# The Magellan M2FS spectroscopic survey of high-redshift galaxies: the
brightest Lyman-break galaxies at $z\sim 6$

Shuqi Fu Department of Astronomy, School of Physics, Peking University,
Beijing 100871, China  Kavli Institute for Astronomy and Astrophysics, Peking
University, Beijing 100871, China  Linhua Jiang Department of Astronomy,
School of Physics, Peking University, Beijing 100871, China  Kavli Institute
for Astronomy and Astrophysics, Peking University, Beijing 100871, China
Yuanhang Ning Department of Astronomy, Tsinghua University, Beijing 100084,
China  Weiyang Liu Department of Astronomy, School of Physics, Peking
University, Beijing 100871, China  Kavli Institute for Astronomy and
Astrophysics, Peking University, Beijing 100871, China  Zhiwei Pan Department
of Astronomy, School of Physics, Peking University, Beijing 100871, China
Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing
100871, China

###### Abstract

We present a study of a sample of 45 spectroscopically confirmed, UV luminous
galaxies at $z\sim 6$. They were selected as bright Lyman-break galaxies
(LBGs) using deep multi-band optical images in more than 2 deg2 of the sky,
and subsequently identified via their strong Ly$\alpha\ $emission. The
majority of these LBGs span an absolute UV magnitude range from $-22.0$ to
$-20.5$ mag with Ly$\alpha\ $equivalent width (EW) between $\sim$10 and
$\sim$200 Å, representing the most luminous galaxies at $z\sim 6$ in terms of
both UV continuum emission and Ly$\alpha\ $line emission. We model the SEDs of
10 LBGs that have deep infrared observations from HST, JWST, and/or Spitzer,
and find that they have a wide range of stellar masses and ages. They also
have high star-formation rates ranging from a few tens to a few hundreds of
Solar mass per year. Five of the LBGs have JWST or HST images and four of them
show compact morphology in these images, including one that is roughly
consistent with a point source, suggesting that UV luminous galaxies at this
redshift are generally compact. The fraction of our photometrically selected
LBGs with strong Ly$\alpha\ $emission ($\mathrm{EW}>25$ Å) is about $0.2$,
which is consistent with previous results and supports a moderate evolution of
the IGM opacity at the end of cosmic reionization. Using deep X-ray images, we
do not find evidence of strong AGN activity in these galaxies, but our
constraint is loose and we are not able to rule out the possibility of any
weak AGN activity.

High-redshift galaxies (734), Lyman-break galaxies (979), Lyman-alpha galaxies
(978), Galaxy properties (615), Reionization (1383)

††software: Astropy (Astropy Collaboration et al., 2013, 2018, 2022), CIGALE
(Noll et al., 2009), GALFIT (Peng et al., 2002, 2010)

##  1 Introduction

High-redshift ($z\geq 6$) galaxies are a key probe to understand the early
Universe, including the early galaxy formation and evolution, the development
of large-scale structures, and the history of cosmic reionization. In the past
twenty years, a number of works have been conducted to search for high-
redshift galaxies, and the number of known galaxies has increased dramatically
thanks to the advances of instrumentation on the Hubble Space Telescope (HST)
and large ground-based telescopes (e.g., Kashikawa et al. 2006; Vanzella et
al. 2009; Hu et al. 2010; Wilkins et al. 2010; Stark et al. 2011; McLeod et
al. 2016; Bouwens et al. 2021; Zheng et al. 2017; Ono et al. 2018; Ning et al.
2020; Wold et al. 2022). The majority of the earlier known galaxies at $z\geq
6$ are photometrically selected Lyman-break galaxies (LBGs) or LBG candidates
selected by the dropout technique. The narrowband technique (or the Ly$\alpha\
$technique) is a complementary method to find high-redshift galaxies. Ground-
based narrowband imaging surveys are efficient in finding Ly$\alpha\ $emitting
galaxies (Ly$\alpha\ $emitters, or LAEs) at certain redshift slices such as
$z\approx 5.7$, 6.6, and 7.0 that correspond to wavelength windows with weak
OH sky lines.

Before the launch of James Webb Space Telescope (JWST), the majority of the
photometrically selected high-redshift galaxies have not been
spectroscopically observed. While narrowband selected LAE candidates typically
have a high success rate of spectroscopic confirmation, only a small fraction
of photometrically selected LBGs are spectroscopically confirmed (e.g.,
Toshikawa et al. 2012; Finkelstein et al. 2013; Watson et al. 2015; Roberts-
Borsani et al. 2016; Song et al. 2016; Larson et al. 2022). Spectroscopic
observations are important to understand LBGs, because they can not only tell
us whether an object is a real LBG, but also provide a key parameter,
redshift. Large samples of high-redshift galaxies have been frequently used to
measure galaxy properties, such as UV slopes (e.g., Dunlop et al. 2012;
Finkelstein et al. 2012a; Bouwens et al. 2014), galaxy morphology (e.g.,
Guaita et al. 2015; Kawamata et al. 2015; Shibuya et al. 2015, 2016; Curtis-
Lake et al. 2016; Kobayashi et al. 2016; Liu et al. 2017; Naidu et al. 2022),
stellar populations, and star-formation rates (e.g., Egami et al. 2005; Stark
et al. 2013; González et al. 2014; Faisst et al. 2016; Castellano et al. 2017;
Karman et al. 2017). These studies are mostly based on photometric samples.

Recently, JWST is revolutionizing our understanding of high-redshift galaxies.
JWST is not only breaking redshift records for the most distant objects (e.g.,
Arrabal Haro et al., 2023; Curtis-Lake et al., 2023; Fujimoto et al., 2023;
Hsiao et al., 2023; Roberts-Borsani et al., 2023), but also rapidly expanding
the sample sizes of high-redshift galaxies, photometrically and
spectroscopically (e.g., Atek et al. 2023; Champagne et al. 2023;
Leethochawalit et al. 2023; Yan et al. 2023). In particular, JWST NIRCam and
NIRISS observations offer slitless spectroscopy that makes it feasible to
obtain spectra for large galaxy samples (e.g., Matthee et al. 2023; Oesch et
al. 2023; Wang et al. 2023). In addition, JWST NIRSpec grating observations
provide medium-resolution spectra that allow detailed studies of line emission
and absorption (e.g., Bunker et al. 2023; Mascia et al. 2023; Prieto-Lyon et
al. 2023; Tang et al. 2023; Tacchella et al. 2023). Despite the great power of
JWST, its field-of-view is small compared to ground-based telescopes.
Therefore, large-area, ground-based observations are highly complementary to
JWST observations.

High-redshift galaxies are also thought to be the major source of ionizing
photons at the epoch of cosmic reionization. Recent studies have suggested
that star-forming galaxies, rather than quasars or AGN, provide most of the
ionizing photons needed for reionization (e.g., Finkelstein et al. 2012b;
Robertson et al. 2015; Onoue et al. 2017; Jiang et al. 2022). Spectroscopic
samples of high-redshift LBGs can be used to constrain the properties of the
IGM during this epoch. For example, Ly$\alpha\ $photons are easily absorbed by
neutral hydrogen, making the Ly$\alpha\ $line a sensitive probe of the
ionization state of the IGM. Therefore, the fraction of LBGs that exhibit
strong Ly$\alpha\ $emission lines can trace the fraction of neutral hydrogen
in the IGM at $z\geq 6$. This so-called Ly$\alpha\ $visibility test from
previous works has shown that the fraction of LBGs with strong Ly$\alpha\
$emission increases steadily from $z\sim 2$ to 6 and then declines sharply
towards $z\sim 7$ (e.g., Stark et al. 2010, 2011; Ono et al. 2012; Schenker et
al. 2012; Finkelstein et al. 2013; Tilvi et al. 2014; Vanzella et al. 2014;
Cassata et al. 2015; Schmidt et al. 2016; Jung et al. 2018, 2022). This is
broadly consistent with the evolving neutral fraction in the IGM at the end of
the reionization epoch.

In this paper, we present a sample of 45 LBGs with spectroscopically confirmed
Ly$\alpha\ $emission lines at $z\sim 6$ from a survey of high-redshift
galaxies using the Magellan telescope (Jiang et al., 2017). In Section 2, we
introduce the survey program, target selection, spectroscopic observations,
and data reduction. In Section 3, we construct our spectroscopic sample of
LBGs. In Section 4, we present the properties of the galaxies using spectra
and images from multi-wavelength observations. We discuss our results in
Section 5, and summarize our paper in Section 6. Throughout the paper, we use
a standard flat cosmology with $\rm H_{0}=70\ km\ s^{-1}\ Mpc^{-1}$,
$\Omega_{m}=0.3$ and $\Omega_{\Lambda}=0.7$. All magnitudes refer to the AB
system.

##  2 Target Selection and Spectroscopic Observations

###  2.1 A Magellan M2FS Survey of $z\sim 6$ Galaxies

Table 1: Survey Fields

Fields | Coordinates | Area | Filters | $R/r^{\prime}$ | $I/i^{\prime}$ | $z^{\prime}$ | Candidates | Good | Possible
---|---|---|---|---|---|---|---|---|---
| (J2000) | (deg2) |  | (mag) | (mag) | (mag) |  |  |
SXDS | 02:18:00–05:00:00 | $1.12$ | $R,i^{\prime},z^{\prime}$ | $27.4$ | $27.4$ | $26.2$ | $368$ | $25$ | $7$
A370a | 02:39:55–01:35:24 | $0.16$ | $R,I,z^{\prime}$ | $27.0$ | $26.2$ | $26.3$ | $86$ | $3$ | $2$
ECDFS | 03:32:25–27:48:18 | $0.22$ | $r^{\prime},i^{\prime},z^{\prime}$ | $27.4$ | $27.5$ | $26.7$ | $105$ | $3$ | $2$
COSMOS | 10:00:29+02:12:21 | $1.26$ | $r^{\prime},i^{\prime},z^{\prime}$ | $26.7$ | $26.3$ | $25.5$ | $145$ | $3$ | $0$

Note. — Col.(1): Field names. Col.(2): Center coordinates. Col.(3): Area
coverage. Col.(4): Broadband filters. Col.(5-7): Magnitude limits ($5\sigma$
detections in a $2^{\prime\prime}$-diameter aperture). Col.(8): Numbers of LBG
candidates. Col.(9-10): Numbers of spectroscopically confirmed LBGs in the
‘good’ sample and the ‘possible’ sample.

We carried out a large spectroscopic survey of galaxies at $5.5<z<6.8$, using
the large field-of-view (FoV), fiber-fed, multi-object spectrograph M2FS
(Mateo et al., 2012) on the 6.5 m Magellan Clay telescope. The overview of the
survey program was provided in Jiang et al. (2017). The survey was designed to
build a large and homogeneous sample of high-redshift galaxies, including LAEs
at $z\approx 5.7$ and 6.6, and LBGs with strong Ly$\alpha\ $emission at
$5.5<z<6.8$. Based on this sample, we can study the properties of these
galaxies, the Ly$\alpha\ $luminosity function (LF) and its evolution at high
redshift, high-redshift protoclusters, cosmic reionization, etc. Taking
advantage of a $30^{\prime}$-diameter FoV, M2FS is very efficient in
identifying relatively bright high-redshift galaxies (e.g., Oyarzún et al.
2016, 2017). The fields that we chose to observe are well-studied deep fields,
including the Subaru XMM-Newton Deep Survey (SXDS), A370, the Extended Chandra
Deep Field- South (ECDFS), COSMOS, etc. They cover a total of $\sim 2$ deg2.
These fields have deep Subaru Suprime-Cam imaging data in a series of broad
bands $BVR(r^{\prime})I(i^{\prime})z^{\prime}$ and narrow bands (e.g., NB816
and NB921). The images have been used to select LAEs at $z\approx 5.7$ and 6.6
and LBGs at $z\sim 6$ in the survey program. The fields are summarized in
Table 1. Some of the fields were later observed by Subaru Hyper Suprime-Cam
(HSC) (Aihara et al., 2022), but we did not use the HSC data by the time of
our observations.

The M2FS observations of the program have been completed and the data have
been reduced. From the survey, Ning et al. (2020) built a large sample of 260
LAEs at $z\approx 5.7$ and Jiang et al. (2018) discovered a giant protocluster
at $z\approx 5.7$. Ning et al. (2022) then assembled a sample of 36 LAEs at
$z\approx 6.6$. By comparing with the $z\approx 5.7$ Ly$\alpha\ $LF, they
confirmed that there is a rapid LF evolution at the faint end, but there is a
lack of evolution at the bright end. Wu et al. (2020) detected diffuse
Ly$\alpha\ $halos around galaxies at $z\approx 5.7$ by stacking 310
spectroscopically confirmed LAEs. In this paper, we focus on luminous LBGs at
$z\sim 6$. The details of the target selection is presented in Section 2.3.

###  2.2 Spectroscopic Observations and Data Reduction

We carried out the M2FS observations in 2015–2018. The resolving power of the
spectra is $R\sim 2000$, and the wavelength coverage is roughly from 7600 to
9600 Å, corresponding to a redshift range of $z=5.3–6.8$ for the detection of
the Ly$\alpha\ $emission line. The selection of M2FS pointing centers was
limited by the number and spatial distribution of bright stars that were used
for guiding, alignment, and primary-mirror wavefront corrections. The layout
of the pointings is shown in Figure 1. The effective integration time per
pointing was about 5 hr on average, and the individual exposure time was 30
min, 45 min, or 1 hr, depending on airmass and weather conditions.

We used our own customized pipeline for data reduction, including bias
(overscan) correction, dark subtraction, flat-fielding, cosmic ray
identification, wavelength calibration, and sky subtraction. For detailed
steps, see Jiang et al. (2017). The pipeline produces combined 1D and 2D
spectra as well as the 2D spectra of individual exposures. This pipeline is
performed for all targets in the same fields, including the candidates of LAEs
and LBGs. The final 1D and 2D spectra were used to identify Ly$\alpha\
$emission lines.

Figure 1: Deep fields used in this work. The large circles represent the M2FS
pointings. All points represent the LBG targets observed by our M2FS survey.
The color-coded points represent the spectroscopically confirmed LBGs with
Ly$\alpha\ $emission: the large points represent LBGs in the ‘good’ sample and
the small points represent LBGs in the ‘possible’ sample. The colors indicate
their spectroscopic redshifts measured from the Ly$\alpha\ $lines. The
histogram on the right shows the the redshift distribution of the ‘good’
sample (blue) and the ‘possible’ sample (orange).

###  2.3 Selection of $z\sim 6$ LBG Candidates

Figure 2: Upper panel: transmission curves of the Suprime-Cam broadband
filters that were used for our LBG candidate selection. Lower panel: expected
values of $i’-z’$ or $I-z’$ as a function of redshift. The simulated LBG
spectra have a UV continuum slope of –2.0 and a Ly$\alpha\ $emission line with
two EW values, and the IGM absorption model from Inoue et al. (2014) is
applied.

Our M2FS observations included a sample of luminous LBG candidates at $z\sim
6$. Deep Subaru Suprime-Cam images were used for the selection of these
candidates. The selection was mainly based on the $i-z^{\prime}$ color (here
$i$ means either $i^{\prime}$ or $I$). The upper panel of Figure 2 shows the
filters that were used for our target selection. The selection limit is
$7\sigma$ detections in the $z^{\prime}$ band. We applied the following color
cuts,

$i-z^{\prime}>1.3\ {\rm or}\ i<3\sigma\ {\rm detection},$ $r-z^{\prime}>2.0\
{\rm or}\ r<3\sigma\ {\rm detection}.$

To illustrate the evolution of the $i-z^{\prime}$ color with redshift, we
produced a simple galaxy spectrum consisting of a power-law continuum and a
Ly$\alpha\ $emission line. The power-law continuum has a fixed slope of –2.0,
and the Ly$\alpha\ $equivalent width (EW) has two values, 20 and 200 Å,
respectively. We then apply the Inoue et al. (2014) IGM attenuation models to
the spectra. The result is shown in the lower panel of Figure 2. The value of
$i-z^{\prime}$ increases rapidly at $z\sim 6$. With our selection criteria,
galaxies with $z\gtrsim 5.6$ can be selected. The actual selection function is
more complex and depends on the galaxy continuum emission and Ly$\alpha\ $line
emission. We also required no detections ($<2\sigma$) in any bands bluer than
$r$ (or $R$), assuming that no flux can be detected at the wavelength bluer
than the Lyman limit. Each candidate was visually inspected.

Compared to the previous selection criteria of LBGs (e.g., Ono et al. 2018;
Bouwens et al. 2021), our selection criteria are relatively conservative.
Previous studies usually applied redder $i-z$ colors (e.g., $i-z>1.5$ in Ono
et al. 2018), and often considered infrared photometry. For example, many
contaminants of high-redshift galaxies are late-type dwarf stars or low-
redshift red (dusty) galaxies, and thus tend to have redder colors in the
near-IR. We did not use near-IR data, despite the fact that some of our fields
are covered by deep near-IR images. Our conservative criteria allow us to
include less promising candidates and thus achieve higher sample completeness.
On the other hand, it means a relatively lower efficiency, i.e., a larger
fraction of contaminants. It is not a concern in our program, since we have
enough fibers to cover almost all these candidates. In Table 1, Column 8 shows
the numbers of the candidates in each field that were observed by our program.

##  3 Spectroscopic Results

###  3.1 Ly$\alpha\ $Line Identification and a Sample of $z\sim 6$ LBGs

In this subsection, we will describe how to identify Ly$\alpha\ $emission
lines in the spectra, and present two samples of spectroscopically confirmed
LBGs, including a ‘good’ sample with high confidence and a ‘possible’ sample
with lower confidence. We will then derive some basic properties of the
Ly$\alpha\ $lines.

We use both 1D and 2D spectra to identify Ly$\alpha\ $emission lines. We first
carry out an initial search. For each galaxy, we bin its 1D spectrum by 3 Å
and search for an emission line with signal-to-noise ratio S/N $>5$ in the
whole wavelength range. For a line in the ‘good’ sample, it needs to cover at
least 5 contiguous pixels with S/N $>1$ in each pixel in the binned spectrum.
This is determined by the typical Ly$\alpha\ $emission line width in our
spectra. For the ‘possible’ sample, we allow a line to cover only 3 or 4
contiguous pixels with S/N $>1$. The S/N of a line is estimated by summing up
the corresponding pixels of the line in the original spectrum. The reason of
adopting a criterion of S/N $>1$ is that most of the regions in the LBG
spectra are contaminated by strong OH sky lines. If a Ly$\alpha\ $line is
close to OH lines, it could be severely affected by sky line residuals after
the sky background subtraction.

After the initial screening above, we visually inspect each identified
emission line in the 2D spectra, including the combined spectrum and the
spectra of individual exposures. Obvious false detections are removed. The
Ly$\alpha\ $emission line of a $z\sim 6$ galaxy is often much broader than
other emission lines at much lower redshift in the observed frame due to the
(1+$z$) broadening. It also shows an asymmetric profile due to strong IGM
absorption and ISM kinematics. Possible contaminant lines from low-redshift
galaxies usually appear narrow and symmetric, including H$\beta$, $[$O III$]$
$\lambda$5007, or H$\alpha$ emission lines. In addition, our resolving power
of $\sim 2000$ can nearly resolve the $[$O II$]$ $\lambda\lambda$3727, 3729
doublet. To quantify the asymmetry of the Ly$\alpha\ $line, we calculate the
weighted skewness $S_{W}$ introduced by Shimasaku et al. (2006). This is the
skewness (or third moment) of the line multiplied by
$(\lambda_{10,r}-\lambda_{10,b})$, where $\lambda_{10,r}$ and $\lambda_{10,b}$
are the wavelengths where the flux drops to $10\%$ of its peak value at the
red and blue sides of the line, respectively. Since the Ly$\alpha\ $emission
of high-redshift galaxies tends to be broader than other emission lines of
lower-redshift galaxies, this line width factor enhances the difference
between Ly$\alpha\ $and other lines. The Ly$\alpha\ $$S_{W}$ values of the
LBGs in our ‘good’ sample and ‘possible’ sample range from 2.3 to 18.4 and
from 2.1 to 12.2, respectively. In comparison, we also calculate $S_{W}$ of 10
emission lines that are identified as low-redshift interlopers based on their
double-peak (e.g., an $[$O II$]$ $\lambda\lambda$3727, 3729 doublet at $z\sim
1.3$), or based on the detection of other lines at the same redshift in the
spectra (e.g., an $[$O III$]$ $\lambda$5007 and corresponding $[$O III$]$
$\lambda$4959 at $z\sim 0.72$). Their $S_{W}$ values span a range from $-12.5$
to $3.3$. Usually $S_{W}>3$ has been used as a threshold to distinguish
Ly$\alpha\ $from other lines, but the asymmetric shape of a high-redshift
Ly$\alpha\ $emission line may not be obvious when its S/N is relatively low
(e.g., Ning et al., 2022). For three LBGs with $2.1<S_{W}<3$, they were not
detected in two blue bands $B$ and $V$, so we put them in the ‘possible’
sample.

We emphasize that in our LBG candidate selection procedure addressed in
Section 2.3, we required non-detections for the candidates in the $B$\- and
$V$-band images. These images reach a great depth of $\geq 28.5$ mag. They can
efficiently exclude low-redshift interlopers.

Figure 3: M2FS 1D and 2D spectra of the 34 LBGs in our $z\approx 6.6$ sample.
In each panel, the 1D spectrum has been binned to 3 Å per pixel in arbitrary
units. The light grey line indicates the $1\sigma$ uncertainty. The best-fit
Ly$\alpha\ $line template is over-plotted in blue. The red dashed line shows
the peak position of the Ly$\alpha\ $emission line. The source numbers
correspond to those shown in Column 1 in Table 2.

Finally, the ‘good’ sample of 34 LBGs has convincing, luminous Ly$\alpha\
$emission lines with S/N $>5$ and asymmetric profiles. Figure 3 shows the 1D
and 2D spectra in the Ly$\alpha\ $region of the 36 LBGs in the ‘good’ sample.
We can see that strong emission lines clearly show asymmetric line shapes due
to the IGM absorption and ISM kinematics. The ‘possible’ sample contains 11
LBGs with less promising Ly$\alpha\ $emission lines. We show all the confirmed
LBGs in Table 2. Column 5 lists the spectroscopic redshifts measured from the
Ly$\alpha\ $lines, and their errors are smaller than 0.001. Figure 1
illustrates the positions of the targets in the five fields, including the
observed candidates (all points) and the spectroscopically confirmed LBGs
(color-coded points). The large circles represent the M2FS pointings. Despite
the fact that the exposure time and depth of the individual pointings are
similar, the numbers of the confirmed LBGs in these pointings are quite
different, suggesting the existence of significant cosmic variance. As
mentioned in Ning et al. (2020, 2022), COSMOS1 and COSMOS3 have some alignment
problems during the observations, so they only have a few LBGs confirmed.

###  3.2 Properties of the Ly$\alpha\ $Emission Lines

We measure redshifts and Ly$\alpha\ $line flux for the LBGs using a Ly$\alpha\
$profile template. The template is a composite Ly$\alpha\ $spectrum of a large
number of LAEs at $z\approx 5.7$ (Ning et al., 2020). For each LBG, we first
estimate an initial redshift using the wavelength of the Ly$\alpha\ $line peak
(1215.67 Å). We then refine this redshift and model the Ly$\alpha\ $profile as
follows. From the Ly$\alpha\ $template, we generate a set of model spectra for
a grid of peak values, line widths, and redshifts. The peak values vary from
0.9 to 1.1 (times of the observed peak value) with a step size of 0.01. The
line widths are from 0.5 to 2.0 times the original width with a step size of
0.1. The redshift values vary within the initial redshift $\pm 0.002$ with a
step size of 0.0001. We find the best-fit model for each LBG using the
$\chi^{2}$ method. The best-fit redshifts are listed in Column 5 of Table 2.

Table 2: Confirmed LBGs with Ly$\alpha\ $emission lines

No. | Field | R.A. | Decl. | Redshift | $i$ | $z^{\prime}$ | log10L(Ly$\alpha$) | $M_{\rm UV}$ | Ly$\alpha\ $EW | $\beta_{\mathrm{UV}}$
---|---|---|---|---|---|---|---|---|---|---
|  | (J2000) | (J2000) |  | (mag) | (mag) | (erg/s) | (mag) | (Å) |
Good Sample
$1$ | A370a | 02:40:21.24 | –01:46:37.52 | $6.043$ | $>27.2$ | $25.43$ | $42.62$ | $-21.31$ | $14.77$ | $-$
$2$ | A370a | 02:40:18.51 | –01:43:51.66 | $6.042$ | $>27.2$ | $24.84$ | $42.73$ | $-21.93$ | $10.66$ | $-$
$3$ | A370a | 02:40:21.60 | –01:33:42.16 | $6.319$ | $>27.2$ | $25.24$ | $43.10$ | $-21.83$ | $27.14$ | $-$
$4$ | ECDFS | 03:31:56.08 | –27:59:06.50 | $5.766$ | $>28.5$ | $25.61$ | $42.58$ | $-20.86$ | $39.40$ | $1.38$
$5$ | ECDFS | 03:32:18.92 | –27:53:02.81 | $5.561$ | $>28.5$ | $24.48$ | $43.37$ | $-21.96$ | $44.83$ | $-1.84$
$6$ | ECDFS | 03:32:30.85 | –27:38:22.20 | $5.808$ | $27.84$ | $24.94$ | $43.26$ | $-22.25$ | $44.38$ | $0.55$
$7$ | COSMOS | 09:59:41.18 | +01:55:51.75 | $6.083$ | $>27.3$ | $24.78$ | $42.65$ | $-21.22$ | $14.87$ | $-2.44$
$8$ | COSMOS | 09:59:56.54 | +02:12:27.15 | $5.992$ | $27.12$ | $24.76$ | $43.27$ | $-21.62$ | $42.13$ | $-2.52$
$9$ | COSMOS | 10:00:12.59 | +02:28:52.08 | $6.146$ | $>27.3$ | $25.03$ | $43.42$ | $-21.36$ | $87.75$ | $-$
$10$ | SXDS1 | 02:18:41.01 | –05:12:47.18 | $6.474$ | $27.9$ | $25.72$ | $42.93$ | $-21.76$ | $19.85$ | $-$
$11$ | SXDS1 | 02:18:00.91 | –05:11:37.77 | $6.029$ | $27.67$ | $24.75$ | $43.35$ | $-21.48$ | $52.53$ | $-2.98$
$12$ | SXDS1 | 02:18:38.92 | –05:09:44.02 | $6.192$ | $>28.4$ | $25.06$ | $43.17$ | $-21.55$ | $41.04$ | $-1.93$
$13$ | SXDS1 | 02:17:43.25 | –05:06:47.60 | $6.087$ | $>28.4$ | $25.90$ | $43.25$ | $-20.08$ | $189.33$ | $-1.98$
$14$ | SXDS1 | 02:17:48.40 | –05:04:10.79 | $6.108$ | $>28.4$ | $25.67$ | $43.25$ | $-19.80$ | $229.40$ | $-2.22$
$15$ | SXDS1 | 02:18:23.34 | –04:58:58.18 | $6.071$ | $>28.4$ | $25.70$ | $43.20$ | $-20.95$ | $53.24$ | $-3.64$
$16$ | SXDS1 | 02:18:07.14 | –04:58:41.50 | $6.050$ | $>28.4$ | $24.84$ | $43.10$ | $-21.61$ | $22.74$ | $-3.64$
$17$ | SXDS1 | 02:18:30.93 | –04:50:58.73 | $5.850$ | $27.04$ | $24.65$ | $42.67$ | $-21.27$ | $13.86$ | $-2.77$
$18$ | SXDS2 | 02:17:28.71 | –04:45:19.61 | $6.104$ | $>28.4$ | $25.67$ | $43.45$ | $-19.48$ | $527.92$ | $-$
$19$ | SXDS2 | 02:18:44.06 | –04:35:54.24 | $6.078$ | $>28.4$ | $25.39$ | $43.26$ | $-20.98$ | $85.69$ | $-$
$20$ | SXDS2 | 02:18:34.48 | –04:34:25.86 | $5.745$ | $26.59$ | $25.19$ | $42.92$ | $-22.21$ | $17.81$ | $-0.21$
$21$ | SXDS2 | 02:17:25.27 | –04:34:12.85 | $6.003$ | $>28.4$ | $25.69$ | $42.98$ | $-20.87$ | $49.57$ | $-$
$22$ | SXDS3 | 02:18:24.72 | –05:35:41.82 | $6.059$ | $27.55$ | $25.67$ | $42.84$ | $-20.97$ | $33.18$ | $-$
$23$ | SXDS3 | 02:18:23.90 | –05:34:49.34 | $6.192$ | $28.19$ | $24.95$ | $42.94$ | $-22.06$ | $24.16$ | $0.32$
$24$ | SXDS3 | 02:18:05.68 | –05:31:21.90 | $6.064$ | $>28.4$ | $25.55$ | $43.29$ | $-20.65$ | $125.98$ | $-$
$25$ | SXDS3 | 02:18:34.47 | –05:20:20.96 | $6.048$ | $>28.4$ | $25.41$ | $43.05$ | $-21.16$ | $44.85$ | $-$
$26$ | SXDS3 | 02:18:06.96 | –05:16:21.93 | $5.928$ | $27.07$ | $25.26$ | $43.04$ | $-20.95$ | $55.84$ | $-1.64$
$27$ | SXDS4 | 02:20:20.49 | –05:01:45.06 | $6.046$ | $>28.4$ | $25.56$ | $43.02$ | $-20.99$ | $49.65$ | $-$
$28$ | SXDS4 | 02:19:26.97 | –04:50:17.71 | $5.848$ | $26.67$ | $25.27$ | $42.67$ | $-21.40$ | $15.23$ | $-$
$29$ | SXDS5 | 02:15:24.62 | –05:06:07.27 | $5.753$ | $26.34$ | $25.07$ | $42.86$ | $-21.57$ | $19.90$ | $-$
$30$ | SXDS5 | 02:16:16.53 | –05:02:17.80 | $6.051$ | $>28.4$ | $25.51$ | $43.15$ | $-20.88$ | $73.98$ | $-1.82$
$31$ | SXDS5 | 02:15:50.69 | –05:00:57.88 | $6.076$ | $27.32$ | $25.50$ | $43.06$ | $-21.62$ | $48.69$ | $0.42$
$32$ | SXDS5 | 02:17:02.70 | –04:56:59.28 | $5.793$ | $26.05$ | $24.28$ | $42.85$ | $-21.96$ | $13.90$ | $-1.73$
$33$ | SXDS5 | 02:16:27.81 | –04:55:34.25 | $6.016$ | $27.36$ | $24.35$ | $43.37$ | $-21.13$ | $77.92$ | $-2.89$
$34$ | SXDS5 | 02:16:02.36 | –04:49:08.81 | $6.043$ | $>28.4$ | $25.60$ | $43.03$ | $-20.94$ | $52.51$ | $-$
Possible Sample
$1$ | A370a | 02:39:26.57 | –01:36:03.84 | $6.463$ | $>27.2$ | $25.59$ | $42.43$ | $-22.05$ | $4.76$ | $-$
$2$ | A370a | 02:39:28.99 | –01:33:31.00 | $6.383$ | $26.73$ | $25.84$ | $42.68$ | $-21.51$ | $13.99$ | $-$
$3$ | ECDFS | 03:32:50.43 | –27:50:40.23 | $5.536$ | $28.45$ | $25.63$ | $42.89$ | $-21.16$ | $55.39$ | $0.85$
$4$ | ECDFS | 03:31:41.99 | –27:46:30.91 | $5.795$ | $>28.5$ | $25.56$ | $42.63$ | $-21.09$ | $18.11$ | $-$
$5$ | SXDS2 | 02:18:14.62 | –04:46:07.52 | $5.778$ | $27.5$ | $26.03$ | $42.47$ | $-20.62$ | $19.60$ | $-$
$6$ | SXDS2 | 02:17:49.61 | –04:22:41.36 | $6.074$ | $>28.4$ | $25.74$ | $43.10$ | $-20.65$ | $81.85$ | $-$
$7$ | SXDS3 | 02:17:13.11 | –05:37:53.43 | $5.768$ | $26.32$ | $24.76$ | $42.64$ | $-21.88$ | $9.04$ | $-$
$8$ | SXDS4 | 02:20:22.93 | –05:04:31.83 | $5.849$ | $25.81$ | $24.23$ | $43.08$ | $-22.74$ | $18.18$ | $0.40$
$9$ | SXDS4 | 02:19:29.35 | –04:53:38.27 | $5.862$ | $27.83$ | $25.38$ | $42.47$ | $-21.69$ | $13.55$ | $1.11$
$10$ | SXDS4 | 02:19:37.99 | –04:52:41.57 | $6.246$ | $28.14$ | $25.65$ | $43.10$ | $-20.98$ | $52.87$ | $-2.41$
$11$ | SXDS5 | 02:15:48.66 | –05:11:58.28 | $5.938$ | $27.32$ | $25.02$ | $43.45$ | $-21.53$ | $79.60$ | $-$

Note. — Col.(1): Object numbers. Col.(2): Field names. Col.(3-4): Source
coordinates. Col.(5): Spectroscopic redshifts (their errors are smaller than
0.001). Col.(6-7): Subaru Suprime-Cam $i$ band and $z^{\prime}$ band
magnitudes. The upper limits indicate $2\sigma$ detections. Col.(8):
Ly$\alpha\ $line luminosities. Col.(9): Absolute UV magnitudes at rest-frame
1500 Å. Col.(10): Ly$\alpha\ $line EWs. Col.(11): UV slopes calculated from
multi-band data.

We measure the Ly$\alpha\ $line flux of each LBG by integrating the best-fit
Ly$\alpha\ $model profile and applying a correction. Line flux directly
calculated from an observed line in faint targets (like our LBGs) can be
significantly underestimated due to several reasons, such as fiber loss,
alignment problems, skyline contamination, etc. For narrowband-selected LAEs,
their Ly$\alpha\ $line flux can be well determined using the combination of
spectroscopic redshifts, narrowband photometry, and broadband photometry. This
has been applied to the LAEs in our fields (Ning et al., 2020, 2022). For 260
LAEs at $z\approx 5.7$ in our fields, we compare their Ly$\alpha\ $flux
derived from the photometric data and from the best-fit Ly$\alpha\ $line
profiles, and the result is shown in Figure 4. We use a hierarchical Bayesian
method to do a linear regression on the Ly$\alpha\ $luminosities calculated by
these two methods, considering the errors on both axes. The best-fit function
$y=0.92x+2.32$ is depicted by the black dashed line in Figure 4, and the
$1\sigma$ and $3\sigma$ confidence intervals are shown in the shaded regions.
Given that these LAEs and the LBGs in this work are in the same fields and
were observed at the same time, the LBGs in our sample should follow the same
relation. We apply this relation to measure the line flux of our LBGs, and the
measured Ly$\alpha\ $luminosities L(Ly$\alpha$) are listed in Column 8 of
Table 2. The IGM absorption blueward of Ly$\alpha\ $is not considered.

Figure 4: Relation between the Ly$\alpha\ $luminosities L(Ly$\alpha$)
calculated from the spectral fitting method and from the photometric data (see
details in Section 3.2). The blue points represent the $z\approx 5.7$ LAE
sample in Ning et al. (2020) and the red points represent our LBG sample. The
best-fit relation from the $z\approx 5.7$ LAE sample is depicted by the black
dashed line, and the shaded regions indicate its $1\sigma$ and $3\sigma$
confidence regions, respectively. We apply this relation to estimate the
Ly$\alpha\ $luminosities of the LBGs in this work.

We use LBGs in the ‘good’ sample to study the dependence of the Ly$\alpha\
$line width (full width at half maximum, or FWHM) on redshift and Ly$\alpha\
$luminosity. We exclude three galaxies whose Ly$\alpha\ $lines are likely
largely affected by strong residuals of the sky subtraction. We then divide
the remaining galaxies into two Ly$\alpha\ $luminosity bins, and produce a
stacked spectrum for each bin. We adjust the number of spectra in each bin so
that the two stacked spectra have similar S/N $\sim 50$. The result is shown
in the upper panel of Figure 5. We also produce two stacked spectra for two
redshift bins using the same method, and the result is shown in the lower
panel of Figure 5. The figure does not show apparent dependence of the line
FWHM on redshift or luminosity. Using a large sample of LAEs at $z\approx 5.7$
and 6.6, Ning et al. (2020, 2022) found that more luminous galaxies tend to
have higher Ly$\alpha\ $FWHMs, because more massive host halos possess higher
HI column densities and higher gas velocities. We do not see this trend in our
LBG sample, likely because the line shape has been severely affected by OH
skylines. Unlike LAEs at $z\approx 5.7$ and 6.6, the Ly$\alpha\ $lines of the
LBGs in our sample are often contaminated by skylines.

##  4 Properties of the LBGs

###  4.1 UV slopes and Ly$\alpha\ $EWs

Figure 5: Stacked Ly$\alpha\ $line spectra for the LBGs in two Ly$\alpha\
$luminosity bins (upper panel) and two redshift bins (lower panel). The
spectra have been normalized so that the peak values are 1. The dashed lines
represent the instrument resolution assuming a Gaussian profile.

In this section, we collect multi-wavelength observations to study the
physical properties and stellar populations of the LBGs in our sample. We make
use of the following data, including the Hyper Suprime-Cam Subaru Strategic
Program (HSC-SSP, Aihara et al. 2022), the UKIRT Infrared Deep Sky Survey
(UKIDSS, Lawrence et al. 2007), the Great Observatories Origins Deep Survey
(GOODS, Giavalisco et al. 2004), the VISTA Deep Extragalactic Observations
Survey (VIDEO, Jarvis et al. 2013), the Cosmic Assembly Near-IR Deep
Extragalactic Legacy Survey (CANDELS, Grogin et al. 2011; Koekemoer et al.
2011), and the Cosmic Dawn Survey by Spitzer Space Telescope (only the 3.6,
4.5 $\mathrm{\mu m}$ data are used, Euclid Collaboration et al. 2022). The No.
13 LBG is covered by the JWST Cycle-1 program (GO 1837), Public Release
IMaging for Extragalactic Research (PRIMER, Dunlop et al. 2021), and has
NIRCam imaging in eight bands (F090W, F115W, F150W, F200W, F277W, F356W,
F410M, and F444W). Ning et al. (2022) carried out a pilot study of seven
spectroscopically confirmed $z\sim 6$ LBGs, including No. 13 LBG, using the
JWST NIRCam imaging data. The No. 7 LBG is covered by another JWST Cycle-1
program COSMOS-Web (GO 1727, Casey et al. 2022), and has NIRCam imaging in
four bands (F115W, F150W, F277W, and F444W).

Most LBGs in our sample except those in the A370a field have multi-wavelength
data that can be used to determine UV continuum slope $\beta_{\mathrm{UV}}$
and other physical properties via SED modeling. The IRAC images of many LBGs
are blended with nearby sources. In this case, GALFIT (Peng et al., 2002,
2010) is used to model and subtract contaminant sources. Photometry of the
target is then done after the de-blending.

We then measure $\beta_{\mathrm{UV}}$ and the absolute UV magnitude $M_{\rm
UV}$ (at rest-frame 1500 Å) for the LBGs using the near-IR data mentioned
above. The median $\beta_{\mathrm{UV}}$ value is $-1.86$, which is consistent
with the median $\beta_{\mathrm{UV}}=-1.73^{+0.14}_{-0.20}$ for $z\sim 6$ LBGs
within the absolute magnitude bin $M_{\rm UV}=-20.75\pm 0.5$ mag from Bouwens
et al. (2014). We also measure the UV slopes of bright LAEs at $z\approx 5.7$
in Ning et al. (2020) and find a median value of $\beta_{\mathrm{UV}}\sim-2$,
which is consistent with the value for the LBGs in this sample. For the LBGs
in A370a that do not have near-IR data, we use the $z^{\prime}$ band
photometry to estimate the UV continuum flux. Since we are not able to
determine $\beta_{\mathrm{UV}}$, we adopt the median
$\beta_{\mathrm{UV}}=-1.86$ from the other fields. For simplicity, we assume
that the flux blueward of Ly$\alpha\ $is completely absorbed. If a Ly$\alpha\
$line is in the $z^{\prime}$ band, its flux is subtracted from the
$z^{\prime}$-band photometry. The calculated $M_{\rm UV}$ and Ly$\alpha\
$rest-frame EW values are listed in Columns 9 and 10 of Table 2.

Figure 6 shows the distribution of the LBG redshifts and Ly$\alpha\ $EWs with
respect to $M_{\rm UV}$ in our sample. These LBGs span a UV magnitude range of
$-22.5$ to $-19.0$ mag, corresponding to $0.3-3.4$ times the characteristic
luminosity of galaxies at $z\sim 6$ (Bouwens et al., 2021), and a Ly$\alpha\
$luminosity range of $(0.4-3)\times 10^{42}$ erg s-1. They represent the most
luminous galaxies at $z\sim 6$ in terms of both UV continuum luminosity and
Ly$\alpha\ $luminosity.

Figure 6:  Distributions of the LBG redshifts (upper panel) and Ly$\alpha\
$EWs (lower panel) with respect to $M_{\rm UV}$. The ‘good’ LBG sample and
‘possible’ LBG sample are both presented. The median errors are shown in the
lower right corner, and the error bar of redshift is too small to be seen.

###  4.2 Stellar populations

Figure 7:  Properties of the ten LBGs measured from the SED modeling. They all
cover wide ranges.

Ten LBGs in the ‘good’ sample have sufficient multi-wavelength imaging data
(especially IRAC $3.6~{}\mu m$ and $4.5~{}\mu m$ photometry) that allow us to
perform SED modeling. We model their SEDs and derive their stellar populations
using the Code Investigating GALaxy Emission (CIGALE; Noll et al. 2009). Our
spectroscopic redshifts remove one critical free parameter in the fitting
process. We use the stellar population synthesis models of Bruzual & Charlot
(2003) and adopt the Salpeter initial mass function. Given the limited number
of available photometric data points, we use as few free parameters as
possible. We use constant SFRs and fix metallicity to be 0.2 $Z_{\sun}$. A
nebular emission template based on Inoue (2011) is included, with ionization
parameter $U$, metallicity, and line width fixed. We do not include AGN
components during the model fitting because these LBGs do not show any AGN
features in the observed bands. Furthermore, Ly$\alpha\ $emission and
radiative transfer in galaxies are very complex (e.g., Charlot & Fall 1993).
Our LBGs are among galaxies with the strongest Ly$\alpha\ $emission, and the
nebular emission model built in CIGALE can not reproduce the Ly$\alpha\
$emission in the SEDs of many LBGs unless we assume an extremely young stellar
population (see Section 5.2). Therefore, we mask out the Ly$\alpha\ $line in
the nebular template of CIGALE when fitting and subtracting the Ly$\alpha\
$contribution from the broadband photometry.

We mainly constrain stellar mass $M_{*}$, age, star formation rate (SFR), and
dust reddening $E(B-V)$. We use the dust extinction law of Calzetti et al.
(2000) with $E(B-V)$ in a range of $0-0.6$. We allow age to vary between 1 and
800 Myr (the age of the Universe at $z=6$ is 914 Myr). The distributions of
the derived properties are shown in Figure 7 and the SED modeling results are
shown in Figure 8. As seen from the figures, the derived values of the
properties all span wide ranges, indicating that these LBGs have a variety of
stellar populations. The LBGs are strongly star-forming galaxies with SFRs
roughly between 30 and 1000 $M_{\odot}$ yr-1. While most of them have SFRs
around 100 $M_{\odot}$ yr-1, two LBGs, (No. 5 and No. 13) have SFRs close to
1000 $M_{\odot}$ yr-1. This is not surprising, because No. 5 is very luminous
with $M_{\rm UV}\approx-22$ mag and No. 13 is also luminous ($M_{\rm
UV}\approx-20$ mag) with a very high Ly$\alpha\ $EW ($\sim 190$ Å). The two
galaxies also have high stellar masses, relatively large ages, and relatively
high dust extinction. No. 13 has been observed by JWST NIR-Cam and will be
further discussed later.

Observational studies of stellar populations in Ly$\alpha\ $galaxies have
suggested that young and low-mass galaxies tend to hold Ly$\alpha\ $lines with
large EWs (e.g., Ono et al., 2010; Hayes et al., 2023; Roy et al., 2023). This
can be explained by increasing gas and dust content in more massive galaxies
and thus lower Ly$\alpha\ $escape fractions, or intrinsically low Ly$\alpha\
$production by more evolved populations. The middle panel of Figure 8 shows
that our galaxies generally follow this trend that less massive galaxies
having higher Ly$\alpha\ $EWs

Figure 8:  Results of the SED modeling for the ten LBGs in our sample. Upper
panel: SFR versus stellar mass, both from SED modeling. Middle panel:
Ly$\alpha\ $line EW from spectra versus stellar mass from SED modeling. Lower
panel: dust reddening $E(B-V)$ versus stellar age of the main stellar
population. The blue circles represent the observed fluxes and the red points
indicate the best-fit model fluxes in the corresponding bands.

###  4.3 Galaxy Morphology

Two LBGs in our sample (No. 7 and No. 13) have high-resolution JWST NIRCam
images, and three LBGs (No. 5, No. 11, and No. 26) have HST WFC3 near-IR
images. The JWST images are retrieved from the Mikulski Archive for Space
Telescopes (MAST) and then reduced by the JWST Calibration Pipeline (version
1.11.4). We basically follow the procedure of the CEERS team for the image
reduction (Finkelstein et al., 2023). The final resampled and combined images
have a pixel scale of $0\farcs 02$ for the short wavelengths (SW; F090W,
F115W, F150W, and F200W) and $0\farcs 04$ for the long wavelengths (LW; F277W,
F356W, F410M, and F444W). The HST data of the three LBGs are from the CANDELS
survey and the images are downloaded from the
website111https://archive.stsci.edu/hlsp/candels. The cutout images of the
five LBGs are shown in Figure 9.

We measure morphological parameters for the five LBGs using GALFIT. For either
of the two LBGs with NIRCam images, we stack its SW images and its LW images
to produce two combined images. This is to increase S/N, assuming that the
object morphology and image quality are similar in individual input bands.
Likewise, we stack the F125W and F160W images for each of the three LBGs with
HST data. A PSF is obtained for each combined image by stacking several
unsaturated stars in the same image, and the resultant FWHM of PSFs are shown
as the red circles in Figure 9. The FWHM values of the PSFs in the NIRCam SW
and LW bands are about $0\farcs 063$ and $0\farcs 148$ ($\approx 0.36$ and
0.84 kpc at $z=6$) , respectively. The PSF FWHM of the HST images is about
$0\farcs 223$ ($\approx 1.3$ kpc at $z=6$).

We then use GALFIT to model the galaxies on the stacked images, and constrain
a few basic parameters, including the effective radius $R_{e}$ along the major
axis, $\rm{S\acute{e}rsic}$ index $n$ (allowed to vary between 0.3 and 4), and
projected minor-to-major axis ratio ($b/a$). We find that all galaxies except
No. 7 can be well fitted by one $\rm{S\acute{e}rsic}$ profile. No. 7 LBG seems
to have two separate components and will be further discussed later. The
fitting results of the $\rm{S\acute{e}rsic}$ profiles are reported in Table 3.

Figure 9:  JWST NIRCam and HST ACS and WFC3 cutout images of five LBGs. The
image size is $2^{\prime\prime}\times 2^{\prime\prime}$. The red circles in
each stamp image indicate the FWHM of the PSF.  Table 3: Galaxy morphological
parameters

No. | bands | $n$ |  $R_{e}$(kpc) | $b/a$
---|---|---|---|---
13 | F090W, F115W, F150W, F200W | $1.76\pm 0.45$ | $0.25\pm 0.03$ | $0.67\pm 0.08$
F277W, F356W, F410M, F444W | $1.10\pm 0.27$ | $0.38\pm 0.03$ | $0.99\pm 0.12$
$7^{a}$ | F115W, F150W | $0.49\pm 0.13$ | $0.59\pm 0.04$ | $0.51\pm 0.04$
F277W, F444W | $0.67\pm 0.11$ | $1.02\pm 0.05$ | $0.61\pm 0.04$
5 | F125W, F160W | $1.18\pm 0.19$ | $0.94\pm 0.09$ | $0.92\pm 0.08$
11 | F125W, F160W | $1.00\pm 0.29$ | $1.16\pm 0.11$ | $0.59\pm 0.09$
26 | F125W, F160W | $0.44\pm 0.19$ | $1.42\pm 0.20$ | $0.70\pm 0.11$

Note. — a. The parameters of $\rm{S\acute{e}rsic}$ profile of the main
component is reported.

Figure 9 and Table 3 show that most galaxies in our sample are compact. For
example, No. 13 is barely resolved. Its effective radius is $R_{e}=0.25$ kpc
in the SW bands and $R_{e}=0.38$ kpc in the LW bands, making it one of the
most compact galaxies in this redshift and luminosity range (see, e.g., Sun et
al. 2023). Its large Ly$\alpha\ $EW, high SFR, and compact size is consistent
with Green Pea (GP) galaxies found at low redshift (Cardamone et al., 2009)
that likely have compact star-forming regions embedded in diffuse, older
stellar components (Amorín et al., 2012; Clarke et al., 2021). The GP galaxies
are thought to have numerous counterparts at the reionization epoch and some
of them may have been discovered recently by JWST (Hall, 2023; Rhoads et al.,
2023). Studies of local GP galaxies have provided valuable information on how
Ly$\alpha\ $photons escape from ISM and CGM, which help us better understand
their high-redshift counterparts (e.g., Henry et al., 2015; Yang et al.,
2017). Another possible explanation for the compactness of the No. 13 galaxy
is that this galaxy holds an AGN that partly powers its strong Ly$\alpha\
$emission.

No. 7 LBG has a quite extended structure and appears to show two components,
including a major component and a much weaker component to the north-west of
the major one. The major component is more than five times brighter than the
minor component in all four bands, so the major component dominates the
radiation in these bands. It is unclear whether the weak component is part of
the galaxy or a foreground object. In addition, mergers and interacting
systems occur more frequently at high redshift (Rodriguez-Gomez et al., 2015),
so it is possible that No. 7 LBG is a merger. To verify that the two
components belong to the same source, we estimate the probability that the
distance between any two random sources is less than the distance between the
two components of No. 7 LBG ($0.36^{\prime\prime}$). Based on the NIRCam
images used above, we find that the probability is only 0.02, suggesting that
the minor component is unlikely a foreground object. Therefore, we use an
additional single $\rm{S\acute{e}rsic}$ profile to model the minor component
of No. 7, and we obtain a much better fitting result. Table 3 shows the result
for the major component.

##  5 Discussion

###  5.1 Fraction of Ly$\alpha\ $emitters in LBGs

The fraction of LAEs among LBGs is an important tracer of the IGM state during
the epoch of reionization, and many works have been done to constrain the
fraction of the neutral hydrogen and its redshift evolution. This method is
also called the Ly$\alpha\ $visibility test. Previous studies have shown that
the fraction of LAEs in LBG samples increases steadily from low redshift to
$z\sim 6$, and drops dramatically towards higher redshift (e.g., Stark et al.,
2010, 2011; Ono et al., 2012; Bian et al., 2015). It is difficult to explain
this using a sudden change in the physical properties of galaxies, but it can
be easily explained by the increase of the fraction of the neutral hydrogen in
the IGM that attenuates Ly$\alpha\ $emission. Before we calculate the LAE
fraction in our LBG sample, we would like to clarify the definitions of LAEs
and LBGs since the definitions are slightly different in the literature. LBGs
mean galaxies selected by the Lyman-break technique, regardless of the
existence of Ly$\alpha\ $emission. For LBGs at $z\geq 6$, they are usually
very faint, and spectroscopic identifications primarily rely on their
Ly$\alpha\ $emission. This means that spectroscopically confirmed LBGs
typically have strong Ly$\alpha\ $emission, and also means that the vast
majority of the known LBGs at $z\geq 6$ are not spectroscopically confirmed
(or just candidates). LAEs are galaxies with strong Ly$\alpha\ $emission
(typically EW $\geq 25$ or 50 Å). Narrowband-selected galaxies are mostly LAEs
by definition. If an LBG has strong Ly$\alpha\ $emission, it is also an LAE,
meaning that most spectroscopically confirmed $z\geq 6$ LBGs to date are also
LAEs. In the following analyses, we use EW $\geq 25$ Å to define LAEs.

We measure the LAE fraction among LBGs at $z\sim 6$ using our
spectroscopically confirmed LBG sample. As mentioned earlier, our LBG
selection criteria are slightly looser than those used in previous studies,
which may result in a slightly higher contamination rate. Therefore, our
result can be regarded as a lower limit. Because of the presence of strong OH
skylines in the wavelength range that we probe, the identification of the
Ly$\alpha\ $line is incomplete. We run simulations to estimate the
completeness for the Ly$\alpha\ $line identification in the spectra. We
generate a grid of model Ly$\alpha\ $lines with a range of redshifts
$z=5.3$–$6.8$ and line strengths $L(Ly\alpha)=10^{42.5}$–$10^{43.5}\
\mathrm{erg/s}$ using the Ly$\alpha\ $template from Ning et al. (2020). For
each spectrum without a Ly$\alpha\ $detection, we insert an artificial
Ly$\alpha\ $line. We then search for these lines using the same method that
was used for real spectra in Section 3.1. The derived completeness function is
the recovery rate of the lines in each redshift and Ly$\alpha\ $luminosity
bin.

We then apply the completeness correction to the LAE fraction and the result
is shown in Figure 10. The upper panel of the figure shows the cumulative
distribution of the Ly$\alpha\ $rest-frame EWs in the ‘good’ LBG sample. The
fraction in a fainter subsample ($-21.75<M_{\mathrm{UV}}<20.25$ mag) is
marginally higher than that in the whole LBG sample
($-21.75<M_{\mathrm{UV}}<-20.25$ mag). The results are generally consistent
with previous studies (Pentericci et al., 2011; Stark et al., 2011; Curtis-
Lake et al., 2012; De Barros et al., 2017).

In the lower panel of Figure 10, we show the LAE fractions
$\chi_{\mathrm{Ly\alpha}}^{25}$ in both ‘good’ and the whole samples, and
compare them with previous studies (Stark et al., 2011; Curtis-Lake et al.,
2012; Ono et al., 2012; Schenker et al., 2014; Tilvi et al., 2014; Cassata et
al., 2015; De Barros et al., 2017) in a redshift range of $4-8$. The UV
magnitude range of the LBGs is $-21.75<M_{\mathrm{UV}}<-20.25$ mag, which
corresponds to the fainter part of our sample and the brighter part of the
previous samples. As seen from the figure, our result is broadly consistent
with previous results, albeit with a large scatter. The large scatter and
error bars reflect complex sample bias and incompleteness. The figure also
shows that $\chi_{\mathrm{Ly\alpha}}^{25}$ increases from lower redshifts to
$z\sim 6$ and then decreases towards higher redshifts, consistent with the
previous claim. The mild decline of $\chi_{\mathrm{Ly\alpha}}^{25}$ may
suggest that the evolution of the IGM opacity from $z\sim 7$ to $z\sim 6$ is
not very dramatic, if the Ly$\alpha\ $visibility mostly depends on the IGM
state. Nevertheless, larger and more complete samples are needed.

Figure 10: Upper panel: cumulative distribution of the Ly$\alpha\ $rest-frame
EWs P($>\mathrm{EW}$) for the $z\sim 6$ LBGs. The red symbols represent LBGs
with $-21.75<M_{\mathrm{UV}}<-20.25$ and the blue circles represent all LBGs
within $-21.75<M_{\mathrm{UV}}<-20.25$. The results are consistent with
previous measurements. The lines are the best fits to the distributions. Lower
panel: fraction of LAEs with $\mathrm{EW}>25$
Å($\chi^{25}_{\mathrm{Ly\alpha}}$) for $-21.75<M_{\mathrm{UV}}<-20.25$
galaxies at $4\leq z\leq 8$. The red filled circles are calculated from the
‘good’ LBG sample and the red open circles are calculated from both ‘good’ and
‘possible’ samples. The results are compared with previous studies.

###  5.2 SED modeling with strong Ly$\alpha\ $emission

In Section 4.2 when we modeled the SEDs of the LBGs, we did not consider the
Ly$\alpha\ $emission due to its complexity. Here we discuss how the results
change if we consider the Ly$\alpha\ $emission in our SED modeling. As has
been pointed out, the SED modeling for $z\sim 6$ galaxies has a strong
degeneracy between young galaxies with prominent nebular emission and old
galaxies with strong Balmer breaks (e.g., Jiang et al., 2015). To include the
Ly$\alpha\ $emission, we make a pseudo narrowband filter with a spectral
resolving power of $R=100$ at the wavelength of Ly$\alpha\ $for each LBG. The
narrowband photometry is then calculated from the Ly$\alpha\ $flux and
implemented for SED modeling. In the modeling procedure, the ionization
parameter $U$, gas metallicity in the nebular emission model, and the ratio of
continuum to line reddening are considered as free parameters.

The derived properties of the stellar populations and the comparison with the
previous results from Section 4.2 are shown in Figure 11. The best-fit
$\chi_{r}^{2}$ values of the two methods are about the same. Figure 11 clearly
shows that when the Ly$\alpha\ $emission is considered in the SED modeling
procedure, these galaxies are much younger with significantly lower stellar
masses. The reason is straightforward. In order to produce strong Ly$\alpha\
$emission seen in the galaxies, the stellar populations must be very young
with high SFRs, which further results in lower stellar masses. It should be
noted, however, that it is difficult to decide how to include the Ly$\alpha\
$emission for SED modeling due to the complexity of the Ly$\alpha\ $emission.
For example, the measurement of the Ly$\alpha\ $flux is almost always a lower
limit, this is mainly because the resonant scattering of the Ly$\alpha\
$photons often forms a large diffuse halo, but the actual measurement is
usually done on the central part. It is also because the Ly$\alpha\ $escape
fraction varies a lot among galaxies. In addition, there are other sources of
uncertainties that are particularly important for $z\geq 6$ galaxies,
including the variation of the IGM absorption along the line-of-sights.

Figure 11:  Comparison of the stellar populations obtained by two SED modeling
methods, with and without Ly$\alpha\ $constraints (see details in Section
5.2).

###  5.3 Search for AGN activity

The LBGs in our sample have strong Ly$\alpha\ $and UV continuum emission. In
addition, some of them are morphologically very compact. It is possible that
they harbor a central AGN that partly contributes to the total emission. We
search for possible evidence of AGN activity in these galaxies. First of all,
they do not have typical Type I AGN components, as seen from their narrow
Ly$\alpha\ $emission lines. Figure 5 shows that the stacked Ly$\alpha\ $line
displays a narrow profile with a velocity dispersion of $\Delta v\sim 250$
km/s (IGM absorption is neglected here), which is much smaller than those in
typical broad-line AGN ($\geq 2000$ km/s).

The wavelength coverage of our spectra is from 7600 Å to 9600 Å, corresponding
to a rest-frame range of 1090-1370 Å for $z\sim 6$ objects. This range covers
the N V 1240 Å emission line that is often regarded as evidence of the
presence of AGN. We do not detect any N V emission in the combined spectrum of
the LBGs. For a typical AGN, however, the N V flux is only a few percent of
the Ly$\alpha\ $flux (e.g., Vanden Berk et al., 2001), so even if any of our
LBGs contain an AGN component, its N V flux is below our detection limit.

We also check these galaxies in deep Chandra X-ray images, including the
Chandra Deep Field-South field (CDF-S) (Luo et al., 2017), the UKIDSS Ultra
Deep Survey Field (Kocevski et al., 2018), and the Chandra Cosmos Legacy
Survey field (Civano et al., 2016). None of them is individually detected.
X-ray detections were actually excluded in the first steps of the target
selection. The No.5 and No.6 LBGs are in the 7 Ms CDF-S field, and their
stacked image have an effective exposure time of over 12 Ms. For the stacked
0.5–7 keV image, we measure the X-ray photon counts in a $1\farcs 5$ radius
aperture, which encloses $90\%$ of the total energy at 6.4 keV. The background
counts are computed in an annular region with the inner and outer radii of
$4\arcsec$ and $8\arcsec$. The $1\sigma$ error of the net counts is calculated
based on the Poisson errors on the extracted source and background counts. The
calculated $1\sigma$ upper limit is 6.3 counts. To estimate the upper limit of
a possible X-ray detection, we assume a typical type 1 quasar with a similar
UV magnitude at the same redshift as the No.5 and No.6 LBGs ($z\sim 5.7$,
$M_{\rm UV}=-22$ mag). We also assume the Shen et al. (2020) SED template for
the quasar. We adopt the Galactic neutral hydrogen column density along the
line-of-sight to the CDF-S $n_{\mathrm{H}}=8.8\times 10^{19}\mathrm{cm}^{-2}$
(Stark et al., 1992). No other absorption is applied. In this case, the 12 Ms
exposure would yield a $2\sigma$ detection (19.2 counts in 0.5–7 keV band) for
this quasar. This simple calculation means that AGN contributes less than one-
third ($1\sigma$ upper limit) of the total luminosity in the two LBGs.
Therefore, we are not able to rule out the possibility of weaker AGN
activities in these galaxies. The stacked images in another two fields are
much shallower and thus cannot provide useful constraints.

##  6 Summary

We have presented a sample of 45 spectroscopically confirmed LBGs at $z\sim 6$
in four well-studied fields, including SXDS, A370, ECDFS, and COSMOS. This
sample is one of the largest samples of spectroscopically confirmed LBGs at
this redshift. The LBG candidates were selected as $i$-band dropout objects
from deep broadband images. The spectroscopic observations were carried out
using M2FS on the Magellan Clay telescope. We identified the Ly$\alpha\ $lines
of the galaxies based on their 1D and 2D M2FS spectra. Their redshifts and
Ly$\alpha\ $luminosities were measured by fitting a composite Ly$\alpha\ $line
template to the individual 1D spectra. The absolute UV magnitude and UV slope
were calculated by fitting a power-law to the available multi-wavelength
photometric data. The UV absolute magnitudes of these LBGs are between –22.5
and –19.0 mag, corresponding to $0.3-3.4$ times the characteristic luminosity
of galaxies at $z\sim 6$, with a Ly$\alpha\ $EW range from $\sim$10 Å to
$\sim$400 Å. They represent the most UV luminous galaxies known at $z\sim 6$.

The SED modeling of ten LBGs in the sample reveals that they have a wide range
of stellar masses and ages with high SFRs. We note that whether to consider
the Ly$\alpha\ $emission in the SED modeling procedure has a significant
impact on the measurement of the stellar populations in these galaxies,
indicating the complexity of the Ly$\alpha\ $emission. Five LBGs have high-
resolution JWST NIRCam images or HST WFC3 near-IR images. Four of them show
compact morphology, and one appears to have two components that might be a
merger. We calculated the LAE fraction among the photometrically selected LBGs
after correcting for the Ly$\alpha$-identification completeness. The fraction
of $\sim 0.2$ is consistent with previous works, and it supports a moderate
evolution of the IGM opacity at the end of cosmic reionization when previous
results at lower and higher redshifts were combined. Finally, we did not find
evidence of strong AGN activities in these galaxies.

We acknowledge support from the National Science Foundation of China
(12225301), the National Key R&D Program of China (2022YFF0503401), and the
China Manned Space Project with No. CMS-CSST-2021-A05 and CMS-CSST-2021-A07.
Magellan: Clay (M2FS).

## References

  * Aihara et al. (2022) Aihara, H., AlSayyad, Y., Ando, M., et al. 2022, Publications of the Astronomical Society of Japan, 74, 247, doi: 10.1093/pasj/psab122
  * Amorín et al. (2012) Amorín, R., Pérez-Montero, E., Vílchez, J. M., & Papaderos, P. 2012, ApJ, 749, 185, doi: 10.1088/0004-637X/749/2/185
  * Arrabal Haro et al. (2023) Arrabal Haro, P., Dickinson, M., Finkelstein, S. L., et al. 2023, arXiv e-prints, arXiv:2303.15431, doi: 10.48550/arXiv.2303.15431
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f
  * Astropy Collaboration et al. (2022) Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, apj, 935, 167, doi: 10.3847/1538-4357/ac7c74
  * Atek et al. (2023) Atek, H., Chemerynska, I., Wang, B., et al. 2023, MNRAS, 524, 5486, doi: 10.1093/mnras/stad1998
  * Bian et al. (2015) Bian, F., Stark, D. P., Fan, X., et al. 2015, ApJ, 806, 108, doi: 10.1088/0004-637X/806/1/108
  * Bouwens et al. (2014) Bouwens, R. J., Illingworth, G. D., Oesch, P. A., et al. 2014, The Astrophysical Journal, 793, 115, doi: 10.1088/0004-637X/793/2/115
  * Bouwens et al. (2021) Bouwens, R. J., Oesch, P. A., Stefanon, M., et al. 2021, The Astronomical Journal, 162, 47, doi: 10.3847/1538-3881/abf83e
  * Bruzual & Charlot (2003) Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000, doi: 10.1046/j.1365-8711.2003.06897.x
  * Bunker et al. (2023) Bunker, A. J., Cameron, A. J., Curtis-Lake, E., et al. 2023, arXiv e-prints, arXiv:2306.02467, doi: 10.48550/arXiv.2306.02467
  * Calzetti et al. (2000) Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682, doi: 10.1086/308692
  * Cardamone et al. (2009) Cardamone, C., Schawinski, K., Sarzi, M., et al. 2009, MNRAS, 399, 1191, doi: 10.1111/j.1365-2966.2009.15383.x
  * Casey et al. (2022) Casey, C. M., Kartaltepe, J. S., Drakos, N. E., et al. 2022, arXiv e-prints, arXiv:2211.07865, doi: 10.48550/arXiv.2211.07865
  * Cassata et al. (2015) Cassata, P., Tasca, L. A. M., Le Fèvre, O., et al. 2015, Astronomy & Astrophysics, 573, A24, doi: 10.1051/0004-6361/201423824
  * Castellano et al. (2017) Castellano, M., Pentericci, L., Fontana, A., et al. 2017, The Astrophysical Journal, 839, 73, doi: 10.3847/1538-4357/aa696e
  * Champagne et al. (2023) Champagne, J. B., Casey, C. M., Finkelstein, S. L., et al. 2023, ApJ, 952, 99, doi: 10.3847/1538-4357/acda8d
  * Charlot & Fall (1993) Charlot, S., & Fall, S. M. 1993, ApJ, 415, 580, doi: 10.1086/173187
  * Civano et al. (2016) Civano, F., Marchesi, S., Comastri, A., et al. 2016, ApJ, 819, 62, doi: 10.3847/0004-637X/819/1/62
  * Clarke et al. (2021) Clarke, L., Scarlata, C., Mehta, V., et al. 2021, ApJ, 912, L22, doi: 10.3847/2041-8213/abf7cc
  * Curtis-Lake et al. (2012) Curtis-Lake, E., McLure, R. J., Pearce, H. J., et al. 2012, Monthly Notices of the Royal Astronomical Society, 422, 1425, doi: 10.1111/j.1365-2966.2012.20720.x
  * Curtis-Lake et al. (2016) Curtis-Lake, E., McLure, R. J., Dunlop, J. S., et al. 2016, Monthly Notices of the Royal Astronomical Society, 457, 440, doi: 10.1093/mnras/stv3017
  * Curtis-Lake et al. (2023) Curtis-Lake, E., Carniani, S., Cameron, A., et al. 2023, Nature Astronomy, 7, 622, doi: 10.1038/s41550-023-01918-w
  * De Barros et al. (2017) De Barros, S., Pentericci, L., Vanzella, E., et al. 2017, A&A, 608, A123, doi: 10.1051/0004-6361/201731476
  * Dunlop et al. (2012) Dunlop, J. S., McLure, R. J., Robertson, B. E., et al. 2012, Monthly Notices of the Royal Astronomical Society, 420, 901, doi: 10.1111/j.1365-2966.2011.20102.x
  * Dunlop et al. (2021) Dunlop, J. S., Abraham, R. G., Ashby, M. L. N., et al. 2021, 1837
  * Egami et al. (2005) Egami, E., Kneib, J.-P., Rieke, G. H., et al. 2005, The Astrophysical Journal, 618, L5, doi: 10.1086/427550
  * Euclid Collaboration et al. (2022) Euclid Collaboration, Moneti, A., McCracken, H. J., et al. 2022, A&A, 658, A126, doi: 10.1051/0004-6361/202142361
  * Faisst et al. (2016) Faisst, A. L., Capak, P., Hsieh, B. C., et al. 2016, The Astrophysical Journal, 821, 122, doi: 10.3847/0004-637X/821/2/122
  * Finkelstein et al. (2012a) Finkelstein, S. L., Papovich, C., Salmon, B., et al. 2012a, The Astrophysical Journal, 756, 164, doi: 10.1088/0004-637X/756/2/164
  * Finkelstein et al. (2012b) Finkelstein, S. L., Papovich, C., Ryan, R. E., et al. 2012b, The Astrophysical Journal, 758, 93, doi: 10.1088/0004-637X/758/2/93
  * Finkelstein et al. (2013) Finkelstein, S. L., Papovich, C., Dickinson, M., et al. 2013, Nature, 502, 524, doi: 10.1038/nature12657
  * Finkelstein et al. (2023) Finkelstein, S. L., Bagley, M. B., Ferguson, H. C., et al. 2023, ApJ, 946, L13, doi: 10.3847/2041-8213/acade4
  * Fujimoto et al. (2023) Fujimoto, S., Arrabal Haro, P., Dickinson, M., et al. 2023, ApJ, 949, L25, doi: 10.3847/2041-8213/acd2d9
  * Giavalisco et al. (2004) Giavalisco, M., Ferguson, H. C., Koekemoer, A. M., et al. 2004, ApJ, 600, L93, doi: 10.1086/379232
  * González et al. (2014) González, V., Bouwens, R., Illingworth, G., et al. 2014, The Astrophysical Journal, 781, 34, doi: 10.1088/0004-637X/781/1/34
  * Grogin et al. (2011) Grogin, N. A., Kocevski, D. D., Faber, S. M., et al. 2011, ApJS, 197, 35, doi: 10.1088/0067-0049/197/2/35
  * Guaita et al. (2015) Guaita, L., Melinder, J., Hayes, M., et al. 2015, Astronomy and Astrophysics, 576, A51, doi: 10.1051/0004-6361/201425053
  * Hall (2023) Hall, S. 2023, Nature, 613, 425, doi: 10.1038/d41586-023-00064-7
  * Hayes et al. (2023) Hayes, M. J., Runnholm, A., Scarlata, C., Gronke, M., & Rivera-Thorsen, T. E. 2023, MNRAS, 520, 5903, doi: 10.1093/mnras/stad477
  * Henry et al. (2015) Henry, A., Scarlata, C., Martin, C. L., & Erb, D. 2015, ApJ, 809, 19, doi: 10.1088/0004-637X/809/1/19
  * Hsiao et al. (2023) Hsiao, T. Y.-Y., Coe, D., Abdurro’uf, et al. 2023, ApJ, 949, L34, doi: 10.3847/2041-8213/acc94b
  * Hu et al. (2010) Hu, E. M., Cowie, L. L., Barger, A. J., et al. 2010, The Astrophysical Journal, 725, 394, doi: 10.1088/0004-637X/725/1/394
  * Inoue (2011) Inoue, A. K. 2011, MNRAS, 415, 2920, doi: 10.1111/j.1365-2966.2011.18906.x
  * Inoue et al. (2014) Inoue, A. K., Shimizu, I., Iwata, I., & Tanaka, M. 2014, MNRAS, 442, 1805, doi: 10.1093/mnras/stu936
  * Jarvis et al. (2013) Jarvis, M. J., Bonfield, D. G., Bruce, V. A., et al. 2013, MNRAS, 428, 1281, doi: 10.1093/mnras/sts118
  * Jiang et al. (2015) Jiang, L., Finlator, K., Cohen, S. H., et al. 2015, The Astrophysical Journal, 816, 16, doi: 10.3847/0004-637X/816/1/16
  * Jiang et al. (2017) Jiang, L., Shen, Y., Bian, F., et al. 2017, The Astrophysical Journal, 846, 134, doi: 10.3847/1538-4357/aa8561
  * Jiang et al. (2018) Jiang, L., Wu, J., Bian, F., et al. 2018, Nature Astronomy, 2, 962, doi: 10.1038/s41550-018-0587-9
  * Jiang et al. (2022) Jiang, L., Ning, Y., Fan, X., et al. 2022, Nature Astronomy, 6, 850, doi: 10.1038/s41550-022-01708-w
  * Jung et al. (2018) Jung, I., Finkelstein, S. L., Livermore, R. C., et al. 2018, The Astrophysical Journal, 864, 103, doi: 10.3847/1538-4357/aad686
  * Jung et al. (2022) Jung, I., Papovich, C., Finkelstein, S. L., et al. 2022, The Astrophysical Journal, 933, 87, doi: 10.3847/1538-4357/ac6fe7
  * Karman et al. (2017) Karman, W., Caputi, K. I., Caminha, G. B., et al. 2017, Astronomy & Astrophysics, 599, A28, doi: 10.1051/0004-6361/201629055
  * Kashikawa et al. (2006) Kashikawa, N., Shimasaku, K., Malkan, M. A., et al. 2006, The Astrophysical Journal, 648, 7, doi: 10.1086/504966
  * Kawamata et al. (2015) Kawamata, R., Ishigaki, M., Shimasaku, K., Oguri, M., & Ouchi, M. 2015, The Astrophysical Journal, 804, 103, doi: 10.1088/0004-637X/804/2/103
  * Kobayashi et al. (2016) Kobayashi, M. A. R., Murata, K. L., Koekemoer, A. M., et al. 2016, The Astrophysical Journal, 819, 25, doi: 10.3847/0004-637X/819/1/25
  * Kocevski et al. (2018) Kocevski, D. D., Hasinger, G., Brightman, M., et al. 2018, ApJS, 236, 48, doi: 10.3847/1538-4365/aab9b4
  * Koekemoer et al. (2011) Koekemoer, A. M., Faber, S. M., Ferguson, H. C., et al. 2011, ApJS, 197, 36, doi: 10.1088/0067-0049/197/2/36
  * Larson et al. (2022) Larson, R. L., Finkelstein, S. L., Hutchison, T. A., et al. 2022, The Astrophysical Journal, 930, 104, doi: 10.3847/1538-4357/ac5dbd
  * Lawrence et al. (2007) Lawrence, A., Warren, S. J., Almaini, O., et al. 2007, MNRAS, 379, 1599, doi: 10.1111/j.1365-2966.2007.12040.x
  * Leethochawalit et al. (2023) Leethochawalit, N., Trenti, M., Santini, P., et al. 2023, ApJ, 942, L26, doi: 10.3847/2041-8213/ac959b
  * Liu et al. (2017) Liu, C., Mutch, S. J., Poole, G. B., et al. 2017, Monthly Notices of the Royal Astronomical Society, 465, 3134, doi: 10.1093/mnras/stw2912
  * Luo et al. (2017) Luo, B., Brandt, W. N., Xue, Y. Q., et al. 2017, ApJS, 228, 2, doi: 10.3847/1538-4365/228/1/2
  * Mascia et al. (2023) Mascia, S., Pentericci, L., Calabrò, A., et al. 2023, A&A, 672, A155, doi: 10.1051/0004-6361/202345866
  * Mateo et al. (2012) Mateo, M., Bailey, J. I., Crane, J., et al. 2012, 84464Y, doi: 10.1117/12.926448
  * Matthee et al. (2023) Matthee, J., Mackenzie, R., Simcoe, R. A., et al. 2023, ApJ, 950, 67, doi: 10.3847/1538-4357/acc846
  * McLeod et al. (2016) McLeod, D. J., McLure, R. J., & Dunlop, J. S. 2016, Monthly Notices of the Royal Astronomical Society, 459, 3812, doi: 10.1093/mnras/stw904
  * Naidu et al. (2022) Naidu, R. P., Oesch, P. A., van Dokkum, P., et al. 2022, ApJ, 940, L14, doi: 10.3847/2041-8213/ac9b22
  * Ning et al. (2022) Ning, Y., Cai, Z., Jiang, L., et al. 2022, arXiv e-prints, arXiv:2211.13620.  https://arxiv.org/abs/2211.13620
  * Ning et al. (2022) Ning, Y., Jiang, L., Zheng, Z.-Y., & Wu, J. 2022, The Astrophysical Journal, 926, 230, doi: 10.3847/1538-4357/ac4268
  * Ning et al. (2020) Ning, Y., Jiang, L., Zheng, Z.-Y., et al. 2020, The Astrophysical Journal, 903, 4, doi: 10.3847/1538-4357/abb705
  * Noll et al. (2009) Noll, S., Burgarella, D., Giovannoli, E., et al. 2009, A&A, 507, 1793, doi: 10.1051/0004-6361/200912497
  * Oesch et al. (2023) Oesch, P. A., Brammer, G., Naidu, R. P., et al. 2023, MNRAS, 525, 2864, doi: 10.1093/mnras/stad2411
  * Ono et al. (2010) Ono, Y., Ouchi, M., Shimasaku, K., et al. 2010, MNRAS, 402, 1580, doi: 10.1111/j.1365-2966.2009.16034.x
  * Ono et al. (2012) Ono, Y., Ouchi, M., Mobasher, B., et al. 2012, The Astrophysical Journal, 744, 83, doi: 10.1088/0004-637X/744/2/83
  * Ono et al. (2018) Ono, Y., Ouchi, M., Harikane, Y., et al. 2018, Publications of the Astronomical Society of Japan, 70, doi: 10.1093/pasj/psx103
  * Onoue et al. (2017) Onoue, M., Kashikawa, N., Willott, C. J., et al. 2017, The Astrophysical Journal, 847, L15, doi: 10.3847/2041-8213/aa8cc6
  * Oyarzún et al. (2017) Oyarzún, G. A., Blanc, G. A., González, V., Mateo, M., & Bailey, J. I. 2017, The Astrophysical Journal, 843, 133, doi: 10.3847/1538-4357/aa7552
  * Oyarzún et al. (2016) Oyarzún, G. A., Blanc, G. A., González, V., et al. 2016, The Astrophysical Journal, 821, L14, doi: 10.3847/2041-8205/821/1/L14
  * Peng et al. (2002) Peng, C. Y., Ho, L. C., Impey, C. D., & Rix, H.-W. 2002, AJ, 124, 266, doi: 10.1086/340952
  * Peng et al. (2010) —. 2010, AJ, 139, 2097, doi: 10.1088/0004-6256/139/6/2097
  * Pentericci et al. (2011) Pentericci, L., Fontana, A., Vanzella, E., et al. 2011, The Astrophysical Journal, 743, 132, doi: 10.1088/0004-637X/743/2/132
  * Prieto-Lyon et al. (2023) Prieto-Lyon, G., Mason, C., Mascia, S., et al. 2023, ApJ, 956, 136, doi: 10.3847/1538-4357/acf715
  * Rhoads et al. (2023) Rhoads, J. E., Wold, I. G. B., Harish, S., et al. 2023, ApJ, 942, L14, doi: 10.3847/2041-8213/acaaaf
  * Roberts-Borsani et al. (2023) Roberts-Borsani, G., Treu, T., Chen, W., et al. 2023, Nature, 618, 480, doi: 10.1038/s41586-023-05994-w
  * Roberts-Borsani et al. (2016) Roberts-Borsani, G. W., Bouwens, R. J., Oesch, P. A., et al. 2016, The Astrophysical Journal, 823, 143, doi: 10.3847/0004-637X/823/2/143
  * Robertson et al. (2015) Robertson, B. E., Ellis, R. S., Furlanetto, S. R., & Dunlop, J. S. 2015, The Astrophysical Journal, 802, L19, doi: 10.1088/2041-8205/802/2/L19
  * Rodriguez-Gomez et al. (2015) Rodriguez-Gomez, V., Genel, S., Vogelsberger, M., et al. 2015, Monthly Notices of the Royal Astronomical Society, 449, 49, doi: 10.1093/mnras/stv264
  * Roy et al. (2023) Roy, N., Henry, A., Treu, T., et al. 2023, ApJ, 952, L14, doi: 10.3847/2041-8213/acdbce
  * Schenker et al. (2014) Schenker, M. A., Ellis, R. S., Konidaris, N. P., & Stark, D. P. 2014, ApJ, 795, 20, doi: 10.1088/0004-637X/795/1/20
  * Schenker et al. (2012) Schenker, M. A., Stark, D. P., Ellis, R. S., et al. 2012, The Astrophysical Journal, 744, 179, doi: 10.1088/0004-637X/744/2/179
  * Schmidt et al. (2016) Schmidt, K. B., Treu, T., Bradač, M., et al. 2016, The Astrophysical Journal, 818, 38, doi: 10.3847/0004-637X/818/1/38
  * Shen et al. (2020) Shen, X., Hopkins, P. F., Faucher-Giguère, C.-A., et al. 2020, MNRAS, 495, 3252, doi: 10.1093/mnras/staa1381
  * Shibuya et al. (2015) Shibuya, T., Ouchi, M., & Harikane, Y. 2015, The Astrophysical Journal Supplement Series, 219, 15, doi: 10.1088/0067-0049/219/2/15
  * Shibuya et al. (2016) Shibuya, T., Ouchi, M., Kubo, M., & Harikane, Y. 2016, The Astrophysical Journal, 821, 72, doi: 10.3847/0004-637X/821/2/72
  * Shimasaku et al. (2006) Shimasaku, K., Kashikawa, N., Doi, M., et al. 2006, PASJ, 58, 313, doi: 10.1093/pasj/58.2.313
  * Song et al. (2016) Song, M., Finkelstein, S. L., Livermore, R. C., et al. 2016, The Astrophysical Journal, 826, 113, doi: 10.3847/0004-637X/826/2/113
  * Stark et al. (1992) Stark, A. A., Gammie, C. F., Wilson, R. W., et al. 1992, ApJS, 79, 77, doi: 10.1086/191645
  * Stark et al. (2010) Stark, D. P., Ellis, R. S., Chiu, K., Ouchi, M., & Bunker, A. 2010, Monthly Notices of the Royal Astronomical Society, 408, 1628, doi: 10.1111/j.1365-2966.2010.17227.x
  * Stark et al. (2011) Stark, D. P., Ellis, R. S., & Ouchi, M. 2011, ApJ, 728, L2, doi: 10.1088/2041-8205/728/1/L2
  * Stark et al. (2011) Stark, D. P., Ellis, R. S., & Ouchi, M. 2011, The Astrophysical Journal, 728, L2, doi: 10.1088/2041-8205/728/1/L2
  * Stark et al. (2013) Stark, D. P., Schenker, M. A., Ellis, R., et al. 2013, The Astrophysical Journal, 763, 129, doi: 10.1088/0004-637X/763/2/129
  * Sun et al. (2023) Sun, W., Ho, L. C., Zhuang, M.-Y., et al. 2023, The Structure and Morphology of Galaxies during the Epoch of Reionization Revealed by JWST.  https://arxiv.org/abs/2308.09076
  * Tacchella et al. (2023) Tacchella, S., Johnson, B. D., Robertson, B. E., et al. 2023, MNRAS, 522, 6236, doi: 10.1093/mnras/stad1408
  * Tang et al. (2023) Tang, M., Stark, D. P., Chen, Z., et al. 2023, MNRAS, 526, 1657, doi: 10.1093/mnras/stad2763
  * Tilvi et al. (2014) Tilvi, V., Papovich, C., Finkelstein, S. L., et al. 2014, The Astrophysical Journal, 794, 5, doi: 10.1088/0004-637X/794/1/5
  * Toshikawa et al. (2012) Toshikawa, J., Kashikawa, N., Ota, K., et al. 2012, The Astrophysical Journal, 750, 137, doi: 10.1088/0004-637X/750/2/137
  * Vanden Berk et al. (2001) Vanden Berk, D. E., Richards, G. T., Bauer, A., et al. 2001, AJ, 122, 549, doi: 10.1086/321167
  * Vanzella et al. (2009) Vanzella, E., Giavalisco, M., Dickinson, M., et al. 2009, ApJ, 695, 1163, doi: 10.1088/0004-637X/695/2/1163
  * Vanzella et al. (2014) Vanzella, E., Fontana, A., Pentericci, L., et al. 2014, Astronomy & Astrophysics, 569, A78, doi: 10.1051/0004-6361/201424285
  * Wang et al. (2023) Wang, F., Yang, J., Hennawi, J. F., et al. 2023, ApJ, 951, L4, doi: 10.3847/2041-8213/accd6f
  * Watson et al. (2015) Watson, D., Christensen, L., Knudsen, K. K., et al. 2015, Nature, 519, 327, doi: 10.1038/nature14164
  * Wilkins et al. (2010) Wilkins, S. M., Bunker, A. J., Ellis, R. S., et al. 2010, Monthly Notices of the Royal Astronomical Society, 403, 938, doi: 10.1111/j.1365-2966.2009.16175.x
  * Wold et al. (2022) Wold, I. G. B., Malhotra, S., Rhoads, J., et al. 2022, The Astrophysical Journal, 927, 36, doi: 10.3847/1538-4357/ac4997
  * Wu et al. (2020) Wu, J., Jiang, L., & Ning, Y. 2020, The Astrophysical Journal, 891, 105, doi: 10.3847/1538-4357/ab7333
  * Yan et al. (2023) Yan, H., Sun, B., Ma, Z., & Ling, C. 2023, arXiv e-prints, arXiv:2311.15121, doi: 10.48550/arXiv.2311.15121
  * Yang et al. (2017) Yang, H., Malhotra, S., Gronke, M., et al. 2017, ApJ, 844, 171, doi: 10.3847/1538-4357/aa7d4d
  * Zheng et al. (2017) Zheng, Z.-Y., Wang, J., Rhoads, J., et al. 2017, The Astrophysical Journal, 842, L22, doi: 10.3847/2041-8213/aa794f