# A Close Look at Ly$\alpha$ Emitters with JWST/NIRCam at $z\approx 3.1$

Yixiao Liu (刘一笑) Chinese Academy of Sciences South America Center for
Astronomy (CASSACA), National Astronomical Observatories(NAOC), 20A Datun
Road, Beijing 100012, China  School of Astronomy and Space Science, University
of Chinese Academy of Sciences, Beijing 101408, China  Y. Sophia Dai (戴昱)
Chinese Academy of Sciences South America Center for Astronomy (CASSACA),
National Astronomical Observatories(NAOC), 20A Datun Road, Beijing 100012,
China Y. Sophia Dai<EMAIL_ADDRESS>Stijn Wuyts Department of Physics,
University of Bath, Claverton Down, Bath BA2 7AY, UK  Jia-Sheng Huang (黄家声)
Chinese Academy of Sciences South America Center for Astronomy (CASSACA),
National Astronomical Observatories(NAOC), 20A Datun Road, Beijing 100012,
China  Harvard-Smithsonian Center for Astrophysics, 60 Garden Street,
Cambridge, MA, 02215, USA  Linhua Jiang (江林华) Kavli Institute for Astronomy
and Astrophysics, Peking University, Beijing 100871, People’s Republic of
China  Department of Astronomy, School of Physics, Peking University, Beijing
100871, People’s Republic of China

###### Abstract

We study 10 spectroscopically confirmed Ly$\alpha$ emitters (LAEs) at
$z\approx 3.1$ in the UDS field, covered by JWST/NIRCam in the PRIMER program.
All LAEs are detected in all NIRCam bands from F090W to F444W, corresponding
to restframe 2200Å–1.2$\mathrm{\mu m}$. Based on morphological analysis of the
F200W images, three out of the 10 targets are resolved into pair-like systems
with separations of $<0.9^{\prime\prime}$, and another three show asymmetric
structures. We then construct the spectral energy distributions (SEDs) of
these LAEs. All sources, including the pairs, show similar SED shapes, with a
prominent flux excess in the F200W band, corresponding to extremely strong [O
iii]+H$\beta$ emission lines (${\rm EW_{rest}}=740$–$6500\,$Å). The median
effective radii, stellar mass, and UV slope of our sample are 0.36 kpc,
$3.8\times 10^{7}\,M_{\odot}$, and –2.48, respectively. The average burst age,
estimated by stellar mass over star formation rate, is $<40\,$Myr. These
measurements reveal an intriguing starbursting dwarf galaxy population lying
off the extrapolations of the $z\sim 3$ scaling relations to the low-mass end:
$\sim 0.7$ dex above the star-forming main sequence, $\sim 0.35$ dex below the
mass–size relation, and bluer in the UV slope than typical high-z galaxies at
similar UV luminosities. We speculate that these numbers may require a larger
main sequence scatter or tail in the dwarf galaxy regime towards the starburst
outliers.

galaxies: formation – galaxies: evolution – galaxies: high-redshift –
galaxies: stellar content – galaxies: structure

††facilities: JWST (NIRCam)††software: astropy (Astropy Collaboration et al.,
2013), GALFIT, CIGALE, emcee, matplotlib

##  1 Introduction

Ly$\alpha$ emitting galaxies, or Ly$\alpha$ emitters (LAEs) have been an
extensively studied population since Partridge & Peebles (1967) first
elucidated the significance of Ly$\alpha$ emission in high-redshift (high-$z$)
galaxies. Especially in recent decades, as telescope capabilities rapidly
enhanced, more and more details about LAEs have been revealed (see Ouchi et
al. 2020 for a review). Today, we have a consensus that typical LAEs are
young, small, and metal-poor galaxies with Ly$\alpha$ emission originating and
escaping from sites of intense on-going star formation (e.g., Nakajima et al.,
2012; Hagen et al., 2014, 2016; Pucha et al., 2022). Galaxies of this type are
often considered to be the progenitors of present-day galaxies like our own
Milky Way (e.g., Gawiser et al., 2007; Hao et al., 2018; Khostovan et al.,
2019). They are also the most competitive contributors of reionization photons
(e.g., Yajima et al., 2012; Finkelstein et al., 2019; Jiang et al., 2022;
Matthee et al., 2022; Simmonds et al., 2023). While other studies about the
high-$z$ Universe focus more on large and/or bright galaxies, which are easier
to find, LAEs provide us with a valuable perspective into early-stage galaxies
when the evolution just starts. Moreover, with respect to the resonant nature
of Ly$\alpha$ emission, the prominent Ly$\alpha$ escape fraction of LAEs is a
pivotal clue for interpreting properties of their interstellar medium (ISM),
circum-galactic medium (CGM), and HI gas in galaxy formation (e.g., Steidel et
al., 2011; Momose et al., 2014; Dijkstra et al., 2016; Leclercq et al., 2020;
Claeyssens et al., 2022; Reddy et al., 2022).

Though an advantageous tool for studying the high-$z$ Universe, many questions
regarding the nature of LAEs are still to be resolved. Besides the
identification of strong Ly$\alpha$ emission, our comprehension about the
galaxies themselves is still inadequate to explain how Ly$\alpha$ is exactly
produced and treads through the surrounding medium. In that sense, revealing
the physical structure and galaxy composition are important steps towards
understanding the whole picture of LAEs and their place in galaxy evolution.
However, due to their low continuum emission and high redshifts, individual
detections at rest-frame optical bands are hard to attain. In practice, a
stacking analysis is usually performed to constrain the average SED of a large
sample (e.g., Gawiser et al., 2006, 2007; Finkelstein et al., 2009; Ono et
al., 2010; Guaita et al., 2011; Vargas et al., 2014; Hao et al., 2018;
Kusakabe et al., 2018). With large survey programs aimed at LAE, their sample
sizes are now growing notably (e.g., a catalogue with over 50k
spectroscopically selected LAEs was assembled by HETDEX, Mentuch Cooper et al.
2023). In contrast, an in-depth study on individual sources is still missing.

With the advent of the James Webb Space Telescope (JWST), we are finally
equipped to inspect these distant, faint targets using resolved images.
Compared to the previous generation infrared telescope Spitzer, JWST
introduces an improvement of about one order of magnitude in both limiting
flux and spatial resolution. Its preeminent power has been confirmed by a
multitude of achievements in searching high-$z$ galaxies within its first year
in service. Yet most of the current research about LAEs focuses on higher
redshifts (e.g, Ning et al. (2023) at $z\simeq 6$; Tang et al. (2023) at
$z=7$–$9$; Jung et al. (2023) at $z\sim 8$; Whitler et al. (2023) at $z\sim
9$; Tang et al. (2023) at $z=7$–$9$). These works investigate the Ly$\alpha$
escape process in the reionization era, while paying relatively less attention
to the intrinsic properties of the galaxies themselves. Where galaxy
morphologies and physical properties are considered, the findings conform to
previous expectations. One notable finding is that these LAEs exhibit
extremely strong optical line emission, as revealed by both spectral and
broadband analyses, which also occurs in the lower redshift ($z\approx 3.1$)
sample explored in this paper. Indeed, extreme emission-line galaxies (EELGs)
selected by their strong optical line emission (e.g., van der Wel et al.,
2011; Tang et al., 2021; Withers et al., 2023) show similar properties as LAEs
in terms of their size, mass and age, and also feature possible Ly$\alpha$
emission. This opens a new way of selecting this type of galaxies in the
future.

In this paper, we zoom in on 10 LAEs at $z\approx 3.1$ with deep JWST/NIRCam
coverage. They were all narrow-band selected and then spectroscopically
confirmed by high-resolution spectrographs, making our sample entirely
reliable. Their relatively low redshift (compared to the most distant sources
now within reach of JWST) eases the observation in terms of signal-to-noise
ratio (S/N) and pushes the wavelength coverage of NIRCam filters to the rest-
frame NIR ($\sim 1\mu m$). These sources at $z\sim 3$ offer a probe of the
star formation process in dwarf galaxies entering cosmic noon, and a link
between star-forming (SF) galaxies in the local and high-$z$ Universe.

Our paper is structured as follows. We briefly introduce our LAE sample and
the relevant observations in §2. We next describe the morphological and SED
analysis in §3. We investigate the LAE properties in the context of the star-
forming main sequence (SFMS) and mass–size relation in §4, discuss their
numbers in §5, and finally conclude in §6.

Throughout, we adopt a $\Lambda-$dominated flat cosmology with
$\mathrm{H_{0}=70\,km\,s^{-1}\,Mpc^{-1}}$, $\mathrm{\Omega_{m}=0.3}$ and
$\mathrm{\Omega_{\Lambda}=0.7}$. All magnitudes quoted are in the AB system.

##  2 Sample and Data

Our sample is drawn from a large spectroscopically-confirmed LAE sample at
$z\approx 3.1$, partly covered by the recently released JWST data from the
Public Release IMaging for Extragalactic Research (PRIMER, Dunlop et al. 2021,
PI: J. Dunlop) survey in the UDS field.

Figure 1: Cutouts of the 10 LAE targets in 8 NIRCam bands and their spectra of
Ly$\alpha$ emission. All images are $2\,^{\prime\prime}\times
2\,^{\prime\prime}$ in size. Blue circles represent apertures with
$\mathrm{radii=0.3^{\prime\prime}}$. Three possible companions (with
consistent SEDs) are also marked by circle apertures. The angluar separations
between the two components are $0.69,0.89,0.47^{\prime\prime}$ for UDS-022,
140, and 141, respectively. Notice that the orientation of images does not
comply with north-south direction. Unsmoothed Ly$\alpha$ spectra of 9 targets
are displayed in the rightmost column. All spectra were observed by M2FS
except UDS-101 using Hectospec. The y-axes of spectral panels are in arbitrary
flux units. The Ly$\alpha$ spectrum of UDS-022 with a subtle double-peak
feature is shown in Figure 3 of Ouchi et al. (2008). In the bottom panel, we
display a LAE model spectrum (which is the best fitted model of UDS-144 in SED
fitting, see §3.3) along with throughput curves of the 8 NIRCam filters to
illustrate the flux contribution in each band. Clearly, emission lines can
take a dominant position in the optical-to-NIR spectrum of LAEs.

###  2.1 LAE Parent Sample

Our parent sample includes 166 spectroscopically-confirmed LAEs presented in
Guo et al. (2020), in which 150 targets were observed with Hectospec
(Fabricant et al., 2005) on the Multi-Mirror Telescope (MMT) or the
Michigan/Magellan Fiber System (M2FS; Mateo et al. 2012) on Magellan, and the
remaining 16 are from Ouchi et al. (2008) observed with the Faint Object
Camera and Spectrograph (FOCAS; Kashikawa et al. 2002) on Subaru and the
Visible Multi-Object Spectrograph (VIMOS; Le Fèvre et al. 2003) on VLT. In
brief, this parent sample is spread across the wider Subaru XMM-Newton Deep
Survey (SXDS; Furusawa et al. 2008) field, which has a coverage of $\sim$1.2
deg2 that fully covers the $\sim$150 arcmin2 UDS field observed by JWST.

The sources in the sample were first selected as LAE candidates at $z\approx
3.1$ by requiring BV$\,-\,$NB$\,>1\,{\rm mag}$, where BV is the weighted
magnitude between B and V bands, and NB is the Subaru narrowband NB497
(central $\lambda=4986\,$Å, $\rm FWHM=78\,$Å) or NB503 (central
$\lambda=5030\,$Å, $\rm FWHM=74\,$Å). An additional narrowband magnitude limit
corresponding to a $>9\,\sigma$ or $10\,\sigma$ (for NB503 and NB497,
respectively) detection is further required to ensure strong Ly$\alpha$
emission. These candidates were then observed with different spectrographs at
resolutions ranging from $R\sim 500$–$2000$. All possible low-z contaminations
(e.g. [O ii], [O iii], H$\alpha$) were carefully removed, before the
confirmation of LAE systems. The rest-frame equivalent width (EW) of the
parent LAE sample has a median value of $\sim 90\,$Å. The redshifts determined
by the peak of the Ly$\alpha$ line are within the range $z=3.05$–$3.16$.

We then matched the parent LAE sample with the PRIMER released data in the UDS
field, and found 10 spectroscopically confirmed LAEs, including three possible
pair systems (see §3.1) that have been observed by JWST. Of the 10 LAEs in our
sample, 9 are confirmed by Guo et al. (2020) and one by Ouchi et al. (2008).
The available Ly$\alpha$ spectra of the 9 LAEs from Guo et al. (2020),
observed with either Magellan M2FS or Hectospec, are shown in Figure 1. We
note that our 10 objects happen to be relatively faint among the parent
sample, with a $V$-band magnitude in the range 25.6–26.8, while the parent
sample has a $V$-band magnitude range spanning ${\rm mag}_{V}=23.4$–$27.4$.

###  2.2 JWST Data

####  2.2.1 Observation and Data Reduction

The PRIMER project surveys the well-observed UDS and COSMOS fields with JWST
NIRCam and MIRI in a parallel mode. For NIRCam imaging, 8 filters are used,
including F090W, F115W, F150W, F200W with the Short Wavelength (SW) detectors,
and F277W, F356W, F410M, F444W with the Long Wavelength (LW) detectors. The
first two epochs of UDS observations were completed in July 2022 and January
2023, respectively.

We retrieve the ‘.uncal’ data that overlap with our parent sample coverage
from the Mikulski Archive for Space Telescopes
(MAST)111https://mast.stsci.edu/. Then we reduce the data using the official
JWST Pipeline (v1.9.4). The calibration reference file involved in the
reduction is ‘jwst$\\_$1046.pmap’. Two additional processes called ‘snowball’
and ‘1/f noise’ are added in Stage-1 and after Stage-2, respectively, to
complement the current pipeline. We note that some exposures of the UDS field
are contaminated by unknown stripes in the NIRCam data. According to the JWST
Help Desk 222https://stsci.service-now.com/jwsts, this contamination may be
caused by the scattered light from some surface or optical path given its
wavelength dependence. To mitigate its effect, we implement an additional step
to first measure and then deduct the median value along the stripes during the
1/f reduction process. The final images are drizzled to a uniform scale of
0.03′′/pixel for the SW and 0.06′′/pixel for the LW data, respectively. We
notice that the WCS of the SW and LW filters often shows an offset, due to the
paucity of reference stars in the field of view. To correct this, we adopt the
F200W image as the SW reference, and apply to the LW images an average WCS
shift, generated by matching the catalogs of each filter to the F200W catalog.
Figure 1 displays the postage stamp images of our 10 targets with a
$2\,^{\prime\prime}\times\,2\,^{\prime\prime}$ size. Since some of the fields
are covered by two pointings, the total exposure time for each source varies,
as summarized in Table 1.

####  2.2.2 Photometry

We measure the fluxes of our objects within circular apertures. Due to their
compact sizes (see §3.2), either a $r=0.1^{\prime\prime}$ or
$r=0.3^{\prime\prime}$ aperture is chosen for the flux measurement. The choice
is made by comparing the flux values after PSF correction for different
apertures (0.1–0.4′′), and when the measured fluxes are consistent between two
apertures, the smaller aperture with smaller uncertainties is adopted.
Typically, if our target is compact with no extended structure or irregular
shapes, a $r=0.1^{\prime\prime}$ aperture is adopted, and vice versa, as noted
in Table 1. We apply a local background measurement and removal in an area of
$3\,^{\prime\prime}\times 3\,^{\prime\prime}$, after masking out all pixels
with $>3\,\sigma$ values. The flux errors are computed by
$\sqrt{n_{pix}}\,\times\,\mathrm{ERR_{max}}$, where $n_{pix}$ is the number of
pixels inside the aperture and $\mathrm{ERR_{max}}$ is the maximum error value
within the aperture. Additionally, to take potential systematic uncertainties
into account, we set a lower error limit of 10% of the total flux. Table 1
lists the measured photometry for all sources in our sample.

###  2.3 Ancillary Data

The UDS and SXDS fields are rich in ancillary data, covering a wide wavelength
range from the X-ray to the submillimeter. For the following analysis, we also
include the photometry in 6 other bands, including the CHFT-MegaCam/$u$ and
the Subaru-SupCam/$B,V,R_{c},i^{\prime},z^{\prime}$ to complement the
observations. These data are taken from the catalogue by Galametz et al.
(2013). Given the low resolution of the UV-optical data (resolution $\sim
0.8^{\prime\prime}$), their photometry was measured by template-fitting with
prior segmentation information based on the CANDELS WFC3 F160W image, whose
resolution is $\rm FWHM=0.2^{\prime\prime}$ and limiting magnitude 27.45 mag.
measured by template-fitting method using the source detection in F160W as
reference. Among the 10 LAEs in our sample, 7 are recorded in their catalogue.
Two (UDS-152, 154) of the remaining three did not have F160W coverage, while
the other one (UDS-140) was covered but not detected. With our new NIRCam
bands, a total of 14 bands are included in the following SED analysis (see
§3.3), spanning from the rest-frame UV to NIR, allowing stellar mass, UV slope
and SFR measurements.

In order to check for potential active galactic nulceus (AGN) radiation, we
also examined the Spitzer/MIPS 24$\mu$m and Chandra full-band images in the
UDS field, which have resolutions of $6^{\prime\prime}$ (24$\mu$m) and
0.2–0.7′′ (Chandra), respectively. No counterpart is matched or found by
visual inspection in any of these bands. Therefore, we assume a negligible AGN
contribution to our sample in the following analysis.

=2.5cm

Table 1: Effective Radii and Photometry for 10 LAEs and Their Possible
Companions at $z\simeq 3.1$

ID | Exp. time | $R_{\mathrm{e,circ}}$ | F090W | F115W | F150W | F200W | F277W | F356W | F410M | F444W |
---|---|---|---|---|---|---|---|---|---|---|---
| (s) | (kpc) | (mag) | (mag) | (mag) | (mag) | (mag) | (mag) | (mag) | (mag) |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) |
UDS-022a | 1675.0 | $0.36\pm 0.04$ | 27.32$\pm$0.11 | 27.62$\pm$0.12 | 27.35$\pm$0.10 | 26.89$\pm$0.10 | 27.47$\pm$0.10 | 28.21$\pm$0.12 | 27.88$\pm$0.18 | 28.18$\pm$0.20 |
UDS-022b | 1675.0 | $0.21\pm 0.08$ | 28.03$\pm$0.19 | 28.17$\pm$0.20 | 27.73$\pm$0.12 | 27.35$\pm$0.10 | 27.84$\pm$0.10 | 29.16$\pm$0.27 | 27.84$\pm$0.17 | 28.20$\pm$0.20 |
UDS-101$\ast$$\ast$footnotemark:  | 837.5(SW) | $0.53\pm 0.12$ | 27.13$\pm$0.34 | 26.73$\pm$0.21 | 26.72$\pm$0.16 | 26.43$\pm$0.11 | 26.96$\pm$0.10 | 27.43$\pm$0.14 | 28.50$\pm$0.58 | 27.66$\pm$0.25 |
1675.0(LW) |
UDS-140a | 1675.0 | $0.23\pm 0.13$ | 28.42$\pm$0.32 | 27.92$\pm$0.19 | 28.73$\pm$0.30 | 27.82$\pm$0.12 | 28.13$\pm$0.11 | 29.42$\pm$0.32 | 28.57$\pm$0.30 | 28.92$\pm$0.34 |
UDS-140b | 1675.0 | $0.38\pm 0.21$ | 28.21$\pm$0.25 | 28.61$\pm$0.32 | 28.18$\pm$0.19 | 27.52$\pm$0.10 | 28.11$\pm$0.11 | 28.17$\pm$0.11 | 27.83$\pm$0.17 | 28.11$\pm$0.17 |
UDS-141a | 837.5 | $0.22\pm 0.03$ | 26.34$\pm$0.10 | 26.52$\pm$0.10 | 26.50$\pm$0.10 | 25.95$\pm$0.10 | 26.70$\pm$0.10 | 27.36$\pm$0.10 | 27.18$\pm$0.14 | 27.18$\pm$0.11 |
UDS-141b | 837.5 | $0.05\pm 0.33$ | 28.86$\pm$0.60 | 29.35$\pm$0.78 | 28.94$\pm$0.49 | 27.59$\pm$0.16 | 28.47$\pm$0.21 | 28.84$\pm$0.28 | 28.59$\pm$0.42 | 28.54$\pm$0.35 |
UDS-143 $\ast$$\ast$footnotemark:  | 837.5 | $0.55\pm 0.05$ | 26.55$\pm$0.21 | 26.25$\pm$0.18 | 26.11$\pm$0.11 | 25.79$\pm$0.10 | 26.17$\pm$0.10 | 26.32$\pm$0.10 | 26.34$\pm$0.14 | 26.30$\pm$0.10 |
UDS-144 $\ast$$\ast$footnotemark:  | 1675.0 | $0.44\pm 0.02$ | 25.86$\pm$0.10 | 25.82$\pm$0.10 | 25.44$\pm$0.10 | 24.75$\pm$0.10 | 25.26$\pm$0.10 | 25.86$\pm$0.10 | 25.61$\pm$0.10 | 25.66$\pm$0.10 |
UDS-146 $\ast$$\ast$footnotemark:  | 1675.0 | $0.27\pm 0.03$ | 26.84$\pm$0.16 | 27.16$\pm$0.21 | 27.03$\pm$0.15 | 26.09$\pm$0.10 | 26.62$\pm$0.10 | 27.10$\pm$0.10 | 27.64$\pm$0.26 | 27.14$\pm$0.16 |
UDS-149 $\ast$$\ast$footnotemark:  | 837.5 | $0.43\pm 0.08$ | 26.60$\pm$0.20 | 26.67$\pm$0.20 | 25.77$\pm$0.10 | 25.74$\pm$0.10 | 26.15$\pm$0.10 | 26.75$\pm$0.11 | 26.41$\pm$0.14 | 26.48$\pm$0.13 |
UDS-152 $\ast$$\ast$footnotemark:  | 1675.0 | $0.98\pm 0.50$ | 26.57$\pm$0.12 | 26.58$\pm$0.12 | 26.46$\pm$0.10 | 25.93$\pm$0.10 | 26.15$\pm$0.10 | 26.57$\pm$0.10 | 26.65$\pm$0.12 | 26.36$\pm$0.10 |
UDS-154 | 837.5 | $0.19\pm 0.03$ | 27.51$\pm$0.21 | 27.34$\pm$0.17 | 27.17$\pm$0.13 | 26.12$\pm$0.10 | 27.10$\pm$0.10 | 28.18$\pm$0.17 | 28.21$\pm$0.29 | 27.65$\pm$0.17 |

∗∗footnotetext: For these relatively large and bright sources, we use r=0.3”
apertures to measure their flux. Different PSF correction factors are adopted
depending on the aperture sizes.

Note. — (1) Object ID. (2) Exposure time in seconds. Different bands share the
same exposure time except in the case of UDS-101, which falls in the gap
between short wavelength detectors (SW) in one pointing, resulting in a
shorter exposure time. (3) Circularized $R_{e}$ in F200W band derived from
GALFIT, which is calculated by the effective radius of semi-major axis times
$\sqrt{b/a}$. The angular-diameter distance is calculated based on spec-z and
the scale at $z\approx 3.1$ is $\mathrm{\sim 7.6\,kpc}$ per arcsec. (4)–(11)
Photometry in 8 NIRCam filters.

##  3 Galaxy Properties

In this section, we introduce the measurement of physical properties of
sources in our sample including their morphology, physical size, and
properties like stellar mass, and SFR derived from the SED fitting. Specific
methods and details are presented in each subsection.

###  3.1 Morphology

The PSF sizes of NIRCam filters are between 0.03–0.14′′ from short to long
wavelengths. Multiplied by the angular scale at $z\approx 3.1$ ($\mathrm{\sim
7.6\,kpc/^{\prime\prime}}$), the NIRCam images allow us to distinguish
structures on scales down to $\sim 0.3\,$kpc. Though their compact nature does
not allow to fully resolve the sources in our sample, we leverage the sharper
view than any pre-JWST observation to place robust constraints on their sizes.

As shown in Figure 1, out of the 10 LAE systems in our sample, 3 exhibit
obvious extended (and asymmetric) structure in JWST images (UDS-143, 144,
149), while the other 7 appear as point-like sources. Among the point sources,
3 of them (UDS-022, 140, 141) show a possible companion with 0.47–0.89′′
separations. We verified the 8-filter NIRCam SEDs of these sources and their
companions, and confirm the presence of a prominent F200W excess in each of
them, similar to what is seen for the other, non-pair LAEs. This excess is
caused by the dominant contribution of optical emission lines (specifically [O
iii]+H$\beta$) that redshift into this filter (see the bottom panel of Figure
1 for an illustration). An imprint of (more modest) line contributions in the
adjacent F277W filter is also commonly seen, and attributed to the H$\alpha$
line which redshifts into this band. We conclude that the companions must be
at similar redshift, and are consistent with being physically associated.
There is no explicit answer whether the Ly$\alpha$ emission comes from one or
both objects in the pair based on the narrowband image or spectroscopy. The
double-peaked nature (with peak separation of $\lesssim 3\,$Å in the
restframe) of the Ly$\alpha$ emission observed for UDS-022 and 144 is not
conclusive in this regard either, as such line profiles are also known to
arise from the complexities of Ly$\alpha$ radiative transfer. What we can
conclude with certainty is that a low-z [O ii] doublet interloper
interpretation is ruled out on the basis of the SED (and specifically the
F200W excess) at high confidence. Considering the similarity of properties in
all aspects, we treat the pair-like sources equally and include the companions
as individual sources in later sections. To distinguish objects in pairs, we
label the brighter one in the F200W image with the letter ‘a’ and the fainter
one with letter ‘b’.

###  3.2 Effective Radii

The size measurement is conducted with GALFIT code (Peng et al., 2002). In the
fitting, we adopt a single Sérsic model to fit the target galaxy and use the
WebbPSF (Perrin et al., 2014) for PSF deconvolution. In general, the semi-
major axis of the ellipse that contains half of the total flux are chosen as
effective radius. But in the case that the target galaxy is small, the
observed flux distribution is largely dominated by the PSF, which means that
changes to the morphological parameters like Sérsic index or ellipticity would
not significantly alter the final model, so that these parameters cannot be
well constrained. When conducting the fittings, we find that the best-fitting
ellipticity and the corresponding semi-major $R_{e}$ vary slightly with the
initial input values, while the circularized $R_{e,circ}$ (defined as
$\sqrt{b/a}\,R_{e}$, where $b/a$ is the ratio between semi-minor and semi-
major axis) is more robust and less affected. Therefore in the following
discussions, we use the circularized radius $R_{e,circ}$ as the physical sizes
of our galaxies. As shown in the bottom panel of Figure 1, the flux of our
objects contains strong emission-line contributions in certain bands (see the
end of §3.3). Since we do not want our size measurement to be biased towards a
specific sub-population, we run the GALFIT in 5 bands, F115W, F150W, F200W,
F277W, and F356W, respectively. We find consistent size measurement in all
five bands using GALFIT, with $R_{e,circ}$ measured in different bands
agreeing within their error margins. In the following analysis, we choose the
sizes derived from F200W images (listed in Table 1) as the representative
size, as it lies in a wavelength range well above the Balmer break and has the
highest imaging quality.

As a sanity check, we also measured the angular sizes of all objects in F200W
by fitting Gaussian functions to their 1D flux distribution, despite the
asymmetrical morphology of some sources. Overall, the observed FWHM of these
sources are 1.30–2.35 $\times$ the PSF size. We deduct the instrumental
resolution in quadrature and obtain the physical effective radius $R_{e}$
through $R_{e}=\mathrm{0.5\times FWHM_{phy}=0.5}\times
d_{A}\times\mathrm{\sqrt{{FWHM_{obs}}^{2}-{FWHM_{PSF}}^{2}}}$, where $R_{e}$
is the radius that contains half of the total flux in a 2-D Gaussian profile,
and $d_{A}$ is the angular scale for the redshift of the source. The final
results agree well with the $R_{e,circ}$ derived from GALFIT except for one
outlier, UDS-152, whose GALFIT size is nearly two times larger than the 1-D
fitted size. The GALFIT value is also distinctly larger than the other
sources. In Table 1 and the following discussion, just as all other sources,
we still adopt the GALFIT size of UDS-152 as the center value, but assign a
large enough uncertainty to cover the result by the two different methods.

The median $R_{e,circ}$ of our sample in F200W band given by GALFIT is 0.36
kpc (0.32 kpc if we exclude UDS-152), which is extremely small for known
galaxies (e.g. the median size value for late-type galaxies in SDSS survey
with similar restframe $r$-band magnitudes is $\sim 2\,$kpc, Shen et al.
2003). In Figure 2, we demonstrate a pseudo color image of the source UDS-154
as an sample (R: F356W, G: F200W, B: F115W, approximately corresponding to the
rest-frame visual color for objects at $z\approx 3.1$). The minuscule size and
green color are two salient characteristics of our sources. These features are
reminiscent of Green Pea galaxies (GPs) (Cardamone et al., 2009), which are
thought to be the local analogs of LAEs.

Figure 2: A false-color image zooming in on the source UDS-154. The RGB color
composite combines F115W (blue), F200W (green) and F356W (red), matching the
real color in restframe. Angular scales are indicated both on the original and
on the zoomed-in frame.  Figure 3: Best-fitting model spectra (gray lines),
model fluxes (red dots) and observed fluxes (blue circles with error bars).
Each panel presents one CIGALE fit, with the ID of its fitted target labelled
in the upper left corner. The SEDs with 14 observed flux points comprise
photometry in CFHT-$u$ \+ SupCam-$B,V,R_{c},i^{\prime},z^{\prime}$ \+ 8 NIRCam
bands. Other spectra are fitted using only the 8 NIRCam bands. All fittings
are conducted under the same parameter space (see Table 2). For the 3 targets
(UDS-022, 140, 141) that have a possible companion within small separations,
we fit each of their components individually based on their NIRCam fluxes.
However, for UDS-022 and UDS-141, we also have their unresolved
$u$-to-$z^{\prime}$ band photometry, so we carry out two additional fits
incorporating the shorter-wavelength photometry and adding the NIRCam fluxes
of their two components together (i.e., regarding the pairs as a whole).

###  3.3 SED Fitting, Stellar mass, and SFR

We utilize the stellar population modelling code CIGALE (Boquien et al., 2019)
to conduct SED fitting with the redshift fixed to its spectroscopic value.
This code allow us to fit SEDs accounting for the estimated nebular emission
based on CLOUDY models. The best-fitting templates are displayed in Figure 3.
As mentioned in Section 2.3, we fit 7 targets with 14-band photometry
(CHFT-$u$ band + 5 Subaru-SupCam bands + 8 NIRcam bands). For UDS-022 and 141
among these 7 targets, since it is hard to separate their two components in
the unresolved ground-based observations, we instead sum the JWST flux of
objects ‘a’ and ‘b’ to treat them as an integral whole. For separate sources
in pairs and other targets without archival optical photometric data, we fit
their SEDs with only 8 NIRCam bands. In all cases, we run CIGALE with
identical models and parameter space as list in Table 2 and described below.
We choose a delayed star formation history with a constant burst in the recent
1–50 Myrs. A wide parameter space is given to both populations to test various
SFHs from single old population to burst-dominated histories. For the stellar
population, we use the classic Bruzual & Charlot (2003, BC03) models and a
Chabrier (2003) stellar initial mass function (IMF). Considering the young age
and strong emission-line that our sample has, we fix the metallicity of the
stellar component to sub-Solar ($Z_{*}=0.2\,Z_{\odot}=0.004$). In the nebular
model, we specify a high range of ionization parameters $\log U$ from –2.2 to
–1.2. Satisfactory fits are obtained for all sources, with
reduced-$\chi^{2}\lesssim 2$.

We check the consistency of SED fitting when using or not using the extra 6
optical bands by comparing the estimated stellar masses of same sources. For
the sample of 7 instances, deviations between the two methods. For the 7 SEDs
where this test was feasible, differences never exceeded 0.033 dex, with a
mean deviation of 0.007 dex, which is negligible. Furthermore, the summed
masses of the two components ‘a’ and ‘b’ for UDS-022 and 141 agree with the
total masses derived directly by modelling the integrated SEDs, within the
margin of error. We thus regard these two fitting methods as consistent.

In Table 3, we list the properties of all 13 separate sources derived by SED
fitting. The UV slopes of the best-fitting spectra have a range of –2.8 to
–2.1 and a median of –2.48. This shows that all of our Lya targets are very
blue with little dust attenuation compared with other high-z SF populations
(Bouwens et al., 2014; Reddy et al., 2018). The median stellar mass of our
sample equals to $3.78\times 10^{7}\,M_{\odot}$.

Using the best-fitting models, we then calculate the SFRs based on their
uncorrected UV luminosities.333Attenuation according to the Calzetti et al.
(2000) law was allowed in the fitting, but effectively not (or negligibly)
used in the best-fitting solutions, such that working with intrinsic (i.e.,
dust-corrected) SFR values would not alter our conclusions. By the same token,
adoption of a steeper attenuation law as appropriate for e.g. the Small
Magellanic Cloud (SMC) would not impact our results either. The luminosity is
averaged among 1500–2800Å and we convert it into SFR using the formula given
by Kennicutt (1998) under the assumption of a Chabrier IMF:

$\mathrm{SFR_{UV}}\,(M_{\odot}\,\mathrm{yr^{-1})=7.8\times 10^{-29}\
}L_{UV}\,\mathrm{(erg\ s^{-1}\,Hz^{-1})}.$ (1)

The calculated SFR values are consistent with the SFR given by CIGALE and are
adopted in the following analysis. We compare the average age computed as
$M_{*}/\mathrm{SFR_{UV}}$ to the burst age fitted by CIGALE. We find that
these two ages are consistent in general, with mean values of 17 and 13 Myr,
respectively. This indicates a dominant burst contribution to the total
stellar mass in our sample. Table 3 lists the calculated $\mathrm{SFR_{UV}}$
and average ages.

We also measure the restframe EWs of the three most prominent lines that fall
in the NIRCam observations, [O iii], H$\alpha$ and H$\beta$. These EW values
are based on the best fitted models. For sources in our sample, the [O iii]
and H$\beta$ lines are redshifted into F200W, and H$\,\alpha$ into the F277W
band. As shown in Figure 3, the flux excesses due to line-emission in these
two bands are well estimated by the fitted model. The results show that EW([O
iii]+H$\beta$)s of our sample have a range of 740–6500 Å, with a median of
1700 Å and EW(H$\alpha$)s have a range of 370–2600 Å with a median of 950 Å.
These high EWs qualify our sample as one of the most extreme emission line
galaxies (EELGs). Correspondingly, over 50% of the F200W flux and 30% of the
F277W flux can be attributed to these line contributions.

In summary, the SED fitting results reveals the extremely young, dust-poor,
and low-mass nature of our sample, which also exhibits extreme emission lines.

Table 2: Parameter Space of the CIGALE Fitting

No. | Parameter | Range
---|---|---
(1) | $\tau_{\mathrm{{del}}}$ |  $50-5000$ Myr
(2) | $age_{\mathrm{{del}}}$ |  $100-1500$ Myr
(3) | $age_{\mathrm{{burst}}}$ |  $1-50$ Myr
(4) | $r_{\mathrm{{SFR}}}$ | $1-10000$
(5) | $Z_{*}$ | 0.004
(6) | $\log\,U$ | $-2.2--1.2$
(7) | $Z_{\mathrm{{gas}}}$ | $0.004,\ 0.008$
(8) | $f_{\mathrm{{esc}}}$ | $0.2-0.7$
(9) | $E(B-V)_{l}$ | $0-0.3$

Note. — (1),(2) The e-folding time and age of the delayed population in star
formation history. (3) Age of the constant burst. (4) Ratio of the SFR
after/before burst. (5) Metallicity of stars. (6) Ionisation parameter. (7)
Metallicity of gas. (8) Escape fraction of Lyman continuum photons. (9) The
color excess of the nebular lines, converting to the color excess of stellar
continuum by multiplying a factor of 0.44.

Table 3: Properties of LAE Sample at $z\simeq 3.1$

ID | $\beta$ | $\log(M_{*}/M_{\odot})$ | $\mathrm{SFR_{UV}}$ | Age | EW([O iii]+H$\beta$) | EW(H$\alpha$)
---|---|---|---|---|---|---
|  |  | ($M_{\odot}\,\mathrm{yr^{-1}}$) | (Myr) | ($10^{3}\,$Å) | ($10^{3}\,$Å)
(1) | (2) | (3) | (4) | (5) | (6) | (7)
UDS-022a | -2.76±0.10 | 7.31±0.17 | 2.6 | 8 | 3.7 | 2.3
UDS-022b | -2.73±0.12 | 7.17±0.18 | 1.5 | 10 | 4.3 | 2.6
UDS-101 | -2.42±0.08 | 7.58±0.15 | 2.6 | 14 | 2.1 | 0.9
UDS-140a | -2.69±0.14 | 7.05±0.18 | 1.3 | 8 | 1.6 | 1.1
UDS-140b | -2.34±0.15 | 7.57±0.18 | 1.0 | 36 | 0.8 | 0.3
UDS-141a | -2.78±0.09 | 7.72±0.19 | 7.2 | 7 | 2.0 | 1.0
UDS-141b | -2.48±0.18 | 7.25±0.24 | 0.5 | 34 | 2.7 | 0.9
UDS-143 | -2.32±0.05 | 8.20±0.09 | 7.0 | 23 | 0.8 | 0.4
UDS-144 | -2.16±0.03 | 8.42±0.08 | 10.7 | 24 | 1.0 | 0.5
UDS-146 | -2.48±0.06 | 7.74±0.15 | 3.9 | 14 | 1.7 | 1.0
UDS-149 | -2.41±0.06 | 8.01±0.13 | 6.4 | 16 | 1.2 | 0.7
UDS-152 | -2.39±0.13 | 8.12±0.17 | 5.8 | 23 | 0.7 | 0.4
UDS-154 | -2.74±0.08 | 7.40±0.13 | 2.6 | 10 | 6.5 | 2.5

Note. — (1) Object ID. (2)(3) UV slope and stellar mass derived from SED
fitting. (4) Uncorrected SFR converted from 1500–2800Å luminosity by equation
1. (5) Age defined as $M_{*}/\mathrm{SFR_{UV}}$. (6)(7) Rest-frame EWs
calculated in the best fitted model.

##  4 Results

Figure 4: SFR to stellar mass distribution of our LAE sample, compared with
calibrations of the star-forming main sequence from the literature (S14, S17,
M23), extrapolated down to our low-mass range of interest. We use $z=3.1$ to
calculate the age of the Universe when plotting the relation given by S14, and
the relations from S17 and M23 are selected to be in the redshift bins closest
to $z=3.1$. All relations are adjusted to Chabrier IMF scale. A uniform
0.3-dex scatter is indicated by the shaded regions around each dashed line.
The SFR uncertainties of our data points are calculated by adding in
quadrature the photometric errors in the rest-frame UV band plus and an
additional 0.25 dex to account for systematic uncertainty in the UV-to-SFR
conversion.

###  4.1 Main Sequence

In Figure 4 we show the SFR to stellar mass distribution of our sample and
compare to the extrapolated star-forming main sequence (MS) given by previous
works (Speagle et al., 2014; Santini et al., 2017; Mérida et al., 2023,
hereafter S14, S17 and M23, respectively). All of our sources lie above the
three given relations with excesses between 0.3–1.5 dex. Here, it is important
to emphasize that all three MS relations shown were established on the basis
of galaxy samples that do not probe as far down as the low-mass ($\lesssim
10^{8.5}\,M_{\odot}$) regime explored here. By lack of further constraints,
and acknowledging that the selection effects inherent to our sample inhibit
its use for fitting of a MS relation at the low-mass end, we thus simply
assume that the same functional form (e.g., linear in the case of S14 and S17)
holds down to $10^{7}$–$10^{8.5}\,M_{\odot}$ as a description of the typical
SF activity in a mass-complete sample of dwarf galaxies. With this ansatz, we
compare our sample with the MS to see whether our LAEs, as a type of star-
forming galaxies, lie on or above the MS, which is an unsettled argument. As
we already alluded to above, all sources in our sample appear as starbursting
outliers residing well above the MS. Taking the MS from S14 as a reference
(the one that has the highest SFR in our mass range), our sample is about 0.7
dex higher on average. There is thus no doubt that our sources feature
unusually high specific SFRs compared to the bulk of star-forming galaxies.
However, it is too premature to decide that the whole Ly$\alpha$-emitting
population necessarily lies above the MS. Our sample is strongly biased to
relatively bright UV continua (which leads to high SFR) through the LAE
candidate narrowband selection and prioritization for subsequent spectroscopic
observation.

Figure 5: Mass-size relation of our LAE sample, with comparison to the V14
relation for late-type galaxies at $z=3.1$ extrapolated to our mass range. The
cyan region represents the linear fitted relation within the 16, 84th
percentiles derived from MCMC chains. Our fitting is conducted with the form
of $\log\,R_{e}=\alpha\,\log\,(M_{*}/10^{7}\,M_{\odot})+\log\,$A , and the
fitted values of ($\log\,$A, $\alpha$) are ($-0.65^{+0.10}_{-0.10}$,
$0.24^{+0.08}_{-0.10}$). The orange dashed line in figure represents the
extrapolated relation of V14, with ($\log\,$A, $\alpha$)=$(-0.31,0.18)$. A
scatter equals to $0.24\,$dex for $R_{e}$ is shown by orange shadow region.
Our sample, although significantly smaller in size and mass from V14, has a
similar slope between $M_{*}$ and $R_{e}$, indicating similar mass-size
relation still holds for less massive star forming galaxies at higher
redshift.

###  4.2 Mass-Size Relation

We show the mass-size relation of our $z\approx 3.1$ LAEs in Figure 5 based on
the effective radii deduced from the F200W (i.e., rest-optical) images (§3.2)
and the stellar masses given by SED fitting (§3.3). In analogy to §4.1, we
here also contrast our sample to the extrapolation of a scaling relation from
the literature, established on the basis of more massive galaxies.
Specifically, we adopt the relation provided by van der Wel et al. (2014,
hereafter V14) at the highest redshift bin (centering at $z=2.75$ with 0.5 as
width) and extroplate it to $z=3.1$ by considering the size evolution as a
function of redshift using the formula, which is also provided by V14,
constructed in the the lowest mass bin ($10^{9}$–$10^{9.5}\,M_{\odot}$). For
consistency of the comparison, we convert the V14 size–mass relation from its
original definition in terms of semi-major axis size to circularised $R_{e}$
by scaling with a median $\rm\sqrt{b/a}$, where the median b/a appropriate for
high-z late-type galaxies is 0.54.444Technically, the CANDELS/3D-HST sample
exploited by V14 reaches up to $z=3$, where its constraints are based on
galaxies with masses $\gtrsim 10^{9.5}\,M_{\odot}$. Our sample occupies a
significantly lower massive regime (by $\sim$ 3 dex), but additionally also
much smaller galaxy sizes, even when accounting for the mass–size relation as
established by V14 (on average $\sim 0.35$ dex smaller). We carry out a linear
regression of the form
$\log\,R_{e}=\alpha\,\log\,(M_{*}/10^{7}\,M_{\odot})+\log\,$A on our sample
using emcee (Foreman-Mackey et al., 2013) and obtain best-fitting values for
($\log\,$A, $\alpha$) and the corresponding uncertainties within the 68%
confidence interval of ($-0.65^{+0.10}_{-0.10}$, $0.24^{+0.08}_{-0.10}$). We
note that, while the zero point is substantially lower than that of the
size–mass relation by V14, the best-fitting slope is consistent.

Other studies on LAEs and EELGs likewise report small sizes, and a correlation
between strong Ly$\alpha$ emission and small physical size is also alluded.
(e.g., Tang et al. 2021 finds that in an extreme-optical-line-selected sample
at $z\simeq 2$–3, galaxies with higher EW(Ly$\alpha$) have a slightly smaller
size ($R_{e}=0.49\,$kpc) comparing to galaxies with weaker Ly$\alpha$
($R_{e}=0.76\,$kpc); Kim et al. 2021 reports a very compact size of GPs with a
typical radius of 0.33 kpc and an anticorrealtion between $R_{e}$ and
EW(Ly$\alpha$).)

To state the obvious, the size–mass relation recovered for our LAEs, with
lower zero point but consistent slope compared to V14, should not be read as
an indication that these galaxies will necessarily maintain their more-
compact-than-average status forever. First, the results presented here on our
sample of starbursting dwarfs do not by themselves confirm that they are
smaller than the average galaxy even at their mass and epoch. It may be that
the size–mass relation itself is not well approximated by a power-law shape
over the full dynamic range of galaxy masses. Secondly, their subsequent
evolution does not need to track the slope of their size–mass relation at the
observed epoch. The evolutionary track through ($M_{*}$, $R_{e}$) space
followed by individual galaxies may differ from the trend-line of their
distribution at a given epoch, as also the zero point of the size–mass
relation evolves (i.e., increases) with time. Using respectively observations
and simulations, both V14 and Genel et al. (2018) argued for steeper
evolutionary size growth tracks for late-type galaxies than the slope of the
size–mass relation (which features little evolution with redshift). Processes
contributing to such growth in size include star formation and merging.
Disentangling the two requires contrasting galaxy sizes measured in a stellar
tracer and an instantaneous star formation tracer. For example, doing so for a
sample of massive ($\gtrsim 10^{9.5}\,M_{\odot}$) star-forming galaxies at
$0.7\lesssim z\lesssim 2.7$ with H$\alpha$ size measurements from integral-
field spectroscopy, Wilman et al. (2020) concluded that their star formation
driven size growth is sufficient only to grow along the size–mass relation,
not to account for its zero-point evolution. Mergers, or preferential
quenching of the more compact star-forming galaxies, would be required to
explain the evolution of the scaling relation. In the low-mass regime we
consider here, quenching is anticipated to impact the population negligibly,
leaving either a strong inside-out trend of star formation or merging as
potential routes to bring our starbursting dwarfs onto the regular size–mass
relation by the time they grow to $\gtrsim 10^{9}\,M_{\odot}$. Alternatively,
they will remain among the more compact objects also at later epochs.

In principle, size biases may contribute to rendering the measured sizes as
compact as observed. As alluded to in §3.2, the F200W and F277W size
measurements may not be ideal as a probe of the galaxies’ stellar extent, with
high-EW line contributions in the median adding up to 50% and 30% of the
broadband flux, respectively. Enhanced excitation levels in the galaxy centres
could boost the central [O iii] (and consequently F200W) emission, thus
skewing the observed sizes to smaller values. In the case of F277W, the main
line contribution comes from H$\alpha$, a tracer of newly formed stars. The
F150W filter at $z=3.1$ samples partly below the Balmer break, and may thus
likewise receive more weight from younger stellar populations. As a counter
argument, however, we raise the conclusion drawn from our SED modelling
(§3.3), namely that no evidence is found for an underlying old population.
This inference is uniquely enabled by NIRCam’s longer wavelength coverage.
Indeed, where the S/N allows, consistently small size measurements are
obtained in the longer wavelength NIRCam images, albeit increasingly of a
marginally resolved nature.

A more in depth assessment of size growth scenarios from the dwarf to normal
galaxy regime will require the collection of more data on the general
distribution of galaxy sizes down to masses of around
$10^{7}$–$10^{8}\,M_{\odot}$.

###  4.3 UV continuum

In Figure 6 we consider the relation between the absolute UV magnitude
($M_{UV}$) and the UV slope ($\beta$) of LAEs in our sample. Specifically, we
quantify $\beta$ on the best-fitting stellar population model. As mentioned in
§3.3, only 5 objects in our sample are modeled with additional restframe-UV
photometry, which constrains the $\beta$ measurement directly. For other
sources, their $\beta$ values are implied by the stellar population model
fitted at longer wavelength. We show the results of both fitting modes in
Figure 6, but with different marks. For reference, we also show the binned
$M_{UV}$–$\beta$ relation for high-z galaxies (at $z\sim 4$) compiled by
Bouwens et al. (2014). Their sample comprises UV-selected galaxies identified
via the Lyman-break (a.k.a. dropout) technique, drawn from the deepest rest-UV
imaging campaigns with HST (XDF, HUDF), and thus extends down to fainter UV
magnitudes. In comparison, our sample occupies the luminous side of the
parameter space, but of significantly steeper slopes, indicating negligible
reddening of the UV continuum.

We see no reason why the offset in UV slopes (particularly in this direction,
towards bluer colours) could be attributed to the modest ($\Delta z\approx
0.9$) offset in redshift between the two samples. If anything, one may expect
the typical galaxy at a given UV luminosity to have matured slightly, in terms
of its ISM composition, over the intervening half billion years. The latter
would constitute an offset towards redder UV slopes. Instead, our LAE selected
objects (which turn out to share rest-optical line characteristics in common
with EELGs) should be taken as representing the tail population of youngest
systems with no/little dust obscuration with respect to the underlying UV-
selected galaxy population. Indeed, similar differences between the LAE and
LBG populations have previously been reported by Stark et al. (2010).

Figure 6:  UV slope $\beta$ as a function of absolute UV magnitude ${M_{UV}}$.
With filled blue circles, we mark the sources in our sample whose SEDs are
fitted with extra restframe-UV bands (see §3.3), which means that their
$\beta$ values are empirically constrained. Sources without photometry
restriction in restframe-UV bands are marked with open circle. The red star
represents the average position of our whole sample, while its error bars show
the standard deviation in two dimensions. The binned $M_{UV}$–$\beta$ relation
of a sample of UV-selected dropout galaxies by Bouwens et al. (2014) is shown
for reference in green diamonds.

##  5 Discussion

From studies in the nearby Universe, and from galaxy formation simulations,
dwarf galaxies are known to experience bursty star formation histories (SFHs).
For this reason, the existence of a population of MS outliers should not
necessarily come as a surprise. While the various selection steps, from NB
selection to spectroscopic targeting, do not guarantee that we are complete,
even to a starbursting population defined by a fixed $\Delta{\rm MS}$
threshold, we can contrast the size of our selected LAE sample to the number
of MS outliers naively expected given a set of simplified conditions.
Specifically, for this back-of-the-envelope estimation, we assume that, at
$z=3.1$:
1) The galaxy stellar mass function established by Weaver et al. (2022) can be
extrapolated down to the low-mass ($10^{7}$–$10^{8.5}\,M_{\odot}$) regime of
consideration here.
2) The MS relation by S14 holds down to such low masses.
3) The distribution of SFR values around the MS is unimodal and has a constant
(i.e., mass-independent) Gaussian scatter of 0.3 dex.

Under these assumptions, and taking into account the exploited survey volume
($\sim 150\,{\rm arcmin}^{2}$ for the overlap between NB imaging and presently
released PRIMER coverage, and $z=3.05$–$3.16$ based on the NB selection), we
estimate there would be 19 galaxies with $\Delta{\rm MS}>0.7$ dex over the
$10^{7}$–$10^{8.5}\,M_{\odot}$ mass range (i.e., overlapping with the
parameter range of our sample). In other words, the 13 sources in our sample,
corresponding to a co-moving number density of $3.5\times
10^{-4}\,{\rm{Mpc}^{-3}}$, could be accommodated under the above conditions.
Not all galaxies feature significant amounts of escaping Ly$\alpha$ photons
though. Sarkar & Samui (2019) compare the UV luminosity function of Lyman-
break galaxies (LBGs) by Reddy et al. (2008) to the UV luminosity function of
LAEs by Ouchi et al. (2008), and estimate a Ly$\alpha$ fraction of $\sim 10\%$
at $z=3.1$, with relatively little dependence on UV luminosity across the
dynamic range probed. If we assume that the same Ly$\alpha$ fraction applies
down to our mass regime and uniformly across all $\Delta{\rm MS}$ (both
potentially questionable assumptions), one would require an enhanced MS
scatter, of $\gtrsim 0.5\,$dex, to account for the 13 observed LAEs (and more
so if other high-$\Delta{\rm MS}$ outliers exist but were missed by the NB
selection or from spectroscopic targeting).

The above numbers were obtained adopting the extrapolated MS from S14. Were we
to adopt extrapolations of the MS calibration by S17 or M23 instead, which has
SFR values dropping more steeply with decreasing mass, the requirement on an
increased gaussian scatter of the MS at the low-mass end (or equivalently, a
super-gaussian tail towards high $\Delta{\rm MS}$) would become
correspondingly more pressing.

We conclude that circumstancial arguments can be made to hint at an enhanced
MS scatter in the dwarf galaxy regime, but increased number statistics, a
well-defined selection function and improved insight in the validity of the
assumed steps in our reasoning are needed to make a firmer case for a more
bursty nature of low-mass galaxies, relative to their more massive
counterparts at the same epoch.

##  6 Summary

In this paper, we present our first results on a sample of spectroscopically
confirmed LAEs at $z\approx 3.1$, observed in the rest-optical to NIR
wavelengths by JWST/NIRCam. With released data from the PRIMER program, we
zoom in on 10 ‘LAE positions’ observed in 8 NIR bands, through which we study
their morphology and stellar properties. Overall, our sample is composed of
galaxies with very similar properties in every aspect, including a small size
(median $R_{e}=0.36\,$kpc), very blue UV continuum (median $\beta=-2.48$),
extreme optical line emission (median ${\rm EW_{rest}}$([O
iii]+H$\beta$)$=1700$Å), low mass ($\log\,(M_{*}/M_{\odot})=7.1$–$8.4$), and
high specific SFR ($0.3$–$1.4\times 10^{-7}\,{\rm yr}^{-1}$).

Among the 10 positions, three are resolved into pair-like compositions with
separations $<0.9^{\prime\prime}$. We deem that the sources in pairs are
plausibly related to each other because they all have the same feature in
their SEDs, namely a F200W excess contributed by extremely strong [O
iii]+H$\beta$ lines redshifted into this filter, as do other sources in our
sample. However, neither the narrowband images nor the spectroscopy allow
determining with certainty whether the Ly$\alpha$ emission is from both
objects or only one of them. In this work, we treat them as individual LAEs.
Besides possible pairs, asymmetrical structures are also captured in three
other sources. Some hints of widening or double-peaked features can be seen in
the Ly$\alpha$ spectra of these asymmetrical and pair-like sources.

Using effective radii measured on the F200W images, stellar masses derived by
SED fitting, and SFRs from $1500$–$2800$Å model fluxes, we compare the mass-
size relation of our sample to the extrapolated empirical one (Figure 5) and
their mass-SFR distribution to the extrapolated main sequence (Figure 4). In
both diagrams, our sample shows large offsets from the extrapolated empirical
relations. Specifically, our selected LAEs are on average $\sim 0.7\,$dex
higher in SFR than the MS, and $\sim 0.35\,$dex smaller in size than the ridge
of the mass-size relation. Also in terms of their inferred UV slope $\beta$,
the LAEs stand out with respect to the underlying population of UV-selected
(dropout) galaxies by their bluer colours.

Considering their numbers, we speculate that this starbursting dwarf galaxy
population hints at an increased MS scatter or more pronounced tail of above-
MS outliers at the low-mass end, although increased number statistics from
ongoing and upcoming JWST programmes are needed to place such constraints more
firmly.

This work is sponsored by the National Key R& D Program of China for grant No.
2022YFA1605300, the National Nature Science Foundation of China (NSFC) grants
No. 12273051 and 11933003. Support for this work is also partly provided by
the CASSACA. The authors gratefully acknowledge support from the Royal Society
International Exchanges Scheme (IES\R1\211140) and the Chinese Academy of
Sciences President’s International Fellowship Initiative (grant no.
2022VMB0004). 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, which is
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 GO-1837. The authors acknowledge the PRIMER team for developing
their observing program with a zero-exclusive-access period.

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