Lyman Continuum Emission from Spectroscopically Confirmed Lyα Emitters at z ∼ 3.1

We present a study of Lyman continuum (LyC) emission in a sample of ∼150 Lyα emitters (LAEs) at z ≈ 3.1 in the Subaru-XMM Deep Survey field. These LAEs were previously selected using the narrowband technique and spectroscopically confirmed with Lyα equivalent widths (EWs) ≥ 45 Å. We obtain deep UV images using a custom intermediate-band filter U J that covers a wavelength range of 3330 ∼ 3650 Å, corresponding to 810 ∼ 890 Å in the rest frame. We detect five individual LyC galaxy candidates in the U J band, and their escape fractions (f esc) of LyC photons are roughly between 40% and 80%. This supports a previous finding that a small fraction of galaxies may have very high f esc. We find that the f esc values of the five LyC galaxies are not apparently correlated with other galaxy properties such as Lyα luminosity and EW, UV luminosity and slope, and star formation rate (SFR). This is partly due to the fact that these galaxies only represent a small fraction (∼3%) of our LAE sample. For the remaining LAEs that are not detected in U J, we stack their U J-band images and constrain their average f esc. The upper limit of the average f esc value is about 16%, consistent with the results in the literature. Compared with the non-LyC LAEs, the LyC LAEs tend to have higher Lyα luminosities, Lyα EWs, and SFRs, but their UV continuum slopes are similar to those of other galaxies.


INTRODUCTION
Lyman continuum (LyC) photons with wavelength λ < 912 Å ionize neutral hydrogen in both galactic and extra-galactic environments.They are considered to originate from two main sources, massive stars in starforming galaxies and active super-massive black holes (SMBHs) in galaxy centers (Vacca et al. 1996;Matthee et al. 2016;Smith et al. 2020).In recent years, studies of the early universe reveal that the intergalactic medium (IGM) began a transition from a neutral state to an ionized state at z ≳ 6 (Fan et al. 2006;Becker et al. 2015;Mason et al. 2018;Keating et al. 2020;Bosman et al. 2022), and sufficient LyC photons are required to complete this reionization process.As the spatial density of AGN/quasars declines rapidly towards high redshift, AGN cannot contribute enough ionizing photons to the UV background at z ≳ 6 (Hopkins et al. 2007;Parsa et al. 2018;Faisst et al. 2022).Jiang et al. (2022) has confirmed from observational data that the AGN population provided a negligible fraction of the total photons required for reionization, and suggested that low-luminosity star-forming galaxies are the dominant ionizing sources.
The contribution of star-forming galaxies critically depends on the fraction (f esc ) of LyC photons escaping into the IGM.It was suggested that f esc ∼10-20% is needed to keep the IGM ionized during the reionization epoch (Finkelstein et al. 2012;Bouwens et al. 2016;Naidu et al. 2020).The required f esc values are also tightly connected with the LyC photon production efficiency in these galaxies.Simulation results have indicated that faint and low-mass galaxies have higher efficiency than brighter and more massive ones (Yung et al. 2020).Nevertheless, the specific LyC contribution of star-forming galaxies remains unclear.
Current searches of LyC emitting galaxies are mainly carried out in two redshift windows.Observations of low-redshift (e.g., z ∼ 0.3 − 0.4) LyC galaxies are made by space telescopes (mainly Hubble Space Telescope, or HST), because they are unfeasible by ground-based telescopes.Several direct detections of low-redshift LyC galaxies show that f esc is around 6-20%.For example, Izotov et al. (2016a) reported a nearby low-mass galaxy with f esc ∼ 8%.Meanwhile, they detected four more LyC galaxies with f esc = 6-13% (Izotov et al. 2016b).Flury et al. (2022) presented a LyC survey of galaxies at z = 0.2-0.4 that detected 35 LyC emitters with high confidence, and 12 of them have f esc ≥ 5 %.These studies usually targeted specific galaxies with strong [O III] line emission that are likely LyC galaxies.
LyC photons from galaxies at z ≥ 3 can be detected by ground-based observations.Steidel et al. (2001) reported the first direct detection of LyC emission from z ≥ 3 galaxies in a composite spectrum.They stacked the spectra of 29 Lyman break galaxies (LBGs) at z ≃ 3.4 and constrained the galaxy contribution to the radiation field.Shapley et al. (2006) detected direct ionizing radiation from two individual galaxies at z ∼ 3.So far, dozens of LyC galaxies have been found using direct, spectroscopic observations in the past ten years (e.g., Mostardi et al. 2013;De Barros et al. 2016;Vanzella et al. 2018;Marques-Chaves et al. 2021).One of the largest samples was provided by the Keck Lyman Continuum Spectroscopic Survey, which detected 15 LyC galaxies at z ∼ 3 and found that their average f esc value was about 9% (Steidel et al. 2018;Pahl et al. 2021).
UV images covering LyC emission provide an alternative method to find LyC galaxies and determine their f esc .Deep UV imaging observations have obtained a number of LyC galaxies or candidates (Vanzella et al. 2012(Vanzella et al. , 2016;;Yuan et al. 2021;Saxena et al. 2022a).These galaxies are often Lyman Break Galaxies (LBGs) or LAEs with strong resonant lines like Lyα.For galaxies that do not show LyC emission in imaging data, image stacking is an efficient approach to derive their average LyC emission, or constrain the upper limit of their LyC emission (Micheva et al. 2016;Grazian et al. 2017;Begley et al. 2022).A reasonable result from previous studies is f esc ≲ 10%.
Due to the increasing IGM opacity, it is very challenging to find LyC galaxies at redshift significantly higher than 3. IGM absorption would result in only a 20% likelihood of detecting LyC leakage from galaxies at z ∼ 4, and a lower probability at higher redshifts (Inoue & Iwata 2008).Therefore, LyC galaxies at z ∼ 3 provide an excellent platform to study the properties of ionizing photons and LyC analogs in the early universe.
Previous studies have shown that f esc is correlated with galaxies properties, and some properties can be used as indirect indicators of LyC leakages.For example, LyC galaxies tend to have high star-formation rates, strong resonant lines, and low metallicities.These properties are similar at both low and high redshifts.Lyα emission is potentially a good indicator, as this resonant line emission implies a low H I density state that can allow LyC photons to escape (Verhamme et al. 2015;Dijkstra et al. 2016).There is a positive correlation between f esc and the Lyα emission line equivalent width W (Lyα) (Steidel et al. 2018;Pahl et al. 2021).In addition, Furtak et al. (2022) found that the blue-peak of Lyα line can be used as a proxy to the LyC emission.A few other emission lines were also reported to be possible indicators of LyC emitters.For example, the [OIII]/[OII] line ratio is likely related with the leakage of LyC photons (Jaskot et al. 2019).Mg II is a resonant line and is likely correlated with with LyC emission at low redshift (Henry et al. 2018;Xu et al. 2022).Furthermore, some LyC galaxies tend to have strong C IV emission lines and very weak S II lines (Wang et al. 2021;Saxena et al. 2022b).It is worth mentioning that some of the above results are not solid yet due to their small sample sizes and large uncertainties.
In this paper, we present a study of LyC emission from z ≈ 3.1 LAEs in the Subaru XMM-Newton Deep Survey (SXDS; Figure 1) field, based on our deep UV imaging observations.The LAE sample consists of ∼200 narrowband selected, spectroscopically confirmed galaxies.The UV filter is a custom filter that covers a restframe 810 ∼ 890 Å for z = 3.1 galaxies.The structure of the paper is as follows.In Section 2, we present our observations and data reduction.In Section 3, we show the main results on individual LyC detections and stacking analyses.We discuss our results in Section 4 and summarize the paper in Section 5. Throughout the paper we use a Λ-dominated flat cosmology with H 0 = 70 km s −1 Mpc −1 , Ω m = 0.3, and Ω Λ = 0.7.All magnitudes are in the AB system.

Observations and Data Reduction
The field that we observed is SXDS.This field has deep optical images in a series of broad and narrow bands taken by Subaru Suprime-Cam (Furusawa et al. 2008) and now by Subaru Hyper-Suprime-Cam (Aihara et al. 2022).The Suprime-Cam imaging data have been widely used to search for LAEs and LBGs at 2 < z < 7 (Ouchi et al. 2008(Ouchi et al. , 2010;;Curtis-Lake et al. 2012;Konno et al. 2014;Matthee et al. 2015;Jiang et al. 2018;Ning et al. 2020;Guo et al. 2020).Our combined images of the Suprime-Cam data reach 27.5 ∼ 28.0 mag in the BV Ri ′ bands and > 26 mag in the z ′ band (Jiang et al. 2018).Guo et al. (2020) selected a large sample of LAE candidates at z ≈ 3.1 based on the images in the B, V , NB497, and NB503 bands, and built a sample of 179 spectroscopically confirmed LAEs.They also built a robust Lyα luminosity function at z ∼ 3.1, which is consistent with previous studies at the similar redshift range (Ciardullo et al. 2012;Sobral et al. 2018).Recently, we obtained 87 more LAEs with spectroscopic redshifts at z ≈ 3.1 in this field.The total number of LAEs at this redshift amounts to 266 and the redshift interval is 3.05 ≤ z ≤ 3.16 (Figure 1).The LAE color selection criterion corresponds to a rest-frame equivalent width EW 0 ≥ 45 Å. AGNs were removed using the optical spectral data and deep X-ray observations (see details in Guo et al. (2020)).We used a custom filter U J to detect LyC radiation from z ≈ 3.1 LAEs.This filter has a wavelength coverage of 3330 ∼ 3650 Å (wavelengths at half maximum; Figure 2) with a full width at half maximum (FWHM) of ∼ 320 Å.It corresponds to a rest-frame wavelength coverage of 810∼890 Å for our LAEs.This range is very close to the Lyman limit and optimizes the detection of LyC emission, because detectable LyC emission decreases rapidly towards short wavelengths due to IGM absorption.The filter was specially designed to have a sharp cutoff at the red end so that the transmission at λ ≈ 3700 Å is nearly zero.This ensures that it does not cover radiation at λ > Lyman limit.We further evaluate non-ionizing radiation that leaks into this filter (referred to as "red-leak") following Smith et al. (2018).We use the SED model spectrum of the galaxies in our sample to quantify the flux from LyC to UV continuum (see SED fitting in Section 3.3).The result reveals that the maximum contribution of nonionizing photons to the filter is only ∼ 0.15% for our sample at z ∼ 3.1, so the effect of the "red-leak" here is negligible.The U J -band observations of the SXDS field were carried out by the 90Prime on the 2.3 m Bok telescope in 2014 and 2015.The 90Prime is a widefield optical imager with a field-of-view of 1 • × 1 • .It was equipped with thin CCDs that were optimized for the UV band (at the time of our observations), so it had a high quantum efficiency at the wavelength range that we probed.The observations were made in dark nights/hours with clear skies.The typical seeing, measured by the point spread function (PSF) in U J , was 1. ′′ 5 ∼ 2. ′′ 0. The typical integration time for individual exposures was 10 min, which ensured that the background noise in the images was dominated by sky background.The total integration time of useful images was 45 hours.
The 90Prime images were reduced in a standard fashion using our own IDL routines.For images taken on each night, we first made a master bias and a master flat image from bias and flat images taken on the same night.We then constructed a bad-pixel mask from the flat image.Bad pixels, saturated pixels, and bleeding trails were later incorporated into weight images.Science images were corrected for overscan and bias, and were flat-fielded and sky-subtracted.We used SCAMP (Bertin 2006) to calculate astrometric solutions and used SWARP (Bertin et al. 2002) to resample and combine all images.The final coadded science image is a weighted average of individual science images, with a native pixel size of 0. ′′ 455.More details can be found in Jiang et al. (2015).

Photometry
In order to measure the photometry of the LAEs in the U J band, we first derived the magnitude zero point of the U J image.It is not straightforward, since U J is a custom filter.We estimated the zero point using SDSS type A5 stars detected in the SXDS field.Figure 2 shows the spectrum of a standard type A5 star.It is quite flat in the wavelength range that U J covers (Gray & Corbally 2002;Allende Prieto & del Burgo 2016), and is thus very suitable for our purpose.Figure 2 also shows that the effective wavelengths of U J and the SDSS u (hereafter referred to as u) are similar.Our procedure consists of two steps.In the first step, we calculated the difference between U J and u for type A5 stars.We collected HST STIS spectra for a sample of A5 stars (Allende Prieto & del Burgo 2016) and found that the average value of their u − U J colors was -0.18 mag.In the second step, we used the SDSS u − g vs. g − r color-color diagram to select type A5 stars or stars with a type close to A5.These stars have nearly the same u − U J color. Figure 3 shows our selection criteria, 0.2<g − r<0.5 and 0.8<u − g<1.2 (Covey et al. 2007).The selected objects are bright and point sources.The U J -band zero point was determined so that the average u − U J color of these objects was -0.18 mag.
We performed U J -band photometry of the LAEs using Python package photutil.The majority of the LAEs were not expected to be clearly detected in U J , so we performed forced aperture photometry based on the object positions from the narrowband images.The aperture size was 3. ′′ 6 in diameter, roughly twice the PSF FWHM.Aperture corrections were obtained from bright point sources and applied to the photometry.The 3σ detection limit is about 26.8 mag.Small spatial offsets among LyC emission, UV/optical continuum emission, and narrowband emission have been found in previous studies (Micheva et al. 2016).Our aperture size is large enough so that these offsets are generally negligible.

RESULTS
As we mentioned earlier, our LAE sample consists of 266 spectroscopically confirmed LAEs in the SXDS field.The U J -band image covers 246 of them.The LAEs were primarily detected and selected based on their narrowband images.They represent the most luminous galaxies in terms of Lyα emission, but they can be very faint in the UV continuum images.We remove 78 LAEs that are fainter than 26.2 mag in the V band (see the upper panel in Figure 4).This selection criterion is determined by the detection limit of the U J -band image that sets a limit for f esc , as shown in the lower panel of Figure 4.In other words, these removed galaxies will not be detected in U J even if their f esc is close to 100%.The f esc limit is calculated using a 3σ detection limit, an average IGM absorption, and an average dust attenuation of E(B − V ) = 0.2.The detailed calculation of f esc is presented in section 3.3.In addition, we remove another 18 LAEs that are apparently contaminated by neighboring objects.Finally, we obtain a sample of 150 LAEs and our following analyses will use this sample.We visually inspect individual LAEs and find that some of them are slightly contaminated by their neighboring objects.For a given LAE, if light of its nearby objects (located outside of the photometric radius) likely reaches our photometric aperture in the U J , we simply model the objects and subtract them before we do photometry for Note-The redshifts are Lyα redshifts from Guo et al. (2020).L900/L1400 and E(B − V ) are obtained from our SED modeling.f abs,m is the escape fraction given by CIGALE and f abs,c is given by our calculation based on the Equation 2. LAE1 has a large and bright neighbor in the Rc, i ′ , z ′ bands, so we do not do SED modeling using its broadband photometry.The upper limits in the table are 2σ upper limits.
the LAE.Deep BV Ri ′ -band images are used to ensure that these nearby objects are real objects.The spatial positions of the LyC emission and UV/optical emission from galaxies are usually consistent with each other.If there are any positional offsets between the two, these offsets are typically smaller than 1 ′′ (e.g., Micheva et al. 2016;Mostardi et al. 2013).We use galfit (Peng et al. 2002) to model nearby objects, and obtain the best-fit positions and profiles simultaneously.A single Sérsic model works well here.

Detections of Individual LyC Galaxies
With the photometric measurements in the U J band, we first identify individual LyC galaxies or candidates.As mentioned earlier, the escape fractions of LyC photons strongly depend on the IGM absorption and dust attenuation.The IGM absorption from z ≈ 3 is substantial.We adopt a criterion of > 3σ detection in U J as the detection of a LyC candidate.With this criterion, we find 5 LyC galaxies.Figure 5 shows the galaxies in three bands, V , narrowband (NB497 or NB503), and U J .Table 1 lists more detailed information about the LyC galaxies.The f esc values will be derived in the following section.As shown in Figure 5 and Table 1, these LyC galaxies are very faint in U J .We also notice that the profile of individual LyC galaxies is non-Sérsic and more irregular than the UV continuum profile.A few of them may have small positional offsets between U J and the other two bands.Such offsets have been reported previously (e.g., Micheva et al. 2016).These phenomena may reflect clumpy and asymmetric structures that create channels for LyC photons to escape from the ISM (Zackrisson et al. 2013;Micheva et al. 2016).
We estimate the possibility of foreground contamination for the LyC galaxies using the deep Subaru imaging data.As we mentioned earlier, these images reach ∼ 27.5 − 28.0 mag.They also have excellent image qualities with PSF as good as ∼ 0. ′′ 5. Therefore, nearby objects with a separation > 0. ′′ 5 can be identified and removed.We calculate the possibility of foreground objects within 0. ′′ 5 from the LyC galaxies.The number counts of z ∼ 3 galaxies are obtained from the ultra-deep VIMOS U -band images in the GOODS-S field (Nonino et al. 2009).Our LyC galaxies have a magnitude range from 25.5 to 26.7 mag in the U J band and the derived surface number density is 145720 deg −2 .Assuming that they are randomly distributed, the calculated probability of foreground contamination for a single object is 0.9%.In our total sample, the likelihood of all five detections being contaminated is 1.1%.If we calculate the contamination rate within the aperture size of 3. ′′ 6 (the size for the U J -band photometry), the contamination rate increases to 6.3% for single objects, which is roughly consistent with the values in Vanzella et al. (2010); Micheva et al. (2016).
We estimate non-ionizing flux at ∼ 1400 Å from the V -band magnitudes provided by Guo et al. (2020).The non-ionizing flux will be used to calculate f esc in the next section.For z ∼ 3.1 LAEs, the Lyα emission line is included in the V band, so we subtract the Lyα contribution from the V -band photometry and obtain nonionizing continuum flux.We measure the Lyα flux using the method given in Guo et al. (2020) and Jiang et al. (2013).The UV continuum and Lyα line emission are modeled as follows, where S Lyα is a model Lyα line profile, β is the UV continuum slope, and A and B are two scaling factors.S Lyα is obtained by co-adding a number of bright Lyα emission lines at z ∼ 3.1, so it has a high S/N.The UV continuum is mainly constrained by the Ri ′ z ′ -band photometry, and the Lyα line emission is mainly estimated by the narrowband photometry.In above procedure, we actually fit the five-band photometry simultaneously.More details can be found in Guo et al. (2020).Figure 6 shows an example of the flux fitting.The results are listed in Table 1.We perform stacking analyses to enhance S/N for the LyC galaxies and to constrain f esc for the remaining galaxies.The stacking procedure will average out the LyC emission from different galaxies and smooth out the variation of the IGM transmission along different lines-of-slights.We first stack the 5 LyC candidates, and the procedure is straightforward.We cut U J -band stamp images for the galaxies.The central positions of the stamp images are determined by the galaxy positions in the corresponding narrowband images.The stacked image is shown in Figure 7.The S/N of the LyC detec- tion in this figure is greater than 8, suggesting that the individual LyC detections are reliable.

Stacking Analyses
Next, we stack the remaining 145 galaxies that are not detected in the U J image.We first combine all 145 galaxies, and the procedure is similar to the above procedure.To efficiently remove outliers, we use sigma-clipping (3σ) to exclude the brightest and faintest pixels when combining images.No detection is found in the center of the combined image.We then divide the sample of the 145 galaxies into 3 groups, including a bright group, a medium group, and a faint group, based on their Vband magnitudes.The galaxies in the individual groups are combined separately, and no detection is found in any of the three combined images.The result is similar to some results in previous studies (Siana et al. 2010;Micheva et al. 2016;Grazian et al. 2017;Saxena et al. 2022a).
For the non-detections in the stacked U J images, we calculate their 2σ upper limits.For each stacked image, we generate ∼ 3000 mock galaxies with magnitudes ranging from 25 to 29 mag.The galaxies are randomly placed on the image.We then perform forced aperture photometry on these sources as we did for real galaxies.By fitting the measured magnitudes and uncertainties, we determine the 2σ upper limit.The results are listed in Table 1.These limits reveal that the overall LyC escape fraction is very low.
We also stack the V -band images to obtain nonionizing flux for the three individual groups.The procedure is the same as we did for the U J -band images, and we also use sigma-clipping (3σ) to exclude outlier pixels.The measurement results (including upper limits) for ionizing and non-ionizing flux in the stacked images are are listed in Table 1 and will be used in the following calculations.

LyC Escape Fractions
We calculate LyC escape fraction f esc using the ionizing and non-ionizing flux obtained earlier.The escape fraction f esc is defined as where f LyC,obs /f UV,obs and f LyC,intr /f UV,intr are respectively the observed and intrinsic flux ratios of ionizing to non-ionizing photons, A UV is the dust attenuation at 1400 Å that can be corrected by dust attenuation law (Calzetti et al. 2000), and τ IGM is the IGM optical depth.We may also define relative escape fraction f esc,rel that assumes no dust extinction (Steidel et al. 2001), Intrinsic flux ratios are roughly between 0.14 and 0.5 in star-forming galaxies with standard stellar populations and different burst ages (ranging from 1 Myr to 0.2 Gyr) (e.g., Bruzual & Charlot 2003;Grazian et al. 2017;Rivera-Thorsen et al. 2022).We perform SED modeling on individual galaxies to derive their intrinsic flux ratios and other properties.These galaxies have broadband photometry in the B, V, R, i ′ , and z ′ bands.Their near-infrared photometric data (J, H, K bands) are obtained from the UKIDSS Ultra-Deep Survey.We model their broadband SEDs using Code Investigating GALaxy Emission (CIGALE; Boquien et al. 2019;Burgarella et al. 2005).Figure 8 shows an example.We apply a SB99 model with the Salpeter IMF (α = 2.35) and a low metallicity of Z = 0.004.The dust reddening E(B − V ) is set to range from 0-1, and the Calzetti et al. (2000) law is used for dust attenuation.We also replace the IGM absorption model in CIGALE with the model in Inoue et al. (2014).We mainly use the SED modeling to obtain dust attenuation and intrinsic flux ratios.The modeling results show that the E(B − V ) values of our LyC galaxies are in the range of 0.1-0.25,suggesting low dust extinction in these galaxies.The derived escape fractions (denoted as f esc,m ) are shown in Table 1.
We also use Equations 2 and 3 to directly calculate the escape fraction (f esc,c ) and apply the IGM model in Inoue et al. (2014).The calculated f esc,c values are between 39% and 84%, comparable to the f esc,m values of 49%-82% derived above.The results are shown in Table 1.As we can see, these galaxies have very high LyC escape fractions, but the fraction of such galaxies among the whole sample is only ∼ 4%.
Finally, we stack broadband images to produce a composite SED for all other galaxies that were not detected in U J , and then measure its f esc by modeling this SED.The combined U J -band photometry is its 2σ upper limit.The redshifts of all the galaxies are in a small range, so the redshift different is neglected when we combine the images and model the SED.The result is f esc,c < 16% (f esc,m < 11%).We further calculate f esc for the three subsamples using the same method, and the values are listed in Table 1.The difference between the subsamples is primarily dependent on the sample size.These results are generally consistent with previous results in the literature, including f esc,rel < 12% in Guaita et al. (2016), f esc < 14% in Micheva et al. (2016), f esc < 9% in Steidel et al. (2018), and f esc < 11% in Saxena et al. (2022a).The detailed dependence of f esc on galaxy properties will be discussed in the following section.
It is worth noting that we have used an average or uniform IGM absorption in the above calculation of f esc .However, IGM absorption has large line-of-sight variations, and galaxies surrounded by more transparent environments tend to have higher LyC escape fractions (Bassett et al. 2021).Therefore, the usage of a uniform IGM absorption or transmission introduces bias for individual LyC or LAE detections (Fletcher et al. 2019;Byrohl & Gronke 2020;Bassett et al. 2021;Yuan et al. 2021).This is particularly important for the five LyC galaxies here.Following previous studies (e.g., Inoue & Iwata 2008;Inoue et al. 2014), we perform Monte Carlo simulations of the IGM transmission by generating 1000 different lines-of-sight (LoS) towards z ∼ 3.1 to estimate the uncertainty.For each LoS, we determine the column density (N HI ), redshift (z HI ), and Doppler parameter (b) distribution of the HI clouds based on the given distributions in the literature.We then calculate the average IGM transmission and dispersion as T IGM = 0.23 ± 0.02 in the wavelength range covered by the U J filter.The results are similar to those in previous studies (Inoue & Iwata 2008;Grazian et al. 2016;Bassett et al. 2021).The IGM absorption exhibits a stochastic nature due to its strong dependence on encounters with dense clouds (N HI > 10 16 ).The final f esc error takes into account all above errors from the photometry, SED modeling, and simulations of the IGM absorption.Our LyC candidates either have intrinsically high f esc or have special environmental conditions.For example, a clear IGM path can be caused by a nearby AGN (Yuan et al. 2021).In addition, f esc can also be overestimated by the average model if the intrinsic ionizing to non-ionizing flux ratio is higher than usual.In this section we discuss possible correlations between f esc and other galaxy properties, including UV continuum emission and continuum slope β, Lyα line emission and EW, star-formation rate (SFR), etc.These properties of our galaxies are listed in Table 1.Most of them are taken from Guo et al. (2020), and the SFRs are from our SED modeling results.One galaxy (LAE1) is close to a much brighter object, and its photometry in long wavelengths is severely affected by this object, so it is not included in most of the following discussions.The correlation results are shown in Figure 9.The two columns in the figure show the model-based f esc (f esc,m ) and directly measured f esc (f esc,c ), respectively.The two sets of measurements are generally consistent with each other.
We first discuss a possible selection effect for our individual LyC galaxies, as shown in the lower panel of Figure 4. Due to the flux limit in the U J and V bands, the LyC detection limit is a strong function of the V -band magnitude.In Figure 4, the individual LyC galaxies are all well above the limit, so this detection limit has a negligible effect on the analyses of the individual LyC galaxies.Furthermore, the limit for the stacked images is very low, so it has a negligible effect when we compare LyC galaxies and stacked non-LyC galaxies below.
Figure 9 shows that, for the individual LyC galaxies, f esc does not significantly correlate with any other properties in the figure.This is partly due to two reasons.One is that the measurement uncertainties of the individual objects are large.The other one is these galaxies represent only a small fraction of our LAEs.Steidel et al. (2018) and Pahl et al. (2021) found that f esc is positively corrected with EW.The EW range in their samples is ∼ 10 − 40 Å.The LyC galaxies in our sample have much larger EWs around 70 − 350 Å, and thus we are not able to draw a conclusion based on this small sample.The correlation coefficient of the SFR and f esc is r ∼ 0.65 while the β is r ∼ 0.8.The weak correlations are not confident due to large uncertainties.Therefore, we mainly compare the LyC galaxies with non-LyC galaxies shown in Figure 9 below.
Compared with the non-LyC galaxies in our sample, the LyC galaxies tend to have higher Lyα luminosities or EWs.This is consistent with previous results that strong Lyα emission is likely an indicator of the LyC leakage.We also divide the non-detections into three subsamples with the same size based on their Lyα EW.We still find no detection in the stacks of these subgroups and the upper limits exhibit little variations with different EW groups.Previous studies also suggest that Lyα luminosity or EW alone is not enough to indicate a LyC leakage (e.g., Bian & Fan 2020;Ji et al. 2020).The combination with a specific Lyα profile, such as a blue peak emission line, can be an additional proxy to search for LyC galaxies (e.g., Furtak et al. 2022).But the blue-peak feature is rare and is not found in our sample.Figure 9 also shows that the LyC galaxies tend to have higher SFRs.This likely reflects the higher Lyα luminosities or EWs above.
Some previous studies reported a correlation between f esc and UV slope β in low-redshift galaxies (e.g., Flury et al. 2022;Chisholm et al. 2022).They found a strong trend that galaxies with steeper slopes have higher f esc and suggested that LyC galaxies tend to have β ≤ −2.In our sample, the slopes of the LyC galaxies are roughly consistent with the non-LyC galaxies.A larger and more representative sample of LyC galaxies is needed.
Previous works also suggested that the LyC escape fractions of star-forming galaxies have a bimodal distribution.The majority of star-forming galaxies have f esc < 10%, while a small fraction of them have much higher f esc .Galaxies with significant LyC detections are rare, but may provide a large fraction of ionizing photons for cosmic reionization (Naidu et al. 2020).Our result tends to support the claim of the f esc bimodal distribution.

SUMMARY
We have presented a study of LyC emission from spectroscopically confirmed galaxies at z ∼ 3.1 in the SXDS field.The galaxy sample consists of ∼150 LAEs and represents the brightest galaxies in terms of Lyα emission.We obtained deep UV images using a custom filter U J that covers a rest-frame range of 810∼890 Å for z = 3.1 galaxies.Five LyC galaxy candidates were detected with S/N > 3 in U J .We estimated their LyC escape fractions using two different methods, including direct calculations and SED modeling.Their escape fractions f esc are roughly between 40% and 80%.We stacked images for the remaining LAEs that were not detected in U J , but did not detect any significant signals in the stacked images.We then estimated the upper limit of For Lyα emission and EW, the triangles show their median values (see Table 1).
their average LyC escape fraction and found f esc < 16%.Our results are generally consistent with previous studies and support a previous claim on the two populations of galaxies: most of the galaxies have small f esc while a minor of galaxies have large f esc .
We have also measured the galaxy properties of this LAE sample, including Lyα emission line luminosity and EW, UV continuum luminosity and slope, and SFR.We discussed their potential correlations with f esc and found that f esc of individual LyC galaxies does not have a strong correlation with these properties.This is likely due to the small size of the sample and the large measurement uncertainties.Compared to the nondetections, however, the LyC galaxies have higher Lyα luminosities, EWs, and SFRs, which is consistent with previous studies.The correlation between UV slope and f esc is not obvious.
Our work adds a sample of individual LyC detections at z ∼ 3. A larger and deeper sample is needed to pro-vide stringent constraints on the relation between f esc and other galaxy properties.In the near future, the China Space Station Telescope (Zhan 2021) will cover ∼400 deg 2 of its deep survey area in the NUV/UV and optical bands.It will provide tens of thousands of LyC detections at z ≤ 3 that should be sufficient for us to achieve robust relations between f esc and galaxy properties.

Figure 1 .
Figure 1.The combined UJ-band image in the SXDS field.The dots represent spectroscopically confirmed LAEs at z ≈ 3.1.The color bar indicates redshifts.

Figure 2 .
Figure 2. Filter transmission curves and a typical spectrum for type A stars.The red curve shows the transmission curve of the UJ filter, which is compared with the SDSS u filter in blue.The Subaru V filter is used to estimate the non-ionizing flux.The transmission curves have included the CCD response curves.The dashed line represents a typical A5 star spectrum.The vertical lines indicate the Lyman limit and Lyα emission at z = 3.1, respectively.

Figure 3 .
Figure 3.The SDSS color-color diagram of bright point sources in the SXDS field.The red rectangle is the selection area for type A stars.The color bar indicates the UJ magnitude.

Figure 4 .
Figure 4. LAEs used in this work.The upper panel shows the V -band magnitudes and redshifts of the LAEs.The symbols indicate all LAEs in SXDS.The dashed line is our selection criterion of V = 26.2mag.Galaxies brighter than V = 26.2mag (in blue) are used in this work.The red crosses represent the galaxies that are rejected due to the contamination from their neighbors in the UJ band.The lower panel shows the detection limits of fesc for the individual LyC galaxies and stacked galaxies assuming an average IGM absorption and an average dust attenuation (see details in section 3).

Figure 5 .
Figure 5. Five LyC galaxies in the V , narrowband (NB497 or NB503), and UJ bands.Nearby objects in the UJ images have been modeled and subtracted.The size of the images is 8 ′′ × 8 ′′ .The red circles in the third column are the aperture used for photometry.

Figure 6 .
Figure 6.Example of our measurement of the Lyα and continuum emission.The red dots show the photometric data points and the horizontal bars indicate their wavelength coverages.The solid line is the best-fit model that combines the Lyα and continuum emission.

Figure 7 .
Figure 7. Median stack of the 5 LyC candidates in the UJ band.The image size is 13.′′ 5 × 13. ′′ 5. Nearby objects have been subtracted.The right panel is a smoothed image.

Figure 8 .
Figure 8. SED modeling of LAE3 and the composite SED.In each panel, the purple circles with error bars represent observed broadband photometry, the black spectrum is the best-fit model, and the red dots are the photometry from the best-fit model.The green curve is the best-fit model without correction for the IGM absorption.We have excluded the Lyα emission line in the fitting process.
Correlations between f esc and Galaxy Properties

Figure 9 .
Figure 9. Relations between the escape fraction (fesc,m and fesc,c) and other galaxy properties, including Lyα emission line luminosity and EW, MUV, SFR and UV slope β.The solid circles represent the five individual LyC galaxies, and the empty ones are the two possible detections.The triangles represent the upper limits from the stacked images for non-detections in UJ.For Lyα emission and EW, the triangles show their median values (see Table1).

Table 1 .
Results of the LyC Measurements