# Constraints on the Lyman Continuum Escape from Low-mass Lensed Galaxies at $1.3 \le z \le 3.0$

Intae Jung, Henry C. Ferguson, Matthew J. Hayes, Alaina Henry, Anne E.

Jaskot, Daniel Schaerer, Keren Sharon, Ricardo O. Amorín, Hakim Atek, Matthew B. Bayliss, et al.

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► To cite this version:

Intae Jung, Henry C. Ferguson, Matthew J. Hayes, Alaina Henry, Anne E. Jaskot, et al. Constraints on the Lyman Continuum Escape from Low-mass Lensed Galaxies at $1.3 \le z \le 3.0$. The Astrophysical Journal, 2024, 971, 10.3847/1538-4357/ad554d. insu-04833957

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Constraints on the Lyman Continuum Escape from Low-mass Lensed Galaxies at
$1.3 \le z \le 3.0$

Intae Jung¹, Henry C. Ferguson¹, Matthew J. Hayes², Alaina Henry¹,³, Anne E. Jaskot⁴, Daniel Schaerer⁵,⁶, Keren Sharon⁷, Ricardo O. Amorín⁸,⁹, Hakim Atek¹⁰, Matthew B. Bayliss¹¹, Håkon Dahle¹², Steven L. Finkelstein¹³, Andrea Grazian¹⁴, Lucia Guaita¹⁵, Göran Östlin¹⁶, Laura Pentericci¹⁷, Swara Ravindranath¹⁸,¹⁹, Claudia Scarlata²⁰, Harry I. Teplitz²¹, and Anne Verhamme⁵

¹Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA; ijung@stsci.edu

²Stockholm University, Department of Astronomy and Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Centre, SE-10691, Stockholm, Sweden

³Center for Astrophysical Sciences, Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA

⁴Department of Astronomy, Williams College, Williamstown, MA 01267, USA

⁵Observatoire de Genève, Université de Genève, Chemin Pegasi 51, 1290 Versoix, Switzerland

⁶CNRS, IRAP, 14 Avenue E. Belin, 31400 Toulouse, France

⁷Department of Astronomy, University of Michigan, 1085 S. University Avenue, Ann Arbor, MI 48109, USA

⁸ARAID Foundation, Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Unidad Asociada al CSIC, Plaza San Juan 1, E-44001 Teruel, Spain

⁹Departamento de Astronomía, Universidad de La Serena, Av. Juan Cisternas 1200 Norte, La Serena 1720236, Chile

¹⁰Institut d'Astrophysique de Paris, CNRS, Sorbonne Université, 98bis Boulevard Arago, 75014, Paris, France

¹¹Department of Physics, University of Cincinnati, Cincinnati, OH 45221, USA

¹²Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, NO-0315 Oslo, Norway

¹³Department of Astronomy, The University of Texas at Austin, Austin, TX, USA

¹⁴INAF-Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, I-35122, Padova, Italy

¹⁵Universidad Andres Bello, Facultad de Ciencias Exactas, Departamento de Física, Instituto de Astrofísica, Fernandez Concha 700, Las Condes, Santiago RM, Chile

¹⁶Department of Astronomy and Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Centre, Stockholm University, SE-10691, Stockholm, Sweden

¹⁷INAF-Osservatorio Astronomico di Roma, via di Frascati 33, 00078 Monte Porzio Catone, Italy

¹⁸Astrophysics Science Division, NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA

¹⁹Center for Research and Exploration in Space Science and Technology II, Department of Physics, Catholic University of America, 620 Michigan Avenue N.E., Washington, DC 20064, USA

²⁰Minnesota Institute for Astrophysics, University of Minnesota, 316 Church Street, SE Minneapolis, MN 55455, USA

²¹IPAC, Mail Code 314-6, California Institute of Technology, 1200 E. California Boulevard, Pasadena, CA 91125, USA

Received 2024 March 3; revised 2024 May 26; accepted 2024 June 5; published 2024 August 16

Abstract

Low-mass galaxies can significantly contribute to reionization due to their potentially high Lyman continuum (LyC) escape fraction and relatively high space density. We present a constraint on the LyC escape fraction from low-mass galaxies at $z = 1.3-3.0$. We obtained rest-frame UV continuum imaging with the ACS/SBC and the WFC3/UVIS from the Hubble Space Telescope for eight strongly lensed galaxies that were identified in the Sloan Giant Arc Survey and the Cluster Lensing and Supernova survey with Hubble. The targeted galaxies were selected to be spectroscopically confirmed, highly magnified, and blue in their UV spectral shapes ($\beta < -1.7$). Our targets include intrinsically low-luminosity galaxies down to a magnification-corrected absolute UV magnitude $M_{UV} \sim -14$. We perform custom-defined aperture photometry to place the most reliable upper limits of LyC escape from our sample. From our observations, we report no significant ($>2\sigma$) detections of LyC fluxes, placing $1\sigma$ upper limits on the absolute LyC escape fractions of 3%–15%. Our observations do not support the expected increased escape fractions of LyC photons from intrinsically UV faint sources. Considering the highly anisotropic geometry of LyC escape, increasing the sample size of faint galaxies in future LyC observations is crucial.

*Unified Astronomy Thesaurus concepts: Reionization (1383); Extragalactic astronomy (506); Dwarf galaxies (416); Ultraviolet astronomy (1736); Strong gravitational lensing (1643)*

1. Introduction

Over the redshift range of around 15 to 6, most of the
hydrogen gas in the intergalactic medium (IGM) changed from
neutral to ionized. The conventional thought is that young stars
in newly formed galaxies played a crucial role in emitting
ionizing photons, although a smaller portion likely came from
accreting black holes (or active galactic nuclei, AGNs; see the
review of Robertson 2022, and the references therein). A flood
of information provided by JWST observations is shedding
light on galaxies and AGNs during this era of reionization,

including direct spectroscopic confirmation of candidate
 galaxies as well as discovery of $z \gtrsim 9$ AGNs (e.g., Arrabal Haro
 et al. 2023a, 2023b; Bunker et al. 2023; Curtis-Lake et al.
 2023; Fujimoto et al. 2023; Harikane et al. 2023; Larson et al.
 2023a; Roberts-Borsani et al. 2023; Maiolino et al. 2024).

The critical measure for assessing the potential of galaxies
to reionize the neutral IGM is their total ionizing output:
$n_{ion,gal} = \rho_{UV} \times \xi_{ion} \times f_{esc}$. Here, $\rho_{UV}$ denotes the nonionizing
ultraviolet (UV) luminosity density, calculated by integrating
the UV luminosity function. $\xi_{ion}$ represents the efficiency of
ionizing-photon production, defined as the number of Lyman-
continuum (LyC) photons produced per unit of UV luminosity
density ($\rho_{UV}$). Lastly, $f_{esc}$ is the fraction of LyC photons that
escape into the IGM (e.g., Finkelstein et al. 2019; Robert-
son 2022; Atek et al. 2024).

<figure><img src="image_4.png" /></figure>

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of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further
distribution of this work must maintain attribution to the author(s) and the title
of the work, journal citation and DOI.
Measurements of the galaxy UV luminosity function at $z \gtrsim 7$ constrain the number densities of the likely sources of ionizing photons in relation to their absolute UV magnitude (e.g., Donnan et al. 2023; Harikane et al. 2023; Finkelstein et al. 2024; McLeod et al. 2024). The spectral energy distributions (SEDs) of galaxies can be used with population-synthesis models to indirectly infer the production rate of ionizing photons, often parameterized by $\xi_{ion}$, the ionizing-photon production rate relative to 1500 Å luminosity $L_{\nu}$ (e.g., Madau et al. 1999; Schaerer 2003; Bouwens et al. 2012). Whereas emission-line information allows more direct measurements of $\xi_{ion}$, comparing the line fluxes to the observed UV (e.g., Bouwens et al. 2016; Nakajima et al. 2016; Matthee et al. 2017; Shivaei et al. 2018; Lam et al. 2019). With access to rest optical wavelength spectra of reionization-era galaxies given by JWST observations, now it also becomes possible to derive $\xi_{ion}$ from the strengths of Balmer emission lines relative to the 1500 Å luminosity (Atek et al. 2024).

Nonetheless, it is challenging to precisely determine the escape of these ionizing photons ($f_{esc}$) and their contribution to reionization. To accurately assess ionizing photon supplies from galaxies during the reionization era, a comprehensive understanding of the escape fraction for ionizing (or LyC) photons originating from these galaxies is essential. Unfortunately, as we venture into the epoch of reionization, the direct measurement of LyC escape becomes infeasible due to the attenuation imposed by the IGM (Madau 1995; Inoue et al. 2014).

The best alternative is to use lower-redshift star-forming galaxies. The systematic trends observed in samples of these low-redshift galaxies can help reveal the conditions that are conducive to LyC escape. Low-redshift samples can also be used to calibrate a set of proxy measurements that might reliably predict the emergent ionizing continuum from a galaxy. UV observations with the Hubble Space Telescope (HST) of $z \sim 0.3$ compact galaxies that are considered as reionization-era analogs have successfully detected LyC emission (e.g., Izotov et al. 2016a, 2018a; Wang et al. 2019; Flury et al. 2022a). Recently, the Low-redshift Lyman-Continuum Survey (LzLCS; PI: A. Jaskot) has significantly enlarged the sample of LyC emitters (Flury et al. 2022a).

These LyC observations enable the investigation of correlations between LyC escape and other galaxy properties that can serve as indirect indicators of LyC escape. This includes, for example, the escape of $Ly\alpha$, the [O III]/[O II] line ratio, Mg II emission, rest-UV $\beta$ slope, C IV/C III] line ratio, and galaxy sizes (e.g., Verhamme et al. 2015; Dijkstra et al. 2016; Chisholm et al. 2018, 2020, 2022; Henry et al. 2018; Izotov et al. 2018a; Izotov et al. 2020; Saldana-Lopez et al. 2022; Saxena et al. 2022a; Schaerer et al. 2022; Xu et al. 2022, 2023). The recent increase in the size and diversity of low-redshift samples has made it possible to undertake a multivariate analysis that substantially reduces the scatter in predicted escape fractions relative to predictions based on a single observable (Flury et al. 2022b; Mascia et al. 2023; Jaskot et al. 2024a, 2024b). JWST observations are beginning to provide access to some of these indirect indicators of LyC escape fraction ($f_{esc}$) for reionization-era galaxies (Cameron et al. 2023; Saxena et al. 2024). The data will get much more extensive as spectroscopic data accumulate. There is thus a realistic prospect of applying these indirect indicators to make a more accurate estimate of the contribution of individual

galaxies to the ionizing photon budget (Mascia et al. 2023, 2024; Jung et al. 2024). However, the current $f_{esc}$ predictions rely on the correlations between indirect indicators and $f_{esc}$ that show generally large scatter and need further testing. This requires an increased data set of direct LyC observations that can be measured at lower redshifts.

Specifically, the applicability of $z \sim 0.3$ relationships to the reionization epoch remains uncertain. Therefore, conducting this study at a modest redshift is paramount to enhancing our understanding, and there has been recent progress on identifying LyC emitters at higher redshift at $z > 2$ (Mostardi et al. 2015; de Barros et al. 2016; Shapley et al. 2016; Vanzella et al. 2016; Bian et al. 2017; Steidel et al. 2018; Vanzella et al. 2018; Fletcher et al. 2019; Ji et al. 2020). However, many of these are high-luminosity galaxies with $M_{UV} \lesssim -19$, comparable to the limit in LzLCS. The LyC contribution may be more significant from lower-luminosity galaxies, which have hotter stellar populations and may be more capable of clearing neutral gas, at least along some sight lines (e.g., Wise et al. 2014; Paardekooper et al. 2015; Xu et al. 2016; Anderson et al. 2017). To fill in the parameter space of calibrating galaxies, the most important complement to the existing data is to measure lower-luminosity galaxies at $z \gg 0$.

The most important redshift range is $1 < z < 3.5$, where the IGM opacity is low enough to allow us to detect LyC radiation and measure the evolutionary trends. This has been attempted with mixed success. There have been successes with detecting leaking LyC photons at $z = 1-3$ but mostly from luminous sources (e.g., Steidel et al. 2001, 2018; Shapley et al. 2006; 2016; Iwata et al. 2009; Vanzella et al. 2012, 2016, 2018; Mostardi et al. 2015; de Barros et al. 2016; Bian et al. 2017; Saha et al. 2020; Marques-Chaves et al. 2021; Pahl et al. 2021; Begley et al. 2022; Rivera-Thorsen et al. 2022; Dhiwar et al. 2024). Meanwhile, many other deep observations found much lower LyC escape fractions, mostly delivering upper limits (e.g., Siana et al. 2010; Rutkowski et al. 2016, 2017; Grazian et al. 2017; Fletcher et al. 2019; Alavi et al. 2020). A more comprehensive overview of previous efforts on detecting LyC leakage at this redshift is available in Kerutt et al. (2024).

Focusing on the observations of lensed galaxies, the Sunburst Arc, a lensed dwarf galaxy at $z = 2.37$, presents an averaged LyC escape fraction of $f_{esc,abs} = 32\%$ (Rivera-Thorsen et al. 2017, 2019; Vanzella et al. 2020; Mainali et al. 2022; Kim et al. 2023). However, Amorín et al. (2014) targeted a strongly lensed sub-$L'$ extreme emission-line galaxy at $z = 3.417$, but finding no clue of $f_{esc,rel} \gtrsim 20\%$. Vasei et al. (2016) obtained $f_{esc,rel} \lesssim 8\%$ (corresponding to $f_{esc,abs} \lesssim 2\%$) for the Cosmic Horseshoe (magnification $\mu \sim 24$). Bian et al. (2017) estimate $f_{esc} = 28\%–57\%$ from a lensed arc at $z = 2.5$ in A2218, but this was the only one of the seven highly magnified arcs they observed that was detected. The six Frontier Fields and cluster A1689 were observed for 6–8 orbits with WFC3/F275W (Program ID 14209, PI: B. Siana) to detect escaping LyC continuum at $z \sim 2.4$. There have been no reports of detections or upper limits, although the analysis is limited only to a few spectroscopically confirmed galaxies. More LyC-leaking galaxies may be found as redshift surveys improve.

In this paper, we present our HST observations aiming to detect leaking LyC photons from eight galaxies strongly boosted by gravitational lensing. We selected highly magnified spectroscopically confirmed sources with blue rest-UV slopes and source plane absolute magnitudes $M_{UV} < -19$, based on
<table><caption>**Table 1**

Lensed Galaxy Sample with the LyC Observation Summary</caption><thead><tr><th>ID<br>(1)</th><th>R.A.<br>(J2000.0)<br>(2)</th><th>Decl.<br>(J2000.0)<br>(3)</th><th>z<sub>cluster</sub><br>(4)</th><th>z<sub>galaxy</sub><br>(5)</th><th>μ<br>(6)</th><th>LyC Filter<br>(7)</th><th>t<sub>exp</sub><br>(hr)<br>(8)</th></tr></thead><tbody><tr><td>SDSS J0851+3331-B</td><td>132.9082792</td><td>33.51857778</td><td>0.3689</td><td>1.3454</td><td>73.5<sup>+4.6</sup><sub>-28.3</sub></td><td>SBC F150LP</td><td>3.0</td></tr><tr><td>SDSS J0915+3826-A</td><td>138.9089458</td><td>38.45128333</td><td>0.3961</td><td>1.501</td><td>42.5<sup>+9.6</sup><sub>-2.2</sub></td><td>SBC F150LP</td><td>2.25</td></tr><tr><td>SDSS J1138+2754-A</td><td>174.5363208</td><td>27.91240278</td><td>0.451</td><td>1.3335</td><td>32.3<sup>+7.7</sup><sub>-1.8</sub></td><td>SBC F150LP</td><td>4.9</td></tr><tr><td>SDSS J1138+2754-C</td><td>174.5367917</td><td>27.91420278</td><td>0.451</td><td>1.455</td><td>66.4<sup>+68.0</sup><sub>-29.5</sub></td><td>SBC F150LP</td><td>4.9</td></tr><tr><td>SDSS J1439+1208-A</td><td>219.7926625</td><td>12.13835833</td><td>0.42734</td><td>1.494</td><td>1831.9<sup>+1304.8</sup><sub>-738.5</sub></td><td>SBC F150LP</td><td>2.25</td></tr><tr><td>M0329-2556</td><td>52.429404</td><td>-2.194035</td><td>0.450</td><td>1.313</td><td>5.5<sup>+0.3</sup><sub>-0.4</sub></td><td>SBC F150LP</td><td>4.5</td></tr><tr><td>M1115-2511</td><td>168.955867</td><td>1.497984</td><td>0.352</td><td>1.599</td><td>7.20<sup>+1.04</sup><sub>-0.01</sub></td><td>SBC F150LP</td><td>6.0</td></tr><tr><td>M1206-4340</td><td>181.560201</td><td>-8.809416</td><td>0.440</td><td>3.036</td><td>5.3<sup>+0.2</sup><sub>-0.3</sub></td><td>UVIS F336W</td><td>6.0</td></tr></tbody></table>

**Note.** Columns: (1) object ID, (2) R.A., (3) decl., (4) cluster redshift (Postman et al. 2012; Sharon et al. 2020), (5) galaxy spectroscopic redshift (Bayliss et al. 2011; Caminha et al. 2017, 2019; Sharon et al. 2020), (6) gravitational lensing magnification, (7) HST imaging filter used to observe LyC fluxes, (8) total exposure time.

the lens models available when the observations were proposed. We constrain LyC escape fractions of our eight sources at $1.3 \le z \le 3.0$ including intrinsically low-luminosity galaxies down to a magnification-corrected $M_{UV} \sim -14$.

This paper is structured as follows. We describe the HST imaging data, data reduction, and photometry of our targets in Section 2. Section 3 presents measurements of LyC escape as well as galaxy physical properties. We discuss our results in Section 4, compared to other studies in the literature. We summarize our findings and conclude in Section 5.

Throughout this work, we assume the Planck cosmology (Planck Collaboration et al. 2016) with $H_0 = 67.8 \text{ km s}^{-1} \text{ Mpc}^{-1}$, $\Omega_M = 0.308$, and $\Omega_\Lambda = 0.692$. All flux densities are given in $f_{\nu}$ and all magnitudes are quoted in the AB system (Oke & Gunn 1983).

## 2. Data and Photometry

### 2.1. Targets

We targeted eight galaxies that are highly magnified by gravitational lensing. All eight galaxies have spectroscopically measured redshifts and blue rest-UV colors. The targets were identified in the Sloan Giant Arc Survey (SGAS; PI: Gladders; Bayliss et al. 2011; Sharon et al. 2020) and the Cluster Lensing and Supernova survey with Hubble (CLASH; PI: M. Postman), including intrinsically lower-luminosity galaxies than previous studies. The targets mostly were detected in their strong emission lines (e.g., [O II] $\lambda\lambda3726,3729$) from ground-based observations (Bayliss et al. 2011; Sharon et al. 2020; Caminha et al. 2019) except for M1206-4340. Strong emission lines are deficient in the MUSE spectra of M1206-4340. Instead, M1206-4340 presents strong absorption features with extended Ly$\alpha$ blobs around the source (Zitrin et al. 2012; Caminha et al. 2017). The majority of sources span redshifts of $1.3 \le z \le 1.6$, except for one $z \approx 3$ galaxy (M1206-4340). Their principal properties are listed in Table 1.

### 2.2. HST Observations

The primary goal of this work is to detect LyC emission from intrinsically less luminous but highly magnified galaxies through gravitational lensing. We obtained rest-frame LyC ($\lambda < 912\AA$) imaging using the F150LP filter of SBC on ACS for seven $z \simeq 1.3-1.6$ targets and the F336W filter of UVIS on WFC3 for a $z = 3$ target (Program ID 15271, PI: H. Ferguson).

The F150LP filter has a significant throughput ($>1\%$) at a wavelength range of $1464\AA < \lambda < 1734\AA$ with a pivot wavelength ($\lambda_{pivot}$) at $1605.7\AA$, which corresponds to $\lambda_{rest} \sim 620-700\AA$ at $z \simeq 1.3-1.6$ (Siana et al. 2010; Alavi et al. 2020). The F336W filter covers $\lambda_{rest} \sim 838\AA$ at $z = 3.0$, having $\lambda_{pivot} = 3355\AA$ with a $>1\%$ throughput at $3016\AA < \lambda < 3708\AA$. The integration time varies depending on the observed apparent magnitude in a band corresponding to the rest-frame 1500 Å ensuring reaching the depth to detect LyC photons with a desired detection significance.

We also use the archival HST multiband imaging data for our sources. Typically, four HST broadband-filter observations are available for SGAS sources from the HST program GO-13003 (PI: Gladders), and the CLASH targets have sixteen broadband-filter-imaging data. We downloaded the fully reduced science mosaic images from the MAST archive for SGAS$^{22}$ and CLASH.$^{23}$ Each of the SGAS clusters was observed using four HST WFC3 filters: the UVIS F390W (the bluest), the IR F160W (the reddest), and two intermediate bands. The selection of these intermediate bands was based on the redshift of the primary arc to cover the 4000 Å break. Depending on our SGAS target, the intermediate bands used were either the F814W and F125W pair or the F775W and F110W pair. By contrast, the CLASH fields were observed using 16 HST filters, ranging from the WFC3/UVIS F225W (the bluest) to the WFC3/IR F160W (the reddest). For details of filter selection, observational strategy, and data reduction, we refer the reader to Sharon et al. (2020) and Postman et al. (2012) for SGAS and CLASH, respectively.

### 2.3. Data Reduction of LyC Observations

We first downloaded the drizzled images (drz.fits files) from the Mikulski Archive for Space Telescopes (MAST) portal for F150LP filter observations (Program ID 15271, PI: H. Ferguson). The images were registered to the existing optical HST images using individually measured positions of sources in the UV images. The reference positions in the world-coordinate systems for the UV images were updated to account for the relatively small shifts due to the use of different guide stars in the different HST observations. The registered individual images were then combined using the drizzle

<footnote>$^{22}$ https://archive.stsci.edu/hlsp/sgas</footnote>

<footnote>$^{23}$ https://archive.stsci.edu/prepds/clash/</footnote>
algorithm (Fruchter & Hook 2002) to produce a single coadded
image per target.

It is known that ACS/SBC data suffer time-dependent dark current rates, which often cause spatial structures in a background (Alavi et al. 2020; Runnholm et al. 2023). To mitigate the effect, we subtracted background substructures from the downloaded drizzled images by estimating a background from bright-sources-masked images using the Background2D class in the BACKGROUND subpackage in PHOTUTILS (Bradley et al. 2023).

For F336W observations, we downloaded the flat-field CTE-corrected images (flc.fits files) to perform better cosmic-ray (CR) removal as the reduced drizzled images of F336W available from the MAST contain numerous CRs uncleaned. We used the ASTRODRIZZLE task within the DRIZZLEPAC package<fnref n="24" /> to combine individual exposures and create the drizzled image (drc.fits). The ASTRODRIZZLE task applies the geometric distortion correction and masks bad pixels that are typically CRs or faulty pixels in the detector. In ASTRODRIZZLE, first, undistorted images are generated using the astrometric and distortion information in the header of flc.fits files. Then, CRs are identified in individual flc.fits frames by comparing them to the median image. We adjusted the *driz_cr_snr* parameters of the CR-detection thresholds and opted for *driz_cr_snr*=[5,1.5]. The first threshold in *driz_cr_snr* was chosen to avoid too many false positives but finding obvious CRs, and the second threshold was selected low enough to capture the faint peripherals of CRs (Zhang & Bloom 2020). We created the drizzled image with the same natural pixel scale (0.′′04) of the input flc images.

## 2.4. Broadband Photometry

It is important that multiband photometry be done with images that have the same point-spread function (PSF). We generated kernels to match the PSF sizes to that of the longest-wavelength image (i.e., F160W image). The CLASH collaboration provides a set of PSF models<fnref n="25" /> for all 16 filters used in the CLASH observations from F225W to F160W. However, currently, no public PSF model is available for F150LP. Thus, we construct the F150LP PSF model separately. We downloaded the latest F150LP calibration-field observations for NGC 6681 with >2000 s exposure time (Program ID: 11387). We selected eight isolated stars that do not have neighboring stars within ~2.′′5 distance. Then, we built the F150LP PSF model using the EPSFBuilder class in the PHOTUTILS.PSF subpackage. Finally, we checked the encircled energy curve within a 2.′′5 radius, which agrees well with the encircled energy curve available on the STScI webpage.<fnref n="26" /> In Figure 1, we present the constructed PSF model (in the inset) and a comparison of the encircled energy curves.

With the PSF models, we created two-dimensional (2D) kernels using the *create_matchring_kernel* function of the PSF Matching subpackage in PHOTUTILS. Then, we confirmed that the convolved PSFs agree well in their encircled energy plots.

Typical source-detection schemes do not generally perform
well for our sources as the sources are strongly lensed, showing

<figure><img src="image_5.png" /><figcaption>**Figure 1.** The encircled energy curve of the F150LP PSF model (blue), compared to the STScI measurement (orange). The inset panel shows the constructed PSF model of F150LP within a 1.′′625 × 1.′′625 box.</figcaption></figure>

highly stretched and elongated morphologies with clumpy
structures. Thus, photometric fluxes in the PSF-matched
images were measured within custom-defined areas, ensuring
extended source boundaries were included. As our lensed
targets are stretched with significant diffuse light, we draw a
boundary encompassing the diffuse components while mini-
mizing contributions from nearby contaminants. These tailored
boundaries are shown as red polygons in Figure 2. For an
improved background subtraction, we also define field areas in
the close vicinity with no obvious neighboring sources. These
background regions are noted as green.

The fluxes in individual broadband filters are measured by
summing all the fluxes included in the tailored boundaries, and
the uncertainties are propagated within the same boundaries
using the weight maps. The photometry is corrected for
Galactic extinction using the *E(B-V)* reddening values
estimated in Schlegel et al. (1998), ranging from 0.022 to
0.032 for SGAS images and 0.039 to 0.062 for CLASH
images. We assume the Pei (1992) dust extinction curve with
*R<sub>V</sub>* = 3.08 to correct the Galactic extinction in each broadband
filter. The flux values measured from our customized aperture
photometry are listed in Table 2 for SGAS, and Table 3
includes our HST photometry of the three CLASH targets.

## 2.5. Lyman-continuum Flux

We used F150LP and F336W filters to detect LyC fluxes
depending on galaxy redshifts. For LyC photometry, we
defined apertures separately based on rest-frame far-UV (FUV)
images that trace confined star-forming regions. We used the
Segmentation subpackage in PHOTUTILS to generate
segmentation maps from the FUV images. We performed
aperture photometry with the segmentation maps on the LyC-
targeting HST filter images that are PSF matched to their FUV
counterparts. Then, we measured LyC fluxes by summing
fluxes within all segments within the tailored boundaries that
we used in our broadband photometry in Section 2.4. We
investigated the LyC filter imaging (either F150LP or F336W)
to find any positive fluxes within the segmentation maps built
with FUV imaging, and we did not find significant (\>2σ)
signals from our targeted sources. Additionally, we performed
photometry on unconvolved LyC images to check if any LyC

<footnote n="24">²⁴ https://drizzlepac.readthedocs.io/en/latest/index.html</footnote>

<footnote n="25">²⁵ https://archive.stsci.edu/missions/hlsp/clash/psf_models/</footnote>

<footnote n="26">²⁶ https://www.stsci.edu/hst/instrumentation/acs/data-analysis/aperture-corrections</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 2.** The 17" × 17" HST postages of our eight targets. In each target, from left to right, we present LyC filter imaging, segmentation maps used for LyC photometry, and an HST broadband filter covering the rest-UV of the targets. In the panels, the red polygons show the tailored boundaries for our broadband photometry, and the background regions are marked as green.</figcaption></figure>

signals were smoothed out, which resulted in no (>2σ) detections as well.

Instead, we place tight upper limits of the LyC escape fraction by deriving realistic photometric uncertainties. The photometric errors in the LyC filter imaging were empirically derived by performing photometry using 100 random pointings of the same size and shape apertures. We first performed aperture photometry (with the same segmentation maps) from 100 random pointings around the sources and took the standard deviation of a sigma-clipped sample, removing 5σ outliers of the 100 random-aperture photometry. This provides empirically derived uncertainties of our customized photometry for the areas of interest where we expect to detect escaping LyC photons. We also corrected the Galactic extinction for the LyC photometry as described in Section 2.4. We take the estimated errors as the upper limits of the LyC fluxes for the rest of the analyses.

# 3. Analysis

## 3.1. Galaxy Properties and Star Formation Histories

To derive galaxy physical properties and study their star formation histories (SFHs), we perform galaxy SED fitting with PROSPECTOR (Leja et al. 2017; Johnson et al. 2021) for our sample. PROSPECTOR uses the Flexible Stellar Population

Synthesis models (Conroy et al. 2009) with the Modules for Experiments in Stellar Astrophysics Isochornes and Stellar Tracks (Choi et al. 2016) and CLOUDY (Ferland et al. 2013) to include the nebular emission lines as described in Byler et al. (2017). PROSPECTOR is capable of modeling SEDs with flexible (so-called “nonparametric”) SFHs. Specifically, PROSPECTOR models nonparametric SFHs with binned SFHs, described as collective piece-wise constant star formation rates of predefined temporal bins. We perform SED fitting with nonparametric SFHs for our CLASH targets, which have 16 band photometric data points. However, only four HST photometric bands are available for SGAS targets, making it infeasible to fit SEDs with nonparametric SFHs. Thus, we adopt a parametric SFH in SED fitting to reduce free parameters to fit for SGAS galaxies. Our targets are spectroscopically confirmed; thus, we fix the redshifts to the spectroscopic redshifts. We model dust attenuation by adopting the Calzetti et al. (2000) dust attenuation curve. In PROSPECTOR, the IGM attenuation is modeled following Madau (1995) with a scaling parameter of the IGM attenuation curve. The IGM scaling parameter accounts for line-of-sight variations in the total IGM opacity.

The free parameters in SED fitting for CLASH targets include dust attenuation, stellar and gas metallicities, an ionization parameter, and IGM attenuation in addition to eight
<table><caption>**Table 2**
HST Customized Aperture Photometry of the SGAS Targets</caption><thead><tr><th>ID</th><th>WFC3/UVIS F390W</th><th>WFC3/UVIS F775W</th><th>WFC3/UVIS F814W</th><th>WFC3/IR F110W</th><th>WFC3/IR F125W</th><th>WFC3/IR F160W</th></tr></thead><tbody><tr><td>SDSS J0851+3331-B</td><td>1.34 ± 0.30</td><td>...</td><td>1.84 ± 0.35</td><td>...</td><td>3.44 ± 0.11</td><td>2.92 ± 0.14</td></tr><tr><td>SDSS J0915+3826-A</td><td>8.84 ± 0.56</td><td>...</td><td>11.87 ± 0.65</td><td>...</td><td>22.85 ± 0.21</td><td>23.84 ± 0.26</td></tr><tr><td>SDSS J1138+2754-A</td><td>4.07 ± 0.78</td><td>6.04 ± 1.15</td><td>...</td><td>11.84 ± 0.17</td><td>...</td><td>14.50 ± 0.37</td></tr><tr><td>SDSS J1138+2754-C</td><td>1.23 ± 0.39</td><td>1.01 ± 0.57</td><td>...</td><td>1.57 ± 0.09</td><td>...</td><td>1.47 ± 0.19</td></tr><tr><td>SDSS J1439+1208-A</td><td>6.46 ± 0.65</td><td>...</td><td>5.57 ± 0.76</td><td>...</td><td>10.13 ± 0.25</td><td>9.76 ± 0.31</td></tr></tbody></table>

**Note.** All flux densities are given in µJy.
<table><caption>**Table 3**
Customized Aperture Photometry of the CLASH Targets</caption><thead><tr><th>Filters</th><th>M0329-2556</th><th>M1115-2511</th><th>M1206-4340</th></tr></thead><tbody><tr><td>WFC3/UVIS F225W</td><td>0.57 ± 0.14</td><td>0.09 ± 0.10</td><td>...</td></tr><tr><td>WFC3/UVIS F275W</td><td>0.65 ± 0.13<sup>a</sup></td><td>0.42 ± 0.08</td><td>...</td></tr><tr><td>WFC3/UVIS F336W</td><td>0.88 ± 0.08</td><td>0.72 ± 0.05<sup>a</sup></td><td>...</td></tr><tr><td>WFC3/UVIS F390W</td><td>1.12 ± 0.04</td><td>0.97 ± 0.03</td><td>0.73 ± 0.04</td></tr><tr><td>ACS/WFC F435W</td><td>1.19 ± 0.03</td><td>1.00 ± 0.02</td><td>1.23 ± 0.03</td></tr><tr><td>ACS/WFC F475W</td><td>1.15 ± 0.02</td><td>1.02 ± 0.01</td><td>1.56 ± 0.02<sup>a</sup></td></tr><tr><td>ACS/WFC F606W</td><td>1.19 ± 0.01</td><td>1.08 ± 0.01</td><td>2.48 ± 0.01<sup>a</sup></td></tr><tr><td>ACS/WFC F625W</td><td>1.11 ± 0.02</td><td>1.05 ± 0.02</td><td>2.93 ± 0.02</td></tr><tr><td>ACS/WFC F775W</td><td>1.22 ± 0.03</td><td>1.08 ± 0.02</td><td>3.11 ± 0.03</td></tr><tr><td>ACS/WFC F814W</td><td>1.40 ± 0.02</td><td>1.04 ± 0.01</td><td>3.10 ± 0.02</td></tr><tr><td>ACS/WFC F850LP</td><td>1.81 ± 0.06</td><td>1.16 ± 0.04</td><td>3.01 ± 0.06</td></tr><tr><td>WFC3/IR F105W</td><td>2.09 ± 0.02</td><td>1.18 ± 0.01</td><td>2.65 ± 0.02</td></tr><tr><td>WFC3/IR F110W</td><td>1.97 ± 0.01</td><td>1.61 ± 0.01</td><td>2.59 ± 0.01</td></tr><tr><td>WFC3/IR F125W</td><td>2.03 ± 0.02</td><td>1.69 ± 0.01</td><td>2.54 ± 0.02</td></tr><tr><td>WFC3/IR F140W</td><td>2.10 ± 0.01</td><td>1.68 ± 0.01</td><td>2.77 ± 0.01</td></tr><tr><td>WFC3/IR F160W</td><td>2.30 ± 0.02</td><td>1.22 ± 0.01</td><td>3.02 ± 0.02</td></tr></tbody></table>

Note. All flux densities are given in µJy.

<sup>a</sup> Filters including Lyα are removed from SED fitting analysis.

temporal bins to model nonparametric SFHs. We adopt top-hat priors to the free parameters, allowing the V-band optical depth ($\tau_V$) from 0 to 4 in dust attenuation, metallicities in the range of $-2.0 \le \log(Z/Z_\odot) \le 2.0$ (gas metallicity is tied to stellar metallicity), and the ionization parameter in the range of $-4.0 \le \log(U) \le -1.0$. The SFHs are modeled in eight temporal bins that include the two most recent temporal bins of [0, 3] Myr and [3, 10] Myr in addition to six evenly spaced bins in logarithmic time between 10 Myr to the age of the Universe at a source redshift. For IGM attenuation, we allow the IGM scaling parameter, which accounts for line-of-sight variations of the total IGM opacity, from 0 to 2, with a Gaussian prior centered at 1.

For SGAS targets where we have far fewer photometric bands, we fix the metallicity to $\log(Z/Z_\odot) = -0.7$ and the ionization parameter to $\log(U) = -2$. These choices are motivated by the mass-metallicity relation (MZR) and the mass-ionization relation (MQR) observed at similar redshifts (e.g., Henry et al. 2021; Sanders et al. 2021; Papovich et al. 2022). Although these MZR and MQR relations were derived from more-massive galaxies than our sample, our parameter choices are still within the extrapolated ranges of metallicity and ionization parameters for galaxies with stellar masses of $10^8-10^9 M_\odot$. Given the significant uncertainties in our galaxy mass estimates and the intrinsic scatter observed in the MZR and MQR at low masses, we adopt a single value for each parameter across all galaxies to provide a consistent approach. Additionally, we set the IGM scaling parameter to unity. The free parameters are dust attenuation ($0 \le \tau_V \le 2$), stellar population age (limited by the age of the Universe at a source redshift), and a $\tau$ value in the delayed-$\tau$ SFH with the range of $-1.0 < \log(\tau) < 10.0$. We allow stellar mass in the range of $5 \le \log(M_*/M_\odot) \le 12$.

Furthermore, to ensure consistency in our SED fitting analysis across all targets, we applied the same parameter choices to our CLASH targets as those used for the SGAS galaxies (with parametric SFHs). There are noticeable differences in the derived physical quantities between non-parametric and parametric SFHs, as detailed in recent studies

(e.g., Tacchella et al. 2022; Gburek et al. 2023). Specifically, SED fitting with parametric SFHs tends to indicate less dust attenuation with zero dust reddening ($E(B-V) = 0$) and bluer UV beta slopes compared to those derived from nonparametric SFHs ($\Delta\beta_{UV} \approx 0.3$). Differences in stellar masses were also observed within $1-2\sigma$ uncertainties, though no systematic biases were detected. Despite these discrepancies, the choice of SFHs in SED fitting does not significantly influence the major trends and findings of this study, which are discussed further in Section 4. Therefore, we have selected nonparametric SFH SED fitting results as the fiducial values for our analysis of CLASH targets.

The rest-frame UV slope ($\beta_{UV}$) is defined as a galaxy UV spectral index ($F_\lambda \propto \lambda^\beta$ or $F_\nu \propto \lambda^{\beta+2}$). We derived the UV slope from best-fit SED models over 1300–2600 Å that use all available photometric data points. To compare to the local LyC sample (see Section 4), we separately derived UV slopes centered at 1550 Å over a spectral window of 1300–1800 Å, as defined in Chisholm et al. (2022). UV slopes can be measured directly as well from photometric power-law fitting. However, we have limited rest-UV coverage for SGAS targets; thus, we rely on SED-based measurements. It has also been suggested that SED-derived UV slopes are less likely biased than those from photometric power-law fitting except for the cases of extremely blue rest-UV slopes ($\beta < -3$) unavailable in SED templates (e.g., Finkelstein et al. 2012; Larson et al. 2023b; Morales et al. 2024).

The best-fit SEDs of our SGAS targets are displayed in Figure 3. We also present the best-fit SEDs of the CLASH targets and their reconstructed nonparametric SFHs in Figure 4. The key quantities derived from SED fitting and the rest-UV slopes are listed in Table 4.

## 3.2. Lensing Models

Our targets are highly magnified with gravitational lensing caused by foreground clusters of galaxies. We obtained the latest available lensing models of the seven foreground clusters behind which our sources are located. The lensing models of SGAS clusters are available in Sharon et al. (2020). We used the lens models in Zitrin et al. (2015) for CLASH clusters. Using the cluster lensing models, we estimated lensing magnifications by averaging the magnification across the entire area of each source as defined for HST photometry (the red polygons in Figure 2). This method provides a more accurate and representative estimation of the lensing effects across the entire galaxy, ensuring that our analysis comprehensively accounts for the varied impact of lensing across the extended regions of our target galaxies. We calculated the magnification uncertainties based on a range of maps for each cluster system, which were derived from Markov Chain Monte Carlo sampling of the lensing parameter space. These random models for SGAS clusters are available in Sharon et al. (2020), while pre-estimated $1\sigma$ uncertainties for lensing maps are provided for CLASH clusters in Zitrin et al. (2015). We present the estimated magnification factors and the associated errors for our sources as listed in Table 1. We corrected the UV absolute magnitudes and stellar masses by dividing them by the estimated magnifications to discuss the intrinsic properties.
<figure><img src="image_7.png" /><figcaption>**Figure 3.** Best-fit SEDs of SGAS targets from our PROSPECTOR SED fitting analysis. The best-fit SEDs are green (MAP; maximum a posteriori), with 100 randomly drawn SEDs from Markov Chain Monte Carlo chains (gray). The observed HST photometric data points are noted with open circles.</figcaption></figure>

### 3.3. LyC Escape Fraction

We measure the upper limits of LyC fluxes from LyC detection bands as described in Section 2.5. The escape fraction of LyC photons is estimated as the ratio of the measured LyC fluxes to the intrinsic LyC fluxes. As we do not find significant LyC fluxes from our observations, we use the upper limits of LyC fluxes to calculate the upper limits of the LyC escape fractions.

The relative escape fractions of LyC fluxes are defined following previous studies (e.g., Steidel et al. 2001; Siana et al. 2007, 2010):

$$f_{\text{esc,rel}} = \frac{(L_{1500}/L_{\text{LyC}})_{\text{stel}}}{(F_{1500}/F_{\text{LyC}})_{\text{obs}}} \exp(\tau_{\text{IGM}}), \quad (1)$$

where $(F_{1500}/F_{\text{LyC}})_{\text{obs}}$ is the observed flux ratio between the flux density ($F_{\nu}$) at 1500 Å ($F_{1500}$) and in the LyC wavelength ($F_{\text{LyC}}$; <900 Å). The 1500 Å fluxes ($F_{1500}$) are averaged in a range of 1450–1550 Å in the rest frame in the best-fit SEDs obtained from the PROSPECTOR runs. $(L_{1500}/L_{\text{LyC}})_{\text{stel}}$ represents the intrinsic flux ratio from stellar populations modeling. Consistent with most of the literature, we adopt an $(L_{1500}/L_{\text{LyC}})_{\text{stel}}$ value of 8

at ~700 Å and 6 at ~900 Å as assumed in Siana et al. (2007). The intrinsic flux ratio could be much larger depending on star formation histories, particularly if galaxies have a single epoch of bursty star formation in the past as the contribution from massive stars decreases rapidly (Siana et al. 2007; Domínguez et al. 2015; Alavi et al. 2020). However, our targets were selected as having blue UV slopes, indicating recent star formation with young stellar ages; adopting the standard value of 6–8 for actively star-forming galaxies thus seems justified. The correction term for IGM attenuation by neutral hydrogen is added as $\exp(\tau_{\text{IGM}})$ where $\tau_{\text{IGM}}$ is the IGM opacity at the LyC wavelength (~620–830 Å). We use the IGM attenuation model (Inoue et al. 2014) and obtain the redshift-dependent mean IGM transmissions of $\exp(-\tau_{\text{IGM}}) \sim 0.6$ at $z \sim 1.3$ and ~0.3 at $z \sim 3$. This IGM transmission value at $z \sim 3$ agrees with the empirically measured IGM transmission at $z \sim 3$ in Steidel et al. (2018). However, we caution that the sight-line variation of IGM transmission could be significant at such high redshifts, which may affect a resulting upper limit of LyC escape up to around a factor of 2. We present the estimated $f_{\text{esc,rel}}$ upper limits.

The definition of $f_{\text{esc,rel}}$ can be related to the absolute escape fraction ($f_{\text{esc,abs}}$) that accounts for dust attenuation of UV
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 4.** Left: best-fit SEDs of CLASH targets from our PROSPECTOR SED fitting analysis. The best-fit SEDs are green, with 100 randomly drawn SEDs from Markov Chain Monte Carlo chains (gray). The observed HST photometric data points are noted with open circles. Right: star formation histories recovered from SED modeling with nonparametric SFHs in PROSPECTOR. The SFHs are modeled in eight temporal bins in look-back time.</figcaption></figure>

<table><caption>**Table 4**

Physical Properties of Lensed Dwarf Galaxy Sample</caption><thead><tr><th>ID<br>(1)</th><th>β<sub>UV</sub><br>(2)</th><th>β<sub>1550</sub><br>(3)</th><th>M<sub>UV,uncor</sub><br>(4)</th><th>M<sub>UV,cor</sub><sup>a</sup><br>(5)</th><th>Log(M<sub>star</sub>/M<sub>☉</sub>)<sup>a</sup><br>(6)</th><th>E(B − V)<br>(7)</th></tr></thead><tbody><tr><td>SDSS J0851+3331-B</td><td>−1.73 ± 0.28</td><td>−1.64 ± 0.16</td><td>−20.45 ± 0.29</td><td>−15.78<sup>+0.36</sup><sub>−0.82</sub></td><td>7.38<sup>+0.39</sup><sub>−0.07</sub></td><td>0.11<sup>+0.06</sup><sub>−0.05</sub></td></tr><tr><td>SDSS J0915+3826-A</td><td>−2.10 ± 0.07</td><td>−2.06 ± 0.08</td><td>−22.70 ± 0.06</td><td>−18.63<sup>+0.28</sup><sub>−0.12</sub></td><td>9.42<sup>+0.02</sup><sub>−0.11</sub></td><td>0.02<sup>+0.02</sup><sub>−0.01</sub></td></tr><tr><td>SDSS J1138+2754-A</td><td>−1.97 ± 0.22</td><td>−1.93 ± 0.26</td><td>−21.60 ± 0.19</td><td>−17.83<sup>+0.42</sup><sub>−0.25</sub></td><td>9.38<sup>+0.02</sup><sub>−0.12</sub></td><td>0.06<sup>+0.07</sup><sub>−0.04</sub></td></tr><tr><td>SDSS J1138+2754-C</td><td>−2.06 ± 0.40</td><td>−2.00 ± 0.46</td><td>−20.11 ± 0.44</td><td>−15.55<sup>+1.21</sup><sub>−1.08</sub></td><td>8.30<sup>+0.26</sup><sub>−0.64</sub></td><td>0.05<sup>+0.10</sup><sub>−0.04</sub></td></tr><tr><td>SDSS J1439+1208-A</td><td>−2.23 ± 0.06</td><td>−2.22 ± 0.07</td><td>−22.30 ± 0.17</td><td>−14.14<sup>+0.75</sup><sub>−0.73</sub></td><td>7.36<sup>+0.22</sup><sub>−0.62</sub></td><td>0.01<sup>+0.02</sup><sub>−0.01</sub></td></tr><tr><td>M0329-2556</td><td>−2.00 ± 0.05</td><td>−1.94 ± 0.07</td><td>−20.20 ± 0.03</td><td>−18.37<sup>+0.09</sup><sub>−0.11</sub></td><td>8.82<sup>+0.13</sup><sub>−0.11</sub></td><td>0.06<sup>+0.02</sup><sub>−0.02</sub></td></tr><tr><td>M1115-2511</td><td>−1.95 ± 0.05</td><td>−1.71 ± 0.06</td><td>−20.48 ± 0.02</td><td>−18.34<sup>+0.16</sup><sub>−0.02</sub></td><td>8.90<sup>+0.07</sup><sub>−0.13</sub></td><td>0.12<sup>+0.01</sup><sub>−0.02</sub></td></tr><tr><td>M1206-4340</td><td>−2.25 ± 0.02</td><td>−2.15 ± 0.03</td><td>−22.88 ± 0.01</td><td>−21.07<sup>+0.05</sup><sub>−0.07</sub></td><td>8.88<sup>+0.09</sup><sub>−0.13</sub></td><td>0.03<sup>+0.01</sup><sub>−0.01</sub></td></tr></tbody></table>

**Notes.** Columns: (1) object ID, (2) rest-UV slope measured from a best-fit SED at a rest-frame wavelength range of 1300 Å–2600 Å, (3) rest-UV slope centered at 1550 Å over a spectral window of 1300 Å–1800 Å, as defined in Chisholm et al. (2022), (4) absolute UV magnitude, (5) magnification-corrected absolute UV magnitude, (6) magnification-corrected stellar mass, (7) dust reddening.

<sup>a</sup> Errors include magnification uncertainties.

photons ($A_{UV}$): $f_{esc,abs} = f_{esc,rel} \times 10^{-0.4A_{UV}}$. Thus, the absolute escape fractions can be lower than the relative escape fractions as dust attenuation becomes significant (e.g., Shapley et al. 2016; Kerutt et al. 2024). We calculated the upper limits of the

absolute LyC escape fraction using the Calzetti et al. (2000) attenuation curve.

We summarize all LyC-escape-related properties of our sources in Table 5.
<figure><img src="image_10.png" /><figcaption>**Figure 5.** Absolute escape fraction of LyC photons vs. absolute UV magnitude (left), dust reddening (middle), and UV $\beta$ slope (right). We present the $1\sigma$ upper limits of LyC escape fractions as red arrows. The diamond symbols show the SGAS targets, and the CLASH targets are marked as the squares. The $z \approx 3$ target is emphasized with the black boundary. We include the known $z \sim 0.3$ sample of LyC leakers in LzLCS+ (Chisholm et al. 2022; Saldana-Lopez et al. 2022). The significant LyC leakers are shown as filled circles, and the gray arrows represent nonleakers in the LzLCS+ sample.</figcaption></figure>

<table><caption>**Table 5**

LyC Escape Properties of Lensed Dwarf Galaxy Sample<sup>a</sup></caption><thead><tr><th>ID<br>(1)</th><th>λ<sub>LyC</sub><br>(Å)<br>(2)</th><th>F<sub>LyC</sub><br>(μJy)<br>(3)</th><th>F<sub>LyC</sub>/F<sub>1500</sub><sup>b</sup><br>(4)</th><th>T<sub>IGM</sub><br>(5)</th><th>(L<sub>1500</sub>/L<sub>LyC</sub>)<sub>stel</sub><br>(6)</th><th>f<sub>esc,rel</sub><br>(7)</th><th>f<sub>esc,abs</sub><br>(8)</th></tr></thead><tbody><tr><td>SDSS J0851+3331-B</td><td>685</td><td>&lt;0.011</td><td>&lt;0.013</td><td>0.61</td><td>8</td><td>&lt;0.106</td><td>&lt;0.046</td></tr><tr><td>SDSS J0915+3826-A</td><td>642</td><td>&lt;0.044</td><td>&lt;0.007</td><td>0.54</td><td>8</td><td>&lt;0.056</td><td>&lt;0.048</td></tr><tr><td>SDSS J1138+2754-A</td><td>688</td><td>&lt;0.023</td><td>&lt;0.005</td><td>0.62</td><td>8</td><td>&lt;0.043</td><td>&lt;0.027</td></tr><tr><td>SDSS J1138+2754-C</td><td>654</td><td>&lt;0.009</td><td>&lt;0.029</td><td>0.56</td><td>8</td><td>&lt;0.222</td><td>&lt;0.152</td></tr><tr><td>SDSS J1439+1208-A</td><td>644</td><td>&lt;0.008</td><td>&lt;0.008</td><td>0.54</td><td>8</td><td>&lt;0.062</td><td>&lt;0.057</td></tr><tr><td>M0329-2556</td><td>694</td><td>&lt;0.010</td><td>&lt;0.014</td><td>0.63</td><td>8</td><td>&lt;0.112</td><td>&lt;0.071</td></tr><tr><td>M1115-2511</td><td>618</td><td>&lt;0.005</td><td>&lt;0.009</td><td>0.50</td><td>8</td><td>&lt;0.075</td><td>&lt;0.030</td></tr><tr><td>M1206-4340</td><td>831</td><td>&lt;0.028</td><td>&lt;0.030</td><td>0.32</td><td>6</td><td>&lt;0.178</td><td>&lt;0.142</td></tr></tbody></table>

**Notes.** Columns: (1) object ID, (2) rest-frame central wavelength of LyC HST filter band, (3) upper limits of LyC flux, (4) flux ratio between the LyC-band flux and rest-UV flux at 1500 Å, (5) mean IGM transmission at a source redshift at $\lambda_{LyC}$ based on Inoue et al. (2014), (6) intrinsic stellar Lyman break adopted in Equation (1), (7) relative LyC escape fraction following Equation (1), (8) absolute LyC escape fraction, UV-dust-attenuation ($A_{UV}$) corrected as $f_{esc,rel} \times 10^{-0.4A_{UV}}$.

<sup>a</sup> $1\sigma$ upper limits are provided.

<sup>b</sup> Corrected for IGM attenuation.

# 4. Discussion

## 4.1. LyC Escape with Galaxy Properties

To place the upper limits on LyC escape in context, it is useful to compare the properties of galaxies in our sample to other samples of galaxies that have been used to study LyC escape. In Figure 5, we present the upper limits of the LyC escape fraction ($f_{esc,abs}$) of our targets in terms of UV luminosity, dust attenuation, and rest-UV slope. We compare our measurements to the known $z \sim 0.3$ sample in LzLCS+ (Chisholm et al. 2022; Saldana-Lopez et al. 2022), which combines the 23 LyC emitters (Izotov et al. 2016a, 2016b, 2018a, 2018b, 2021; Wang et al. 2019) and the LzLCS sample (Flury et al. 2022a, 2022b).

Compared to the literature studies, we explore a much fainter regime down to $M_{UV} \sim -14$ thanks to gravitational lensing magnification, as shown in the left panel of Figure 5. Interestingly, we constrain $f_{esc}$ upper limits from three faint sources ($M_{UV} > -16$), which are comparable to those from relatively brighter targets ($M_{UV} \lesssim -18$). This mainly suggests

no evidence of the increased escape fractions of LyC photons from intrinsically UV faint sources although this must be further explored with additional observations.

Also, our SED fitting analysis suggests low dust content in these galaxies with $E(B-V) \lesssim 0.1$ (middle panel). There is a significant increasing trend of $f_{esc}$ with lower dust content seen from the LzLCS+ sample. Although we do not find evidence of LyC photon escape from our sources, we place $f_{esc}$ upper limits around the lower bound of the LyC-leaker distribution of LzLCS+, yet compatible with findings from the low-redshift sample.

In the last panel, we present the $f_{esc}$ upper limits versus the rest-UV slope at 1550 Å ($\beta_{1550}$). Chisholm et al. (2022) find a correlation between $f_{esc}$ and $\beta_{1550}$ from the LzLCS+ sample where they find significant LyC leakers with blue UV slopes ($\beta < -1.5$). Our targets exhibit blue UV slopes similar to the LyC leakers in the LzLCS+ sample. Despite nondetections of LyC fluxes, similar to what we find for $E(B-V)$, our results on the $f_{esc}$ upper limits lie along with the correlation suggested in Chisholm et al. (2022).
<figure><img src="image_11.png" /><figcaption>**Figure 6.** Similar to Figure 5, but showing the ratio of LyC fluxes to UV fluxes at 1500 Å as a function of absolute UV magnitude (left), dust reddening (middle), and UV β slope (right).</figcaption></figure>

Separately, for comparison of more direct observables, we derived the upper limits for the ratio of observed LyC flux to FUV continuum fluxes ($F_{LyC}/F_{1500}$), which are corrected for IGM attenuation, dropping the assumptions of the intrinsic flux ratios ($L_{1500}/L_{LyC}$). The $F_{LyC}/F_{1500}$ values are listed in the fourth column in Table 5. For a comparison, UV continuum fluxes ($F_{1500}$) of the LzLCS+ sample are converted from their $M_{1500}$ values (Flury et al. 2022b). In Figure 6, we show the upper limits of $F_{LyC}/F_{1500}$ of our targets as well as the LzLCS+ sample with the same physical properties to Figure 5. In this analysis, the galaxies in our sample tend to depart from the trend for LzLCS+ LyC leakers with low $E(B-V)$ or very blue UV slopes to have larger $F_{LyC}/F_{1500}$. This result could be further tested even for the current sample by obtaining more complete multiwavelength photometry for the SGAS sample galaxies to understand better their SFHs and emission-line properties to measure emission-line-based $f_{esc}$ (e.g., Rutkowski et al. 2016; Fletcher et al. 2019; Alavi et al. 2020).

## 4.2. Interpretations of the Nondetections

Our targets pose as potential LyC leakers with galaxy properties similar to those of confirmed LyC leakers from the literature. The low dust contents and blue UV slopes found in our targets suggest that the galaxies are young and in an active star-forming phase. As described in Section 3.1, we further examine SFHs of our CLASH targets thanks to the capability of building nonparametric SFHs in PROSPECTOR. The reconstructed SFHs of CLASH targets are displayed in the right panels in Figure 4. All three targets show recent bursty star formation within ~100 Myr in the past. This implies young stellar ages and is consistent with blue UV slopes. Such galaxy properties suggest that the galaxies are likely leaking LyC photons. Particularly, higher LyC escape fractions in faint and less-massive galaxies have been suggested in many theoretical studies (e.g., Wise et al. 2014; Paardekooper et al. 2015; Xu et al. 2016; Anderson et al. 2017; Yeh et al. 2023). However, our findings do not support the enhanced escape fraction of LyC photons from faint sources.

This seems puzzling at a glance, but it is understandable if we consider scenarios of highly anisotropic geometry of LyC escape with varying interstellar medium conditions depending on sight lines. This has been suggested in theoretical studies where they present significant line-of-sight variations in the

escape fraction of LyC photons (e.g., Cen & Kimm 2015; Ma et al. 2015; Paardekooper et al. 2015; Witten et al. 2024; Choustikov et al. 2024). Observationally, Kim et al. (2023) reported significant spatial variations of LyC leakage from their spatially resolved analysis of HST imaging of the Sunburst Arc: a strongly lensed LyC emitter at $z=2.37$. Such an anisotropic nature of LyC escape is consistent, in general, with the relatively large scatter found in relations between individual galaxy physical properties and the LyC escape fraction (e.g., Izotov et al. 2018a; Chisholm et al. 2022; Flury et al. 2022b). Indeed, similar to what is reported for the Sunburst Arc, a possible anisotropy of LyC escape has been suggested by the complex ionized gas kinematics (i.e., asymmetry of line profiles) of LzLCS LyC leakers (Amorín et al. 2024) and the lack of significant correlation of LyC leakage with galaxy properties from the analysis of $3.1 \lesssim z \lesssim 3.5$ star-forming galaxies (Saxena et al. 2022b).

Alternatively, the nondetections of escaping LyC fluxes in our study may simply indicate no significant increase in the LyC escape fraction for fainter galaxies. A turnover of increasing LyC escape fraction with lower stellar mass has been discussed due to less efficient star formation in low-mass-end populations with $M_* \lesssim 10^7 M_\odot$ (Ma et al. 2020; Rosdahl et al. 2022), although our targets are suggested to be slightly more massive than this threshold. Interestingly, such low-luminosity galaxies have been observed in Ly$\alpha$, the emission of which is dependent primarily on H I covering/column density and dust, in a qualitatively similar way to LyC (e.g., Hayes 2015; Verhamme et al. 2015, for a review). Indeed, Ly$\alpha$ escape and LyC escape correlate well in some existing samples (Steidel et al. 2018; Izotov et al. 2020; Pahl et al. 2021; Flury et al. 2022b). Some such low-luminosity galaxies were targeted early with HST: specifically IZw18 ($M_{UV} \sim -15.2$), SBS 0335–052E ($M_{UV} \sim -16.2$), Tol 65 ($M_{UV} \sim -14.6$), and SBS 1415+437 ($M_{UV} \sim -15.4$) overlap with the low-luminosity end of our lensed sample. These galaxies all show very strong Ly$\alpha$ absorption, with EWs $\lesssim -25$ Å (Kunth et al. 1994; Thuan & Izotov 1997; James et al. 2014), but show very strong H$\alpha$ emission implying vigorous levels of ongoing star formation. The damped Ly$\alpha$ with no hints of emission implies the starbursts are covered by thick layers of neutral hydrogen with column densities $\sim 2 \times 10^{21} \text{ cm}^{-2}$, with similar phenomena observed in numerous galaxies from the CLASSY sample (Hu et al. 2023). These galaxies mostly show high atomic gas mass
fractions, and we have previously speculated that the very youthful star formation in these galaxies has not yet accelerated or disrupted the absorbing material. At least along the line of sight, these galaxies must almost inevitably show zero LyC emission if the observation could be made. Broadly speaking, we speculate that similar phenomena could be responsible for the lack of LyC emission we report in our very faint lensed dwarfs. For example, the MUSE spectra for some of our targets (M0329-2556 and M1206-4340) present either a strong damped Ly$\alpha$ feature or abundant Balmer and metal absorption lines. By contrast, the ground-based spectra of our SGAS targets are relatively shallow, providing limited spectral information beyond redshift confirmation (Caminha et al. 2017; Richard et al. 2021).

Lastly, it is worth noting that $f_{esc}$ measurements from imaging may be more complicated to interpret than what is measured from spectra. They rely on, for example, the exact shape of a filter transmission curve (e.g., see discussion in Steidel et al. 2018). A further comparison of LyC measurements from photometry to those from spectra will help in understanding potential biases.

## 5. Summary

We present HST imaging observations with the ACS/SBC F150LP and WFC3/UVIS F336W filters, aiming to detect LyC photons from eight highly magnified sources at $z = 1.3–3.0$ with blue UV slopes ($\beta < -1.7$). Our targets include intrinsically faint galaxies in their rest-frame UV, down to $M_{UV} \sim -14$. We perform photometry with custom-defined apertures to derive reliable measurements of LyC escape dealing with complex morphologies in our lensed targets. Our findings are summarized as follows.

1. We perform SED fitting with PROSPECTOR to derive key physical quantities, including absolute UV luminosity, dust reddening, and UV $\beta$ slope. Our targets pose as potential LyC leakers with low dust content and are faint in UV and blue in UV color. We model SEDs with nonparametric SFHs for three CLASH targets, which recovers bursty star formation within the recent $\lesssim 100$ Myr in these galaxies.

2. We derive tight upper limits on the escape fraction of LyC photons by estimating empirically derived photometry errors. From our observations, we report no significant ($>2\sigma$) detections of LyC fluxes, placing $1\sigma$ upper limits at 3%–15% of the LyC escape fractions ($f_{esc,abs}$).

3. We constrain $f_{esc}$ upper limits from three faint sources ($M_{UV} > -16$) that are comparable to those from relatively brighter targets ($M_{UV} \lesssim -18$). Albeit with a relatively small sample—and with relatively large uncertainties in some of the magnification estimates—our results do not show the expected increase of LyC escape fraction from very low-luminosity galaxies.

UV faint galaxies have been suspected to be the main drivers of reionization. Understanding their contribution to ionizing photon supplies to the IGM can be critical to constrain the detailed reionization processes. Recent JWST observations suggest that UV faint galaxies are likely efficient in producing ionizing photons (e.g., Atek et al. 2024; Simmonds et al. 2024). However, unknown LyC escape makes it challenging to diagnose the actual capability of these faint galaxies in supplying ionizing photons to the IGM. In particular, we find

no significant enhancement of LyC escape in UV faint galaxies. Despite the nondetections of LyC fluxes, the $f_{esc,abs}$ upper limits of our sources are in general compatible with those of the LyC leakers in the LzLCS+ sample that share similar physical properties with our targets (i.e., less dusty and blue in rest-UV color). However, the galaxies in our sample tend to depart from the trend for the low-redshift LyC leakers with low $E(B-V)$ or very blue UV slopes ($\beta$) to have larger $F_{LyC}/F_{1500}$. This result could be further tested even for the current sample by obtaining more complete multiwavelength photometry for the SGAS sample galaxies to understand better their SFHs and emission-line properties to study emission-line-based $f_{esc}$. Overall, increasing the sample of these faint and low-mass galaxies is critical in future LyC observations to understand their relative contributions to reionization.

## Acknowledgments

The authors would like to thank the anonymous referee for the detailed reading and the constructive suggestions on this paper. This work is primarily based on observations taken by the HST Cycle 25 program (GO 15271) with the NASA/ESA HST, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for this work was provided by NASA through a grant program ID HST-GO-15271 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Some of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (MAST). These data are associated with programs GO-13003 (SGAS; Sharon 2022), GO-12065 (CLASH; Postman 2011), and GO-11387 (NGC 6681). H.A. is supported by the Centre National d'Etudes Spatiales (CNES).

**Facility:** HST (ACS and WFC3).

**Software:** astropy (Astropy Collaboration et al. 2013, 2022, The Astropy Collaboration et al. 2018), IDL Astronomy Library: idlastro.gsfc.nasa.gov (Landsman 1993), matplotlib (Hunter 2007), NumPy (Harris et al. 2020), SciPy (Virtanen et al. 2020), Photutils (Bradley et al. 2023), DrizzlePac (Fruchter et al. 2010).

## ORCID iDs

Intae Jung https://orcid.org/0000-0003-1187-4240
Henry C. Ferguson https://orcid.org/0000-0001-7113-2738
Matthew J. Hayes https://orcid.org/0000-0001-8587-218X
Alaina Henry https://orcid.org/0000-0002-6586-4446
Anne E. Jaskot https://orcid.org/0000-0002-6790-5125
Daniel Schaerer https://orcid.org/0000-0001-7144-7182
Keren Sharon https://orcid.org/0000-0002-7559-0864
Ricardo O. Amorín https://orcid.org/0000-0001-5758-1000
Hakim Atek https://orcid.org/0000-0002-7570-0824
Matthew B. Bayliss https://orcid.org/0000-0003-1074-4807
Håkon Dahle https://orcid.org/0000-0003-2200-5606
Steven L. Finkelstein https://orcid.org/0000-0001-8519-1130
Andrea Grazian https://orcid.org/0000-0002-5688-0663
Lucia Guaita https://orcid.org/0000-0002-4902-0075
Göran Östlin https://orcid.org/0000-0002-3005-1349
Laura Pentericci https://orcid.org/0000-0001-8940-6768
Swara Ravindranath https://orcid.org/0000-0002-5269-6527
Claudia Scarlata https://orcid.org/0000-0002-9136-8876

Harry I. Teplitz https://orcid.org/0000-0002-7064-5424

Anne Verhamme https://orcid.org/0000-0002-2201-1865

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