11institutetext:  Department of Astronomy, University of Geneva, 51 Chemin
Pegasi, 1290 Versoix, Switzerland 22institutetext: CNRS, IRAP, 14 Avenue E.
Belin, 31400 Toulouse, France 33institutetext: INAF – OAS, Osservatorio di
Astrofisica e Scienza dello Spazio di Bologna, via Gobetti 93/3, I-40129
Bologna, Italy 44institutetext: Department of Astronomy, University of Texas
at Austin, 2515 Speedway, Austin, Texas 78712, USA 55institutetext: Department
of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
66institutetext: Centro de Astrobiología (CAB), CSIC-INTA, Ctra. de Ajalvir km
4, Torrejón de Ardoz, E-28850, Madrid, Spain

# Witnessing an extreme, highly efficient galaxy formation mode with resolved
Ly$\alpha$ and LyC emission

R. Marques-Chaves e-mail<EMAIL_ADDRESS>an
extreme, highly efficient galaxy formation mode with resolved Ly$\alpha$ and
LyC emissionWitnessing an extreme, highly efficient galaxy formation mode with
resolved Ly$\alpha$ and LyC emission D. Schaerer Witnessing an extreme, highly
efficient galaxy formation mode with resolved Ly$\alpha$ and LyC
emissionWitnessing an extreme, highly efficient galaxy formation mode with
resolved Ly$\alpha$ and LyC emissionWitnessing an extreme, highly efficient
galaxy formation mode with resolved Ly$\alpha$ and LyC emissionWitnessing an
extreme, highly efficient galaxy formation mode with resolved Ly$\alpha$ and
LyC emission E. Vanzella Witnessing an extreme, highly efficient galaxy
formation mode with resolved Ly$\alpha$ and LyC emissionWitnessing an extreme,
highly efficient galaxy formation mode with resolved Ly$\alpha$ and LyC
emission A. Verhamme Witnessing an extreme, highly efficient galaxy formation
mode with resolved Ly$\alpha$ and LyC emissionWitnessing an extreme, highly
efficient galaxy formation mode with resolved Ly$\alpha$ and LyC emission M.
Dessauges-Zavadsky Witnessing an extreme, highly efficient galaxy formation
mode with resolved Ly$\alpha$ and LyC emissionWitnessing an extreme, highly
efficient galaxy formation mode with resolved Ly$\alpha$ and LyC emission J.
Chisholm Witnessing an extreme, highly efficient galaxy formation mode with
resolved Ly$\alpha$ and LyC emissionWitnessing an extreme, highly efficient
galaxy formation mode with resolved Ly$\alpha$ and LyC emission F. Leclercq
Witnessing an extreme, highly efficient galaxy formation mode with resolved
Ly$\alpha$ and LyC emissionWitnessing an extreme, highly efficient galaxy
formation mode with resolved Ly$\alpha$ and LyC emission A. Upadhyaya
Witnessing an extreme, highly efficient galaxy formation mode with resolved
Ly$\alpha$ and LyC emissionWitnessing an extreme, highly efficient galaxy
formation mode with resolved Ly$\alpha$ and LyC emission J. Alvarez-Marquez
Witnessing an extreme, highly efficient galaxy formation mode with resolved
Ly$\alpha$ and LyC emissionWitnessing an extreme, highly efficient galaxy
formation mode with resolved Ly$\alpha$ and LyC emission L. Colina Witnessing
an extreme, highly efficient galaxy formation mode with resolved Ly$\alpha$
and LyC emissionWitnessing an extreme, highly efficient galaxy formation mode
with resolved Ly$\alpha$ and LyC emission T. Garel Witnessing an extreme,
highly efficient galaxy formation mode with resolved Ly$\alpha$ and LyC
emissionWitnessing an extreme, highly efficient galaxy formation mode with
resolved Ly$\alpha$ and LyC emission M. Messa Witnessing an extreme, highly
efficient galaxy formation mode with resolved Ly$\alpha$ and LyC
emissionWitnessing an extreme, highly efficient galaxy formation mode with
resolved Ly$\alpha$ and LyC emission

(Received –; accepted –)

J1316+2614 at $z$=3.613 is the UV-brightest ($M_{\rm UV}=-24.7$) and strongest
Lyman continuum (LyC, $f_{\rm esc}^{\rm LyC}\approx$90%) emitting star-forming
galaxy known, showing also signatures of inflowing gas from its blue-dominated
Ly$\alpha$ profile. Here, we present high-resolution imaging with the Hubble
Space Telescope (HST) and the Very Large Telescope (VLT) of the LyC,
Ly$\alpha$, rest-UV, and optical emission of J1316+2614. Detailed analysis of
the LyC and UV light distributions reveals compact yet resolved profiles, with
LyC and UV morphologies showing identical half-light radii of $r_{\rm
eff}\simeq 220$ pc. The continuum-subtracted Ly$\alpha$ emission, obtained
with the HST ramp-filter FR551N, reveals an extended filamentary structure of
$\simeq 6.0$ kpc oriented south-north with only weak/residual flux within the
stellar core, suggesting a Ly$\alpha$ ”hole”. Our SED analysis shows that
J1316+2614 is characterized by a young (5.7$\pm$1.0 Myr), nearly un-obscured
stellar population with a high star formation rate ($\rm SFR=898\pm 181$
$M_{\odot}$ yr-1) and a stellar mass of $M_{\star}^{\rm young}=(4.8\pm
0.3)\times 10^{9}M_{\odot}$. Additionally, the SED analysis supports the
absence of an underlying old stellar population ($M_{\star}^{\rm old}\leq
2.8\times 10^{9}M_{\odot}$, 3$\sigma$). J1316+2614 presents remarkably high
SFR and stellar mass surface densities of log($\Sigma SFR[M_{\odot}\rm
yr^{-1}kpc^{-2}])=3.47\pm 0.11$ and log($\Sigma M_{\star}[M_{\odot}\rm
pc^{-2}])=4.20\pm 0.06$, respectively, which are among the highest observed in
star-forming galaxies and are more typically observed in local young massive
star clusters and Globular clusters. Our findings indicate that J1316+2614 is
a powerful, young, and compact starburst, leaking significant LyC photons due
to the lack of gas and dust within the starburst. We explore the conditions
for gas expulsion using a simple energetic balance and find that, given the
strong binding force in J1316+2614, a high star formation efficiency
($\epsilon_{\rm SF}\geq 0.7$) is necessary to remove the gas and explain its
exposed nature. Our results thus suggest a close link between high
$\epsilon_{\rm SF}$ and high $f_{\rm esc}^{\rm LyC}$. This high efficiency can
also naturally explain the remarkably high SFR, UV-luminosity, and efficient
mass growth of J1316+2614, where at least 62% of its mass formed in the last 6
Myr. J1316+2614 may exemplify an intense, feedback-free starburst with a high
$\epsilon_{\rm SF}$, similar to those proposed for UV-bright galaxies at high
redshifts.

###### Key Words.:

Galaxies: starburst – Galaxies: high-redshift – Cosmology: dark ages,
reionization, first stars

##  1 Introduction

UV-bright star-forming galaxies were once considered extremely rare at any
redshift, even at the Epoch of Reionization (EoR, at $6<z<16$). However,
recent James Webb Space Telescope (JWST) observations have dramatically
changed this picture by revealing a large number of UV-bright and sometimes
massive galaxies at $z\simeq 7-14$ (see e.g., Arrabal Haro et al., 2023;
Bunker et al., 2023; Carniani et al., 2024; Castellano et al., 2024, for some
spectroscopically confirmed sources). The derived volume densities of these
sources exceed predictions from galaxy formation models and pre-JWST
observations by an order of magnitude (e.g., Bouwens et al., 2021; Kannan et
al., 2023; Lovell et al., 2023). These results are enigmatic based on the
common wisdom of galaxy formation and evolution, challenging our understanding
of the nature of UV-bright galaxies and the potential role these sources play
in cosmic reionization.

Several scenarios have been proposed to explain this tension. One suggestion
is that the star formation efficiency ($\epsilon_{\rm SF}$), i.e., the
efficiency in converting gas into stars, is higher than assumed in current
models and measured locally (of a few percent, e.g., Megeath et al. 2016). In
this framework (Dekel et al., 2023; Li et al., 2023; Boylan-Kolchin, 2024),
high-density environments and low metallicities, properties expected at early
times, may favor the formation of so-called “feedback-free starbursts” (Dekel
et al., 2023) through the collapse of gas clouds within very short free-fall
times. This would increase the star formation efficiency since the cloud
collapse occurs before the onset of strong feedback, thus enhancing star-
formation rates (SFRs), UV luminosities, and stellar masses. Other works have
related the excess of UV-bright sources to variations of the initial mass
function (IMF) that allow the formation of more massive stars (e.g., Inayoshi
et al., 2022; Finkelstein et al., 2023; Trinca et al., 2024). This excess of
massive stars, also referred to as a “top-heavy” IMF, boosts the UV radiation
and the luminosity-to-mass ratio making these sources appear (UV) brighter at
fixed mass. On the other hand, Ferrara et al. (2023) (see also Ziparo et al.
2023) proposed that radiation-driven outflows originating from recent star
formation could temporarily remove dust as soon as it is produced. Dust
ejection by strong radiative feedback would decrease the dust optical depth,
making these galaxies appear brighter in the UV. Other frameworks invoke the
stochastic nature of star formation at high redshifts (e.g., Mason et al.,
2023; Shen et al., 2023), or even the contribution from active galactic nuclei
(Hegde et al., 2024; Maiolino et al., 2024).

In parallel, extremely UV-bright star-forming galaxies at $z\simeq 2-4$ have
been discovered in the wide Sloan Digital Sky Survey by Marques-Chaves et al.
(2020a, 2021, 2022). These galaxies present remarkably high UV absolute
magnitudes of $M_{\rm UV}\sim-24$ and are characterized by very young ($\leq
10$ Myr) stellar populations without signs of AGN activity by the detection of
photospheric absorption lines and wind line features and UV/optical BPTs. They
show star-formation rates up to $\rm SFR\simeq 1000$ $M_{\odot}$ yr-1, but
residual dust attenuation with UV continuum slopes as steep as $\beta_{\rm
UV}\simeq-2.6$ (e.g., Marques-Chaves et al., 2022). As such, these sources are
among the most vigorous and almost un-obscured star-forming galaxies known,
with specific star formation rates sSFR $>50-100$ Gyr-1. Furthermore, they
also show complex gas kinematics, including outflows (Álvarez-Márquez et al.,
2021; Marques-Chaves et al., 2021) and inflows (Marques-Chaves et al., 2022).
Recently, the analysis of the rest-UV spectra of these sources by Upadhyaya et
al. (2024) have revealed signatures of very massive stars (VMS, with initial
masses $>100M_{\odot}$) for most of them, suggesting that VMS might be common
in UV-bright galaxies. Last but not least, the few sources with Lyman
continuum (LyC) observations so far, J0121+0025 ($z=3.2$) and J1316+2614
($z=3.6$), showing copious LyC leakage, with absolute escape fractions up to
$f_{\rm esc}^{\rm LyC}\approx 90\%$ (Marques-Chaves et al., 2021, 2022). As
the UV-brightest star-forming galaxies known, they are ideal laboratories to
test the various scenarios proposed to explain the overabundance of UV-bright
EoR sources.

Here we present high spatial-resolution observations of J1316+2614 at $z=3.61$
(Marques-Chaves et al., 2022), the UV-brightest star-forming galaxy ($M_{\rm
UV}=-24.7$) and also the strongest LyC emitter known ($f_{\rm esc}^{\rm
LyC}\simeq 90\%$). J1316+2614 is a powerful starburst with negligible dust
attenuation given by its steep UV slope ($\beta_{\rm UV}=-2.59\pm 0.05$). It
shows relatively weak nebular emission (e.g., $EW_{0}(\rm H\beta)=34.7\pm 6.8$
Å) due to the high fraction of ionizing photons escaping its interstellar
medium ($f_{\rm esc}^{\rm LyC}\approx 90\%$ and log($Q_{\rm H}^{\rm
esc}/s^{-1})=55.86\pm 0.11$, Marques-Chaves et al. 2022). Finally, J1316+2614
also shows a peculiar Ly$\alpha$ spectral profile with a blue-to-red peak line
ratio $I_{\rm blue}/I_{\rm red}\simeq 3.7$, suggesting inflows.

This work is organized as follows. In Section 2 we described high-resolution
observations taken with the Hubble Space Telescope (HST) and the Very Large
Telescope (VLT) probing the LyC, Ly$\alpha$, and the rest-UV and optical
emission of J1316+2614. In Section 3 we describe the methodology and present
the main results, including the morphology, photometry, and the spectral
energy distribution (SED) of J1316+2614. The discussion of the results is
presented in Section 4, and, finally, we present the summary of our main
findings in Section 5. Throughout this work, we use a concordance cosmology
with $\Omega_{\rm m}=0.274$, $\Omega_{\Lambda}=0.726$, and $H_{0}=70$ km s-1
Mpc-1. Magnitudes are given in the AB system.

##  2 Observations

###  2.1 HST imaging

High-resolution imaging of J1316+2614 was obtained with the UVIS/IR imager
Wide Field Camera 3 (WFC3) and the Advanced Camera for Surveys (ACS) of Wide
Field Channel (WFC) aboard the HST. These observations were carried out
between June 26 and July 3 2023 under the Cycle 30 program ID 17286 (PI: R.
Marques-Chaves). J1316+2614 was observed with the WFC3 in the medium-band
F410M and broad-band filters F775W and F160W, with total exposure times of
5004 s, 2372 s, and 2412 s, respectively. These filters probe the rest-frame
LyC ($\simeq$871-914 Å), UV ($\simeq$1650 Å), and optical ($\simeq$3310
Å)111The F410M filter response at $\lambda_{0}>912$ Å is less than $\sim
0.08$, and therefore, the contamination of non-LyC emission in F410M is
negligible. emission of J1316+2614. Additional ACS/WFC observations were
obtained with the narrow-band ramp filter FR551N (transmission width of
$\simeq 97$ Å) centered at $\lambda_{\rm obs}=5604$ Å to cover the Ly$\alpha$
emission of J1316+2614 at $z=3.612$. The ACS total exposure time was 2008 s.
Table 1 summarizes the HST observations.

Data were reduced using AstroDrizzle version 3.6.2 from the DrizzlePac package
(Fruchter & Hook, 2002) and retrieved from MAST. The final images have pixel
scales of $0.04^{\prime\prime}$ pix-1 (F410M and F775W), $0.05^{\prime\prime}$
pix-1 (FR551N), and $0.12^{\prime\prime}$ pix-1 (F160W). The astrometry was
corrected and aligned to the GAIA DR3 (Gaia Collaboration et al., 2023). The
astrometry r.m.s precision is $\simeq
0.09^{\prime\prime}-0.12^{\prime\prime}$. The instrumental point-spread
function (PSF) in each image was modeled using the Point Spread Function
reconstruction (PSFr, Birrer et al. 2021, 2022) code by stacking several (3-5)
isolated bright stars within the field of view (FoV) of the observations. We
measured PSF FWHM of 0.075′′, 0.109′′, 0.080′′, 0.197′′ for F410M, FR551N,
F775W, and F160W, respectively. Figure 1 shows the F775W image of J1316+2614
and the contours from F410M.

Figure 1: Cutout image of J1316+2614 showing the HST F775W (background image)
and F410M (orange contours, 5$\sigma$, 10$\sigma$, and 50$\sigma$) which probe
the rest-UV and LyC emission of J1316+2614, respectively.  Table 1: Summary of
the HST and VLT imaging observations of J1316$+$2614\.

Filter |  $\lambda_{\rm rest}$ [Å] |  $t_{\rm exp}$ [s] | Scale [′′/pix] | PSFFWHM [′′] | Mag. [AB] | $n$ | $b/a$ |  $\theta$ [deg] |  $r_{\rm eff}$ [pc]
---|---|---|---|---|---|---|---|---|---
$\rm(1)$ | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
F410M | 871-914 | 5004 | 0.0394 | 0.0745 | $23.32\pm 0.06$ | $2.12\pm 0.91$ | $0.71\pm 0.19$ | $198\pm 36$ | $262\pm 64$
FR551N | 1204-1225 | 2008 | 0.0500 | 0.1085 | $20.81\pm 0.10$ | — | — | — | —
F775W | 1489-1859 | 2372 | 0.0396 | 0.0796 | $21.25\pm 0.04$ | $2.90\pm 0.42$ | $0.72\pm 0.05$ | $162\pm 5$ | $220\pm 12$
F160W | 3004-3686 | 2412 | 0.1272 | 0.1968 | $21.66\pm 0.05$ | — | — | — | $\leq 442$
$K_{\rm s}$ | 4301-5003 | 1350 | 0.1065 | 0.2960 | $21.73\pm 0.06$ | — | — | — | $\leq 550$

Notes. — (1) and (2) Filter and corresponding bandwidth in the rest-frame; (3)
exposure time; (4) pixel scale; (5) PSF FWHM obtained from stars in the field-
of-view; (6) aperture photometry of J1316+2614; (7) Sersic index; (8) minor-
to-major axis; (9); orientation (north=0, east=90); and (10) half-light
effective radius.

###  2.2 VLT/HAWK-I imaging

Additional near-IR imaging of J1316+2614 was obtained in the $K_{\rm s}$-band
with the HAWK-I on the VLT UT4. These observations were conducted on May 31
2023 as part of the program ID 111.251K.001 (PI: R. Marques-Chaves). $K_{\rm
s}$-band observations were obtained with the GRound layer Adaptive optics
system Assisted by Lasers (GRAAL), enhancing the final image quality down
$\simeq 0.296^{\prime\prime}$, as measured from the light profiles of several
stars in the HAWK-I FoV. The on-source exposure time was 1350 s. Data were
reduced using the standard ESO pipeline version 2.4.12
222https://www.eso.org/sci/software/pipelines/hawki/hawki-pipe-recipes.html.
and were flux calibrated against 2MASS stars in the field. The astrometry was
calibrated using the GAIA DR3 catalog (Gaia Collaboration et al., 2023)
yielding an r.m.s precision of $\simeq 0.10^{\prime\prime}$, similar to the
native pixel-scale (0.107′′).

##  3 Methodology and Results

Figure 2: HST and VLT images of J1316+2614. From left to right, we show the
HST F410M (LyC), FR551N (Ly$\alpha$), F775W (rest-UV), F160W (rest-optical),
and VLT HAWK-I $K_{\rm s}$ (rest-optical) images. The FWHM PSF of image is
represented with a red circle. Each stamp has a size of
$3.2^{\prime\prime}\times 3.2^{\prime\prime}$. North is up and East is to the
left. The bottom panels show the normalized radial profiles (to their maxima)
of J1316+2614 in each band (solid blue with uncertainties in shadow), the
best-fit Sersic model (dashed green), and the PSF used in the fit (red dotted
dashed). J1316+2614 shows a compact stellar morphology, only resolved in F410M
and F775W ($r_{\rm eff}\simeq 220$ pc). The FR551N, which probes the
Ly$\alpha$ emission (and stellar continuum), shows a more extended morphology.

###  3.1 Size measurements

As shown in Figure 2, the HST and VLT images reveal a compact morphology in
the bands probing the stellar continuum of J1316+2614 (F410M, F775W, F160W,
and $K_{\rm s}$). In contrast, the ACS/FR551N image, which predominantly
traces the Ly$\alpha$ emission, shows a well-resolved and extended profile.

####  3.1.1 Stellar morphology

The light distribution of J1316+2614 is investigated using the PySersic code
(Pasha & Miller, 2023), which uses a Bayesian framework to understand the
degeneracies between different parameters. PySersic fits the light
distribution of a source using morphological models convolved with a given
PSF. As described in Section 2, the PSF of each image/band is obtained by
stacking several bright stars within the FoV using the PSFr code (Birrer et
al., 2021, 2022). We fit the morphology of J1316+2614 using both 2D Sersic
(with a Sersic index varying from 0.5 to 6.0) and point-like profiles to
investigate whether the light distribution of J1316+2614 is resolved in each
band.

We start fitting the light profile of J1316+2614 using the HST F775W (rest-
UV). Assuming a Sersic profile, PySersic finds an effective radius $r_{\rm
eff}=0.76\pm 0.04$ pix (or $r_{\rm eff}=220\pm 12$ pc with our adopted
cosmology) and a Sersic index $n=2.90\pm 0.42$. The normalized residuals (NR),
measured within a circular aperture of 0.6′′ around J1316+2614, are $\rm
NR\simeq 8\%$ (Fig. 3). While a Sersic profile recovers most ($\gtrsim 90\%$)
of the light emission in F775W, the model-subtracted image shows some
residuals that are not perfectly accounted for and may suggest additional
underlying structures. If instead a point-like profile is used in the fit,
PySersic cannot recover well the light profile of J1316+2614 yielding
substantial residuals in the model-subtracted image ($\rm NR\simeq 22\%$,
right middle panel of Figure 3). Our results thus indicate that J1316+2614 has
a resolved morphology in the rest-UV continuum ($r_{\rm eff}=220\pm 12$ pc),
as also indicated through its radial profile (bottom panel of Fig. 2).

Similar to F775W, the profile of J1316+2614 in the HST F410M (LyC) appears
resolved. Assuming a Sersic profile, the PySersic best-fit predicts an
effective radius $r_{\rm eff}=0.79\pm 0.21$ pix or $r_{\rm eff}=262\pm 64$ pc
and a Sersic index $n=2.12\pm 0.91$. The normalized residuals from this fit,
measured within $r\leq 0.6^{\prime\prime}$), are significantly better ($\simeq
7\%$) than those obtained assuming a point-like source ($\simeq 28\%$, Fig.
3). This suggests that the LyC emission seen in F410M is resolved and has a
similar morphology to the rest-UV emission. To investigate this, we inspect
the residuals obtained from the PSF-subtracted images. As shown in Figure 3,
the PSF-subtracted images in F410M and F775W show almost identical residuals
(highlighted with blue arrows), indicating that the even faintest resolved
emission in F775W is present in F410M. In addition, we inspect the F410M and
F775W normalized radial profiles of J1316+2614 and find that they are
indistinguishable within the uncertainties (Figure 2). Finally, we model the
F410M emission using the F775W image of J1316+2614 as a PSF and assuming a
point-like source. The normalized residuals are slightly better than the ones
obtained assuming a Sersic model. Altogether, our results indicate that the
LyC (F410M) and rest-UV (F775W) light profiles of J1316+2614 are essentially
the same, and consistent with $r_{\rm eff}=220$ pc. This strongly supports
that the LyC and UV emissions have similar origins.

Figure 3: HST F410M (LyC, left) and F775W (UV, right) images of J1316+2614
(top) and the residuals obtained after subtracting the PSF and Sersic best-fit
models (middle and bottom, respectively). The normalized residuals (NR),
measured around a circular aperture of 0.6′′ around J1316+2614, are also
indicated. Each stamp has a size of $1.0^{\prime\prime}\times
1.0^{\prime\prime}$. North is up and East is to the left. The PSF-subtracted
residuals are identical in F410M and F775W, indicating similar LyC and rest-UV
morphologies.

Turning to longer wavelengths, the light distribution of J1316+2614 in the HST
F160W and VLT $K_{\rm s}$ bands appears unresolved. This is expected given the
slightly poorer spatial resolution in these bands and the fact that they still
probe the young stellar population of J1316+2614 ($r_{\rm eff}\simeq 220$ pc).
Our best-fit models assuming Sersic or point-like profiles yield essentially
similar residual images. Given the oversampling of the HST/F160W PSF ($\rm
FWHM\simeq 1.6$ pix) we use the minimum resolvable size of $r_{\rm eff}\leq
0.47$ pix estimated in Messa et al. (2022) for the same instrument and filter
considered here to infer the upper limit $r_{\rm eff}\leq 442$ pc in the
HST/F160W. Since the HAWK-I PSF is well sampled ($\rm FWHM\simeq 2.8$ pix), we
derive the upper limit in the $K_{\rm s}$-band of $r_{\rm eff}\leq 550$ pc
assuming $\rm FWHM_{\rm min}\leq\rm FWHM(PSF)/2$.

####  3.1.2 Ly$\alpha$ morphology

Finally, we analyze the HST ACS/FR551N image of J1316+2614 which includes the
Ly$\alpha$ emission ($EW_{0}=20.5\pm 1.9$ Å, Marques-Chaves et al. 2022). As
shown in the top left panel of Figure 4, the ACS/FR551N image reveals a
complex morphology consisting of a bright central clump co-spatial with the
compact stellar emission (e.g., as seen in F410M or F775W) and a more diffuse,
filamentary-like emission oriented south-north with a $3\sigma$ scale length
of $\simeq 0.8^{\prime\prime}$ or $\simeq 6.0$ kpc.

Figure 4: Ly$\alpha$ spatial distribution of J1316+2614. The top left panel
shows the cutout images of J1316+2614 in the ACS/HST ramp-filter FR551N (with
a total size of $1.2^{\prime\prime}\times 1.2^{\prime\prime}$, North is up and
East to the left), which includes the Ly$\alpha$ emission and the underlying
stellar continuum (blue contours mark the 3$\sigma$, 15$\sigma$, and
50$\sigma$ emission). The orange dashed circle represents the position and
total size of the stellar continuum as measured in the F775W after deconvolved
with the PSF (i.e., radius of $2\times r_{\rm eff}\simeq
0.06^{\prime\prime}$). The top right panel shows the GTC spectrum of
J1316+2614 (black, Marques-Chaves et al., 2022) and the FR551N transmission
curve (dashed green). The orange dashed-dotted line represents our best fit of
the stellar continuum around the Ly$\alpha$ emission (blue). The bottom panels
show the continuum-subtracted FR551N images using two different methods (see
text). Ly$\alpha$ appears weak/residual within the UV-bright stellar clump
(orange) and is predominantly emitted in the outskirts. The blue contours mark
the 2.5$\sigma$ level.

We employ two different methodologies to subtract the underlying stellar
emission in the FR551N band. For the first one (method 1 in Figure 4), we use
the WFC3/F775W as the reference image of the stellar emission of J1316+2614,
which is first resampled to the FR551N native pixel size (0.05′′ pix-1) using
the MAGNIFY task from Iraf. We repeat this step in an individual star and find
no significant differences between the PSF FWHM measured in FR551N and the
resampled F775W images. Since the astrometry uncertainties in both filters
($\simeq 0.10^{\prime\prime}$) are larger than the pixel size, we choose to
spatially match both images of J1316+2614 using their centroid emission and
the corresponding shifts in pixels using the Iraf task imshift. This step
assumes that the centroid emission in FR551N is dominated by the stellar
continuum, which is a fair assumption since the continuum emission represents
$\simeq 50\%$ of the total flux in FR551N (see next) and is way more compact
than the extended Ly$\alpha$ emission. We infer the contribution of the
stellar continuum in the FR551N passband using the low-resolution optical
spectrum of J1316+2614 obtained with GTC/OSIRIS, which was previously rescaled
to the $R$-band photometry to account for slit losses (see Marques-Chaves et
al., 2022). As highlighted in the top right panel of Figure 4, the
contribution of the stellar emission is obtained by fitting a linear
polynomial function using two spectral windows on each side of Ly$\alpha$
(5480-5527 Å and 5757-5841 Å). Using
PyPhot333https://github.com/mfouesneau/pyphot and the FR551N transmission
profile centered at $\lambda=5604$ Å, we measure the synthetic photometry of
the polynomial function, which probes only the stellar continuum. We find
$f_{\nu}^{\rm cont}\simeq 9.62\times 10^{-29}$ erg s-1 cm-2 Hz-1 which
represents roughly $\simeq 50\%$ of the total emission in FR551N. Finally, we
rescale the flux of the resampled F775W image to that obtained from the
synthetic photometry and subtract it from the FR551N image.

The bottom left panel of Figure 4 shows the continuum-subtracted FR551N image
(method 1), i.e., the Ly$\alpha$ emission of J1316+2614. As seen in this
figure, Ly$\alpha$ is predominantly emitted in the outskirts of the UV-bright
stellar core, whose total size is represented by an orange circle with a
radius of $2\times r_{\rm eff}$ ($\simeq 0.06^{\prime\prime}$). This bright UV
continuum in the center of the galaxy leads to a Ly$\alpha$ hole with
weak/residual Ly$\alpha$ emission being emitted at the position of the stellar
core. It is important to note that the continuum-subtracted Ly$\alpha$ image,
especially its faint and diffuse emission, is affected by additional noise due
to the subtraction process of the F775W image from the FR551N image.

For consistency, we explore an alternative method for subtracting the stellar
contribution in FR551N (method 2 in Figure 4). Using PySersic, we model a
Sersic profile with the best-fit parameters obtained for the stellar continuum
in F775W (i.e., $r_{\rm eff}=220$ pc, $n=2.90$, Table 1) and convolved it with
the PSF of FR551N obtained from stars in the field-of-view. After rescaling
the flux, we subtract this model from the FR551N image. Consistent with our
previous method, we recover the weak/residual Ly$\alpha$ emission within the
stellar core. However, we note that the spatial distribution of the bright
Ly$\alpha$ emission around the stellar component differs slightly from the
previous method, as seen in the bottom panels of Figure 4. Lastly, we
investigate the uncertainties on the assumed flux and contribution of the
stellar continuum in FR551N. We repeat our analysis, conservatively assuming a
stellar contribution in FR551N of $\simeq 40\%$. Under this assumption, the
Ly$\alpha$ ”hole” appears less prominent but is still present, with the bulk
of Ly$\alpha$ photons emitted around (and far away) from the stellar core.

While the detailed characterization of this hole (e.g., its size) is difficult
and requires deeper data, given the low significance of the Ly$\alpha$
emission and other uncertainties in our methodology, our results strongly
support a deficit of Ly$\alpha$ co-spatial with the stellar continuum. Such a
configuration was discussed and predicted in Marques-Chaves et al. (2022) in
order to reconcile the high $f_{\rm esc}^{\rm LyC}\simeq 90\%$, requiring a
gas column density $N_{\rm HI}\lesssim 10^{17}$ cm-2, and the large Ly$\alpha$
velocity peak separation observed in J1316+2614 ($\Delta v=680\pm 70$ km s-1),
which suggests $N_{\rm HI}\sim 10^{21}$ cm-2 according to the radiative models
of Verhamme et al. (2015) under standard conditions. We further discuss the
connection between the Ly$\alpha$ and LyC-UV spatial distributions in Section
4.2.

###  3.2 Photometry

Using Sextractor (Bertin, 2006) we perform aperture photometry on J1316+2614
assuming an aperture of $0.8^{\prime\prime}$ diameter. For F410M, we measure
$\rm F410M=23.32\pm 0.06$, which is in excellent agreement with that inferred
from the optical GTC/OSIRIS spectrum presented in Marques-Chaves et al. (2022)
($23.33\pm 0.06$). Similarly, we obtain $\rm F775W=21.25\pm 0.04$ and $\rm
F160W=21.66\pm 0.05$ which is consistent with previous ground-based photometry
probing similar spectral ranges ($I=21.24\pm 0.08$ and $H=21.70\pm 0.14$,
Marques-Chaves et al. 2022). For the HAWK-I $K_{\rm s}$-band, we measure
$K_{\rm s}=21.73\pm 0.06$ which is substantially different than that obtained
with GTC/EMIR ($K_{\rm s}=21.31\pm 0.07$). These differences are likely due to
the shorter spectral coverage of the HAWK-I $K_{\rm s}$-band
($\lambda=1.984-2.308\mu$m) compared to the GTC/EMIR one
($\lambda=2.080-2.388\mu$m), therefore, not including the contribution of the
redshifted [O iii] $\lambda 5008$ emission ($\lambda\simeq 2.310\mu$m) in the
former. The ACS/FR551N image of J1316+2614 shows a more extended profile due
to the Ly$\alpha$ emission, as shown in Figure 2. Given its extended emission,
we use a large aperture of $1.2^{\prime\prime}$ diameter, obtaining $\rm
FR551N=20.81\pm 0.10$. Table 1 summarizes the photometry of J1316+2614.

In addition to the photometry of the UV-bright and compact starburst, we
constrain the flux densities of an underlying stellar population in
J1316+2614. So far, the SED analysis by Marques-Chaves et al. (2022) using
unresolved photometry supports the absence of a significant old stellar
population. We assume that the underlying old stellar population has a
Gaussian profile with an effective radius of 1.5 kpc centered at the position
of the UV-bright emission. Its size is motivated by the characteristic
effective radius of LBGs at similar redshifts ($r_{\rm eff}^{\rm LBGs}\simeq
1.3$ kpc; e.g., Ribeiro et al., 2016) and the size of the dust emission of
J1316+2614 detected by ALMA ($r_{\rm eff}^{\rm dust}\simeq 1.7$ kpc), which
could already be produced before the UV-bright starburst in J1316+2614 (as
discussed in Dessauges-Zavadsky et al. in prep.). Given the fact that
J1316+2614 is unresolved in the HST/F160W and VLT/$K_{\rm s}$ images (section
3.1), we thus simulate the maximum flux of the underlying stellar population
needed to resolve the total emission in these bands. If more extended than the
UV-bright component, we find that the underlying old population should be
fainter than $\rm F160W>24.95$ and $K_{\rm s}>23.98$ to keep the total
emission unresolved in F160W and $K_{\rm s}$, respectively.

###  3.3 Spectral Energy Distribution

Using the photometry from the new images along with the previous ones obtained
and discussed in Marques-Chaves et al. (2022), we re-analyze the spectral
energy distribution (SED) of J1316+2614. Following Marques-Chaves et al.
(2022), we perform SED-fitting with CIGALE version 2022.1 (Burgarella et al.,
2005; Boquien et al., 2019) using the available photometry and flux
measurements of the H$\beta$ and [O iii] $\lambda\lambda$4960,5008. Two
stellar components are considered to probe the young UV-bright starburst
(assuming a constant star-formation history) and a burst model with an age of
1.4 Gyr to probe the maximum light and mass of an underlying, old stellar
population, which corresponds to a formation redshift of $\simeq 12.5$. We
assume the Calzetti et al. (2000) dust attenuation law and the Chabrier (2003)
initial mass function. Stellar population models from Bruzual & Charlot (2003)
with the metallicity of $Z=0.008$ are considered (Marques-Chaves et al.,
2022). We also let $f_{\rm esc}^{\rm LyC}$ as a free parameter.

Overall, the properties of the UV-bright starburst obtained from CIGALE agree
with those previously derived in Marques-Chaves et al. (2022). Figure 5 shows
the best-fit SED of J1316+2614. The UV-bright starburst is characterized by a
young stellar population with an age of $5.7\pm 1.0$ Myr and a continuous $\rm
SFR=898\pm 181M_{\odot}$ yr-1 with residual dust attenuation ($E(B-V)=0.03\pm
0.01$). The SFR derived here reflects the total SFR within 5.7 Myr, i.e., the
age of the young stellar population. If instead we use the 10 Myr-weighted SFR
indicator, we obtain $\rm SFR=492\pm 35\,M_{\odot}$ yr-1 that is consistent
with the value reported in Marques-Chaves et al. (2022), $\rm SFR=496\pm
92\,M_{\odot}$ yr-1. The mass formed in this young starburst is
log($M_{\star}^{\rm young}/M_{\odot})=9.68\pm 0.03$, in excellent agreement
with previous measurements (log($M_{\star}^{\rm young}/M_{\odot})=9.67\pm
0.07$, Marques-Chaves et al. 2022). Our best-fit model also predicts $f_{\rm
esc}^{\rm LyC}=0.75\pm 0.16$.

Figure 5: Best-fit SED model (blue) of J1316+2614. The fit uses the new
photometry obtained with HST and VLT (black circles) and the one presented in
Marques-Chaves et al. (2022) (grey squares). The SED of J1316+2614 is
dominated by a young stellar population with an age of $5.7\pm 1.0$ Myr and a
continuous star formation rate $\rm SFR=898\pm 181M_{\odot}$ yr-1. The mass
formed in this starburst is log($M_{\star}^{\rm young}/M_{\odot})=9.68\pm
0.03$ with a residual dust attenuation ($E(B-V)=0.03\pm 0.01$). The red upper
limits represent the maximum flux of the underlying stellar population needed
to resolve the emission in the F160W and $K_{\rm s}$ bands (see Section 3.2).

On the other hand, the new and deeper photometry in HST/F160W and VLT/$K_{\rm
s}$ presented in this work, which probes the rest-optical stellar continuum,
provides significantly improved constraints on the properties of the old
stellar population. Our best-fit model predicts an old stellar component,
assumed here as a 1.4 Gyr old burst model, with a stellar mass of
log($M_{\star}^{\rm old}/M_{\odot})=9.00^{+0.29}_{-1.36}$ or
log($M_{\star}^{\rm old}/M_{\odot})\leq 9.46$ (3$\sigma$). The strong
constraints on the mass of the old stellar component are due to the fact that
the HST/F160W and VLT/$K_{\rm s}$ photometry is fully dominated by the
starlight from the young starburst, leaving minimal room for an additional,
older stellar component.

In short, our results strongly support that the extremely UV-bright starburst
not only dominates the rest-UV and optical light emission of J1316+2614
($\simeq 100\%$) but also its stellar mass, with a mass fraction of the galaxy
formed in the last $\simeq 6$ Myr of $f_{\rm burst}=M_{\star}^{\rm
young}/(M_{\star}^{\rm young}+M_{\star}^{\rm old})\geq 62\%$ (3$\sigma$). We
further discuss the implications of these findings in Section 4.5.

##  4 Discussion

###  4.1 J1316+2614 with cluster-like surface densities

J1316+2614 is the UV-brightest star-forming galaxy known ($M_{\rm UV}=-24.7$)
and one of the most compact. Using the derived mass and SFR from Section 3.3,
along with its size ($r_{\rm eff}=220\pm 12$ pc), we measure the stellar mass
and SFR surface densities, defined as $\Sigma M_{\star}=M_{\star}/(2\pi r_{\rm
eff}^{2})$ and $\Sigma SFR=SFR/(2\pi r_{\rm eff}^{2})$. J1316+2614 shows
remarkably high mass and SFR surface densities of log($\Sigma
M_{\star}[M_{\odot}\rm pc^{-2}])=4.20\pm 0.06$ and log($\Sigma
SFR[M_{\odot}\rm yr^{-1}kpc^{-2}])=3.47\pm 0.11$, respectively. Figure 6 shows
the position of J1316+2614 (blue star) in the mass (top) and SFR (middle)
versus $r_{\rm eff}$ diagrams. For comparison, similar measurements are
provided for various compilations of galaxies at $z\simeq 1-5$ (red: van der
Wel et al., 2012), star-forming clumps in lensed galaxies (green: Claeyssens
et al., 2023; Fujimoto et al., 2024; Messa et al., 2024), star-clusters and
young massive clusters (YMC) at different redshifts (yellow: Norris et al.,
2014; Vanzella et al., 2023; Adamo et al., 2024), and local globular clusters
(GCs), ultracompact dwarfs (UCDs) and compact elliptical galaxies (cEs) from
Norris et al. (2014) (orange).

Figure 6: Stellar mass (top) and star-formation rate (middle) as a function of
effective radius. J1316+2614 is represented with a blue star. Measurements of
other compilations of galaxies at $z=1-5$ (red circles: van der Wel et al.,
2012), star-forming clumps in lensed galaxies (green squares: Claeyssens et
al., 2023; Fujimoto et al., 2024; Messa et al., 2024), and star-clusters and
young massive clusters at different redshifts (yellow diamonds: Norris et al.,
2014; Vanzella et al., 2023; Adamo et al., 2024) are also shown. For star-
clusters and star-forming clumps without SFR measurements, we assume star-
formation ages of 1 Myr and 10 Myr, respectively, and $\rm SFR=M_{\star}/age$.
The bottom panel shows the $\Sigma M_{\odot}$ vs. $\Sigma SFR$ of J1316+2614
along with other galaxies at higher redshift (black), including very compact
sources with strong nitrogen emission (violet) which exhibit abundance
patterns resembling those seen in globular clusters.

As shown in Figure 6, the $\Sigma M_{\star}$ and $\Sigma SFR$ of J1316+2614
deviate considerably from those of $z\simeq 1-5$ galaxies, by approximately
$1-4$ dex on average. At these redshifts, star-forming galaxies with high
$\Sigma SFR$ are indeed extremely rare, with only very few dusty sub-mm
selected galaxies presenting $\Sigma SFR$ values approaching those of
J1316+2614 (Oteo et al., 2017). In addition, very few galaxies exhibit similar
$\Sigma M_{\star}$, such as UCDs (e.g., M32) and cEs in the local Universe
(Norris et al., 2014), or extremely massive and compact quiescent galaxies at
$z\sim 2-5$ (e.g., van Dokkum et al., 2008; Barro et al., 2017; de Graaff et
al., 2024; Glazebrook et al., 2024). However, these evolved galaxies have
residual star formation. At higher redshifts ($z>5$), star-forming galaxies
tend to show higher $\Sigma M_{\star}$ and $\Sigma SFR$ than their lower-$z$
counterparts, as recently shown by Langeroodi & Hjorth (2023) and Morishita et
al. (2024). Still, even the densest sources at $z>5$ struggle to reach the
densities observed in J1316+2614 (bottom panel in Figure 6). To our knowledge,
only a few star-forming galaxies at $z>6$ show comparable densities to
J1316+2614 (Bunker et al., 2023; Williams et al., 2023; Castellano et al.,
2024; Schaerer et al., 2024b; Topping et al., 2024, Alvarez-Marquez et al. in
prep.), several of them are UV-bright and exhibiting peculiar abundance
patterns resembling those seen in globular clusters (Charbonnel et al., 2023;
Marques-Chaves et al., 2024; Schaerer et al., 2024b; Senchyna et al., 2024).

The densities derived for J1316+2614 are indeed extreme in star-forming
galaxies, and more closely resemble those observed in young massive stellar
clusters, which are among the densest systems known (Figure 6). Following
Kruijssen (2012), J1316+2614 would have a very high cluster formation
efficiency, $\Gamma\simeq 85\%$, given its high $\Sigma SFR$. However, while
the surface densities of J1316+2614 are similar to those of massive star
clusters, its starburst mass and UV-luminosity differ significantly ($\gtrsim
3-5$ dex). It remains unclear whether J1316+2614 consists of a large number of
normal star clusters ($N\sim 5\times 10^{4}$ clusters with $10^{5}M_{\odot}$
each) compacted in a $\sim 220$ pc radius, or if its luminosity and mass
originate from a single, supermassive star cluster with a total mass
$M_{\star}\sim 5\times 10^{9}M_{\odot}$.

###  4.2 Spatially resolved LyC and gas distribution

J1316+2614 represents the first example of resolved LyC in a strong LyC
emitter star-forming galaxy (see also Meštrić et al. 2023 for resolved LyC in
a star cluster). As shown in Section 3.1.1 and highlighted in Figure 7, the
LyC emission is not only resolved but its size and morphology are remarkably
similar to that of the non-ionizing UV (with $r_{\rm eff}\simeq 220$ pc). This
is further highlighted in the bottom right panel of Figure 7, where the LyC
and UV (normalized) radial profiles are shown (black and yellow,
respectively). Despite potential variations in the PSF between F410M and
F775W, which are residual (Table 1) and were accounted for in our
morphological analysis with PySersic (Section 3.1.1), the figure shows that
the LyC and UV radial profiles are indistinguishable within the uncertainties.
Together with the high $f_{\rm esc}^{\rm LyC}\approx 90$% measured in Marques-
Chaves et al. (2022), the almost identical LyC and UV morphologies suggest
that the covering fraction of neutral gas and dust, the two known sources of
LyC opacity, is residual or negligible. It also suggests that the UV starlight
is dominated by O-type stars that emit both LyC and UV photons, which is
consistent with the strong wind line profiles seen in the rest-UV spectrum
(e.g., N iv $\lambda$1240, C iv $\lambda$1550; Marques-Chaves et al. 2022).
Our results thus support the very high $f_{\rm esc}^{\rm LyC}\simeq 90\%$
directly measured from the optical spectroscopy analyzed in Marques-Chaves et
al. (2022). The non-detection of low-ionization ISM absorption lines in the
optical spectrum of J1316+2614 and its steep UV slope ($\beta_{\rm
UV}\simeq-2.60$, Marques-Chaves et al. 2022) are also consistent with
weak/residual gas and dust along the line-of-sight (e.g., Gazagnes et al.,
2018; Chisholm et al., 2022; Saldana-Lopez et al., 2022).

Figure 7: The left panel shows the LyC emission of J1316+2614 from the
HST/F410M image ($0.8^{\prime\prime}\times 0.8^{\prime\prime}$ size, north is
up and east is to the left). The continuum-subtracted Ly$\alpha$ emission is
shown in blue with three contours representing the $2.5\sigma-5\sigma$,
$5\sigma-8\sigma$, and $8\sigma-15\sigma$ levels. The emission from the non-
ionizing UV (F775W, $\lambda_{0}\simeq 1650$ Å) is represented in orange and
has the size corresponding to its observed FWHM ($\simeq
0.09^{\prime\prime}$). The top right panel shows the GTC optical and near-IR
spectra analyzed in Marques-Chaves et al. (2022), highlighting the Ly$\alpha$
$\lambda$1216 Å (blue) and [O iii] $\lambda$5008 Å (violet) spectral profile
at rest-velocity. The right bottom panel shows the normalized (to their
maxima) radial profiles obtained for the LyC (black), UV (orange), and
Ly$\alpha$ emission (blue).

The left panel of Figure 7 shows the continuum-subtracted Ly$\alpha$ emission
obtained from HST/FR551N (blue). Ly$\alpha$ photons are predominantly emitted
around (and far from) the compact stellar emission as traced by LyC
(background image) and UV (orange). This is also highlighted in its radial
profile seen in the bottom right panel of Figure 7 where Ly$\alpha$ (blue)
seems weak within the stellar component ($r<0.1^{\prime\prime}$). It is worth
noting that one of the most puzzling aspects of J1316+2614, as discussed in
Marques-Chaves et al. (2022), is the reconciliation of its high LyC escape
fraction with the large Ly$\alpha$ peak separation observed in its spectrum
($\Delta v\simeq 680$ km s-1, top right panel of Figure 7). Since density-
bounded H ii regions leak LyC photons by $f_{\rm esc}^{\rm
LyC}=e^{-\sigma_{\nu_{0}}N_{\rm HI}}$ where $\nu_{0}=6.3\times 10^{-18}$ cm2
is the ionization cross-section, the observed $f_{\rm esc}\simeq 90\%$ in
J1316+2614 implies a low column density of neutral gas of a few $10^{16}$
cm-2. This contrasts with the large $\Delta v\rm(Ly\alpha)$ observed in
J1316+2614 for which radiative transfer models predict log($N_{\rm HI}/\rm
cm^{-2})\gtrsim 21.5$ under standard assumptions (Verhamme et al., 2015). The
high $\Delta v$ observed in J1316+2614 can still be reconciled with a low
column density of neutral gas of a few $10^{16}$ cm-2, but this requires a
fairly high Doppler broadening parameter suggestive of e.g., turbulent gas
(Dijkstra, 2019). Whether the gas traced by Ly$\alpha$ is optically thick or
thin but highly turbulent, this apparent discrepancy seems now solved:
Ly$\alpha$ photons are predominantly emitted far from the LyC regions of
J1316+2614, and, therefore, the high $f_{\rm esc}^{\rm LyC}$ and large $\Delta
v\rm(Ly\alpha)$ can be naturally reconciled.

Furthermore, the Ly$\alpha$ spectral profile analyzed in Marques-Chaves et al.
(2022) also reveals relatively weak emission at the systemic velocity, which
should trace the closest gas around the stars. Given that a low column density
of neutral gas (of a few $\sim 10^{16}$ cm-2) is necessary for the high
$f_{\rm esc}^{\rm LyC}\simeq 90\%$, the weak Ly$\alpha$ emission at the
systemic velocity may suggest low amount of ionized gas within and in front
the UV stellar component, consistent with the Ly$\alpha$ geometry and its hole
shown in Figure 7. A substantial offset between H ii regions and stars in
J1316+2614 could also explain its relatively low $O32=$[O iii] $\lambda$5008 /
[O ii] $\lambda$3727 $=4.8\pm 2.1$ (Marques-Chaves et al., 2022) compared to
other strong LyC emitters, (e.g., Jaskot & Oey 2013; Izotov et al. 2018), and
therefore its low ionization parameter ($\propto d^{-2}$, where $d$ is the
distance between the ionized gas and stars). This should be confirmed with
high-spatial resolution observations of the nebular emission traced by non-
resonant lines.

All the aforementioned points refer to the LyC, UV, and gas distributions
along the line-of-sight, and variations of $f_{\rm esc}^{\rm LyC}$ and
Ly$\alpha$ properties with sight-line are certainly expected (e.g., Verhamme
et al., 2012; Mauerhofer et al., 2021; Blaizot et al., 2023; Gazagnes et al.,
2024). However, the analysis by Marques-Chaves et al. (2022) relating the
observed H$\beta$ luminosity with the production rate of LyC photons suggests
that the total ($\approx 4\pi$) LyC escape fraction in J1316+2614 is globally
high ($f_{\rm esc}^{\rm LyC,4\pi}\approx 80\%$). This conclusion arises from
the simple conservation of ionizing photons444The H$\beta$ luminosity should
be proportional to the production rate of ionizing photons, $Q_{\rm H}$, in
the form $L(\rm H\beta)\propto$ $Q_{\rm H}\times[1-f_{\rm esc}^{\rm LyC}]$.
and the fact that the non-resonant H$\beta$ emission is weakly affected by
sight-line variations, in particular when dust-attenuation levels are residual
(as in the case of J1316+2614).

Finally, we discuss the ALMA observations of J1316+2614 presented in
Dessauges-Zavadsky et al. (in prep). J1316+2614 was observed in Bands 3 and 6
to probe the molecular gas and dust emission, respectively. The molecular gas,
traced by CO(4-3), is not detected with a $4\sigma$ velocity-integrated
intensity limit of $I_{\rm CO}\leq 108$ mJy km s-1. This places an upper limit
on the molecular gas of $M_{\rm molgas}\leq 6.3\times 10^{9}M_{\odot}$. On the
other hand, dust emission is significantly detected (6.2$\sigma$), and a dust
mass of $M_{\rm dust}=(3.5\pm 1.0)\times 10^{7}M_{\odot}$ is inferred
(Dessauges-Zavadsky et al. in prep.). As discussed in that work, the origin of
the dust remains unclear. It might have formed from SNe in the UV-bright
starburst region, although the derived dust mass slightly exceeds standard
predictions (Gall & Hjorth, 2018) even without considering dust destruction.
The observed dust could also be produced before the UV-bright starburst by an
older, still undetected stellar population. Despite the relatively low spatial
resolution (beam size of $1.70^{\prime\prime}\times 1.33^{\prime\prime}$), the
dust emission is resolved with an effective radius of $r_{\rm eff}^{\rm
dust}=1.7\pm 0.8$ kpc. If dust and gas are coupled, the dust distribution
could follow that traced by Ly$\alpha$, which might explain its relatively
large size. We would expect that the dust emission also shows a “hole” or is
distributed in a shell, similar to Ly$\alpha$. High angular resolution
observations will be needed to test this. In any case, the steep UV slope
($\beta_{\rm UV}\simeq-2.60$) and the fairly blue ($f_{\nu}$) SED of
J1316+2614 indicate residual dust attenuation in the starlight. Thus, it is
likely that the dust and stellar emission from the UV-bright starburst are not
co-spatial.

In short, the various independent observations analyzed in this section all
indicate that the young, UV-bright starburst in J1316+2614 is likely exposed,
i.e., nearly devoid of gas and dust. While gas and dust are present around the
starburst, these appear to be residual within it. Under these conditions, LyC
photons are free to escape.

###  4.3 Energetics and the need for high star-formation efficiency

The exposed nature of J1316+2614 raises an important question: how can such a
vigorous starburst be almost devoid of gas? Although these conditions are
extreme on a galaxy-wide scale, they are common in local star clusters and
have been studied extensively over the past decade (e.g., Baumgardt et al.,
2008; Bastian & Strader, 2014; Krause et al., 2016). The basic principle is
that feedback from mechanical and radiative outflows must surpass the
gravitational binding force, ejecting the remaining gas from star-forming
clouds and leaving an exposed stellar component. In the following, we
investigate the different energetic processes associated with J1316+2614.

Figure 8: The left panel shows the different energies associated with
J1316+2614. Binding energies are shown in dark red (horizontal dashed lines)
for star-formation efficiencies of 0.4, 0.7, and 0.95. The total kinetic
energy is shown in black and includes the contribution of stellar winds (green
dashed line) and supernovae (yellow dashed line). These are obtained from
BPASS models assuming a continuous star formation history with $\rm SFR=898$
$M_{\odot}$ yr-1, $Z=0.008$ and the Chabrier (2003) IMF. The age of J1316+2614
and the corresponding uncertainty are marked in blue. The right panel shows
the critical star formation efficiency for gas expulsion by stellar winds
(green), normal supernovae ($10^{51}$ erg, yellow), and hypernovae ($10^{53}$
erg, red) as a function of the compactness index $C_{5}$ as proposed by Krause
et al. (2016). The location of J1316+2614 is shown in blue. The compactness
indexes of other star clusters, including the Sunburst cluster, are marked
with grey dashed lines.

We assume the Plummer star cluster model, in which the gravitational binding
energy of the gas is given by $E_{\rm b}=k(1-\epsilon_{\rm SF})GM^{2}_{\rm
T}/r_{h}$ (Baumgardt et al., 2008). Here, $k$ is a dimensionless constant
($\approx 0.4$), $\epsilon_{\rm SF}$ is the star formation efficiency, and
$M_{\rm T}$ is the total mass enclosed within the half-mass radius $r_{\rm h}$
(where $r_{\rm h}\simeq 1.7\times r_{\rm eff}$ in a Plummer sphere). The
factor $(1-\epsilon_{\rm SF})$ accounts for the fact that a fraction of the
gas is converted into stars. We estimate $E_{\rm b}$ as a function of
$\epsilon_{\rm SF}$ assuming that $M_{\rm T}\simeq M_{\star}+M_{\rm gas}$ and
$\epsilon_{\rm SF}=M_{\star}/M_{\rm T}$. The left panel of Figure 8 shows the
binding energies for J1316+2614 obtained with $\epsilon_{\rm SF}$ of 0.4, 0.7,
and 0.95 (horizontal red lines). For simplicity, we assume that $E_{\rm b}$
remains constant over time.

We also examine the mechanical energy from stellar winds and supernovae as a
function of age. Predictions for the kinematic energy of J1316+2614 were
obtained from BPASS v2.2.1 models (Stanway & Eldridge, 2018), assuming a
constant star formation of $\rm SFR=898$ $M_{\odot}$ yr-1, a metallicity of
$Z=0.008$ and the Chabrier (2003) IMF, reflecting the properties of the young
starburst derived in Section 3.3. The outputs of wind and SN energy of
J1316+2614 are shown in the left panel of Figure 8 in green and yellow,
respectively. As shown, the total mechanical energy (winds and SNe) surpasses
the binding energy feedback only if the star-formation efficiency in
J1316+2614 is $\epsilon_{\rm SF}\geq 0.7$ (at the age of J1316+2614). In other
words, gas expulsion from stellar winds and SNe can only occur if
$\epsilon_{\rm SF}\geq 0.7$. Before the onset of SNe feedback ($\lesssim 3.5$
Myr), stellar winds appear relatively inefficient in removing the gas,
requiring star-formation efficiencies as high as $\epsilon_{\rm SF}\gtrsim
0.95$.

Given that binding energy is proportional to $M^{2}/r$ and the mechanical
energy proportional to $M$, Krause et al. (2016) introduced the compactness
index $C_{5}=M_{\odot}/r_{h}$. This index relates the critical star formation
efficiency, above which the kinetic energy surpasses the gravitational
binding, leading to gas expulsion. The right panel of Figure 8 shows the
$C_{5}$ derived for J1316+2614, $C_{5}=128\pm 11$ ($10^{5}M_{\odot}$ pc-1),
along with the critical star formation efficiency needed for gas expulsion by
stellar winds (green), supernovae (yellow, $E_{0}=10^{51}$ erg) and hypernovae
(red, $E_{0}=10^{53}$ erg) derived in Krause et al. (2016). Overall, the
$C_{5}$ derived for J1316+2614 is much higher than typical values in star
clusters ($C_{5}\lesssim 1$, Krause et al. 2016), implying also a much higher
$\epsilon_{\rm SF}$ to remove the gas within the stellar core of J1316+2614.
However, note that the critical star formation efficiencies shown in this
figure were calibrated for star clusters (i.e., assuming a single age burst,
Krause et al. 2016). Whether J1316+2614 can be described as a single burst is
still unclear (see Section 4.1).

We also explore the effects of radiative-driven outflows, which were recently
proposed to explain the overabundance of UV-bright galaxies at high redshifts
(Ferrara et al., 2023). Following Ziparo et al. (2023), we determine the
conditions under which radiation pressure can drive an outflow by comparing
the Eddington ratio as a function of $\Sigma\rm SFR$. Considering $\Sigma\rm
SFR\simeq 3\times 10^{3}M_{\odot}$ yr-1 kpc-2 derived for J1316+2614, a
radiative-driven outflow can occur when the burstiness parameter is $k_{\rm
s}\gtrsim 56$, which quantifies the deviation from the Kennicutt-Schmidt
relation (i.e., $\Sigma$SFR $\propto k_{\rm s}\Sigma_{\rm gas}^{1.4}$). This
translates to an upper limit of the gas surface density of $\Sigma_{\rm
gas}\lesssim 6\times 10^{3}M_{\odot}$ pc-2. Assuming gas and stars had the
same size, we find that $\epsilon_{\rm SF}\gtrsim 0.72$ is needed to
efficiently launch radiation-driven outflows.

Our results thus support a very high star-formation efficiency in J1316+2614.
The exposed, gas-free nature of the UV-bright starburst in J1316+2614 suggests
that either all the gas was converted into stars ($\epsilon_{\rm SF}\sim 1$)
or it was partially ejected by mechanical or radiative feedback, still
requiring a fairly high $\epsilon_{\rm SF}\gtrsim 0.7$. Feedback seems indeed
ineffective in J1316+2614 to suppress star formation, as seen from the
inflowing signatures suggested from its Ly$\alpha$ profile. This inefficient
feedback could enhance the star formation efficiency and SFR of J1316+2614,
explaining also its remarkably high UV luminosity (e.g., Renzini, 2023). The
high star-formation efficiency is also corroborated by the non-detection of
molecular gas using ALMA ($M_{\rm gas}\leq 6.3\times 10^{9}M_{\odot}$), for
which an $\epsilon_{\rm SF}\geq 0.4$ was derived (Dessauges-Zavadsky et al. in
prep.). On the other hand, we acknowledge that these analytic expressions are
likely too simple to explain the complex ISM conditions and kinematics of
J1316+2614, not considering, for example, possible effects of hot X-ray-
emitting gas, turbulence, the multi-phase nature of the ISM, or even the
presence of an AGN (see e.g. Krause et al., 2020; Thompson & Heckman, 2024,
and references therein), although there are currently no signs of such
phenomena in our target (Marques-Chaves et al., 2022). Additionally, the
energies and $\epsilon_{\rm SF}$ considered here also depend on the stellar
mass derived for J1316+2614, which is sensitive to the adopted IMF (e.g.,
Menon et al., 2024). In this context, VMS have been suggested in J1316+2614
(and in other similar UV-bright galaxies, Upadhyaya et al. 2024) from its
intense and broad He ii $\lambda 1640$ emission (e.g., Martins & Palacios,
2022; Martins et al., 2023). However, they appear to provide only modest
changes on the UV mass-to-light ratio, decreasing it by $\approx\times 1.5$
(Schaerer et al., 2024a).

###  4.4 High star-formation efficiency and high LyC escape: cause-effect

Several surveys have been conducted to understand the conditions under which
LyC photons can escape from star-forming galaxies (e.g., Steidel et al., 2018;
Flury et al., 2022). The standard paradigm assumes that LyC leakage occurs
through ionized channels in the ISM originated by strong feedback mechanisms
(e.g., Heckman et al. 2001). Observations do suggest the importance of
mechanical and radiative driven winds in the escape of LyC photons (e.g.,
Komarova et al., 2021; Bait et al., 2023; Amorín et al., 2024).

In the case of J1316+2614, mechanical and radiative feedback alone seems
insufficient to clear the gas within the starburst, at least from a simple
energetic balance. As highlighted before, gas clearance from mechanical and
radiative feedback requires a fairly high star-formation efficiency.
Regardless of the presence of strong feedback, an $\epsilon_{\rm SF}\gtrsim
0.7$ is necessary to account for the exposed nature of J1316+2614 and its
resulting high LyC leakage. If instead J1316+2614 had a more typical star
formation efficiency (e.g., $\lesssim 0.1$), it would likely contain large
amounts of gas ($M_{\rm gas}\gtrsim 4\times 10^{10}M_{\odot}$), increasing
considerably the gravitational binding energy ($E_{\rm b}\gtrsim 10^{59}$
erg). Under these conditions, the kinetic energy ($E_{\rm kin}\simeq 10^{57}$
erg, Figure 8) would be insufficient to expel the gas from the stellar core,
likely preventing LyC leakage. Our results thus support that, although
mechanical and radiative outflows may be significant in J1316+2614 (though not
detected so far), the high star-formation efficiency seems to be the primary
driver for the high LyC escape in J1316+2614.

A causal relationship between high star-formation efficiencies and increased
LyC production/leakage is indeed expected (c.f., Jecmen & Oey 2023, Kimm et
al. 2019). Simply put, higher $\epsilon_{\rm SF}$ within a star-forming region
inevitably results in less residual gas to absorb LyC photons. Additionally,
this remaining gas would be more easily removed from the starburst region, as
higher $\epsilon_{\rm SF}$ enhances both mechanical and radiative energies
(both proportional to SFR or $M_{\star}$, i.e., $\propto\epsilon_{\rm
SF}M_{\rm T}$), and decreases the binding energy ($\propto(1-\epsilon_{\rm
SF})M_{\rm T}^{2}$). Moreover, an enhanced $\epsilon_{\rm SF}$ would boost the
SFR, leading to the formation of more massive stars and thereby increasing LyC
emission. This could also lead to density-bounded regions, which facilitates
LyC escape (e.g., Jaskot et al., 2017). Hence, the impact of high
$\epsilon_{\rm SF}$ on LyC escape is twofold: it not only enhances the
production of ionizing photons but also facilitates their escape.

While J1316+2614 may represent an extreme case with LyC leakage possibly
enhanced by its high star formation efficiency, similar conditions might be
already present in other cases. For example, the well-studied, gravitationally
lensed Sunburst cluster at $z=2.37$ is known to leak large amounts of LyC
photons (Dahle et al., 2016; Rivera-Thorsen et al., 2017, 2019; Vanzella et
al., 2020). Meštrić et al. (2023) showed that the LyC region is slightly
smaller ($r_{\rm eff}^{\rm LyC}\simeq 5$ pc) than the non-ionizing region
($r_{\rm eff}^{\rm UV}\simeq 8$ pc), suggesting that the Sunburst cluster is,
at least, partially exposed555It can still be fully exposed if the LyC
emitting stars are segregated in the center of the cluster (see the discussion
in Meštrić et al., 2023).. Using the stellar mass derived in Vanzella et al.
(2022) of $10^{7}M_{\odot}$ and the half-mass radius of $r_{\rm h}\simeq
1.7\times r_{\rm eff}^{\rm UV}$, the Sunburst cluster shows a high compactness
index of $C_{5}\simeq 7.5$ ($10^{5}M_{\odot}$ pc-1), which is a factor of
$\approx\times 10$ higher than in local star clusters (e.g., Bastian &
Strader, 2014; Krause et al., 2016). If the outflows detected by Mainali et
al. (2022) and Vanzella et al. (2022) are responsible for the gas clearance in
the Sunburst cluster, then its high $C_{5}$ suggests a high $\epsilon_{\rm
SF}$, at least $\gtrsim 0.45$ as seen in the right panel of Figure 8.

In short, our results suggest a close relationship between high $\epsilon_{\rm
SF}$ and high escape of ionizing photons. This may be particularly relevant at
higher redshifts, where star-formation efficiencies are expected to be higher
due to the higher densities and lower metallicities of the ISM in high-$z$
galaxies (e.g., Dekel et al., 2023; Ceverino et al., 2024). Thus, high star-
formation efficiencies could not only be crucial for the mass growth of
high-$z$ galaxies (e.g., Xiao et al., 2023; de Graaff et al., 2024; Glazebrook
et al., 2024; Weibel et al., 2024), but may also have important implications
for cosmic reionization.

###  4.5 Feedback-free starburst within an extreme formation mode

####  4.5.1 J1316+2614 as an intense feedback-free starburst?

The high star-formation efficiency in J1316+2614 likely plays a key role in
enhancing its star formation rate and burst mass. In this context, high star-
formation efficiencies have been recently proposed to explain the high-number
density of UV-bright and massive sources at early times (Dekel et al., 2023;
Li et al., 2023; Ceverino et al., 2024). Following Dekel et al. (2023), high-
density environments and low metallicities could favor the formation of so-
called feedback-free starbursts (FFB, Dekel et al. 2023) through the collapse
of gas clouds within very short free-fall times. This would promote higher
star formation efficiencies, as the cloud collapse occurs before the onset of
mechanical feedback. High-mass galaxies could thus form quickly through
several generations of FFBs.

The very high mass density of J1316+2614 indeed suggests a rather short free-
fall time. Assuming a spherical gas geometry with a radius of $r_{\rm eff}$,
and a star formation efficiency of $0.7$, we derive the free-fall time $t_{\rm
ff}\simeq 1.1$ Myr, where $t_{\rm ff}=\sqrt{3\pi/(32\,G\,\rho)}$ and
$\rho=3\,M_{\rm gas}/(4\pi\,r_{\rm eff}^{3})$. Therefore, the derived free-
fall time in J1316+2614 is within the range predicted by the FFB scenario
($\sim 1$ Myr, Dekel et al. 2023). Additionally, J1316+2614 shows a very
compact morphology ($r_{\rm eff}\simeq 220$ pc) which aligns with predictions
for galaxies in the FFB phase ($r_{\rm eff}\sim 300$ pc) as discussed in Li et
al. (2023).

On the other hand, the metallicity inferred for J1316+2614 using the $R23$
method (12+log(O/H) $=8.45\pm 0.12$, Marques-Chaves et al. 2022) is higher
than expected in the FFB scenario ($\sim 0.1Z_{\odot}$, Dekel et al. 2023).
However, the derived O/H abundance should also reflect the likely efficient
chemical enrichment of the starburst itself over the last 5-6 Myr, potentially
differing from the gas metallicity in the pre-FFB phase. Furthermore, the
derived abundance in J1316+2614 should be treated with caution due to the
underlying effect of high $f_{\rm esc}^{\rm LyC}$, as discussed by Marques-
Chaves et al. (2022). We also compare the star-formation history of J1316+2614
with those expected in an FFB galaxy (Li et al., 2023). Using the derived $\rm
SFR=898\,M_{\odot}$ yr-1 and the upper limit on the molecular mass $M_{\rm
molgas}\leq 6.3\times 10^{9}M_{\odot}$, the gas depletion timescale is $t_{\rm
depl}=M_{\rm molgas}/\rm SFR\lesssim 7$ Myr. Considering its age, the duration
of the UV-bright starburst in J1316+2614 should be around $\Delta t\simeq
6-13$ Myr. The star-formation history of J1316+2614 appears slightly different
(higher SFR and higher $\Delta t$) than the predictions by Li et al. (2023)
(see their Section 4).

In short, being among the most powerful starbursts known and showing no
evidence of feedback so far, J1316+2614 may represent a case of an intense
feedback-free starburst with high star-formation efficiency. This would
support the link between high star-formation efficiencies and high UV-
luminosities, as suggested for galaxies at very high redshifts (Dekel et al.,
2023; Li et al., 2023).

Figure 9: Contribution (in %) of the starburst mass ($\leq 10$ Myr) to the
total mass of J1316+2614 (blue star) and other starbursting galaxies,
including UV-bright galaxies at $z\simeq 2-3$ (blue circles, Marques-Chaves et
al., 2020a, 2021), extreme [O iii] $\lambda$5008 emitters at $z\sim 1-4$
(violet squares, Tang et al., 2022), and local Green Pea galaxies (red
diamonds, Amorín et al., 2012). Green crosses mark the measurements of highly
magnified galaxies at $z\gtrsim 6$ for which young star clusters or star-
forming regions are resolved (Vanzella et al., 2023; Adamo et al., 2024;
Fujimoto et al., 2024). FirstLight simulated sources at $z\simeq 5-6$ and
$z\gtrsim 10$ are also shown with orange and cyan dots, respectively (Ceverino
et al., 2017).

####  4.5.2 Very efficient stellar mass growth

We further investigate the impact of this extreme UV-bright starburst on the
stellar mass growth of J1316+2614. Our multi-wavelength SED analysis in
Section 3.3 indicates that the young starburst dominates the light (UV-
optical) and likely the mass of J1316+2614. Even with conservative assumptions
for the old stellar population (1.4 Gyr old), our best-fit CIGALE model
predicts a relatively faint stellar component with log($M_{\star}^{\rm
old}/M_{\odot})\leq 9.46$ (3$\sigma$). If so, it could also explain the origin
of the dust observed in J1316+2614 ($M_{\rm dust}=3.5\times 10^{7}M_{\odot}$,
Dessauges-Zavadsky et al. in prep.). Following the $M_{\rm dust}-M_{\star}$
relation derived by Magnelli et al. (2020), we would expect a stellar mass of
the underlying old stellar population of log($M_{\star}^{\rm
old}/M_{\odot})\simeq 9.2$, i.e., consistent with our upper limit. Assuming
log($M_{\star}^{\rm old}/M_{\odot})\leq 9.46$, the UV-bright starburst
accounts for a large fraction of the stellar mass of J1316+2614, $f_{\rm
burst}=M_{\star}^{\rm young}/(M_{\star}^{\rm young}+M_{\star}^{\rm old})\geq
62\%$ (3$\sigma$).

Figure 9 shows the $f_{\rm burst}$ derived for J1316+2614 (blue star). We also
show measurements obtained for other galaxies, including other similar UV-
bright galaxies (blue circles, Marques-Chaves et al., 2020a, 2021), extreme [O
iii] $\lambda$5008 emitters at $z\sim 1-4$ (squares, Tang et al., 2022), and
local Green Pea galaxies (diamonds, Amorín et al., 2012). Green symbols mark
the measurements of highly magnified galaxies at $z\gtrsim 6$ for which young
star clusters or star-forming regions are resolved (Vanzella et al., 2023;
Adamo et al., 2024; Fujimoto et al., 2024).

Green Pea and extreme [O iii] emitters are vigorous star-bursting galaxies,
but their young ($\lesssim 10$ Myr) stellar populations account for a
relatively small fraction of the total mass (with a mean a standard deviation
of $f_{\rm burst}=6\pm 5\%$). This figure also shows the $f_{\rm burst}$
derived for two other UV-bright galaxies, J1220+0842 ($f_{\rm burst}\geq
50\%$, Marques-Chaves et al. 2020a) and J0146-0220 ($f_{\rm burst}\geq 24\%$,
Marques-Chaves et al. 2021), whose properties closely resemble those of
J1316+2614 (e.g., $M_{\rm UV}<-24$). Interestingly, Dessauges-Zavadsky et al.
(in prep.) find high star formation efficiencies for these two sources, up to
$\epsilon_{\rm SF}\geq 24\%$. For more normal, main-sequence galaxies, the
$f_{\rm burst}$ parameter is likely even smaller. This is highlighted in
Figure 9 where we show the predictions from FirstLight simulations (Ceverino
et al., 2017). Simulated sources at $z\simeq 5-6$ (orange dots) show
relatively modest $f_{\rm burst}\simeq 5\%$ on average. At higher redshifts,
FirstLight simulated sources at $z\gtrsim 10$ (cyan dots) show higher stellar
mass growth efficiencies, with $f_{\rm burst}\simeq 15\%$ on average, likely
due to the more burstier nature of high-$z$ sources and the limited time to
form evolved stellar populations. Star-forming clumps at $z\sim 6-10$ recently
observed in lensed galaxies seem indeed to contribute substantially to the
total mass of these early galaxies, up to $f_{\rm burst}\simeq 30\%$ (green in
Figure 9, Vanzella et al. 2023; Adamo et al. 2024; Fujimoto et al. 2024).

If the star formation efficiency in J1316+2614 is effectively high, our
results suggest that it can have a huge impact on the stellar mass growth in
the galaxy. Indeed, the high stellar mass fraction formed in the starburst in
J1316+2614 ($f_{\rm burst}\geq 62\%$) resembles traditional models of
monolithic collapse, where most of its mass is assembled within a remarkably
short period of time (e.g., Eggen et al., 1962; Larson, 1976; Matteucci,
1994).

###  4.6 Possible formation paths

How can J1316+2614 be so UV-bright, compact, massive, and young? Here, we
explore possible formation paths for this extreme starburst. Extended
Ly$\alpha$ halos, like the one seen in J1316+2614, are commonly observed
around high redshift star-forming galaxies (e.g., Leclercq et al., 2017;
Kusakabe et al., 2022). However, signatures of inflowing gas indicated by
blue-dominated Ly$\alpha$ profiles are extremely rare (e.g., Erb et al., 2014;
Martin et al., 2015). Typically, star-forming galaxies show Ly$\alpha$
profiles dominated by redshifted emission along with blueshifted ISM
absorption lines, both consistent with large-scale outflows (e.g., Shapley et
al., 2003; Steidel et al., 2010; Leclercq et al., 2020; Marques-Chaves et al.,
2020b). Therefore, it is tempting to associate the extreme nature of
J1316+2614 with the inflowing gas suggested by its Ly$\alpha$ profile (see
discussion in Marques-Chaves et al. 2022).

The rapid mass assembly history of J1316+2614, forming $\simeq 5\times
10^{9}M_{\odot}$ of stars in just $\simeq 5-6$ Myr, along with its compactness
and the absence of a significant old stellar population, suggests an extreme
formation path, potentially monolithic. Inflowing streams or massive gas
collapse could trigger and feed the young starburst in J1316+2614. This could
provide enough gas supply for a globally high star formation efficiency (e.g.,
as required for the FFB; Dekel et al., 2023). Thus, the filamentary-like gas
distribution traced by Ly$\alpha$ emission (see Figure 7) could represent
remnants of the infalling streams, supporting its Ly$\alpha$ spectral profile
(e.g., Dijkstra et al., 2006). However, the real extent of this inflowing gas
and whether it consists of pristine or recycled material from previous star
formation episodes (e.g., galactic fountains) remains unknown.

Alternatively, the inflowing gas kinematics could be related to dissipative
compaction of the gas disc induced by a wet-merger or by violent disc
instabilities (e.g., Zolotov et al., 2015), as discussed in Marques-Chaves et
al. (2022). However, simulations of the compaction phase predict a modest
increase of the sSFR with respect to the main sequence, of $\Delta\rm
log(sSFR)\simeq 0.3-0.7$ dex (Zolotov et al., 2015; Tacchella et al., 2016),
while J1316+2614 shows $\Delta\rm log(sSFR)\simeq 1.7$ dex (assuming $\rm
sSFR=188\pm 40$ Gyr-1). Furthermore, the (stellar) disc remains undetected in
our deep, high-resolution images. Finally, typical major merger processes
involve timescales that are likely too long to explain the observed properties
of J1316+2614 (e.g., Lotz et al., 2008). Given the very young age of
J1316+2614, we would expect to observe multiple merging clumps or galaxies.
However, HST images reveal only a very compact stellar morphology with a half-
light radius of $\simeq 220$ pc. The Ly$\alpha$ emission shows a complex,
filamentary-like morphology (oriented south-north, Figures 4 and 8), which
could, in principle, represent tidal tails from merging galaxies. However,
such a configuration is unlikely given the short timescales involved in
J1316+2614 ($\simeq 6$ Myr). Moreover, merging galaxies would likely present
evolved stellar populations, but these have not been detected so far in
J1316+2614. Therefore, a typical major merger seems unlikely to be the direct
cause of this intense starburst, though a rare merging configuration cannot be
ruled out.

##  5 Summary and Conclusions

In this work, we have presented high-resolution Hubble Space Telescope (HST)
and Very Large Telescope (VLT) imaging observations of J1316+2614 at $z=3.613$
discovered by Marques-Chaves et al. (2022). J1316+2614 is so far the UV-
brightest ($M_{\rm UV}=-24.7$) star-forming galaxy known and one of the
strongest LyC emitters with an escape fraction of $f_{\rm esc}^{\rm
LyC}\approx 90\%$. It also shows a steep UV slope ($\beta_{\rm
UV}\simeq-2.60$) and a peculiar, blue-dominated Ly$\alpha$ emission indicating
inflowing gas. The new HST observations probe the LyC, Ly$\alpha$, and the
rest-UV and optical emission of J1316+2614 with WFC3/F410M, ACS/FR551N,
WFC3/F775W, and WFC3/F160W, respectively. Seeing enhanced $K_{\rm s}$-band
observations were obtained with VLT/HAWK-I ($\rm FWHM\simeq
0.30^{\prime\prime}$). From the analysis of these data, we arrived at the
following main results:

  * •

J1316+2614 shows a very compact, but resolved morphology in the LyC and rest-
UV. Using PySersic we find similar half-light radii for LyC and UV emission of
$r_{\rm eff}^{\rm LyC}=262\pm 64$ pc and $r_{\rm eff}^{\rm UV}=220\pm 12$ pc,
respectively. J1316+2614 represents the first case known with resolved LyC
emission in a star-forming galaxy. The LyC and UV radial profiles and
residuals obtained from the PSF-subtracted images are also indistinguishable
within the uncertainties. Our results suggest that the LyC and UV morphologies
and sizes are essentially the same ($r_{\rm eff}\simeq 220$ pc), indicating a
residual/null covering fraction of neutral gas and very high LyC leakage. On
the other hand, J1316+2614 appears unresolved at longer wavelengths in
HST/F160W and VLT/$K_{\rm s}$ ($r_{\rm eff}^{\rm opt}\leq 440$ pc).

  * •

The HST ACS/FR551N ramp-filter image ($\lambda_{\rm eff}\simeq 5604$ Å and
width of $\simeq 97$ Å), which traces the Ly$\alpha$ emission of J1316+2614,
shows a well-resolved morphology with a filamentary-like emission with a total
scale length of $\simeq 6.0$ kpc ($3\sigma$) oriented south-north. After
subtracting the contribution of the underlying stellar continuum, Ly$\alpha$
appears residual at the position of the stellar (LyC and UV) emission. Our
results indicate a Ly$\alpha$ hole with weak/residual Ly$\alpha$ co-spatial
with the stellar continuum. This configuration, combined with its steep UV
slope, lack of ISM absorption lines, similar LyC and UV morphologies, and the
high LyC escape fraction, suggests that gas and dust are residual within the
starburst (though present around it).

  * •

Using the photometry obtained from the new images, we re-analyzed its spectral
energy distribution (SED). We find that J1316+2614 is dominated by an almost
un-obscured ($E(B-V)=0.03\pm 0.01$) young stellar population with an age of
$5.7\pm 1.0$ Myr and a continuous $\rm SFR=898\pm 181$ $M_{\odot}$ yr-1. The
mass formed in this young starburst is $M_{\star}^{\rm young}=(4.8\pm
0.3)\times 10^{9}$ $M_{\odot}$. The SFR and stellar mass surface densities,
log($\Sigma SFR[M_{\odot}\rm yr^{-1}kpc^{-2}])=3.47\pm 0.11$ and log($\Sigma
M_{\star}[M_{\odot}\rm pc^{-2}])=4.20\pm 0.06$, are among the highest found in
star-forming galaxies, resembling those observed in local young massive star
clusters.

  * •

We also investigated the presence of an underlying old stellar population,
which is not detected. Assuming a 1.4 Gyr old burst model, we place an upper
limit on its mass of $M_{\star}^{\rm old}\leq 2.8\times 10^{9}M_{\odot}$
(3$\sigma$). Our results suggest that the UV-bright starburst not only
dominates the light emission of J1316+2614 ($\simeq 100\%$) but also its
stellar mass, with a mass fraction of the galaxy formed in the last $\simeq 6$
Myr of $f_{\rm burst}=M_{\star}^{\rm young}/(M_{\star}^{\rm
young}+M_{\star}^{\rm old})\geq 62\%$ (3$\sigma$). Our results suggest that
the bulk of the stellar mass in J1316+2614 was assembled within a remarkably
short period of time, resembling models of monolithic collapse.

The emerging picture of J1316+2614 consists of a very powerful, young, and
compact starburst leaking a significant fraction of LyC photons due to the
lack of gas and dust within its stellar core. Using simple analytic
expressions and assumptions, we explore the different energetic processes
associated with J1316+2614 and the conditions leading to its exposed nature.
Feedback seems ineffective in J1316+2614 under normal conditions, and a very
high star formation efficiency ($\epsilon_{\rm SF}\geq 0.7$) is suggested to
expel the remaining gas from the starburst region. Thus, our results support
that, although mechanical and radiative outflows may be present in J1316+2614
(though not detected so far), the high star-formation efficiency is likely the
main driver for the high LyC escape in J1316+2614.

Overall, the high star formation efficiency in J1316+2614 provides a natural
explanation for its remarkably high $f_{\rm esc}^{\rm LyC}$, star formation
rate and UV luminosity, and at the same time, the lack of molecular gas
($M_{\rm molgas}\leq 6.3\times 10^{9}M_{\odot}$, Dessauges-Zavadsky et al in
prep.). It also explains the very efficient stellar mass growth in J1316+2614,
with at least 62% of its mass formed in the last 6 Myr. In this context,
J1316+2614 may represent an intense feedback-free starburst with enhanced star
formation efficiency, similar to those proposed for UV-bright galaxies at very
high redshifts. If similar conditions are present in their higher-$z$
counterparts, our results suggest that enhanced star formation efficiencies
could be crucial not only for the accelerated mass build-up of high-$z$
galaxies but also for promoting the LyC production and escape, with possible
implications for cosmic reionization.

###### Acknowledgements.

We would like to thank Angela Adamo and Adélaïde Claeyssens for sharing the
data presented in Figure 6. This research is based on observations made with
the NASA/ESA Hubble Space Telescope obtained from the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5–26555. These observations are
associated with program ID 17286. Based on observations collected at the
European Southern Observatory under ESO programme 111.251K.001.

## References

  * Adamo et al. (2024) Adamo, A., Bradley, L. D., Vanzella, E., et al. 2024, arXiv e-prints, arXiv:2401.03224
  * Álvarez-Márquez et al. (2021) Álvarez-Márquez, J., Marques-Chaves, R., Colina, L., & Pérez-Fournon, I. 2021, A&A, 647, A133
  * Amorín et al. (2012) Amorín, R., Pérez-Montero, E., Vílchez, J. M., & Papaderos, P. 2012, ApJ, 749, 185
  * Amorín et al. (2024) Amorín, R. O., Rodríguez-Henríquez, M., Fernández, V., et al. 2024, A&A, 682, L25
  * Arrabal Haro et al. (2023) Arrabal Haro, P., Dickinson, M., Finkelstein, S. L., et al. 2023, ApJ, 951, L22
  * Bait et al. (2023) Bait, O., Borthakur, S., Schaerer, D., et al. 2023, arXiv e-prints, arXiv:2310.18817
  * Barro et al. (2017) Barro, G., Faber, S. M., Koo, D. C., et al. 2017, ApJ, 840, 47
  * Bastian & Strader (2014) Bastian, N. & Strader, J. 2014, MNRAS, 443, 3594
  * Baumgardt et al. (2008) Baumgardt, H., Kroupa, P., & Parmentier, G. 2008, MNRAS, 384, 1231
  * Bertin (2006) Bertin, E. 2006, in Astronomical Society of the Pacific Conference Series, Vol. 351, Astronomical Data Analysis Software and Systems XV, ed. C. Gabriel, C. Arviset, D. Ponz, & S. Enrique, 112
  * Birrer et al. (2022) Birrer, S., Bhamre, V., Nierenberg, A., Yang, L., & Van de Vyvere, L. 2022, PSFr: Point Spread Function reconstruction, Astrophysics Source Code Library, record ascl:2210.005
  * Birrer et al. (2021) Birrer, S., Shajib, A., Gilman, D., et al. 2021, The Journal of Open Source Software, 6, 3283
  * Blaizot et al. (2023) Blaizot, J., Garel, T., Verhamme, A., et al. 2023, MNRAS, 523, 3749
  * Boquien et al. (2019) Boquien, M., Burgarella, D., Roehlly, Y., et al. 2019, A&A, 622, A103
  * Bouwens et al. (2021) Bouwens, R. J., Oesch, P. A., Stefanon, M., et al. 2021, AJ, 162, 47
  * Boylan-Kolchin (2024) Boylan-Kolchin, M. 2024, arXiv e-prints, arXiv:2407.10900
  * Bruzual & Charlot (2003) Bruzual, G. & Charlot, S. 2003, MNRAS, 344, 1000
  * Bunker et al. (2023) Bunker, A. J., Saxena, A., Cameron, A. J., et al. 2023, A&A, 677, A88
  * Burgarella et al. (2005) Burgarella, D., Buat, V., & Iglesias-Páramo, J. 2005, MNRAS, 360, 1413
  * Calzetti et al. (2000) Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682
  * Carniani et al. (2024) Carniani, S., Hainline, K., D’Eugenio, F., et al. 2024, arXiv e-prints, arXiv:2405.18485
  * Castellano et al. (2024) Castellano, M., Napolitano, L., Fontana, A., et al. 2024, arXiv e-prints, arXiv:2403.10238
  * Ceverino et al. (2017) Ceverino, D., Glover, S. C. O., & Klessen, R. S. 2017, MNRAS, 470, 2791
  * Ceverino et al. (2024) Ceverino, D., Nakazato, Y., Yoshida, N., Klessen, R., & Glover, S. 2024, arXiv e-prints, arXiv:2404.02537
  * Chabrier (2003) Chabrier, G. 2003, ApJ, 586, L133
  * Charbonnel et al. (2023) Charbonnel, C., Schaerer, D., Prantzos, N., et al. 2023, A&A, 673, L7
  * Chisholm et al. (2022) Chisholm, J., Saldana-Lopez, A., Flury, S., et al. 2022, MNRAS, 517, 5104
  * Claeyssens et al. (2023) Claeyssens, A., Adamo, A., Richard, J., et al. 2023, MNRAS, 520, 2180
  * Dahle et al. (2016) Dahle, H., Aghanim, N., Guennou, L., et al. 2016, A&A, 590, L4
  * de Graaff et al. (2024) de Graaff, A., Setton, D. J., Brammer, G., et al. 2024, arXiv e-prints, arXiv:2404.05683
  * Dekel et al. (2023) Dekel, A., Sarkar, K. C., Birnboim, Y., Mandelker, N., & Li, Z. 2023, MNRAS, 523, 3201
  * Dijkstra (2019) Dijkstra, M. 2019, Saas-Fee Advanced Course, 46, 1
  * Dijkstra et al. (2006) Dijkstra, M., Haiman, Z., & Spaans, M. 2006, ApJ, 649, 14
  * Eggen et al. (1962) Eggen, O. J., Lynden-Bell, D., & Sandage, A. R. 1962, ApJ, 136, 748
  * Erb et al. (2014) Erb, D. K., Steidel, C. C., Trainor, R. F., et al. 2014, ApJ, 795, 33
  * Ferrara et al. (2023) Ferrara, A., Pallottini, A., & Dayal, P. 2023, MNRAS, 522, 3986
  * Finkelstein et al. (2023) Finkelstein, S. L., Bagley, M. B., Ferguson, H. C., et al. 2023, ApJ, 946, L13
  * Flury et al. (2022) Flury, S. R., Jaskot, A. E., Ferguson, H. C., et al. 2022, ApJ, 930, 126
  * Fruchter & Hook (2002) Fruchter, A. S. & Hook, R. N. 2002, PASP, 114, 144
  * Fujimoto et al. (2024) Fujimoto, S., Ouchi, M., Kohno, K., et al. 2024, arXiv e-prints, arXiv:2402.18543
  * Gaia Collaboration et al. (2023) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1
  * Gall & Hjorth (2018) Gall, C. & Hjorth, J. 2018, ApJ, 868, 62
  * Gazagnes et al. (2018) Gazagnes, S., Chisholm, J., Schaerer, D., et al. 2018, A&A, 616, A29
  * Gazagnes et al. (2024) Gazagnes, S., Cullen, F., Mauerhofer, V., et al. 2024, ApJ, 969, 50
  * Glazebrook et al. (2024) Glazebrook, K., Nanayakkara, T., Schreiber, C., et al. 2024, Nature, 628, 277
  * Heckman et al. (2001) Heckman, T. M., Sembach, K. R., Meurer, G. R., et al. 2001, ApJ, 558, 56
  * Hegde et al. (2024) Hegde, S., Wyatt, M. M., & Furlanetto, S. R. 2024, arXiv e-prints, arXiv:2405.01629
  * Inayoshi et al. (2022) Inayoshi, K., Harikane, Y., Inoue, A. K., Li, W., & Ho, L. C. 2022, ApJ, 938, L10
  * Izotov et al. (2018) Izotov, Y. I., Worseck, G., Schaerer, D., et al. 2018, MNRAS, 478, 4851
  * Jaskot & Oey (2013) Jaskot, A. E. & Oey, M. S. 2013, ApJ, 766, 91
  * Jaskot et al. (2017) Jaskot, A. E., Oey, M. S., Scarlata, C., & Dowd, T. 2017, ApJ, 851, L9
  * Jecmen & Oey (2023) Jecmen, M. C. & Oey, M. S. 2023, ApJ, 958, 149
  * Kannan et al. (2023) Kannan, R., Springel, V., Hernquist, L., et al. 2023, MNRAS, 524, 2594
  * Kimm et al. (2019) Kimm, T., Blaizot, J., Garel, T., et al. 2019, MNRAS, 486, 2215
  * Komarova et al. (2021) Komarova, L., Oey, M. S., Krumholz, M. R., et al. 2021, ApJ, 920, L46
  * Krause et al. (2016) Krause, M. G. H., Charbonnel, C., Bastian, N., & Diehl, R. 2016, A&A, 587, A53
  * Krause et al. (2020) Krause, M. G. H., Offner, S. S. R., Charbonnel, C., et al. 2020, Space Sci. Rev., 216, 64
  * Kruijssen (2012) Kruijssen, J. M. D. 2012, MNRAS, 426, 3008
  * Kusakabe et al. (2022) Kusakabe, H., Verhamme, A., Blaizot, J., et al. 2022, A&A, 660, A44
  * Langeroodi & Hjorth (2023) Langeroodi, D. & Hjorth, J. 2023, arXiv e-prints, arXiv:2307.06336
  * Larson (1976) Larson, R. B. 1976, MNRAS, 176, 31
  * Leclercq et al. (2020) Leclercq, F., Bacon, R., Verhamme, A., et al. 2020, A&A, 635, A82
  * Leclercq et al. (2017) Leclercq, F., Bacon, R., Wisotzki, L., et al. 2017, A&A, 608, A8
  * Li et al. (2023) Li, Z., Dekel, A., Sarkar, K. C., et al. 2023, arXiv e-prints, arXiv:2311.14662
  * Lotz et al. (2008) Lotz, J. M., Jonsson, P., Cox, T. J., & Primack, J. R. 2008, MNRAS, 391, 1137
  * Lovell et al. (2023) Lovell, C. C., Harrison, I., Harikane, Y., Tacchella, S., & Wilkins, S. M. 2023, MNRAS, 518, 2511
  * Magnelli et al. (2020) Magnelli, B., Boogaard, L., Decarli, R., et al. 2020, ApJ, 892, 66
  * Mainali et al. (2022) Mainali, R., Rigby, J. R., Chisholm, J., et al. 2022, ApJ, 940, 160
  * Maiolino et al. (2024) Maiolino, R., Scholtz, J., Witstok, J., et al. 2024, Nature, 627, 59
  * Marques-Chaves et al. (2020a) Marques-Chaves, R., Álvarez-Márquez, J., Colina, L., et al. 2020a, MNRAS, 499, L105
  * Marques-Chaves et al. (2020b) Marques-Chaves, R., Pérez-Fournon, I., Shu, Y., et al. 2020b, MNRAS, 492, 1257
  * Marques-Chaves et al. (2021) Marques-Chaves, R., Schaerer, D., Álvarez-Márquez, J., et al. 2021, MNRAS, 507, 524
  * Marques-Chaves et al. (2022) Marques-Chaves, R., Schaerer, D., Álvarez-Márquez, J., et al. 2022, MNRAS, 517, 2972
  * Marques-Chaves et al. (2024) Marques-Chaves, R., Schaerer, D., Kuruvanthodi, A., et al. 2024, A&A, 681, A30
  * Martin et al. (2015) Martin, C. L., Dijkstra, M., Henry, A., et al. 2015, ApJ, 803, 6
  * Martins & Palacios (2022) Martins, F. & Palacios, A. 2022, A&A, 659, A163
  * Martins et al. (2023) Martins, F., Schaerer, D., Marques-Chaves, R., & Upadhyaya, A. 2023, A&A, 678, A159
  * Mason et al. (2023) Mason, C. A., Trenti, M., & Treu, T. 2023, MNRAS, 521, 497
  * Matteucci (1994) Matteucci, F. 1994, A&A, 288, 57
  * Mauerhofer et al. (2021) Mauerhofer, V., Verhamme, A., Blaizot, J., et al. 2021, A&A, 646, A80
  * Megeath et al. (2016) Megeath, S. T., Gutermuth, R., Muzerolle, J., et al. 2016, AJ, 151, 5
  * Menon et al. (2024) Menon, S. H., Lancaster, L., Burkhart, B., et al. 2024, ApJ, 967, L28
  * Messa et al. (2024) Messa, M., Dessauges-Zavadsky, M., Adamo, A., Richard, J., & Claeyssens, A. 2024, MNRAS, 529, 2162
  * Messa et al. (2022) Messa, M., Dessauges-Zavadsky, M., Richard, J., et al. 2022, MNRAS, 516, 2420
  * Meštrić et al. (2023) Meštrić, U., Vanzella, E., Upadhyaya, A., et al. 2023, A&A, 673, A50
  * Morishita et al. (2024) Morishita, T., Stiavelli, M., Chary, R.-R., et al. 2024, ApJ, 963, 9
  * Norris et al. (2014) Norris, M. A., Kannappan, S. J., Forbes, D. A., et al. 2014, MNRAS, 443, 1151
  * Oteo et al. (2017) Oteo, I., Zwaan, M. A., Ivison, R. J., Smail, I., & Biggs, A. D. 2017, ApJ, 837, 182
  * Pasha & Miller (2023) Pasha, I. & Miller, T. B. 2023, The Journal of Open Source Software, 8, 5703
  * Renzini (2023) Renzini, A. 2023, MNRAS, 525, L117
  * Ribeiro et al. (2016) Ribeiro, B., Le Fèvre, O., Tasca, L. A. M., et al. 2016, A&A, 593, A22
  * Rivera-Thorsen et al. (2019) Rivera-Thorsen, T. E., Dahle, H., Chisholm, J., et al. 2019, Science, 366, 738
  * Rivera-Thorsen et al. (2017) Rivera-Thorsen, T. E., Dahle, H., Gronke, M., et al. 2017, A&A, 608, L4
  * Saldana-Lopez et al. (2022) Saldana-Lopez, A., Schaerer, D., Chisholm, J., et al. 2022, A&A, 663, A59
  * Schaerer et al. (2024a) Schaerer, D., Guibert, J., Marques-Chaves, R., & Martins, F. 2024a, arXiv e-prints, arXiv:2407.12122
  * Schaerer et al. (2024b) Schaerer, D., Marques-Chaves, R., Xiao, M., & Korber, D. 2024b, A&A, 687, L11
  * Senchyna et al. (2024) Senchyna, P., Plat, A., Stark, D. P., et al. 2024, ApJ, 966, 92
  * Shapley et al. (2003) Shapley, A. E., Steidel, C. C., Pettini, M., & Adelberger, K. L. 2003, ApJ, 588, 65
  * Shen et al. (2023) Shen, X., Vogelsberger, M., Boylan-Kolchin, M., Tacchella, S., & Kannan, R. 2023, MNRAS, 525, 3254
  * Stanway & Eldridge (2018) Stanway, E. R. & Eldridge, J. J. 2018, MNRAS, 479, 75
  * Steidel et al. (2018) Steidel, C. C., Bogosavljević, M., Shapley, A. E., et al. 2018, ApJ, 869, 123
  * Steidel et al. (2010) Steidel, C. C., Erb, D. K., Shapley, A. E., et al. 2010, ApJ, 717, 289
  * Tacchella et al. (2016) Tacchella, S., Dekel, A., Carollo, C. M., et al. 2016, MNRAS, 458, 242
  * Tang et al. (2022) Tang, M., Stark, D. P., & Ellis, R. S. 2022, MNRAS, 513, 5211
  * Thompson & Heckman (2024) Thompson, T. A. & Heckman, T. M. 2024, arXiv e-prints, arXiv:2406.08561
  * Topping et al. (2024) Topping, M. W., Stark, D. P., Senchyna, P., et al. 2024, MNRAS, 529, 3301
  * Trinca et al. (2024) Trinca, A., Schneider, R., Valiante, R., et al. 2024, MNRAS, 529, 3563
  * Upadhyaya et al. (2024) Upadhyaya, A., Marques-Chaves, R., Schaerer, D., et al. 2024, A&A, 686, A185
  * van der Wel et al. (2012) van der Wel, A., Bell, E. F., Häussler, B., et al. 2012, ApJS, 203, 24
  * van Dokkum et al. (2008) van Dokkum, P. G., Franx, M., Kriek, M., et al. 2008, ApJ, 677, L5
  * Vanzella et al. (2020) Vanzella, E., Caminha, G. B., Calura, F., et al. 2020, MNRAS, 491, 1093
  * Vanzella et al. (2022) Vanzella, E., Castellano, M., Bergamini, P., et al. 2022, A&A, 659, A2
  * Vanzella et al. (2023) Vanzella, E., Claeyssens, A., Welch, B., et al. 2023, ApJ, 945, 53
  * Verhamme et al. (2012) Verhamme, A., Dubois, Y., Blaizot, J., et al. 2012, A&A, 546, A111
  * Verhamme et al. (2015) Verhamme, A., Orlitová, I., Schaerer, D., & Hayes, M. 2015, Astronomy and Astrophysics, 578, A7
  * Weibel et al. (2024) Weibel, A., Oesch, P. A., Barrufet, L., et al. 2024, arXiv e-prints, arXiv:2403.08872
  * Williams et al. (2023) Williams, H., Kelly, P. L., Chen, W., et al. 2023, Science, 380, 416
  * Xiao et al. (2023) Xiao, M., Oesch, P., Elbaz, D., et al. 2023, arXiv e-prints, arXiv:2309.02492
  * Ziparo et al. (2023) Ziparo, F., Ferrara, A., Sommovigo, L., & Kohandel, M. 2023, MNRAS, 520, 2445
  * Zolotov et al. (2015) Zolotov, A., Dekel, A., Mandelker, N., et al. 2015, MNRAS, 450, 2327