by the Poisson error and
the cosmic variance.

We find that our measurements for both galaxies and AGNs are consistent with
the previous photometric measurements, except for the brightest $M_{\rm UV}$
bin in the $z\sim 9$ UVLF. This exceptional data point consists of our two
brightest sources, ID3686 at $z=9.33$ and ID10646 at $z=8.51$. These two
sources are located at different redshifts, indicating that the excess from
the previous UVLF measurements is not caused by an overdensity but by their
uniquely UV bright properties. Interestingly, both of these sources show some
implications as AGNs from the identification of the high ionization emission
lines such as N iv] $\lambda$1749, C iv $\lambda$1549, and He ii $\lambda$1640
and the uniquely high [O iii] $\lambda$5008/H$\beta$ ratio of $>10$ (Section
3.1). Although both of these sources are spatially resolved in the NIRCam
filters, many BL AGNs have been identified in spatially-resolved sources in
recent NIRSpec studies (e.g., Harikane et al. 2023c; Larson et al. 2023). Even
if the AGN contribution to the total UV luminosity is 50%, the $M_{\rm UV}$
value moves towards the bright end by $\sim$0.7 mag, which may easily impact
the bright-end shape of the UVLF. These UVLF measurements offer another
independent implication of the potential AGN nature of these UV brightest
sources.

In the left panel of Figure 6, we also show the AGN LF estimated at $z\sim 6$
for X-ray AGNs (the magenta dashed line; Giallongo et al. 2019). This X-ray
AGN LF shows an excellent agreement with the lower boundaries obtained from
the BL AGN of ID20466 at $z=8.50$ and the X-ray luminous AGN (ID26185) at
$z=10.07$. This indicates that a comprehensive AGN LF at $z\gtrsim 9$ could
have a comparable, even higher amplitude than the previous measurement at
$z\sim 6$. We summarize our lower limit constraints on UVLFs of galaxies and
AGNs in Table 2 and Table 3, respectively.

Table 2: Spectroscopic Constraints on $z\simeq 9$–12 UVLFs

$M_{\rm UV}$ |  $\Phi$ (UNCOVER) |  $\Phi$ (UNCOVER+Fields)
---|---|---
[AB mag] | [$10^{-5}$ Mpc-3 dex-1]
(1) | (2) | (3)
$z\sim 9$
$-21.5$ | $>19.9_{-17.6}^{+25.9}$ | $>2.16_{-1.69}^{+2.81}$
$-20.5$ |  $\cdots$ | $>2.16_{-1.59}^{+2.81}$
$-19.5$ |  $\cdots$ | $>1.08_{-0.95}^{+2.49}$
$-18.5$ |  $\cdots$ | $>2.16_{-1.49}^{+2.81}$
$z\sim 10$
$-20.5$ | $>7.45_{-6.98}^{+17.1}$ | $>2.43_{-1.53}^{+2.34}$
$-19.5$ |  $\cdots$ | $>2.43_{-1.47}^{+2.34}$
$-18.5$ |  $\cdots$ | $>0.81_{-0.69}^{+1.86}$
$-17.5$ | $>22.4_{-13.5}^{+21.6}$ | $>22.4_{-13.5}^{+21.6}$
$z\sim 12$
$-20.5$ |  $\cdots$ | $>0.69_{-0.62}^{+1.58}$
$-19.5$ | $>10.6_{-7.88}^{+13.8}$ | $>2.06_{-1.27}^{+1.99}$
$-18.5$ |  $\cdots$ | $>4.08_{-2.90}^{+5.31}$

Note. — (1): Absolute UV magnitude. (2): UVLF constraints with spec-$z$
confirmed sources in UNCOVER, except for two AGNs (see text), resulting in
$N=8$. (3): UVLF constraints with spec-$z$ confirmed sources in UNCOVER,
CEERS, and JADES, except for two AGNs (Larson et al. 2023; Maiolino et al.
2023c) and the sources in the $z=8.7$ overdensity in the CEERS field reported
in the literature (Larson et al. 2022), resulting in $N=23$. Errors and upper
limits are 1$\sigma$, evaluated with the Poisson uncertainty (Gehrels 1986)
and the cosmic variance (Trapp & Furlanetto 2020).

Table 3: Spectroscopic Constraints on $z\simeq$9–10 AGN LFs

Redshift |  $M_{\rm UV}$ |  $\Phi$ (AGN)
---|---|---
| [AB mag] | [$10^{-5}$ Mpc-3 dex-1]
$z\sim 9$ | $-18.1$ | $>9.96_{-8.81}^{+22.9}$
$z\sim 10$ | $-18.9$ | $>7.45_{-6.63}^{+17.1}$

Note. — Same as Table 2, but for AGN LFs constrained from two spec-$z$
confirmed AGNs of ID20466 and ID26185.

Figure 7:  Comparison of the luminosity functions with the theoretical
predictions in the literature at $z\sim 9$, $z\sim 10$, and $z\sim 12$. The
symbols are the same as Figure 6, The color dashed lines denote the
theoretical predictions of SC-SAM (Yung et al. 2019), FLARES (Lovell et al.
2022; Vijayan et al. 2021; Wilkins et al. 2023), DELPHI (Dayal et al. 2014;
Mauerhofer & Dayal 2023), Thesan (Kannan et al. 2022), Bluetides (Wilkins et
al. 2017), and Universe Machine (Behroozi et al. 2020). In each redshift
range, our lower limit estimate in the brightest $M_{\rm UV}$ challenges
several theoretical predictions, confirming the earlier arguments of the high
abundance of UV-bright ($M_{\rm UV}\lesssim-20$) galaxies in previous
photometric studies in a spectroscopic manner at $z\sim 9$–12.

###  4.2 UVLF from UNCOVER+CEERS+JADES

To benefit from the complementary survey layers enabled by the lensing cluster
surveys and the general field surveys, we also evaluate the UVLF together with
public spec-$z$ confirmed sources at $z\geq 8.5$ in recent JWST/NIRSpec MSA
studies (e.g., Tang et al. 2023; Fujimoto et al. 2023b; Bunker et al. 2023b,
a; Hainline et al. 2023; Arrabal Haro et al. 2023b, a; Harikane et al. 2023c;
Hsiao et al. 2023). We include the sources spectroscopically confirmed at
$z\geq 8.5$ in two general field surveys of CEERS (e.g., Finkelstein et al.
2023; Arrabal Haro et al. 2023a; Fujimoto et al. 2023a) and JADES in GOODS-S
(hereafter JADES-GS) (e.g., Bunker et al. 2023a; Curtis-Lake et al. 2023;
Robertson et al. 2023; Hainline et al. 2023) to our spectroscopically
confirmed sources in UNCOVER. We also use the sources spectroscopically
confirmed in a JWST DDT follow-up observation with NIRSpec/prism MSA, which
primarily aims to confirm a remarkably UV-bright galaxy candidate at $z\sim
16$ (Arrabal Haro et al. 2023b). We obtain 12 and 7 spec-$z$ confirmed sources
from CEERS (+DDT) and JADES-GS, respectively, covering a wide $M_{\rm UV}$
range of $\in[-22.2:-18.0]$. In conjunction with our UNCOVER sample, our final
spec-$z$ sample in this analysis results in a total number of 29.

We calculate the survey volume as follows. In JADES-GS, the NIRSpec
observations had small dithers ($<1^{\prime\prime}$) with one pointing, and
the NIRSpec pointing center was not re-optimized to the late addition of the
high-priority NIRCam sources (Bunker et al. 2023a). Therefore, we regard the
JADES-GS NIRSpec observations as a pure general field survey almost with a
single NIRSpec pointing and adopt the NIRSpec Field-of-View (FoV) of 9
arcmin2.333https://jwst-docs.stsci.edu/jwst-observatory-characteristics/jwst-
field-of-view In CEERS, the NIRSpec observations were initially designed with
six paintings, where one pointing was added from the DDT NIRSpec observations
(#2750: PI, P. Arrabal-Haro; Arrabal Haro et al. 2023a) for the $z\sim 16$
candidate (Donnan et al. 2023). Among the original six pointings in CEERS, the
prism observations in two pointings were affected by the electrical short and
thus rescheduled (Arrabal Haro et al. 2023a). Although the pointing centers of
the rescheduled two NIRSpec observations were optimized to maximize the yield
of the NIRCam-selected high-redshift galaxy candidates, we assume that the
potential bias from this optimization for the targets is insignificant, given
the ratio to the total number of the paintings (= 2/9 $\lesssim 20\%$). Since
the primary target in the DDT observation is the $z\sim 16$ candidate, we
assume that the potential bias in the DDT observation for other $z\gtrsim 9$
galaxies within the NIRSpec FoV is also minimal. In a similar manner as
Harikane et al. (2023a), we count the area overlapped between the FoVs of the
NIRSpec and NIRCam in CEERS and obtain 37.5 arcmin2. We add the survey areas
from JADES-GS and CEERS to that of UNCOVER, and re-derive the UVLFs with the
three redshift bins at $z_{\rm spec}=$ 8.5–9.5, 9.5–11.0, 11.0–13.5. We do not
include CEERS-D28 at $z=8.763$, CEERS1025 at $z=8.715$, CEERS1019 at
$z=8.679$, CEERS80083 at $z=8.638$, and CEERS1029 at $z=8.610$ (Arrabal Haro
et al. 2023a) in our estimates, as the $z=8.7$ overdensity has been reported
in literature (e.g., Larson et al. 2022; Castellano et al. 2023; Harikane et
al. 2023c).

In the right panel of Figure 6, we present the UVLF measurements with the
spec-$z$ confirmed sources in UCNOVER, CEERS, and JADES. For comparison, we
also present the recent NIRSpec spec-$z$ based measurements (the orange
squares; Harikane et al. 2023c). We confirm that our measurements are
generally consistent with the previous spec-$z$ based measurements and improve
the lower constraints owing to the comprehensive spec-$z$ sample, including
the lensing cluster and general field surveys. We find that the brightest
$M_{\rm UV}$ bin in the $z\sim 9$ UVLF still shows the excess from the
previous photometric UVLF measurements beyond the errors, which still consists
of ID10646 and ID3686. This indicates that the excess is unlikely explained by
the cosmic variance. A similar excess has also been reported in recent JWST
studies (e.g., Castellano et al. 2023; Harikane et al. 2023c), and this has
been interpreted as galaxy overdensity. However, we do not include the sources
in the $z=8.7$ overdensity (Larson et al. 2022) in our measurements. Besides,
ID3686 and ID10646 are at different redshifts. Thus, the excess is more likely
caused by their uniquely UV-bright properties than the excess in abundance,
offering independent implications that they are the AGNs, as discussed in
Section 4.1. In Table 3, we also summarize the UVLF measurements using the
spec-$z$ sources from UNCOVER, CEERS, and JADES.

###  4.3 Comparison with Models

We compare our UVLF measurements with theoretical predictions. In Figure 7, we
show theoretical predictions of the UVLF at $z\sim 9$, $z\sim 10$, and $z\sim
12$, together with our UVLF measurements using the spec-$z$ confirmed sources
in UNCOVER, CEERS, and JADES. We find that our lower limit estimate in the
brightest $M_{\rm UV}$ bin challenges some theoretical predictions in every
redshift range. This indicates that we confirm the earlier reports of the high
abundance of UV-bright ($M_{\rm UV}\lesssim-20$) galaxies argued in the
photometric studies (e.g., Adams et al. 2022; Atek et al. 2022, 2023b; Bouwens
et al. 2022b; Bradley et al. 2022; Castellano et al. 2022; Donnan et al. 2023;
Finkelstein et al. 2022b, 2023; Harikane et al. 2023b; Labbe et al. 2022;
Morishita & Stiavelli 2022; Naidu et al. 2022c; Yan et al. 2022; Williams et
al. 2023; Austin et al. 2023; Leung et al. 2023) in a spectroscopic manner at
$z\sim 9$–12. Several possible scenarios for the high abundance have been
discussed, including preferential detection of galaxies upscattered compared
to the main sequence, lower dust attenuations with increasing redshift, a top-
heavy initial mass function or even UV luminosity contribution from an AGN
component (e.g., Ferrara et al. 2022; Inayoshi et al. 2022; Pacucci et al.
2022; Naidu et al. 2022b; Finkelstein et al. 2023; Bouwens et al. 2022a;
Harikane et al. 2023c). Given that the most stringent lower limit obtained at
$z\sim 9$ is dominated by possible AGN sources (Section 4.1 & 4.2), it seems
increasingly plausible that the bright end of the UV LF is shaped by sources
where the UV luminosity is contributed by both star formation and black hole
accretion. Although further observational evidence is necessary to conclude
whether those possible sources are truly AGNs or not, such observations will
prove crucial in baselining theoretical models and shedding light on black
hole seeding & growth at these early epochs.

###  4.4 AGN fraction

Figure 8:  AGN fraction at $z\geq 8.5$. The blue and red histograms present
the number of AGNs and the sources that are spectroscopically confirmed in our
studies at each $M_{\rm UV}$ bin. The histogram with a red outline represents
the two possible AGN sources of ID10646 and ID3686 that fall in the brightest
$M_{\rm UV}$ bin. The red circles indicate the AGN fraction for the spec-$z$
confirmed UNCOVER sources at $z\geq 8.5$, where we show the brightest $M_{\rm
UV}$ bin in the case that both possible sources are the AGNs. The error bars
represent the confidence intervals for the binomial proportion, derived using
the Jeffreys interval at 1$\sigma$. The red-hatched area shows the 1$\sigma$
range for the AGN fraction over the entire $M_{\rm UV}$ range ($=2/10$). This
may be a lower limit, as more sources, including ID10646 and ID3686, might be
confirmed to be AGNs in future observations. The black shaded area denotes the
recent reports of $\simeq 5-10\%$ from the BL AGN identifications in recent
NIRSpec studies at $z\simeq 4$–7 (Harikane et al. 2023a; Maiolino et al.
2023b).

We investigate the AGN fraction at $z\geq 8.5$. Note that here we count the
spec-$z$ confirmed sources in UNCOVER alone, since the homogeneous data and
sensitivity are required to examine the AGN fraction. Figure 8 presents the
AGN fraction as a function of $M_{\rm UV}$ from our spec-$z$ sample. We
calculate the 1$\sigma$ uncertainty from the confidence intervals for the
binomial proportion, derived using the Jeffreys interval. The red-hatched area
indicates the 1$\sigma$ range of the AGN fraction over the entire $M_{\rm UV}$
range with our secure AGNs from the BL and X-ray detections ($=2/10$), while
we also show the possible AGN fraction in the brightest $M_{\rm UV}$ bin which
consists of the possible AGN sources of ID10646 and ID3686. For comparison, we
also show the BL AGN fraction of $\approx$5–10% estimated at $z\simeq 4$–7 in
the recent JWST/NIRSpec studies (Harikane et al. 2023a; Maiolino et al.
2023b).

We find that our results suggest a relatively high AGN fraction of $>10$–35%
compared to the previous measurements from the BL AGNs. Our higher AGN
fraction than the previous measurements can be interpreted as a more
comprehensive approach adopted in the AGN identification than the BL
identification alone. Since the weak-line quasars have also been identified at
$z>6$ (e.g., Andika et al. 2020; Fujimoto et al. 2022a), the BL approach can
be hampered by the observational bias for the sources whose equivalent width
of BL is high ($\approx$ high $M_{\rm BH}/M_{\rm star}$) and/or whose BL width
is sufficiently broad ($\approx$ more massive $M_{\rm BH}$) to be resolved
with JWST instruments. On the other hand, in addition to the successful
identification of the BL AGN at $z=8.50$, we identify the X-ray luminous AGN
at $z=10.07$ and several potential AGN sources from multiple angles, owing to
the deep NIRSpec/prism spectroscopy leveraged by the lensing effect and the
ancillary deep X-ray data (e.g., Bogdan et al. 2023). Although further
observational evidence is necessary, the AGN confirmation, at least from
ID10646 and ID3686, suggests the increase of the AGN fraction towards the
bright end. Such a trend has been confirmed at $z\sim 2$–7 (e.g., Sobral et
al. 2018; Ono et al. 2018; Bowler et al. 2021; Finkelstein & Bagley 2022).
Further comprehensive AGN searches and follow-up observations may unveil even
higher AGN fractions at $z\gtrsim 9$ and provide the reasonable answer to the
origin of the high abundance of UV-bright galaxy candidates at $z\gtrsim 9$
(Section 4.3).

##  5 Bubbles in the Shadow at $z=8.5$

Figure 9:  Zoom-in 1D+2D prism spectra of ID10646 (left) and ID20466 (right).
The magenta vertical line and dashed curve indicate the expected Ly$\alpha$
line wavelength and the best-fit spline model using msaexp based on $z_{\rm
line}$, respectively. The blueward of the Ly$\alpha$ continuum or line is
clearly detected in both sources. The red curve in ID10646 represents our
best-fit IGM absorbed model with an ionized bubble, yielding the best-fit
$R_{\rm p}$ value of $7.69\pm 0.18$ pMpc. The red vertical line corresponds to
the expected wavelength of the Ly$\alpha$ line based on the redshift of the
ionization front of the ionized bubble along the line of sight. Because of the
lack of the blueward Ly$\alpha$ continuum and the difficulty in modeling the
intrinsic Ly$\alpha$ line profile in ID20466, we perform the $R_{\rm p}$
measurement only for ID10466. For reference, the red dashed vertical line in
ID20466 is drawn at the same wavelength as the red vertical line in the left
panel.  Figure 10:  Schematic illustration of the relative 3D positions of
ID20466 and ID10646 in the source plane. The source plane coordinates of
ID20466 and ID10646 are (RA, Dec) = (3.63506157, $-30.44818861$) and
(3.63209972, $-30.46295758$), respectively. The light blue shaded sphere
denotes an isotropic sphere of the ionized bubble with $R_{\rm p}=7.7$ pMpc
measured from the blueward Ly$\alpha$ line and continuum emission in the prism
spectrum of ID10646. Their physical distance of 0.38 pMpc indicates that
ID20466 also resides in the same ionized bubble, which facilitates the
blueward Ly$\alpha$ emission also observed from ID20466, and the AGN activity
in ID20466 (and ID10646) may contribute to forming this ionized bubble.

In Section 3.1, we find that the $z_{\rm break}$ measurements are
underestimated in ID20466 and ID10646, compared to their $z_{\rm line}$
measurements. This is caused by the non-zero fluxes at the blueward of the
Ly$\alpha$ emission in the prism spectra. Such an enhanced transmission of the
Ly$\alpha$ line and continuum is thought to be attributed to the presence of
the so-called proximity zone, which has often been observed around high-
redshift luminous quasars due to their strong radiation making the surrounding
IGM neutral gas fully ionized (e.g., Eilers et al. 2017). In addition to the
unambiguous AGN feature observed in ID20466 via the broad H$\beta$ line,
ID10646 also shows several uniquely high ionization lines (e.g., N iv]
$\lambda$1487, C iv $\lambda$1549, He ii $\lambda$ 1640), suggesting the
presence of an AGN and/or star-forming activities that produce the strong
radiation. Furthermore, ID20466 and ID10646 turn out to be the same redshift
with a physical distance of 380 kpc in the source plane, where they might
reside in the same ionized bubble.

Figure 9 presents the zoom-in 2D+1D prism spectra of ID10646 and ID20466 with
the expected wavelength of the Ly$\alpha$ break based on $z_{\rm line}$
(magenta vertical line). In both spectra, we clearly identify the emission in
the blueward of the Ly$\alpha$ break, indicating the presence of ionized
bubbles around these systems. To evaluate the proximity zone radius $R_{\rm
p}$, we model the IGM absorption in the same manner as Totani et al. (2006).
For the intrinsic rest-frame UV spectrum, we perform a power-law fit at
1.2–2.0$\mu$m, masking the $\pm 0.05\mu$m range of the bright emission lines
detected in the spectrum. We then convolve the best-fit power law with the
spectral resolution of NIRSpec/prism, multiply the IGM absorption model, and
infer the best-fit $R_{\rm p}$ value from the minimum $\chi^{2}$ method.
Although the blueward of the Ly$\alpha$ line is also clearly detected from
ID20466, we conduct this measurement only for ID10646, because of the
difficulties from i) the absence of the blueward of the Ly$\alpha$ continuum
in the spectrum, ii) the uncertainty in modeling the intrinsic SED with its
heavily dust-reddened nature, and iii) the uncertainty in modeling the
intrinsic Ly$\alpha$ line profile with the current spectral resolution.

In Figure 9, we show the best-fit IGM absorbed SED for ID10646 (red curve). We
obtain the best-fit value of $R_{\rm p}=7.69\pm 0.18$ proper Mpc (pMpc). To
evaluate the potential effect from a weak Ly$\alpha$ line whose flux may
spread into a Gaussian on both sides of the Ly$\alpha$ break (Jones et al.
2023), we also test the fit, including a Gaussian component on the power law.
However, the measured $R_{\rm p}$ values consistently remain at $R_{\rm p}>7$
pMpc with the rest-frame Ly$\alpha$ equivalent widths of 10–100${\rm\AA}$. We
thus use the best-fit value from the single power-law fit as a fiducial
estimate in this paper. In Figure 10, we also illustrate the ionized bubble
and relative positions of ID10646 and ID20466 in the source plane. The best-
fit $R_{\rm p}$ value exceeds the physical distance between ID20466 and
ID10646. This indicates that these two sources reside in the same ionized
bubble. Since ID20466 is the BL AGN, the ongoing and/or past quasar active
phases in ID20466 might play a key role in contributing to forming the ionized
bubble. Yet, we cannot rule out the possibility that ID10646 is the main
driver of the formation of this ionized bubble, given its numerous detections
of the high ionization lines. A galaxy overdensity might also be related,
where many faint galaxies contribute to forming the ionized bubble.

Figure 11:  Sizes of the proximity zones ($R_{\rm p}$) as a function of
$M_{\rm UV}$. The red-filled circle indicates the potential AGN source of
ID10646, and the red open circle represents the dusty BL AGN of ID20466 after
the dust correction. The blue circles indicate the previous measurements for
luminous quasars at $z\sim 6$ (Eilers et al. 2018; Ishimoto et al. 2020). The
blue and black curves are the best-fit relations for the observation (Ishimoto
et al. 2020) and the radiative transfer simulations (Eilers et al. 2017).
ID10646 and ID20466 show remarkable gaps compared to the previous measurements
and theoretical trends. In line with the bright Ly$\alpha$ line detection from
the dusty BL AGN of ID20466, one interpretation is that the IGM gas density
around these two sources is lower than the environment around the luminous
quasars at $z\sim 6$ and illuminated by the ionizing (and Ly$\alpha$) photons
escaped from the dusty cloud with a low covering fraction around the AGN.
Together with the high AGN abundance from the UVLF measurements at $z\sim
9$–10 (Section 4), the identification of one of the most giant ionized bubbles
to date around the dusty BL AGN and the possible AGN source indicates the non-
negligible contributions of AGNs to cosmic reionization.

In Figure 11, we also compare our $R_{\rm p}$ measurement with those of
luminous quasars at $z\gtrsim 6$ in the literature (Eilers et al. 2017;
Ishimoto et al. 2020). Because ID20466 also resides in the same ionized bubble
and might play a key role in its formation, we also show the dust-corrected
measurement for ID20466.444We use the bolometric luminosity estimate of
$L_{\rm bol}=6.6\times 10^{45}$ erg s-1 (Kokorev et al. 2023) and assume the
bolometric luminosity correction factor of 4.5 at 1500${\rm\AA}$ (Richards et
al. 2006).  For comparison, we also present the best-fit $R_{\rm p}-M_{\rm
UV}$ relation for the $z\sim 6$ quasars estimated in Ishimoto et al. (2020)
and the trend obtained from the radiative transfer simulations presented in
Eilers et al. (2017). These empirical and theoretical predictions show the
positive correlation between $M_{\rm UV}$ and $R{\rm p}$. Remarkably, we find
that ID10646 and ID20466 fall in significantly faint $M_{\rm UV}$ and large
$R_{\rm p}$ parameter space, $\sim 1$–2 orders of magnitude fainter $M_{\rm
UV}$ than what is predicted from the typical positive correlation obtained
both from the previous observational and theoretical results. These remarkable
gaps indicate the following three possible interpretations: i) ID20466 and/or
ID10646 had more luminous quasar phases until recently, ii) the IGM gas
density is much lower around these two sources than those of the luminous
quasars at $z\sim 6$, which enables to form a large $R_{\rm p}$ with a
relatively low luminosity555Strömgren radius $\propto L^{1/3}\times n_{\rm
gas}^{-2/3}$, and iii) there exist many faint galaxies around that are the
main drivers of the ionized bubble. If the first interpretation is the case,
the correlations of $M_{\rm UV}$ and $R_{\rm p}$ suggest that the more
luminous phase of these objects could reach $M_{\rm UV}\lesssim-26$. From the
survey volume in UNCOVER at $z\sim 8.5$, the predicted number of such luminous
quasars ($M_{\rm UV}\lesssim-26$) is $\ll 10^{-5}$ (e.g., Dayal et al. 2019),
indicating that the presence of such a single luminous quasar is already
extremely challenging to our current BH formation and evolution models. In the
interpretation of ii), given that Strömgren radius $\propto n_{\rm
gas}^{-2/3}$, a gas density lower than the environment around the luminous
quasars by a factor of $\sim 100$ may explain that ID20466 provides a
sufficient amount of the ionizing photon budget to form the observed proximity
zone. Nevertheless, this interpretation still requires the covering fraction
of the dusty cloud around the AGN to be low, where most ionizing photons
successfully escape from the system to ionize the surrounding neutral IGM. In
the interpretation of iii), although we do not find evidence of a galaxy
overdensity at $z\sim 8.5$ in our SED catalog (B. Wang et al. submitted),
these galaxies fall close to the edge of the primary area of the UNCOVER
NIRCam observations (Figure 1), which might make it difficult to identify the
nearby faint galaxies at the same redshift.

Interestingly, we also observe the Ly$\alpha$ line from ID20466, despite its
heavily dusty nature with $A_{\rm V}=2.1$ (Section 3.1). The giant ionized
bubble may facilitate the Ly$\alpha$ line, including the blueward emission,
while the heavily dusty nature indicates that the origin of the Ly$\alpha$
line is not the emission of the BL AGN from the line of sight. Instead, there
are the following three possible scenarios for the origin of the Ly$\alpha$
line from ID20466: a) cold gas inflow, b) a blue, un-obscured host galaxy, and
c) scattered light escaped from angles different from the dust-obscured AGN
line of sight.

In the scenario of a), we include a single Gaussian to the power law function,
convolve with the wavelength-dependent spectral resolution of the prism, and
fit it to the prism spectra at $0.9\text{--}1.6\,\mu\mathrm{m}$ to measure the
velocity offset of Ly$\alpha$ line peak. We find that the Ly$\alpha$ peak is
blue-shifted by $2500\pm 300\,\mathrm{km}\,\mathrm{s}^{-1}$ ($\simeq
0.01\,\mu\mathrm{m}$) with respect to the systemic redshift determined by
other emission lines ($z_{\rm line}$). However, the velocity scale of the cold
gas inflow is regulated by the gravitational potential (e.g., Laursen et al.
2019), which would be comparable to the escape velocity of $\sqrt{2GM_{\rm
h}/R_{\rm vir}}$, where $M_{\rm h}$ and $R_{\rm vir}$ are the halo mass and
virial radius, respectively. Assuming the maximum $M_{\rm h}$ of $\sim
10^{11}\,M_{\rm h}$ at $z=8.5$ from our survey volume Behroozi et al. (2020)
and its $R_{\rm vir}$, the dynamical velocity is estimated to be $\sim
200\,\mathrm{km}\,\mathrm{s}^{-1}$. While the resonance scattering nature of
the Ly$\alpha$ line can increase the velocity offset by a factor of $\sim 2$
(e.g., Verhamme et al. 2006), this indicates that the measured blue-shifted
velocity is still too high to be explained by the cold gas inflow. Instead, a
degeneracy between velocity and morphology arises if the Ly$\alpha$ emission
is spatially extended and the emitting peak position differs from other
emission lines within the MSA shutter. Based on the line spread function for a
uniformly-illuminated slit and assuming the resolution element for the prism
is 2.2 pixels (Jakobsen et al. 2022), we estimate this effect to be up to
$\sim 0.016$ $\mu$m at 1.1 $\mu$m if the peak of the Ly$\alpha$ distribution
is located on the opposite side of the microshutter compared to the other
line-emitting gas. The measured Ly$\alpha$ offset is equal to $\sim 0.01$
$\mu$m, indicating that the Ly$\alpha$ offset in the prism may be explained by
this differential morphology effect within the shutter, although we do not
find any clear evidence of the differential morphology in the F115W that
includes the Ly$\alpha$ line emission. To give a definitive answer, we need a
high spectral resolution follow-up and the detailed Ly$\alpha$ line profile.
In the scenario of b), it might be the case that the AGN core is heavily dust
reddened, while the host galaxy is a blue, un-obscured galaxy from which
Ly$\alpha$ is emitted. From the Gaussian and power-law fitting above, we
obtain the Ly$\alpha$ flux of $\simeq 3.7\times 10^{42}$ erg s-1. Assuming no
dust attenuation and the IGM absorption, we estimate SFR from this Ly$\alpha$
luminosity of $\simeq$4 $M_{\odot}$/yr using a calibration of Kennicutt
(1998). This SFR value is comparable to a UV luminosity observed at 27.8 mag
in F150W, using the Kennicutt (1998) calibration. However, ID20466 is as faint
as 28.8 mag in F150W with the compact morphology, indicating that the emission
in F150W is still dominated by the AGN component and that the UV magnitude of
the host galaxy is $\gg 28.8$ mag. These properties suggest the scenario of b)
is unlikely. In the scenario of c), the strong Ly$\alpha$ emission is
originally from the AGN, and its resonance scattering nature helps to avoid
the dusty cloud in the line of sight. Similarly, this might also be the case
that a patchy dusty cloud only covers the BL region, not the narrow line (NL)
region sufficiently, and the observed Ly$\alpha$ line directly comes from the
NL region. It has also been argued that the rest-UV light in these red compact
objects like ID20466 may be caused by the scattered light (e.g., Assef et al.
2020; Glikman et al. 2023) based on their unique SED shape of the blue in UV
and red in optical colors (Labbe et al. 2023). The escape of the ionizing
photon together with Ly$\alpha$ is also in line with the giant ionized bubble
identified around ID20466, where such successful ionizing photon escapes
contribute to forming the ionized bubble.

In short, c) is the most likely scenario among these three, which is also in
line with the interpretation of the remarkable gap observed in the $M_{\rm
UV}-R_{\rm p}$ relation that ID20466 (and ID10646) forms the giant ionized
bubble in a relatively low-density IGM environment (interpretation ii).
Despite the small survey volumes, the dozens of dust-reddened compact objects
have been identified in recent HST and JWST studies at $z\sim 4-7$ (e.g.,
Fujimoto et al. 2022a; Furtak et al. 2023b; Labbe et al. 2023), and some have
already been spectroscopically confirmed to be AGNs from the BL Balmer line
detection (Kocevski et al. 2023; Matthee et al. 2023; Furtak et al. 2023a).
These identifications indicate a high abundance of the dusty AGNs at high
redshifts, resulting in steeper faint-end slopes of AGN LFs at $z\sim 4-7$
(e.g., Labbe et al. 2023; Matthee et al. 2023) than what is estimated from
previous Type-I quasar measurements (e.g., Akiyama et al. 2018; McGreer et al.
2018; Matsuoka et al. 2018). While their dusty nature has implied that their
contributions to cosmic reionization are minimal, the discovery of the giant
ionized bubble and the bright Ly$\alpha$ line detected from ID20466 suggests
its potential contributions to forming the ionized bubble, despite its heavily
dusty nature. Importantly, a similarly bright Ly$\alpha$ line is also observed
in another dusty BL AGN at $z=7.0$ ($A_{\rm V}\sim 3$; Furtak et al. 2023a).
If a situation similar to ID20466 is also taking place in other dusty BL AGNs,
the ionizing photon escape from dusty AGNs may be a recurrent event at the
heart of the epoch of cosmic reionization. While recent spectroscopic
observations for faint galaxies (down to $M_{\rm UV}=-15$) at $z\simeq 6$–8
provide firm evidence that the main driver of cosmic reionization is galaxies
(Atek et al. 2023a), our results imply that the abundant (dusty) AGNs at
$z\gtrsim 9$ may still have non-negligible contributions to cosmic
reionization.

##  6 Summary

In this paper, we present JWST NIRSpec prism follow-up observations in the
multi-object spectroscopy mode (MOS) using the multi-shutter array (MSA) for
$z\gtrsim 9$ galaxy candidates. These candidates were identified in the Cycle
1 Treasury program of UNCOVER (#2561, PIs: I. Labbe & R.Bezanson; Bezanson et
al. 2022) behind the massive galaxy cluster A2744. Owing to its extensive
designs of the NIRSpec observations among the lensing cluster surveys in JWST
Cycle 1, these new deep prism spectra, leveraged by the gravitational lensing
effect, afford us unparalleled opportunities to perform the initial
spectroscopic census of these early galaxies and investigate the UV luminosity
function (LF), the AGN fraction, and their contributions to cosmic
reionization out to the redshift frontier in a wide UV luminosity range. The
major findings of this paper are summarized below:

  1. 1.

Of the 680 distinct targets in our NIRSpec MSA, we confirm the source redshift
via emission lines and/or the Ly$\alpha$ break feature in the prism spectra
for 10 lensed galaxies ($\mu=$1.3–12.8) ranging from $z=8.50$ to $13.08$.
These galaxies have a $M_{\rm UV}$ range of $\in[-21.72:-17.28]$ after lensing
corrections. This increases the spec-$z$ confirmed sample so far known in a
high-redshift ($z\gtrsim 9$) and UV-faint ($M_{\rm UV}\gtrsim-19$) regime by a
factor of 3.

  2. 2.

Although the ten spec-$z$ confirmed sources are initially selected through
several different selection criteria, four sources are the sample selected
from a systematic NIRCam analysis presented in Atek et al. (2023b) (hereafter
A23), which achieves a high confirmation rate of 100%. Six sources show robust
multiple emission line detections, providing the most secure redshift
estimates. The other four sources are mainly constrained with the Ly$\alpha$
break feature.

  3. 3.

For the homogeneous sample from A23, we do not find systematic overestimates
in $z_{\rm phot}$ from $z_{\rm spec}$ reported in recent NIRSpec studies,
probably owing to the deep blue NIRCam filters (F115W, F150W) taken in UNCOVER
and some strict selection criteria adopted in the A23 selection. Using six
sources with multiple emission line detection, we also evaluate the offset of
the redshift estimates between the lines ($z_{\rm line}$) and the Ly$\alpha$
break ($z_{\rm break}$). We find that the offset can be as large as out to
$\pm 0.2$. This offset can be even worse with lower S/N data, which raises
caution in designing future follow-up spectroscopy for the break-only sources,
especially with ALMA.

  4. 4.

In addition to the X-ray luminous AGN confirmed at $z=10.07$ (Goulding et al.
2023), we newly identify a dusty broad-line (BL) AGN at $z=8.50$ (Kokorev et
al. 2023). Besides, the prism spectra for the two most UV-luminous galaxies in
our spec-$z$ sample cohort hint at AGN activity. This is inferred from several
highly-ionized gas emission lines detected at high significance levels (e.g.,
N iv] $\lambda$1487, C iv $\lambda$1549, He ii $\lambda$1640) and an elevated
[O iii] $\lambda$5008/H$\beta$ ratio exceeding 10 observed in ID10646 and
ID3686.

  5. 5.

In conjunction with the spec-$z$ confirmed sources in UNCOVER and other
general field surveys of CEERS and JADES, we infer lower bounds on the UV LFs
at $z\sim 9$, $z\sim 10$, and $z\sim 12$. Our results align with previous
photometric measurements and improve the lower constraints previously
established from recent spectroscopic studies. Our results also confirm the
high abundance of the UV-bright ($M_{\rm UV}\lesssim-20$) galaxies at
$z\gtrsim 9$, which challenges several current theoretical models. In the
$z\sim 9$ UVLF, we find a significant excess in the brightest $M_{\rm UV}$
bin, spanning $[-22:-21]$, comprising ID10646 and ID3686. Given their
different redshifts, this excess is attributable not to an overdensity but to
their uniquely UV-bright properties. This further reinforces the hypothesis
that these UV-luminous sources, characterized by multiple high-ionization
emission lines, are indeed AGNs.

  6. 6.

With the spec-$z$ confirmed BL AGN and X-ray luminous AGN, we also evaluate
the lower limits on the AGN LF at $z\sim 9$ and $z\sim 10$. These lower limits
require the AGN LFs at $z\sim$ 9–10 comparable or even higher amplitude than
the X-ray AGN LF estimated at $z\sim 6$.

  7. 7.

Our results suggest a relatively high AGN fraction of $>10$–35% even at
$z\gtrsim 9$, compared to the previous reports of $\approx$ 5-10% from the BL
AGN identification at $z\sim 4$-7. This high AGN fraction is likely attributed
to the comprehensive AGN recognition made feasible by our intensive 2.7–-11.8
hours prism exposures (cf. $\sim$1–-2.6 hours in previous NIRSpec studies for
BL AGN search) and the ancillary deep X-ray data, both of which benefit
substantially from the gravitational lensing effect. These results indicate
the plausible cause of the high abundance of $z>9$ galaxies claimed in the
recent photometric studies may be the AGNs.

  8. 8.

We identify the non-zero fluxes at the blueward of Ly$\alpha$ emission in the
prism spectra of the dusty BL AGN of ID20466 at $z=8.50$ and the potential AGN
source of ID10646 at $z=8.51$. The proximity zone size measurement shows that
these two sources resided in the same ionized bubble with $R_{\rm p}=7.69\pm
0.18$ proper Mpc. Both these sources notably deviate from the established
$M_{\rm UV}-R_{\rm p}$ relationship observed in luminous quasars at $z\sim 6$.
Despite its heavily dusty nature with $A_{\rm V}=2.1$, the Ly$\alpha$ line is
also detected from ID20466. A plausible explanation is that the covering
fraction of the dusty cloud surrounding the AGN is minimal, thereby
facilitating significant ionizing photon escape. This is in line with our
identification of the giant ionized bubble. Our results, taken in concert with
indications of the high AGN fraction even at $z\gtrsim 9$, suggest that AGNs
might have played a non-negligible role during cosmic reionization.

We thank Peter Larson, Darach Watson, Charlotte Mason, Kohei Inayoshi, and
Akio Inoue for helpful discussions on the proximity zone size measurements and
the interpretation of the ionized bubble identified at $z=8.5$. We are also
grateful to Steven Finkelstein and Pablo Arrabal-Haro for valuable discussions
and for sharing the materials for the survey volume calculations for the
NIRSpec programs conducted in the CEERS field. We also thank Rohan Naidu for
discussing the spec-$z$ confirmation results for $z>10$ galaxies, Nikko Cleri
for discussing the UV emission line properties, and Maximilien Franco for
sharing the UVLF measurements. This work is based on observations made with
the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the
Mikulski Archive for Space Telescopes at the Space Telescope Science
Institute, operated by the Association of Universities for Research in
Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. These observations
are associated with program JWST-GO-2561. Support for program JWST-GO-2561 was
provided by NASA through a grant from the Space Telescope Science Institute,
which is operated by the Association of Universities for Research in
Astronomy, Inc., under NASA contract NAS 5-03127. This project has received
funding from NASA through the NASA Hubble Fellowship grant HST-HF2-51505.001-A
awarded by the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Incorporated, under
NASA contract NAS5-26555. H.A. and IC acknowledge support from CNES, focused
on the JWST mission, and the Programme National Cosmology and Galaxies (PNCG)
of CNRS/INSU with INP and IN2P3, co-funded by CEA and CNES. 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.
AZ and LJF acknowledge support by Grant No. 2020750 from the United States-
Israel Binational Science Foundation (BSF) and Grant No. 2109066 from the
United States National Science Foundation (NSF), and by the Ministry of
Science & Technology, Israel. This work has received funding from the Swiss
State Secretariat for Education, Research and Innovation (SERI) under contract
number MB22.00072, as well as from the Swiss National Science Foundation
(SNSF) through project grant 200020_207349. The Cosmic Dawn Center (DAWN) is
funded by the Danish National Research Foundation under grant No. 140. The
work of CCW is supported by NOIRLab, which is managed by the Association of
Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation. MS acknowledges support from the
CIDEGENT/2021/059 grant, from project
PID2019-109592GB-I00/AEI/10.13039/501100011033 from the Spanish Ministerio de
Ciencia e Innovación - Agencia Estatal de Investigación. MST also acknowledges
the financial support from the MCIN with funding from the European Union
NextGenerationEU and Generalitat Valenciana in the call Programa de Planes
Complementarios de I+D+i (PRTR 2022) Project (VAL-JPAS), reference
ASFAE/2022/025.

Some/all of the data presented in this paper were obtained from the Mikulski
Archive for Space Telescopes (MAST) at the Space Telescope Science Institute.
The specific observations analyzed can be accessed via
http://dx.doi.org/10.17909/bvf5-mp20 (catalog 10.17909/bvf5-mp20). The reduced
data is also available via https://jwst-uncover.github.io/.

##  Appendix A Details of Individual Sources

Below, we briefly summarize the information for the spec-$z$ confirmed ten
UNCOVER sources presented in this paper.

20466 ($z=8.50$)

– This source is included in the MSA as a high-redshift dusty AGN candidate
due to the red color and compact morphology (ID13556 in Labbe et al. 2023). We
observed this source once in MSA2 with an exposure time of 2.7 hours. In
addition to the Ly$\alpha$ break feature, multiple emission lines are detected
at SNR $\geq$ 2.5, such as Ly$\alpha$, Mg ii $\lambda\lambda$2796, 2803, [Ne
iii] $\lambda$3869, [Ne iii] $\lambda$3968, [O iii] $\lambda$4363, [O iii]
$\lambda$4960, [O iii] $\lambda$5008, H$\delta$, H$\gamma$, and H$\beta$,
constraining its redshift at $z=8.500^{+0.000}_{-0.001}$. The unambiguous
broad line (BL) emission is identified in H$\beta$, being the highest redshift
BL AGN whose Balmer BL is securely (SNR $>$ 5) detected so far (see also
Larson et al. 2023). The Ly$\alpha$ line, bluer than its rest-frame
1216${\rm\AA}$, is also detected, and we discuss its possible physical origins
in Section 5. The photometric catalog ID is 21347 (Weaver et al. 2023).
Further details of the sample selection and characterizations will be
presented in J. Greene et al. in prep. and Kokorev et al. (2023).

10646 ($z=8.51$)

– This source is included in the MSA due to its uniquely red color
(F277W–F444W = 1.2 mag). We observed this source once in MSA2 with an exposure
time of 2.7 hours. In addition to the unambiguous Ly$\alpha$ break, multiple
emission liens are detected at SNR $\geq 2.5$, such as N iv] $\lambda$1487, C
iv $\lambda$1549, O iii] $\lambda\lambda$1661,1666, He ii $\lambda$1640, C
iii] $\lambda\lambda$1907,1909, Mg ii $\lambda\lambda$2796,2803, [Ne v]
$\lambda$3346, [O ii] $\lambda\lambda$3727,3730, [Ne iii] $\lambda$3869, [Ne
iii] $\lambda$3968, [O iii] $\lambda$4363, [O iii] $\lambda$4960, [O iii]
$\lambda$5008, H$\gamma$, H$\delta$, H$\beta$, and He i, constraining its
redshift at $8.511^{+0.000}_{-0.001}$. Note that the [Ne v] $\lambda$3426/[Ne
v] $\lambda$3346 ratio is almost constant at 2.73. We confirm [Ne v]
$\lambda$3426 is also observed in our spectrum with SNR $\sim 2$, while it
indicates [Ne v] $\lambda$3426/[Ne v] $\lambda$3346 $\sim 1$. This might
suggest that the [Ne v] $\lambda$3346 line detection could be spurious,
although it is challenging to conclude with their current SNRs. ID10646 is
spatially separated from ID20466 by a physical scale of 380 kpc in the source
plane, and their redshift difference is only 0.01. We thus interpret these
sources as residing in the same massive dark matter halo. Similar to ID20466,
the continuum blueward of the Ly$\alpha$ line is also detected in ID10646, and
we discuss its possible physical origins in Section 5. ID10646 is uniquely UV
bright. With $M_{\rm UV}=-21.5$ mag, it is comparably bright to GNz11 (e.g.,
Bunker et al. 2023b) and shows several highly ionized gas emission lines at
high significance levels (e.g., N iv] $\lambda$1487, C iv $\lambda$1549, He ii
$\lambda$1640). However, we cannot rule out the possibility that the galaxy
emission is driven by star-forming activity rather than AGN based on rest-
frame UV-optical line diagnostics alone (e.g., Feltre et al. 2016). The
photometric catalog ID is 11701 (Weaver et al. 2023). Further details and
characterizations will be presented in J. Weaver et al. in prep.

3686 ($z=9.33$)

– This source is included in the MSA as one of the robust $z>9$ candidates
selected in Atek et al. (2023b) (hereafter A23). We observed this source once
in MSA2 with an exposure time of 2.7 hours. In addition to the unambiguous
Ly$\alpha$ break, multiple emission lines are detected at SNR $\geq$ 2.5, such
as N iv] $\lambda$1487, [Ne v] $\lambda$3426, [O ii]
$\lambda\lambda$3723,3730, [Ne iii] $\lambda$3869, [O iii] $\lambda$4960, [O
iii] $\lambda$5008, and H$\gamma$, constraining its redshift at
$z=9.325_{-0.001}^{+0.000}$. As part of the GLASS-JWST survey (#1324; PI. T.
Treu; Treu et al. 2022) and a follow-up DDT program (#2756; PI. W. Chen), a
consistent NIRSpec/prism spectroscopic confirmation has also been reported in
Boyett et al. (2023), while the previous prism observations only cover the
wavelength range of $\sim 1.1$–4.5 $\mu$m with detector gaps. The full prism
spectrum coverage of $\sim 0.6$–5.2$\mu$m newly detects several emission lines
from this source, including N iv] $\lambda$1487, H$\beta$ and [O iii]
$\lambda$4960, 5008. On the other hand, the [Ne v] $\lambda$3426 line is not
detected in the previous observations, although its observed wavelength was
covered by the previous observations. This suggests that the [Ne v]
$\lambda$3426 line could be spurious, while the shutter configurations of MSA
are not exactly the same between previous and our observations. The source is
spatially extended, indicative of an interacting system (Boyett et al. 2023).
ID3686 is the most luminous high-redshift galaxy candidate at $z\gtrsim 9$ in
the original photometric catalog with $M_{\rm UV}=-21.7$. Employing a nearby
empty shutter, we also produce spectra for the three shutters with the global
background subtraction, where the [O iii] $\lambda$5008/H$\beta$ shows
uniquely high ratios of $\sim 11$–18 in the central and Southern East shutters
(see Section 3.1). These ratios exceed the maximum value of $\sim 10$ observed
in recent NIRSpec studies for galaxies at $z\sim 2$-9 and fall in the AGN
regime in the [N ii], [S ii], and [O i] BPT diagrams (Sanders et al. 2023).
Such a high ratio may also be induced by the shock excitation (e.g., Kewley et
al. 2013; Hirschmann et al. 2022), while the fact that the similarly high
ratio also observed in the Southern East shutter, where the emission is
dominated by the compact component in the NIRCam map, indicates that these
line properties may be caused by a strong radiation of an AGN. The photometric
catalog ID is 4745 (Weaver et al. 2023).

22223 ($z=9.57$)

– This source is included in the MSA as one of $z>9$ candidates selected from
the SED analysis using eazy and prospector (B. Wang et al. submitted). We
observed this source once in MSA4 with an exposure time of 4.4 hours. In
addition to the unambiguous Ly$\alpha$ break, multiple emission lines are
detected at SNR $\geq$ 2.5, including C iv $\lambda$1549, [O iii]
$\lambda$4960, [O iii] $\lambda$5008, H$\delta$, H$\gamma$, and H$\beta$. In
the 2D spectrum, we also identify an unknown line at $\sim$0.9$\mu$m, probably
due to a failed open shutter, though our extraction does not include either
the positive and negative features from this line, and thus this does not
affect our results. The prism spectrum shows a softened Ly$\alpha$ break
shape, also reported in other $z>9$ prism-observed galaxies. This shape is
likely caused by some combination of effects of the Ly$\alpha$ damping wing,
the intrinsic SED shape, and/or an additional DLA system (e.g., Curtis-Lake et
al. 2023; Arrabal Haro et al. 2023a; Umeda et al. 2023; Heintz et al. 2023).
The photometric catalog ID is 23089 (Weaver et al. 2023).

31028 ($z=9.74$)

– This source is included in the MSA as one of $z>9$ candidates with a high
magnification ($\mu>5$) selected from SED analysis using eazy and prospector
(B. Wang et al. submitted). We observe this source in MSA3 and MSA6, with a
total exposure time of 6.9 hours. However, due to the lack of an obvious
continuum trace in the 2D spectrum taken in MSA3, probably because of more
significant slitloss (see Fig. 2) and the potential systematic uncertainty in
the slitloss correction in the coadd process, we only use the data taken in
MSA6 in this paper (4.4h). Our template fitting supports the high-$z$ solution
from the Ly$\alpha$ break feature (see also the blue curve representing the
forced low-$z$ best-fit solution in Fig. 3), constraining its redshift at
$z=9.740^{+0.000}_{-0.001}$, where the Ly$\alpha$ line is tentatively detected
at SNR$\sim$3\. No emission lines are detected above SNR $\geq 2.5$. The
redshift estimate subsequently leads to a magnification estimate of
$\mu=6.73^{+1.50}_{-0.05}$ and $M_{\rm UV}=-17.31$ mag, making it
intrinsically the faintest source among the spec-$z$ confirmed objects at
$z\geq 8.5$ with JWST so far (e.g., Williams et al. 2022; Roberts-Borsani et
al. 2022; Fujimoto et al. 2023b; Arrabal Haro et al. 2023b, a; Hainline et al.
2023). The photometric catalog ID is 31955 (Weaver et al. 2023).

13151 ($z=9.88$)

– This source is included in the MSA as one of $z>9$ candidates with a high
magnification ($\mu>5$) selected from the SED analysis using eazy and
prospector (B. Wang et al. submitted). We observed this source three times in
MSA5, MSA6, and MSA7, with a total exposure time of 11.8 hours. In addition to
the unambiguous Ly$\alpha$ break, multiple emission lines are detected at SNR
$\geq$ 2.5, including O iii] $\lambda\lambda$1661,1666, and C iii]
$\lambda\lambda$1907,1909. Previous NIRSpec/prism observations detect the
Ly$\alpha$ break feature, providing the redshift solution of $z=9.79$ via a
similar eazy template fitting method Roberts-Borsani et al. (2023), while the
multiple emission line identification and the better sensitivity in the
Ly$\alpha$ break make the redshift solution firmly improved. The photometric
catalog ID is 14088 (Weaver et al. 2023).

26185 ($z=10.07$)

– This source is included in the MSA as one of the robust $z>9$ candidates
selected in A23 (see also e.g., Castellano et al. 2023). Moreover, an X-ray
luminous AGN has been reported from a 1.25 Ms deep Chandra observation, making
this the highest-$z$ X-ray AGN known (Bogdan et al. 2023). We observe this
source twice in MSA1 and MSA4, with a total exposure time of 7.1 hours. In
addition to the unambiguous Ly$\alpha$ break, multiple emission lines are
detected at SNR $\geq$ 2.5, such as C iii] $\lambda\lambda$1709,1909, [O ii]
$\lambda\lambda$3727, 3730, [Ne iii] $\lambda$3869, [Ne iii] $\lambda$3968,
and H$\gamma$, constraining its redshift at $z=10.071_{-0.001}^{+0.000}$. The
photometric catalog ID is 27025 (Weaver et al. 2023). Further details and
characterizations have been presented in Goulding et al. (2023) as UHZ1.

37126 ($z=10.23$)

– This source is included in the MSA as one of the robust $z>9$ candidates
selected in A23. We observed this source twice in MSA3 and MSA4, with a total
exposure time of 6.9 hours. The source failed to be successfully extracted
from MSA3 in our early reduction, and thus we use the data from MSA4 (4.4h) in
this analysis. The peaky feature at $\sim 4.8\mu$m in the spectrum is an
artifact, and we mask the relevant pixels in our template fitting. From the
unambiguous Ly$\alpha$ break, the redshift is securely estimated at
$z=10.255^{+0.001}_{-0.001}$ with N iii] $\lambda\lambda$1747,1749 detection
at SNR $\sim$ 3\. The photometric catalog ID is 38095 (Weaver et al. 2023).

38766 ($z=12.39$)

– This source is included in the MSA as one of the robust $z>12$ candidates
selected in A23. We observed this source once in MSA4, with an exposure time
of 4.4 hours. The unambiguous Ly$\alpha$ break, a tentative He i
(SNR$\sim$2.5) are detected, constraining the source redshift at
$z=12.393^{+0.004}_{-0.001}$. At a consistent redshift, tentative [O ii]
$\lambda\lambda$3727,3730 and Mg ii $\lambda\lambda$2796,2803 are also
detected (SNR$\sim$2). Within a $\sim$2 arcmin on the sky, a remarkably UV
bright galaxy is identified with a very close photometric redshift ($z_{\rm
phot}=12.4^{+0.1}_{-0.3}$; Naidu et al. 2022b, see also Castellano et al.
2022; Donnan et al. 2022; Harikane et al. 2023b; Bouwens et al. 2022a), where
there might exist a galaxy overdensity. The photometric catalog ID is 39753
(Weaver et al. 2023). Further details and characterizations have been
presented in Wang et al. (2023b) as UNCOVER-z12.

13077 ($z=13.08$)

– This source is included in the MSA as one of $z>12$ candidates selected from
the SED analysis using eazy and prospector (B. Wang et al. submitted). We
observe this source twice in MSA5 and MSA7, with a total exposure time of 7.4
hours. No emission lines are detected above SNR $\geq 2.5$, while our template
fitting shows the high-$z$ solution from the Ly$\alpha$ break feature (see
also the blue curve representing the forced low-$z$ best-fit solution in Fig.
3), constraining its redshift at $z=13.079^{+0.014}_{-0.001}$. Although the
Ly$\alpha$ break feature is less secure than other sources, the template
fittings to both individual spectra taken in MSA5 and MSA7 show the high-$z$
solution as well. The photometric catalog ID is 14019 (Weaver et al. 2023).
Further details and characterizations have been presented in Wang et al.
(2023b) as UNCOVER-z13.

##  Appendix B IDs in different literature

Our ten spec-$z$ confirmed sources have also been reported in previous studies
in various contexts. Here, we summarize the IDs of the ten spec-$z$ confirmed
sources presented in different literature.

Table 4: IDs of the ten spec-$z$ confirmed sources at $z\geq 8.5$ in our
UNCOVER/NIRSpec observations

ID (This) | ID (We23) | ID (Other)
---|---|---
(1) | (2) | (3)
20466 | 21347 | 13556 (L23)
10646 | 11701 |  $\cdots$
3686 | 4745 | Gz9p3 (B23), 2065 (A23)
22223 | 23089 |  $\cdots$
31028 | 31955 |  $\cdots$
13151 | 14088 | JD1 (Z14), (RB23)
26185 | 27025 | UHZ1 (C23), 21623 (A23)
37126 | 38095 | 39074 (A23)
38766 | 39753 | 42329 (A23), UNCOVER-z12 (Wa23)
13077 | 14019 | UNCOVER-z13 (Wa23)

Note. — (1) Source ID used in the MSA design and this paper. (2) Source ID
used in the UNCOVER photometric catalog of (Weaver et al. 2023). (3) Source ID
or name used in other literature (L23; Labbe et al. 2023, A23; Atek et al.
2023b, B23; Boyett et al. 2023, C23; Castellano et al. 2023, RB23; Roberts-
Borsani et al. 2023, G23; Goulding et al. 2023, Wa23; Wang et al. 2023b, Z14;
Zitrin et al. 2014).

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