Lyman Continuum Galaxy Candidates in COSMOS

High-resolution HST data are required for this work to identify any potential low-redshift contaminants along the line of sight. The new HST data presented here were taken in Cycle 25 (GO 15100; PI: Cooke; 30 orbits) in three blocks between 2018 February 21 and 2018 April 15. The data were taken using two filters in parallel: F336W on the Wide Field Camera 3 (WFC3)/UVIS and F435W on the Advanced Camera for Surveys (ACS)/WFC.

For galaxies at z = 3–5, LyC flux (<912 Å) is cleanly sampled in the WFC3/F336W band at z > 3.087 and the ACS/F435W band at z > 4.391. These limits assume a <0.3% red leak (≳8 mag fainter than the UV continuum) as used in Smith et al. (2018), and we refer to these limits as z_lim. Figure 1 shows an LBG composite (∼200 spectra binned by Lyα strength) from Shapley et al. (2003). The LBG composite is redshifted to z_lim = 3.087 (gray) and z_lim = 4.391 (black). Transmission curves for photometric bands used in this work are overlaid. The HST bands WFC3/F336W, ACS/F435W, ACS/F606W, and ACS/F814W and three ground-based Hyper-Suprime Cam (HSC) bands, g, r, and i, are shown. We also highlight key features on the LBG template at z = 4.391 (black) with vertical dark blue lines: the Lyman break at rest ∼912 Å (dashed), Lyα at rest ∼1216 Å (dotted–dashed), and nonionizing UV continuum at rest ∼1500 Å (dotted).

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The 30 orbits of HST data were originally intended to be taken in two F336W pointings with two parallel F435W pointings. Given observation scheduling constraints, the first F336W pointing (F336W_1) was observed in two overlapping visits with different position angles (PAs) for a total of 15 orbits. This means that the parallel F435W pointings are split up into F435W_1a (five orbits) and F453W_1b (10 orbits). The second F336W pointing (F336W_2) and F435W parallel (F435_2) both include the full 15 orbits. The total area of all pointings is ∼40 arcmin² at various depths. Figure 2 shows all five HST pointing footprints (two F336W and three F435W), with names and respective orbit depths, overlaid on the COSMOS-ACS/F814W background image cutout (Koekemoer et al. 2007). We also show the CANDELS-ACS/F606W (Grogin et al. 2011; Koekemoer et al. 2011) footprint (light green) overlaid.

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We use full-orbit exposures to reduce the total background contribution caused by postflashing each exposure to 12 e⁻ (as recommended in Anderson et al. 2012). The longer exposures also reduce read noise and maximize the counts per exposure for faint sources. This enables improved charge transfer efficiency (CTE) correction, which is better suited for higher count levels. We use a five-point dither pattern per visit to subsample the point-spread function (PSF). We employ a larger dither pattern between each visit to remove the chip gap and low-level, large-scale pattern noise (Rafelski et al. 2015). The total exposure time of both F336W pointings shown in Figure 2 is ∼44,000 s. The exposure time of the deepest F435W pointing (F435W_2) is ∼40,000 s, and this exposure time is split by a 1:2 ratio between F435W_1a and F435W_1b, respectively. See Table 1 for a summary.

Table 1. HST Image Properties and Contamination Probabilities in the LyC Filters (F336W or F435W)

Filter	No. Orbits	Exposure	5σ Depth a	PSF FWHM	Zeropoints	LyC Contamination b
		Time (s)	(mAB)	(003 pixels)	(mAB)	Probability
COSMOS-ACS/F814W c	1	2028	27.20	3.9	25.952	⋯
CANDELS-ACS/F606W d	2	3300	28.50	3.8	26.491	⋯
New ACS/F435W_1a	5	13,326	28.52	3.3	25.650	0.025
New ACS/F435W_1b	10	26,652	29.11	3.4	25.650	0.018
New ACS/F435W_2	15	39,978	29.78	3.4	25.650	0.013
New WFC3/F336W_1	15	44,091	29.77	3.0	24.689	0.050
New WFC3/F336W_2	15	44,091	30.11	3.0	24.689	0.014

Notes.

^a The rms depth measured within a 02 radius aperture. ^b Probability of a 3σ contamination within a 05 aperture in the LyC band. ^c Koekemoer et al. (2007). ^d Grogin et al. (2011) and Koekemoer et al. (2011).

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Given the faint nature of potential LCG candidates in the rest far-UV (FUV), having the best-quality HST images is essential. We therefore make several improvements to the standard Space Telescope Science Institute (STScI) WFC3/UVIS reduction pipeline to clean and calibrate our images beyond what was previously available from the Mikulski Archive for Space Telescopes (MAST). We also develop and apply new additional calibrations to the CTE-corrected single-exposure calibrated images (called FLCs). Some of these improvements have been added to the standard WFC3/UVIS MAST pipeline (detailed in Section 2.2.1), while others are additional calibration improvements (outlined in Section 2.2.2). We provide further information and plots (Figure A1) to demonstrate our improvements in Appendix A.

2.2.1. HST/WFC3 Darks Pipeline Improvements

2.2.2. Additional Calibrations

2.3.1. Ancillary Data

2.3.2. Creating Mosaics

2.4.1. Point-spread Functions

2.4.2. Isophotal Flux Measurements

2.4.3. LyC Contamination Calculations

2.4.4. Ground-based Photometry

As seen in Figure 2, not all of our HST images are covered by CANDELS-F606W that we use in our analysis of LCGs. For F435W_2, we require ground-based data that span the field and a similar wavelength range as F606W for making color–color plots for illustrative purposes rather than sample selection. We opt to use HSC on the 8.2 m Subaru telescope on Maunakea. The HSC Deep+UltraDeep coverage of COSMOS (Public Data Release 2; Aihara et al. 2019) ²¹ has depths of 28.4 mag in g, 28.0 mag in r, and 27.7 mag in i (bands shown in Figure 1). We take the seeing FWHM values from Aihara et al. (2019) of 061 for HSC-r and 081 for HSC-i and create a Gaussian PSF for each band. We then create a convolution kernel to PSF-match the F435W images to the HSC-i band.

Due to the large size of the ground-based PSFs relative to the HST bands, when convolving the F435W band to the HSC-i PSF, the flux from the faint sources that we are interested in is lost altogether. We therefore derive a correction to convert the F435W isophotal fluxes to 1'' aperture– and HSC PSF-matched fluxes. We achieve this by measuring 1'' aperture fluxes on our F435W image convolved to the HSC-i PSF for all sources. We then plot the HST isophotal fluxes against all of the valid PSF- and aperture-matched F435W fluxes and derive the following relation for converting between the two:

$$\begin{eqnarray}&&{F}_{{\rm{F}}435{\rm{W}},1^{\prime\prime} \mathrm{ap}}=0.6{F}_{{\rm{F}}435{\rm{W}},\ \mathrm{iso}}+0.063.\end{eqnarray} \tag{ 1 }$$

Here F_F435W,1''ap is the F435W flux measured in 1'' apertures from the HSC-i PSF-matched image, and F_F435W,iso is the measured F435W isophotal flux. We apply this correction to the F435W isophotal fluxes to convert them to 1''-aperture HSC-i PSF-convolved fluxes so that they can be directly compared to the ground-based HSC bands.

To select LCGs, we require a sample of high-redshift galaxies not selected with the Lyman-break technique. We use ZFOURGE (Straatman et al. 2016) as our primary source of redshifts, as it comprises 30 bands of imaging, including medium IR FourStar bands (Persson et al. 2013) from the 6.5 m Magellan Baade telescope at Las Campanas Observatory. These medium IR bands accurately sample the region around the Balmer break for well-constrained photometric redshifts (δz ∼ 2% quoted accuracy; Straatman et al. 2016) of 1 < z < 4 galaxies (van Dokkum et al. 2009). ZFOURGE spans a roughly 11' × 11' (13' × 13' with dithering) region of COSMOS (yellow footprint in Figure 2). As shown in Figure 2, the ZFOURGE footprint does not span the full area of our new HST F435W images (blue footprints), with about one-third of F435W_1b and F435W_2 outside the ZFOURGE area.

The ZFOURGE is useful in the search for LCGs, as these medium bands sample the Balmer break. This means that we are less dependent on the Lyman break, which may be less prominent in these galaxies, for determining photometric redshifts. Strong emission lines can bias photometric redshift measurements. Narrow bands that are sensitive to emission were omitted in the ZFOURGE photometric redshift calculations; the medium bands are less sensitive to emission and were included but may still bias the results. We therefore draw from multiple redshift sources where possible for selecting LCG candidates.

Then ZFOURGE sources are K_s band–selected in images with 5σ depths of 26.2–26.5 mag at a typical seeing of ∼04. As ZFOURGE galaxies are K_s band–selected, the candidates must be sufficiently bright in this red band to be detected, and we will miss some faint bluer sources. We therefore collate other available redshift information in the COSMOS field to construct a more complete parent sample. These include photometric redshifts from the COSMOS2015 catalog (Laigle et al. 2016) and the CANDELS catalog of COSMOS (Nayyeri et al. 2017).

We compiled a catalog of available spectroscopic redshifts in the field from 3D-HST (Brammer et al. 2012; Momcheva et al. 2016), CANDELSz7 (Pentericci et al. 2018), DEIMOS 10K (Hasinger et al. 2018), DEIMOS-C3R2 (Masters et al. 2017), IMACS (Trump et al. 2009), FMOS (Kartaltepe et al. 2015), FORS2 (George et al. 2011; Comparat et al. 2015), GEEC2 Gemini-S GMOS (Balogh et al. 2014), hCOSMOS (MMT/Hectospec; Damjanov et al. 2018), LEGA-C (VLT/VIMOS; van der Wel et al. 2016), MOSDEF (MOSFIRE; Kriek et al. 2015), PRIMUS (Magellan/IMACS; Coil et al. 2011; Cool et al. 2013), VUDS (VLT/VIMOS; Le Fèvre et al. 2015), zCOSMOS, and zBRIGHT (VLT/VIMOS; Lilly et al. 2009). We note that many targets in spectroscopic surveys are preselected using color selection and photometric redshifts. Many of these are biased toward objects with the strongest Lyman breaks. Therefore, many of the publicly available spectroscopic catalogs may be biased against bright leaking LyC.

We first spatially crop all catalogs down to our region of interest (shown in Figure 2). We then cross-match the redshift catalogs within 1'' apertures (05 search radii). We start by matching everything in COSMOS to ZFOURGE, then add any candidates from COSMOS that do not overlap. We then cross-match the other catalogs, starting with CANDELS, and then the spectroscopic redshift catalog. The CANDELS catalog contains photometric redshifts produced by six different authors and methods with the same data. We therefore calculate an average CANDELS photometric redshift (as shown to be most accurate in, e.g., Dahlen et al. 2013; Barro et al. 2019) and standard deviation of the available redshifts and use both in our redshift constraints for selecting our samples.

Within our F336W and F435W footprints, there are 8311 unique sources at all redshifts (our "all-z sample"). This reference sample splits into 3065 objects in the F336W footprints and 6430 sources in the F435W footprints (with overlap). We create a comprehensive "parent sample" from the all-z sample by selecting all objects from the catalogs with a redshift above the LyC z_lim for the F336W or F435W filters. We remain as agnostic as possible at the candidate selection phase and include any galaxy in the parent sample that has at least one redshift to place it above z_lim for F336W or F435W to probe LyC. The CANDELS redshift constraint we use for selecting our parent sample was our calculated average minus one standard deviation of the CANDELS photometric redshifts. There are 574 unique objects in the parent sample: 380 objects have at least one redshift z > 3.087 and are in the F336W footprints, and 242 objects have at least one redshift z > 4.391 and are in the F435W footprints (with overlap).

We visually inspect all objects in the parent sample with at least three different investigators examining each. We inspect the sources in all four HST bands described here and their NEQ and source-detection segmentation maps to evaluate whether there is any visible LyC flux. If any of the investigators notes a detection of possible flux in the filter probing the rest-frame LyC (F336W and/or F435W), they are reevaluated multiple times. We remove any obvious erroneous redshifts (large bright local galaxies, star spikes, and bright saturated stars) from the sample. We end up with a long list of 77 unique objects that have varying degrees of confidence both in their LyC detection (strength, offset, confusion over the source for close objects) and in redshift. We rank these candidates based on their number of visual confirmations, LyC confidence, and redshift confidence. All 77 sources are used as potential candidates for spectroscopic follow-up to remain as agnostic as possible and because a relatively high density on the sky is required for multiobject slit spectroscopy (MOS).

We present Keck/LRIS data of our LCG candidates taken on 2016 February 9 and 10 (2016A_W034LA; PI: Cooke) and 2020 January 20–22 (2019B_N010; PI: Rafelski). We require good seeing (<1''), clear skies, and dark nights for our observations. To spectroscopically detect the LyC, we require the objects to have optical magnitudes of ∼24 mag. We then need around a half night (∼6 hr) in our optimal conditions to achieve spectroscopic detection of LyC flux. This assumes that there is no contamination from neighboring sources or LRIS detector issues. The conditions for the 2016 run were relatively poor, spread over 2 nights, but we were able to obtain some usable exposures for zf_9775. In 2020, ∼80% of the time was usable but with a relatively poor average seeing of ∼12 (relative to what is possible at Keck). This poorer seeing disperses light over the edges of the LRIS slit and therefore increases the exposure time required to get sufficient S/N.

The LRIS instrument uses precut metal masks with slits to disperse the light of our targets across blue and red spectroscopic arms. We use the 400/3400 grism on the blue side and the 400/8500 grating for the red side with the 560 dichroic. We create LRIS masks with the autoslit software. The slit widths are ∼12, and longer-length slits are preferred to improve background subtraction. The masks are designed to encompass as many of our high-priority candidates as possible. We fill any remaining space with lower-priority LCG candidates and fillers that include extreme emission-line galaxies, Lyα emitters, and LBGs. We then select at least four stars, and ideally five to six, placed as near as possible to the edge of the LRIS masks for acquisition on the sky and mask alignment.

The highest-priority objects are placed as close to the north of the detector (with PA = 0) as possible due to amplifier issues with the red side. At the time of observations, both chips could not reliably be read out, leaving no coverage at redder wavelengths for half the mask. The best objects are placed in the central third of the detector, when possible (in x and y), to accommodate full wavelength coverage and minimize instrument distortion at the edges. With an optimal distribution on the sky, ∼25 candidates fit on a mask, including ∼five high-priority targets. However, when factoring in all of the observational constraints, fewer than that are often in the prime detector and dispersion positions. We aim to observe each mask for a total of ∼6 hr in 1200 s exposures to reduce data loss in variable weather conditions and contamination by cosmic rays. Typically, we observed just a few hours per mask, if at all.

The Keck/LRIS spectra are reduced using IRAF (Tody 1986) following the standard reduction procedure for multislit spectroscopy. We also use twilight flats to aid with the blue flux calibrations. A 2 × 2 binning was used for the 2016 observations, and a 1 × 1 binning was used for the 2020 data.

The Keck/LRIS observations yielded redshifts for three LCG candidates: zf_9775, zf_11754, and zf_14000. Only 14 (seven >3σ in F336W/F435W) galaxies from our long candidate list were successfully observed due to the weather conditions limiting the number of masks we could observe and their spatial distribution. We present spectra for three of the >3σ candidates but were unable to get redshifts for the other four observed. A full analysis of the spectroscopic properties of the candidates (e.g., Lyα profiles) is planned to be presented in a future paper. Sources with confident spectroscopic LRIS redshifts and nondetections of LyC are the focus of another paper (Meštrić et al. 2021).

Figure 3 shows 3 pixel boxcar-smoothed LRIS spectra (black) and a composite of ∼200 LBGs with a similar Lyα strength to the galaxy overlaid (blue; Shapley et al. 2003). The postage stamps on the left show the LRIS mask slits (top; 30'' across) and candidate orientation (bottom; 5'' across). Below each spectrum, we show zoom-ins on some spectroscopic features. We also highlight other spectroscopic features with shading: the UV continuum redward of Lyα (≳1216 Å; yellow), the Lyα forest (green), the Lyβ forest (violet), and the LyC (<912 Å; blue panel).

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To determine redshifts for the candidates, we compare each spectrum to an LBG composite from Shapley et al. (2003) and look at the fit to the profile of the UV continuum. We also investigate all of the highlighted spectroscopic information available, including the flux decrement as a result of the Lyα forest, the presence of a Lyα emission/absorption feature, and the fit to ∼6–12 interstellar medium (ISM) absorption features (depending on the wavelength coverage of the spectrum). We summarize the properties of the three spectra shown in Figure 3 and the redshifts we determine from each below.

• 1.  
  zf_9775. We show the blue and red halves of the 2016 LRIS spectrum. The profile of the LRIS spectrum matches the LBG composite, with distinctive breaks and ∼10 well-aligned common strong UV ISM absorption features, all assessed to determine the redshift (e.g., see zoom-ins below). This spectrum has a confident redshift of z = 4.365 (with δz ∼ 0.003 for all spectra). However, there is some ambiguity over the nature of this detection. The spectrum is dominated by the optically bright component (left), and we are unable to resolve the component emitting the blue flux (right; see components in Figure 4). Therefore, zf_9775 remains a spectroscopic candidate rather than a confirmed LyC detection.
• 2.  
  zf_11754. We show just the red side of the spectrum, as the blue side is contaminated by the close bright source in the upper right part of the postage stamp. The red half of the spectrum shows a distinct Lyα line (panel below) and a break on either side from the UV continuum (yellow) to Lyα forest (green). We are confident in the redshift from the red side of the spectrum of z = 4.470 (using ∼six common ISM lines). However, due to the blue side contamination and the fact that it is so close to the other source, there remains some ambiguity as to the nature of the LyC detection seen in the HST F435W images. This contamination could be increasing the blue flux through the Lyα forest (green) and even redward of Lyα. The red side of the spectrum also shows some deviation from the composite that could be real (i.e., a very young population of stars and clean line of sight) or a product of extraction with such a close neighboring source. Therefore, zf_11754 remains a spectroscopic candidate rather than a confirmed detection.
• 3.  
  zf_14000. There is a tentative broad feature that could be Lyα, and it exists at a slight break in the spectrum between what would be the UV continuum (yellow) and Lyα forest (green). This smaller decrement, if it is indeed a physical Lyα forest, could be due to the source being observed along a cleaner line of sight. This could be the case if considering the strong LyC detection, which would require a high IGM transmission sight line. There is contamination seen in the 2D spectrum (upper line) due to slight slit drift throughout the observations from alignment star catalog inconsistencies or length of observations. However, the upper line does not affect the extraction of zf_14000 due to their sufficient separation. The tentative redshift we determine for this source is z = 3.727, and it remains a spectroscopic candidate rather than a confirmation. We rule out the possibility that this object is a star, as its blue temperature is consistent with it being a K star, but the spectrum does not support that. Its spectral energy distribution (SED) is also not consistent with a late M-type star. Most catalogs list this source as nonstellar, but they do have a variety of redshifts (z = 0.301–3.953; see Table 5). For it to be a K4–M0 star, it needs to be 30–128 kpc away to be as faint as it is. Only the reddest M dwarf would be realistic (at ∼2–10 kpc), and they are too red for the SED.

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Table 5. LCG Candidate IDs, Coordinates, Assigned Groups, LyC Band and Limit, and Redshifts

ID a	Group b	R.A.	Decl.	LyC c	zlim d	zphot e	zphot f	$\overline{{z}_{\mathrm{phot}}}$ g	Δzphot h	zspec i	zspec j	zconf k
				Pointing		(ZF)	(CS)	(CA)	(CA)	(Lit.)	(LRIS)
zf_9775	A	150.102478	2.281554	F336W_2	3.087	4.266	4.246	4.231	0.074	0.446 l	4.365	1
zf_11754	A	150.047912	2.303804	F435W_2	4.391	4.453	0.705	⋯	⋯	⋯	4.470	1
zf_14000	A	150.208221	2.328479	F336W_1	3.087	3.953	0.301	⋯	⋯	3.779 m	3.727	1
zf_11423	B	150.201065	2.300642	F336W_1	3.087	0.796	0.716	0.813	0.094	3.655 m	⋯	2
zf_12283	B	150.192413	2.309807	F336W_1	3.087	3.520	0.372	3.592	0.126	⋯	⋯	2
zf_8333	B	150.114257	2.266746	F336W_2	3.087	3.223	3.117	0.285	0.056	⋯	⋯	2
zf_8461	B	150.118164	2.268226	F336W_2	3.087	3.197	0.443	0.350	0.016	⋯	⋯	2
zf_13836	B	150.196579	2.326127	F336W_1	3.087	3.622	⋯	0.338	0.324	⋯	⋯	2
zf_14198	B	150.196670	2.330944	F336W_1	3.087	3.826	2.180	0.619	0.020	⋯	⋯	2
zf_13312	B	150.201431	2.320581	F336W_1	3.087	3.159	3.165	2.748	1.283	⋯	⋯	2
zf_6745	B	150.115646	2.249375	F435W_1a	4.391	5.461	⋯	1.213	0.772	⋯	⋯	2
zf_14060	B	150.211822	2.329048	F336W_1	3.087	3.158	⋯	⋯	⋯	⋯	⋯	2
zf_13676	B	150.220871	2.324596	F336W_1	3.087	4.779	4.557	⋯	⋯	⋯	⋯	2
cs_658350	C	150.207800	2.300505	F336W_1	3.087	⋯	3.171	⋯	⋯	⋯	⋯	3
cs_621227	C	150.106355	2.244453	F336W_2	3.087	⋯	3.931	⋯	⋯	⋯	⋯	3
cs_626018	C	150.111087	2.251412	F336W_2	3.087	⋯	3.578	⋯	⋯	⋯	⋯	3
cs_667332	C	150.035636	2.314277	F435W_2	4.391	⋯	5.419	⋯	⋯	⋯	⋯	3
cs_621890	C	150.121013	2.245430	F435W_1a	4.391	⋯	4.567	⋯	⋯	⋯	⋯	3
cs_681305	C	150.011024	2.334490	F435W_2	4.391	⋯	4.656	⋯	⋯	⋯	⋯	3
zf_8009	C	150.114654	2.263270	F336W_2	3.087	0.833	3.218	0.656	0.328	⋯	⋯	4
zf_9669	C	150.098083	2.280273	F336W_2	3.087	0.415	3.871	0.377	0.029	⋯	⋯	4
zf_12022	C	150.193847	2.306703	F336W_1	3.087	0.652	3.164	0.723	0.038	⋯	⋯	4
zf_14044	C	150.199768	2.32866	F336W_1	3.087	0.545	3.939	0.483	0.017	⋯	⋯	4
cs_671985	C	150.192170	2.321238	F336W_1	3.087	⋯	3.301	2.025	0.565	⋯	⋯	4
zf_9963	C	150.10466	2.284251	F336W_2	3.087	0.332	3.095	0.436	0.052	⋯	⋯	4
cs_643060	C	150.104563	2.277120	F336W_2	3.087	⋯	3.496	0.579	0.194	⋯	⋯	4
cs_723862	C	150.109444	2.398033	F435W_1b	4.391	⋯	5.286	2.249	0.154	⋯	⋯	4
zf_12042	C	150.222595	2.307420	F336W_1	3.087	1.080	4.122	⋯	⋯	⋯	⋯	4
zf_8356	C	150.13797	2.267169	F336W_2	3.087	2.009	3.231	1.303	0.639	⋯	⋯	4
zf_10407	C	150.205856	2.289908	F336W_1	3.087	1.061	3.45	⋯	⋯	⋯	⋯	4
zf_13775	C	150.044174	2.326125	F435W_2	4.391	0.632	4.988	⋯	⋯	⋯	⋯	4
zf_5935	C	150.118850	2.241288	F435W_1a	4.391	2.460	4.807	2.024	0.549	⋯	⋯	4
zf_13099	C	150.195251	2.318458	F336W_1	3.087	0.312	3.453	1.869	1.692	⋯	⋯	4
zf_6857	C	150.125915	2.250819	F336W_2	3.087	2.447	3.227	0.371	0.457	⋯	⋯	4
cs_611354	C	150.107760	2.229506	F435W_1a	4.391	⋯	5.338	1.687	0.369	⋯	⋯	4

Notes.

^a Prefixes show ID and coordinate survey origin (zf_* is ZFOURGE, cs_* is COSMOS). ^b LCG group assigned in this work, described in Section 5.1. ^c HST filter probing LyC flux and the pointing name. ^d Redshift limit above which the LyC filter will cleanly sample LyC flux. ^e ZFOURGE photometric redshift (Straatman et al. 2016). ^f COSMOS2015 photometric redshift (Laigle et al. 2016). ^g CANDELS photometric redshift average (Nayyeri et al. 2017). ^h CANDELS photometric redshift standard deviation (Nayyeri et al. 2017). ⁱ Spectroscopic redshifts from the literature (see Section 3.1). ^j New Keck/LRIS spectroscopic redshift presented in this paper. ^k Redshift confidence parameter defined in Section 5.1. ^l Low-confidence spectroscopic redshift from 3D-HST (Brammer et al. 2012; Momcheva et al. 2016); see Section 4.2 and Appendix B. ^m Low-confidence spectroscopic redshift from DEIMOS 10K (Hasinger et al. 2018); see Section 4.2 and Appendix B.

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Three of the LCG candidates have low-quality ancillary spectra. Two of the spectra place the candidates above the redshift limit of their respective bands for LyC to be detected if present (z_lim), and one places it below z_lim. Two spectra (Figure B1) are from the DEIMOS 10K survey and assigned their lowest-quality redshift flag (hereafter DM18; Hasinger et al. 2018). The spectra are for zf_14000 (DM18 ID: L677152; z_DM18 = 3.779) and zf_11423 (DM18 ID: L658665; z_DM18 = 3.655). There is a tentative feature that could add weight to the LRIS redshift for zf_14000, but with low confidence. The spectrum for zf_11423 shows two very tentative features and conflicts with three photometric redshifts for this source, so we cannot be confident of its DM18 redshift. There is a 3D-HST G141 grism spectrum (Brammer et al. 2012; Momcheva et al. 2016) for zf_9775 (3D-HST ID: 9997; z_3DHST = 0.446) in Figure B2. There are no strong features to provide evidence for either the 3D-HST or LRIS redshift. The 3D-HST value also conflicts with the closely matching independent redshifts from ZFOURGE, COSMOS, average CANDELS, and our confident LRIS redshift (z ∼ 4.2–4.4). We therefore deem the 3D-HST redshift unreliable. See Appendix B for more details.

We refine our LCG candidates and categorize them based on our confidence in their detection and redshift. We select only LCG candidates with 3σ flux detections in their LyC probing band (determined from the available redshifts). We then remove candidates with close neighboring sources (within 12 apertures) and those contaminated by bright saturated nearby stars. To help rule out the possibility that our candidates are active galactic nuclei (AGNs), we check the spectra (where available) for AGN FUV emission features. We then cross-match the candidate list against the public XMM-Newton X-ray (Cappelluti et al. 2009) and Chandra COSMOS legacy (Marchesi et al. 2016) catalogs within 05 radii and find no matches.

This refinement results in a final sample of 35 sources, with 26 sources in the F336W pointings and 9 in F435W. With cross-matching and overlap, our final LCG candidate sample has redshifts from ZFOURGE (25), COSMOS (32), CANDELS (22), the spectroscopic catalog (3), and our new LRIS spectroscopic redshifts (3). This is within just our four untargeted HST fields (∼40 arcmin²).

The three LCG candidates for which we have Keck/LRIS spectra, zf_9775, zf_11754, and zf_14000, are the spectroscopic candidates that we categorize as group A. We then categorize the remaining sample of 32 sources as "photometric" LCG candidates. We define a redshift confidence parameter (z_conf) to categorize the LCG candidates, with z_conf = 1 being most confident and z_conf = 4 being least confident.

• 1.  
  z_conf = 1 (most confident). Has at least one high-quality spectroscopic redshift and at least two redshifts total, both above the redshift for F336W or F435W to probe LyC flux (z_lim). This only applies to the three group A candidates with LRIS spectra.
• 2.  
  z_conf = 2. Has more than two photometric redshifts >z_lim or one or more redshifts from a reliable source >z_lim. We consider a reliable source a tentative public spectroscopic redshift that we have inspected (i.e., zf_11423; see Section 4.2 and Figure B1), photometric redshifts from ZFOURGE or the CANDELS average minus one standard deviation. This is group B, which contains 10 LCG candidates.
• 3.  
  z_conf = 3. Has one photometric redshift >z_lim from a less reliable source (i.e., COSMOS2015, which we found to deviate more from the other available redshifts) and no other redshifts (i.e., not enough information to rule the redshift reliable or not). We place these candidates in group C.
• 4.  
  z_conf = 4 (least confident). Has one photometric redshift >z_lim from a less reliable source (COSMOS2015) and other conflicting redshifts that place the source at <z_lim. We place these candidates in group C along with the z_conf = 3 sources, with a total of 22 LCG candidates.

In Figure 4, we show 3'' postage stamps of the three group A spectroscopic LCG candidates (with z_conf = 1), ordered by magnitude in F814W (m_F814W) from brightest to faintest. In Figure 5, we show the 10 group B photometric LCG candidates ordered by m_F814W (with z_conf = 2, which includes the tentative spectroscopic redshift of zf_11423; see Section 4.2 and Figure B1). In Figure 6, we show our 22 group C photometric LCG candidates (with z_conf = 3 and 4), also ordered by m_F814W.

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For each of the LCG candidate figures, we show the available HST bands for the targets (new F336W and F435W, CANDELS-F606W, and COSMOS-F814W), the NEQ combined image, and the source-detection segmentation map of the NEQ image (NEQ-Seg) used for isophotal fluxes (right stamp). We apply minor smoothing to the blue bands by convolving the images with a 2D Gaussian kernel (1.5 pixel standard deviation) to highlight the often-faint flux. We indicate which of the blue bands contain clean LyC flux if their >z_lim redshifts are accurate. Above the row of stamps for each candidate, we show their IDs, any >z_lim redshifts, the S/N of their LyC flux, z_conf, and m_F814W values. We overplot a 12 aperture for scale. See Figure 2 for the spatial distribution of the candidates split by groups A (with IDs shown), B, and C. See Table 5 for a summary of all of the LCG candidate details and redshift information and Table 6 for their photometry.

Table 6. LCG Candidate Isophotal Area, Isophotal Magnitude, and S/N Values

ID	Isophotal a	mF336W	S/N	mF435W	S/N	mF435W b	mF606W	S/N	mF814W	S/N
	Area (pixels)		(F336W)		(F435W)	(HSC Match)		(F606W)		(F814W)
zf_9775	391	27.68 ± 0.11	9.1	27.25 ± 0.18	5.7	27.39 ± 0.18	25.29 ± 0.04	23.4	24.15 ± 0.05	18.3
zf_11754	323	⋯	⋯	28.65 ± 0.31	3.4	28.14 ± 0.31	⋯	⋯	24.92 ± 0.09	11.0
zf_14000	126	27.52 ± 0.06	16.6	⋯	⋯	⋯	25.41 ± 0.04	26.1	24.92 ± 0.05	21.1
zf_11423	196	28.29 ± 0.15	6.9	⋯	⋯	⋯	27.17 ± 0.25	4.2	25.75 ± 0.11	9.1
zf_12283	204	27.95 ± 0.12	8.9	⋯	⋯	⋯	26.70 ± 0.12	8.8	26.29 ± 0.22	4.7
zf_8333	193	29.07 ± 0.31	3.4	27.74 ± 0.21	5.1	27.70 ± 0.21	27.09 ± 0.20	5.2	26.60 ± 0.41	2.5
zf_8461	156	27.90 ± 0.09	11.2	27.26 ± 0.12	8.7	27.40 ± 0.12	26.65 ± 0.11	9.7	26.73 ± 0.37	2.8
zf_13836	106	28.23 ± 0.11	9.4	⋯	⋯	⋯	27.15 ± 0.17	6.2	26.75 ± 0.20	5.2
zf_14198	128	28.10 ± 0.10	9.9	⋯	⋯	⋯	27.48 ± 0.26	4.1	26.90 ± 0.29	3.7
zf_13312	112	28.92 ± 0.22	4.9	⋯	⋯	⋯	27.60 ± 0.27	3.9	27.41 ± 0.41	2.5
zf_6745	80	28.36 ± 0.10	10.3	28.06 ± 0.20	5.3	27.88 ± 0.20	28.16 ± 0.39	2.7	27.51 ± 0.60	1.8
zf_14060	74	28.61 ± 0.13	7.8	⋯	⋯	⋯	28.35 ± 0.48	2.2	27.52 ± 0.38	2.8
zf_13676	96	28.50 ± 0.17	6.1	⋯	⋯	⋯	⋯	⋯	27.57 ± 0.31	3.4
cs_658350	127	27.76 ± 0.08	13.2	⋯	⋯	⋯	27.51 ± 0.39	2.7	27.29 ± 0.39	2.7
cs_621227	111	29.53 ± 0.34	3.1	27.97 ± 0.23	4.6	27.83 ± 0.23	28.37 ± 0.44	2.4	27.72 ± 0.86	1.2
cs_626018	57	29.62 ± 0.28	3.7	29.33 ± 0.56	1.9	28.34 ± 0.56	29.39 ± 0.82	1.3	27.99 ± 0.72	1.4
cs_667332	61	⋯	⋯	29.23 ± 0.25	4.2	28.32 ± 0.25	⋯	⋯	28.01 ± 0.73	1.4
cs_621890	119	28.20 ± 0.11	9.1	28.15 ± 0.27	3.9	27.92 ± 0.27	28.23 ± 0.51	2.1	28.21 ± 1.36	0.7
cs_681305	44	⋯	⋯	29.20 ± 0.21	5.1	28.31 ± 0.21	⋯	⋯	28.32 ± 0.82	1.3
zf_8009	191	27.52 ± 0.07	14.0	27.16 ± 0.12	8.5	27.33 ± 0.12	27.11 ± 0.18	5.8	26.26 ± 0.28	3.8
zf_9669	170	28.19 ± 0.12	8.7	27.71 ± 0.18	5.7	27.69 ± 0.18	26.90 ± 0.13	8.0	26.27 ± 0.26	4.1
zf_12022	159	27.76 ± 0.08	12.2	⋯	⋯	⋯	27.07 ± 0.15	7.0	26.36 ± 0.19	5.6
zf_14044	154	28.39 ± 0.15	7.1	⋯	⋯	⋯	27.24 ± 0.23	4.6	26.49 ± 0.21	4.9
cs_671985	108	28.32 ± 0.11	9.0	⋯	⋯	⋯	27.22 ± 0.19	5.5	26.95 ± 0.29	3.6
zf_9963	159	28.44 ± 0.15	6.9	⋯	⋯	⋯	27.21 ± 0.18	5.7	26.98 ± 0.51	2.0
cs_643060	143	27.76 ± 0.08	13.4	27.28 ± 0.12	8.9	27.42 ± 0.12	27.24 ± 0.15	7.0	27.07 ± 0.40	2.6
cs_723862	106	⋯	⋯	27.39 ± 0.07	13.6	27.49 ± 0.07	27.39 ± 0.25	4.2	27.19 ± 0.32	3.3
zf_12042	72	28.39 ± 0.10	9.9	⋯	⋯	⋯	28.65 ± 0.80	1.3	27.27 ± 0.27	3.8
zf_8356	152	28.28 ± 0.17	6.1	27.13 ± 0.10	10.3	27.31 ± 0.10	27.39 ± 0.25	4.2	27.35 ± 0.72	1.5
zf_10407	100	27.47 ± 0.05	19.2	⋯	⋯	⋯	27.13 ± 0.16	6.4	27.54 ± 0.43	2.5
zf_13775	54	⋯	⋯	29.50 ± 0.28	3.7	28.38 ± 0.28	28.85 ± 1.27	0.8	27.74 ± 0.53	2.0
zf_5935	145	28.32 ± 0.22	4.7	27.27 ± 0.13	8.1	27.41 ± 0.13	27.75 ± 0.32	3.3	28.06 ± 1.25	0.8
zf_13099	40	29.01 ± 0.17	6.3	⋯	⋯	⋯	28.55 ± 0.40	2.7	28.16 ± 0.55	1.9
zf_6857	123	28.44 ± 0.16	6.4	27.66 ± 0.18	5.7	27.66 ± 0.18	27.31 ± 0.21	4.9	28.50 ± 2.03	0.5
cs_611354	109	⋯	⋯	27.15 ± 0.09	11.0	27.32 ± 0.09	27.39 ± 0.21	5.0	29.20 ± 3.14	0.3

Notes.

^a Measured from the source-detection segmentation map with a 003 pixel scale (see Section 2.4). ^b F435W isophotal fluxes converted to HSC PSF-matched 1'' aperture fluxes (see Section 2.4.4).

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We summarize the number of LCG candidates by both LyC photometric band (>3σ in F336W and F435W) and assigned category (groups A, B, and C). We also indicate the candidate IDs that do not have F606W coverage, which is relevant for the illustrative color–color plots in Section 5.3.

• 1.  
  LCG candidates in F336W: 26

  • (a)  
    group A: 2
  • (b)  
    group B: 9 (zf_13676 not covered by F606W)
  • (c)  
    group C: 15;
• 2.  
  LCG candidates in F435W: 9

  • (a)  
    group A: 1 (zf_11754 not covered by F606W)
  • (b)  
    group B: 1
  • (c)  
    group C: 7 (cs_667332 and cs_681305 not covered by F606W).

We find the following detection rates for our >3σ LCG candidates relative to the parent and all-z samples within their respective LyC-band footprints:

• 1.  
  F336W candidates/parent: 26/380 = 6.84%,
• 2.  
  F435W candidates/parent: 9/242 = 3.72%,
• 3.  
  F336W candidates/all-z: 26/3065 = 0.85%,
• 4.  
  F435W candidates/all-z: 9/6430 = 0.14%.

We find the following number densities for the >3σ LCGs in different pointings:

• 1.  
  F336W candidates (z > 3.087, two 15 orbit images, m_AB = 29.77, 30.11 at 5σ depth): ∼1.8 arcmin⁻²;
• 2.  
  F435W candidates (z > 4.391):

  • (a)  
    F435W_1a (5 orbits, m_AB = 28.52 at 5σ): ∼0.1 arcmin⁻²,
  • (b)  
    F435W_1b (10 orbits, m_AB = 29.11 at 5σ): ∼0.4 arcmin⁻²,
  • (c)  
    F435W_2 (15 orbits, m_AB = 29.78 at 5σ): ∼0.4 arcmin⁻².

Color selections are often used to identify high-redshift galaxies and LBGs (e.g., Steidel et al. 1996). We therefore plot our LCG candidates on color–color plots with the available bands to show their colors. However, these filter combinations are not the normal bands used for high-redshift LBG selection, nor are they optimal for it. Given that we do not select any galaxies based on colors, we use these purely for illustrative purposes.

Figure 7 shows the LCG candidates split by category: groups A (red stars), B (blue circles), and C (dark blue diamonds). We show the parent sample of all galaxies $\gt {z}_{\mathrm{lim}}$ (black points) and the all-z sample within our HST footprints (gray points). The evolutionary tracks for four Shapley et al. (2003) LBG composites with increasing Lyα strength (red, yellow, green, and turquoise) redshifted from z = 2.7 to 5 are shown. We show LBGs with no LyC flux (dotted curves) and increasing LyC flux as observed from Earth (rest <912 Å) as compared to observed rest ∼1500 Å flux (i.e., R_obs = 1%, 2%, 5%, 10%, and 20%; see Cooke et al. 2014) that peels the tracks off at different colors from the top. Note that these tracks are not at derived f_esc values but observed flux ratios (see Section 5.4 for more details). The tracks are marked at increasing redshift (left to right) with plus signs at z = 3.5, 4, and 5.

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We show the color–color plots for the HST bands (Figure 7, top row) with colors calculated from our isophotal magnitudes. The isophotal magnitudes are extracted within the same footprints on each band for each respective source (see Figures 4–6). The F336W_iso–F606W_iso versus F606W_iso–F814W_iso plot (top left) shows all but one of our LCG candidates selected within the F336W band. The missing candidate is zf_13676 from group B (a lower-priority candidate), as it is not covered by F606W. The F435W_iso–F606W_iso versus F606W_iso–F814W_iso plot (top right) is missing one of the top group A candidates (zf_11754), as it does not have F606W coverage. We therefore use our derived correction (see Section 2.4.4, Equation (1)) to directly compare our HSC PSF- and aperture-matched F435W fluxes with ground-based HSC bands (bottom plot). The F435W_1''ap–HSC_{r_1''ap} versus HSC_{r_1''ap}–HSC_{i_1''ap} shows zf_11754 (red star). Some LCG candidates (mostly in group C) are not shown on the axis ranges we present. This may indicate contamination of the lower-confidence LCG candidates if they are that far away from the all-z cloud (gray points).

The LBG selection boxes for z = 2–4 galaxies (higher-redshift LBGs are off the plot) with these filter combinations are shown in gray in Figure 7. The boxes are comprehensive to span the possible LBG regions. However, they are purely illustrative and should not be used for the clean selection of LBGs. We start with the boxes for a similar filter combination presented in Alavi et al. (2016; F336W−F435W versus F435W−F814W). The box is defined by the location of the color–color evolution tracks of star-forming galaxies for these filters (not shown here; see Alavi et al. 2016). The star-forming galaxy tracks are model predictions from Bruzual & Charlot (2003) synthetic stellar populations with constant star formation, 0.2Z_⊙, 100 Myr ages, and color excesses E(B − V) = [0, 0.1, 0.2, 0.3]. We apply the Madau (1995) cosmic opacity prescription and dust extinction law from Calzetti et al. (2000). We translate these model-based LBG boxes in color space to our filter combinations. We then expand them to encompass the Shapley et al. (2003) tracks (dotted lines shown here) as needed. Most of the LCG candidates, including all of the top group A targets, sit outside of the comprehensive illustrative LBG boxes.

In determining f_esc, the escape fraction of ionizing UV flux relative to the nonionizing continuum, many assumptions are required that have significant degeneracies. These include the SED of a galaxy, its star formation history (SFH), its metallicity, and the assumed line-of-sight IGM distribution through which it is observed. There are often a variety of escape fraction–related parameters quoted in the literature that can further complicate the picture.

The simplest observational parameter for measuring LyC emission is the flux ratio of the observed LyC to the observed UV continuum (R_obs(λ); see Cooke et al. 2014). We measure R_obs = 4%, 3%, and 9% for zf_9775, zf_11754, and zf_14000, respectively (see Table 4 for a summary). These values assume the LyC flux to be in F336W (for zf_9775 and zf_14000) or F435W (zf_11754) and the UV continuum to be F814W for the redshifts (z ∼ 3.7–4.4) of our sources (see Figure 1). The R_obs values vary slightly from the color–color plot approximations (where they overlap with the tracks) given the different filter combinations and galaxy properties.

The parameter required to constrain cosmic reionization is the absolute f_esc, or ${f}_{\mathrm{esc}}^{\mathrm{abs}}$. This is the fraction of escaping LyC photons produced by O and B stars in star-forming galaxies that reach the IGM without being absorbed by the ISM or circumgalactic medium (CGM; e.g., Wyithe & Cen 2007; Wise & Cen 2009). However, direct measurements of this value are not possible due to the severe attenuation of ionizing photons by the IGM. The quantity used to constrain ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ from observations is the relative f_esc (${f}_{\mathrm{esc}}^{\mathrm{rel}};$ Steidel et al. 2001),

$$\begin{eqnarray}&&{f}_{\mathrm{esc}}^{\mathrm{rel}}=\displaystyle \frac{{({F}_{\mathrm{LyC}}/{F}_{1500})}_{\mathrm{obs}}}{{({L}_{\mathrm{LyC}}/{L}_{1500})}_{\mathrm{int}}}\exp ({\tau }_{\mathrm{IGM}}^{\mathrm{LyC}}).\end{eqnarray} \tag{ 2 }$$

Here ${({F}_{\mathrm{LyC}}/{F}_{1500})}_{\mathrm{obs}}$ is the observed rest-frame LyC-to-UV flux ratio, ${({L}_{\mathrm{LyC}}/{L}_{1500})}_{\mathrm{int}}$ is the ratio of the intrinsic ionizing to nonionizing luminosity density, and ${\tau }_{\mathrm{IGM}}^{\mathrm{LyC}}$ is the redshift-dependent IGM attenuation along the line of sight. Both ${({L}_{\mathrm{LyC}}/{L}_{1500})}_{\mathrm{int}}$ and ${\tau }_{\mathrm{IGM}}^{\mathrm{LyC}}$ are highly model- and assumption-dependent. This ${f}_{\mathrm{esc}}^{\mathrm{rel}}$ parameter can be converted to an ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ estimate (proposed in Inoue et al. 2005; Siana et al. 2007) using

$$\begin{eqnarray}&&{f}_{\mathrm{esc}}^{\mathrm{abs}}={f}_{\mathrm{esc}}^{\mathrm{rel}}\times {10}^{-0.4({k}_{1500}E(B-V))},\end{eqnarray} \tag{ 3 }$$

where k_λ is the reddening law (Calzetti et al. 2000) and E(B − V) is the total dust attenuation (see, e.g., Meštrić et al. 2020, for a summary).

We determine ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ for the three group A candidates using the equations above, as is traditionally done in the literature. We first determine average IGM transmission of the LyC probing filter using the commonly adopted models from Inoue et al. (2014; ${T}_{{\rm{IGM}},{\rm{I}}14}^{{\rm{LyC}}}$). These models consider only the IGM contributions along the line of sight and do not include attenuation by the CGM. We find average ${T}_{{\rm{IGM}},{\rm{I}}14}^{{\rm{LyC}}}=0.0118$, 0.0261, and 0.0429 for zf_9775, zf_11754, and zf_14000, respectively. The intrinsic ratio between the luminosity in the LyC band over the nonionizing band is measured for the best-fitting Binary Population and Spectral Synthesis (BPASSv2.1; Eldridge et al. 2017) model for each candidate. We determine ${f}_{\mathrm{esc}}^{\mathrm{rel}}$ using Equation (2), and, since our best-fitting E(B − V) =0, ${f}_{\mathrm{esc}}^{\mathrm{abs}}={f}_{\mathrm{esc}}^{\mathrm{rel}}$, so no further correction for dust is applied. With the attenuation values from Inoue et al. (2014), we find escape fractions of ${f}_{\mathrm{esc},{\rm{I}}14}^{\mathrm{abs}}=8.75,3.63$, and 5.87 for zf_9775, zf_11754, and zf_14000, respectively.

We then calculate a new average IGM transmission of the LyC probing filter (${T}_{{\rm{IGM}}}^{{\rm{LyC}}}$) by generating 10,000 sight lines that include contributions from both the IGM and CGM (see Appendix C for more details). We find average ${T}_{{\rm{IGM}}}^{{\rm{LyC}}}=0.0015$, 0.0141, and 0.0125 for zf_9775, zf_11754, and zf_14000, respectively. Using the same calculation as before with these new attenuation estimates, we find ${f}_{\mathrm{esc}}^{\mathrm{abs}}=111.3,9.8$, and 20.23 for zf_9775, zf_11754, and zf_14000, respectively. Note that these are not percentages but fractions, so they are well over 100% (i.e., 980% for zf_11754) and not physical given these assumptions.

To further investigate the f_esc of the group A candidates, we also adopt a statistical approach to generate realistic f_esc probability distribution functions (PDFs), ${f}_{\mathrm{esc}}^{\mathrm{PDF}}$, that account for some of the sources of uncertainty. We use the probabilistic method described in Bassett et al. (2021b) that we outline in more detail in Appendix C. Probabilistic approaches to estimating f_esc have also been adopted in previous studies (Vasei et al. 2016; Vanzella et al. 2016). We show the f_esc PDFs for one LCG candidate, zf_11754, in Figure 8 (left panel). The PDFs are scaled by the maximum probability (max(P)) assuming the model flux is equal to the observed flux. The PDFs are shown at each of the 25 BPASS model ages and for the best-fitting model (zem5 = Z_* = 1e⁻⁵, $\mathrm{log}(\mathrm{age})=6.0$) and the weighted average at this fixed metallicity (red line). We also show the probability-weighted average f_esc PDF at each metallicity (Figure 8, middle panel). The red line shows the weighted average for all 275 BPASS metallicities and ages. See Figure C1 for grids of weights for each BPASS model for zf_11754.

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The f_esc estimates are constrained from zero to 1, and the maximum is at 1. These plots show that the most consistent ${f}_{\mathrm{esc}}^{\mathrm{PDF}}$ for zf_11754 is 100%. The right panel of Figure 8 shows a histogram of fluxes (blue) across all 10,000 sight lines for the redshift of zf_11754 (z = 4.470) and 10,000 f_esc values between zero and 1 (10⁸ trials). The observational data for zf_11754 are represented by a Gaussian (black curve) with a mean of its observed LyC flux in F435W (μ) and width of the flux error (σ). Where the blue histogram tails off on the right is ${f}_{\mathrm{esc}}^{\mathrm{PDF}}=100 \%$ and high transmission. The peak for zf_11754, i.e., its highest probability ${f}_{\mathrm{esc}}^{\mathrm{PDF}}$, sits even further right of that tapered tail. The right panel therefore shows that the actual probability of this estimate being realistic is low and that it is likely >100%. See Table 4 for a summary of all f_esc values and related parameters.

From the full range of f_esc and IGM transmission combinations tested, ∼1/10,000 sight lines would produce a high enough transmission to obtain the observed LyC flux provided f_esc = 1. Given the very low likelihood of this happening, we deem that the more likely explanation is that f_esc > 1. If adopting a similar approach to Inoue et al. (2014), where the CGM is not included in the sight lines, the likelihood of this high transmission and escape combination only slightly increases, and the models become less physical. We are unable to provide absolute probabilities of these values being possible, since they would depend on the intrinsic PDF of f_esc for a population of star-forming galaxies at the redshifts of the group A candidates (z = 3.7–4.4), which is unknown. All of the probabilities we present are relative, so we quote only the f_esc value that has the highest relative probability within the framework of our analysis.

Quantifying the errors is not possible, as the PDF analysis indicates that the most likely true value of ${f}_{\mathrm{esc}}^{\mathrm{PDF}}$ is >100% and therefore not constrained. The main limitation here is that even in the 99th percentile, IGM transmission is ∼0.2 in the F435W band at the redshift of zf_11754 (see Appendix C, Figure C2). Even for the most transparent sight lines with the largest intrinsic LyC fluxes and f_esc = 1 as inputs, the resulting flux of the model is more than three times the measured uncertainty below the measured flux (i.e., they are too faint). This is also the case for the other two spectroscopic candidates, zf_9775 and zf_14000, so we only present the plots for zf_11754 to illustrate the method. An additional caveat for zf_14000 is that from the full array of SEDs, there are no models that fit the data well, whereas the best-fit models to zf_11754 and zf_9775 are realistic. We therefore have additional doubts about the validity of the ${f}_{\mathrm{esc}}^{\mathrm{PDF}}$ measurement, and therefore LyC detection, of zf_14000.

The most likely value of ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ and ${f}_{\mathrm{esc}}^{\mathrm{PDF}}$ for all three group A spectroscopic candidates is >100% and therefore not physical with these models and assumptions. It is possible that some assumptions that go into the ${f}_{\mathrm{esc}}^{\mathrm{PDF}}$ calculations may not be appropriate for our candidates. Many of the assumptions are those commonly adopted by others for the more traditional f_esc estimates (e.g., ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ calculated with Equation (3)). The models (BPASSv2.1; Eldridge et al. 2017), metallicity ranges (Steidel et al. 2018; Fletcher et al. 2019; Bassett et al. 2021a), and IGM sight-line calculations (Inoue et al. 2014; Steidel et al. 2018; Bassett et al. 2021a) are all based on established methods but do not include strong emission lines in the SEDs, only exponentially declining SFHs. However, as the best-fitting model for all three group A candidates is "zero-age" for BPASS (equivalent to a single, instantaneous burst with an age of 10⁶ yr), the choice of SFH will not affect the fact that ${f}_{\mathrm{esc}}^{\mathrm{PDF}}$ is unconstrained at >100% (see Appendix C).

The statistical ${f}_{\mathrm{esc}}^{\mathrm{PDF}}$ estimate approach presented here has been tested on a spectroscopically confirmed z = 3.64 galaxy (VUDS 511227001; Le Fèvre et al. 2015) in Bassett et al. (2021b). The CLAUDS (Sawicki et al. 2019) U band shows a LyC detection for this galaxy. The resulting PDF has a peak within the zero to 1 range, with ${f}_{\mathrm{esc}}^{\mathrm{PDF}}={0.45}_{-0.28}^{+0.39}$. If we derive many more possible sight lines (10⁷ rather than 10⁴), it is possible that at least one would be transparent enough to match the observed flux for our candidates. However, all three would be unlikely to be within our four untargeted HST pointings.

The f_esc is a valuable parameter that is highly unconstrained, with estimates in the literature ranging from zero to 100%. The clean sample of 13 KLCS LyC emitters (Steidel et al. 2018; Pahl et al. 2021) has ${f}_{\mathrm{esc}}^{\mathrm{abs}}=0.21\pm 0.03$, with a full sample estimate (including 107 non-LyC-detected z ∼ 3 galaxies) of ${f}_{\mathrm{esc}}^{\mathrm{abs}}=0.06\pm 0.01$. Meštrić et al. (2020) presented two promising LCG candidates with spectroscopic redshifts, high-resolution optical HST imaging (to identify contaminants), and CLAUDS U-band LyC detections. Meštrić et al. (2020) estimated ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ for these two candidates in the ranges ∼5%–73% and ∼30%–93%. The spectroscopically confirmed LyC emitter, Ion2, at z = 3.2 (Vanzella et al. 2015; de Barros et al. 2016; Vanzella et al. 2016) has an ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ range of ∼50%–100%, depending on IGM attenuation. For the confirmed LyC emitter Q1549-C25 at z = 3.15, Shapley et al. (2016) found ${f}_{\mathrm{esc}}^{\mathrm{abs}}\geqslant 0.51$ at 95% confidence but ${f}_{\mathrm{esc}}^{\mathrm{abs}}\leqslant 1$ at 45% confidence. Ion3 at z = 4.0 has a quoted ${f}_{\mathrm{esc}}^{\mathrm{rel}}\sim 60 \%$ (Vanzella et al. 2018). An additional five z ∼ 3–3.6 galaxies from LACES have average LyC ${f}_{\mathrm{esc}}^{\mathrm{abs}}=0.35\pm 0.14$ (Nakajima et al. 2020), while a lensed z = 2.5 dwarf galaxy was found to have ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ ≃28%–57% from imaging (Bian et al. 2017). The lensed "Sunburst Arc" at z = 2.37 (Rivera-Thorsen et al. 2017) has line-of-sight ${f}_{\mathrm{esc}}^{\mathrm{abs}}={32}_{-4}^{+2} \%$, although the global escape fraction is expected to be much lower (Rivera-Thorsen et al. 2019).

This large uncertainty can exist even for individual sources as measured in simulations (e.g., Paardekooper et al. 2015; Trebitsch et al. 2017; Rosdahl et al. 2018). The true form of ${f}_{\mathrm{esc}}^{\mathrm{PDF}}$ could also vary by several factors, including galaxy mass, which further complicates its accurate estimation (e.g., Finkelstein et al. 2019; Naidu et al. 2020; Bassett et al. 2021a). The broad range of f_esc estimates in the literature, and even for each individual source, makes it hard to infer meaningful interpretations for the ionizing flux contributions from high-redshift galaxies. There only exists a relatively small sample of individually detected LyC candidates, and they make up a diverse population of chance detections.

A key conclusion from Meštrić et al. (2020) was that only the cleanest lines of sight could work for observing LCGs. Therefore, these detections tell us as much about the random line of sight of the galaxies as they do about the galaxies themselves. It is likely that a population of high-redshift (z ∼ 3–5) galaxies may hold some of the most valuable clues about the sources that reionized the universe due to their proximity in time and likely their physical properties. However, given the severe attenuation of LyC photons by the intervening IGM, this population remains incredibly elusive.

Only in large statistical numbers can we average over possible IGM sight lines. Even then, many of those that we observe in the LyC may exist along the cleanest lines of sight. Nondetections of LyC may be the best path forward for constraining the global ionizing photon budget. The KLCS clean nondetection (<3σ) sample of 107 galaxies has ${f}_{\mathrm{esc}}^{\mathrm{abs}}=0.05\pm 0.01$ (Steidel et al. 2018; Pahl et al. 2021). Bian & Fan (2020) stacked 54 Lyα emitters at z ≃ 3.1 and found no visible LyC but 3σ upper limits of ${f}_{\mathrm{esc}}^{\mathrm{abs}}\lt$ 14%–32%. The LBG stacks from Ji et al. (2020) give upper limits of ${f}_{\mathrm{esc}}^{\mathrm{abs}}\lesssim 0.63 \%$. The spectroscopic assessment in Cooke et al. (2014) gives ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ upper limits of 0.086 for z ∼ 3 galaxies. Using a simplified stacking method of ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ for galaxies without AGNs at z ∼ 2.3–4.3, Smith et al. (2018, 2020) found limits of 0.08, 0.06, and 0.57 for F225W, F275W, and F336W, respectively, from their stacks. Meštrić et al. (2021) analyzed quoted upper limits in the literature and found global ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ values of 0.086 at 2 ≲ z ≤ 3, 0.105 at 3 ≤ z ≤ 4, and 0.084 at 2 ≲ z < 6.

Even with deep HST LyC imaging and secure LRIS redshifts for zf_9775 and zf_11754, the LCGs presented in this paper remain candidates. This is in part due to the quality of the spectra given consistently poor weather conditions for our observations (see Table 3) and slit positioning on our targets. Nevertheless, from the spectra and imaging alone, these appear to be promising candidates. However, the ${f}_{\mathrm{esc}}^{\mathrm{abs}}$ values and statistical ${f}_{\mathrm{esc}}^{\mathrm{PDF}}$ estimates (that explore a broader range of possible assumptions than are usually adopted), we find that the most likely f_esc is >100% and therefore not physical given these models and assumptions.

The candidates shown on the color–color plots (Figure 7) mostly sit outside the comprehensive LBG region. This was hypothesized by Cooke et al. (2014) and found with a small number of LCG candidates by Meštrić et al. (2020). The group A candidates sit on the LBG tracks with observed LyC flux artificially added (R_obs ∼ 5% for zf_9775 and R_obs ∼ 10% for zf_11754 and zf_14000; see Table 4 for calculated values). This could imply that these LCGs are similar to LBGs that exhibit LyC flux (Pahl et al. 2021), or they have flux contamination.

Are the group A spectroscopic LCG candidates contaminated by low-redshift interlopers? Spatially resolving the LyC in high-resolution imaging is one of the best ways to identify low-redshift contaminants (e.g., Vanzella et al. 2012). We find that the chance of contamination is higher than the LCG candidate detection rates of sources in the field. We derive 1.3%–5.0% probabilities of 3σ overlapping sources in our deep HST F336W and F435W images probing the LyC (see Section 2.4.3, Table 1). The redshift-independent contamination rates are higher than the detection rates relative to the all-z sample from the combined redshift catalog (0.85% in F336W, 0.14% in F435W). Therefore, it is possible that our candidates are high-redshift sources contaminated by low-redshift interlopers and our selection method is biased toward finding these chance alignments.

Our blue HST images (∼29–30 mag depths at 5σ) are deeper than other searches for LyC emitters. Comparable surveys from Siana et al. (2015) reach ∼29.27 mag at 5σ and Smith et al. (2018, 2020) reach ∼29.11 mag at 5σ in F336W (with data from Oesch et al. 2018). Deeper bluer filter images could help to resolve the question of possible contamination. However, with deeper images, picking up faint foreground sources is more likely (e.g., Alavi et al. 2014). At the high redshift of our candidates (z ∼ 3.7–4.4), the sight line is long; therefore, the chance of coincident sources is higher, compared with z ∼ 1 (e.g., Siana et al. 2007, 2010).

Higher-S/N spectra with maximal spatial separation of components along the slit of zf_9775 might help us identify the true nature of the candidate. If detected, emission lines in the LyC part of the spectrum could confirm this double source as a low-redshift interloper rather than a physical merger. The LyC emission for zf_11754 is also slightly offset from the optical emission and could also be contaminated. Candidate zf_14000 is very centered, but this is the group A candidate with the largest uncertainties with respect to its nature, redshift, and f_esc estimates. However, it may be that LyC flux does not trace nonionizing flux; for example, mergers can disrupt gas in galaxies, inhomogeneously exposing star-forming regions.

At higher redshifts, the IGM opacity increases significantly. This further reduces the chance of identifying strong LyC detection, particularly at the redshifts of our group A spectroscopic candidates (z ∼ 3.7–4.4). For zf_9775 and zf_14000, the band cleanly sampling their LyC flux is F336W (zf_9775 also has F435W, which contains some forest lines), which would be around ∼560–695 Å. The expected LyC flux is low in F336W; e.g., intrinsic: F_int = 0.034 μJy, attenuated: F_att = 5.2e⁻⁵ ±3.2e⁻⁴ μJy, ≈34.6 ± 6.6 mag. However, Ion3 does show faint LyC down to 750 Å (Vanzella et al. 2018). The results presented in this work are a cautionary tale that even with a blue spectroscopic redshift, detection in a "LyC" probing band, and HST imaging to remove contamination, the true nature of the sources may still not be clear.

The group A spectroscopic candidates are the three brightest galaxies of all of our LCG candidates, with isophotal m_F814W < 25 mag. Given the poor-to-moderate observing conditions (with poorer-than-optimal seeing), obtaining spectra for galaxies fainter than m_F814W ∼ 25 proved challenging. Of the three top candidates, additional improved spectra are required to confirm them as genuine LCGs. A slit orientation to maximally spatially resolve the two components of zf_9775 is needed. A slit for zf_11754 placed to avoid its bright neighboring sources is also required. We have already attempted to target these three group A candidates with these optimized slit positions (2020B_N168; PI: Prichard; weathered out). We were recently reawarded this time for 2022 January (2021B_N87; PI: Prichard).

The remaining group B and C photometric candidates are relatively faint with isophotal optical magnitudes (≳26 mag, down to 28.3 mag). Note that the isophotal magnitudes are a conservative clean flux estimate (best for accurate colors) that may not include all the flux of a source. In good conditions, with seeing <1'', we expect to get redshifts in 4–6 hr down to m_F814W ∼ 26. If a candidate has a strong line, assumed to be Lyα in emission, a redshift can be determined for a source fainter than m_F814W ∼ 26.

High-S/N spectroscopy is essential for identifying genuine LCGs. In a recent complimentary LCG study with MOSFIRE, Bassett et al. (2021b) found that the ZFOURGE photometric redshifts for all seven LCG candidates were overestimated by δ z ∼ 0.2, most likely due to template mismatch. These candidates were therefore ruled out as LCGs, as their true spectroscopic redshift placed them at a redshift such that the U band was not cleanly sampling the LyC. Although the ZFOURGE stated accuracy is ∼2% errors (Straatman et al. 2016), Bassett et al. (2021b) concluded that the search for LCGs is biased toward finding overestimated redshifts (with 94% confidence). The results of this paper further emphasize that HST data are required for removing low-redshift interlopers and demonstrate the requirement of blue spectra to aid with the removal of contaminants.

Redder wavelengths can be used to confirm redshifts but may miss blue features to aid with contaminant removal. We have had supporting programs at redder wavelengths using Keck/MOSFIRE (2018B_W151; PI: Bassett) that focused on the [O iii]/[O ii] relation with LyC (Bassett et al. 2019, 2021b). The combination of MOS observations spanning the bluest wavelengths does provide the best opportunity for getting redshifts and removing low-redshift contaminants efficiently, along with the opportunity to spectroscopically detect the LyC in optimal observing conditions if bright enough. Keck/LRIS is not the only blue MOS option we have tried; we were awarded telescope time with the LBT/MODS that was also weathered out (see Table 3 for a summary). Integral field units could be valuable for exploring the spectroscopic properties of individual LyC emission regions and removing contaminants. However, this requires a high pixel resolution (<1'') for these small sources and is less efficient for building up statistical samples.

Additional information in the blue part of the spectrum can help reveal the nature of the detection and if it is contaminated. This expensive spectroscopic campaign will be handled with superior efficiency for galaxies such as our candidates with the new class of blue MOS instruments on 30 m telescopes. Additionally, the proposed Keck Wide-Field Imager (KWFI; Gillingham et al. 2020) would provide photometry down to ∼29 mag in u in just ∼5 hr and ∼3 hr in g over an area ∼150× that of HST to rapidly identify photometric candidates for spectroscopic follow-up. This combination could efficiently detect and confirm statistical samples of LCGs that could help to constrain valuable cosmic reionization parameters.