# Candidate $z\sim 2.5$ Lyman Continuum Sources in the GOODS Fields

L. H. Jones Department of Astronomy, University of Wisconsin-Madison, 475 N.
Charter Street, Madison, WI 53706, USA  A. J. Barger Department of Astronomy,
University of Wisconsin-Madison, 475 N. Charter Street, Madison, WI 53706, USA
Department of Physics and Astronomy, University of Hawaii, 2505 Correa Road,
Honolulu, HI 96822, USA  Institute for Astronomy, University of Hawaii, 2680
Woodlawn Drive, Honolulu, HI 96822, USA  L. L. Cowie Institute for Astronomy,
University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA

###### Abstract

We use the wealth of deep archival optical spectroscopy on the GOODS-South
field from Keck, the VLT, and other facilities to select candidate high-
redshift Lyman continuum (LyC) leakers in the Hubble Deep UV Legacy Survey
(HDUV) dataset. We select sources at $2.35<z<3.05$, where the _HST_ /WFC3
F275W filter probes only the redshifted LyC. We find five moderately
F275W-bright sources (four detected at $\gtrsim 3\sigma$ significance) in this
redshift range. However, two of these show evidence in their optical spectra
for contamination by foreground galaxies along the line-of-sight. We then
perform an F275W error-weighted sum of the fluxes of all 129 galaxies at
$2.35<z<3.05$ in both the GOODS-N and GOODS-S HDUV areas to estimate the total
ionizing flux. The result is dominated by just five candidate F275W-bright LyC
sources. Lastly, we examine the contributions to the metagalactic ionizing
background, finding that, at the sensitivity of the HDUV F275W data and
allowing for the effects of LyC transmission in the intergalactic medium
(IGM), star-forming galaxies can match the UV flux required to maintain an
ionized IGM at $z\sim 2.5$.

cosmology: observations — galaxies: active — galaxies: distances and redshifts
— galaxies: evolution — galaxies: formation

##  1 Introduction

For the past few decades, one of the most active areas of research in
observational astronomy has been the identification of sources that contribute
to the metagalactic ionizing background. This has been particularly important
for building a cohesive picture of reionization — an important epoch in the
history of the Universe in which the first galaxies formed and the bulk of
hydrogen in the intergalactic medium (IGM) transitioned from neutral to
ionized (e.g., Bouwens et al. 2006, 2012, 2015; Ouchi et al. 2009; Robertson
et al. 2015). Massive stars and quasars/active galactic nuclei (AGN) both
produce ionizing photons, though their relative importance to the global
ionizing background appears to evolve over time. Most evidence currently
favors a scenario in which dwarf star-forming galaxies (SFGs) are the primary
driver of hydrogen reionization (Riccoti & Shull, 2000; Bouwens et al., 2006;
Fontanot et al., 2007, 2014; Robertson et al., 2010, 2015; Japelj et al.,
2017), while AGN contributions to the ionizing background are small until
$z\sim$ 2 – 3 (Barger et al., 2003; Bolton et al., 2005; Cowie, Barger, &
Trouille, 2009; Cristiani et al., 2016; Smith et al., 2020). However, because
these scenarios typically rely on an extrapolation of observed galaxy counts
to faint absolute magnitudes unobtainable even in the deepest HST imaging,
some authors have argued that quasars/AGN could produce a non-negligible or
even dominant fraction of UV photons during the era of reionization (e.g.,
Fontanot et al. 2012; Madau & Haardt 2015). Of course, arguments for or
against this alternate scenario depend critically on the assumed number
density of AGN at high redshift, which is still a subject of significant
debate (see, e.g., Giallongo et al. 2019; Cowie et al. 2020; Grazian et al.
2020 and Shin et al. 2020 for some recent analyses).

Another major uncertainty in determining the relative importance of SFGs and
AGN to reionization is constraining the escape fraction $f_{esc}$, defined as
the fraction of all Lyman continuum (LyC, rest frame $\lambda$ $<$ 912 Å)
photons that manage to escape their galaxy of origin to interact with the IGM.
Most theoretical and semi-analytical models of reionization require an average
$f_{esc}$ for SFGs of about 10% or greater, if SFGs are to be the primary
driver of reionization (e.g., Bolton & Haehnelt 2007; Vanzella et al. 2012a;
Feng et al. 2016; Price et al. 2016; Kimm et al. 2017; see, however, Faucher-
Giguère et al. 2008 and Matthee et al. 2017), though at the highest redshifts,
$f_{esc}$ remains largely unconstrained by observations. For sources at
$z\gtrsim$ 4, the rising density of intervening neutral hydrogen absorption
systems leads to much lower transmissivity of the IGM to LyC photons (Madau,
1995; Songaila, 2004; Inoue et al., 2014). This effectively prohibits direct
detections of LyC emission (and hence estimates of $f_{esc}$) along most
sightlines at redshifts where such measurements are most needed, though some
exceptions have been reported in recent years (e.g., the $z=4$ source Ion3 in
Vanzella et al. 2018 and the $z=3.8$ source Ion1 in Ji et al. 2020). Thus,
observations focused on analogous objects at slightly lower redshifts are
often used to constrain the ionization history of the Universe.

Literature reports of individual or stacked LyC detections suggest that most
galaxies have small values of $f_{esc}$, at most $\sim 1-3\%$ (e.g., Leitherer
et al. 1995; Steidel et al. 2001; Grimes et al. 2009; Cowie et al. 2010;
Leitet et al. 2013; Rutkowski et al. 2016), and that the typical escape
fraction increases with redshift (e.g., Mitra et al. 2013; Fontanot et al.
2014; Faisst 2016; Khaire et al. 2016; Japelj et al. 2017). The latter
observation is based on a growing number of LyC detections at $z\sim 2-3$
(e.g., Vanzella et al. 2010b, 2012b, 2018; Mostardi et al. 2015; Grazian et
al. 2016; Shapley et al. 2016; Jones et al. 2018; Steidel et al. 2018;
Fletcher et al. 2019; Rivera-Thorsen et al. 2019; Saha et al. 2020), though it
is now well known that direct LyC searches can be affected by contamination
from foreground galaxies (e.g., the projections from Vanzella et al. 2010a or
the reexamination of sources first reported in Shapley et al. 2006 by Siana et
al. 2015). Stacking analyses also tend to give a relatively weak average LyC
signal at these redshifts (e.g., Siana et al. 2010; Grazian et al. 2017;
Rutkowski et al. 2017; Marchi et al. 2018; Naidu et al. 2018; Fletcher et al.
2019; see, however, Steidel et al. 2018).

However, some studies have suggested that particular subgroups of galaxies are
more likely to have significant LyC escape. For example, moderately large
Ly$\alpha$ equivalent width in emission (e.g., Micheva et al. 2017; Marchi et
al. 2018; Steidel et al. 2018; Fletcher et al. 2019) or multiply-peaked
Ly$\alpha$ line profiles (Verhamme et al., 2017; Vanzella et al., 2020) appear
to be signposts of nonzero $f_{esc}$; see, however, the confirmed LyC leaker
Ion1, which shows Ly$\alpha$ in absorption only (Ji et al., 2020). A high flux
ratio of [OIII]$\lambda\lambda 4959,5007$ to [OII]$\lambda\lambda 3727,3729$
(O32) has also recently been proposed as an optical marker of LyC escape
(e.g., Nakajima & Ouchi 2014; Izotov et al. 2016a, b, 2018; Steidel et al.
2018; Fletcher et al. 2019; Tang et al. 2019). However, this connection
remains tenuous, with several studies reporting that large O32 by itself is
insufficient to guarantee significant LyC escape (e.g., Reddy et al. 2016b;
Izotov et al. 2017; Rutkowski et al. 2017; Naidu et al. 2018; Barrow et al.
2020).

Legacy fields like the GOODS-North and South (Giavalisco et al., 2004) tend to
be especially attractive targets for LyC leaker searches, due to the abundance
of deep multiwavelength imaging and thorough spectroscopic coverage. In
particular, the advent of the Hubble Deep UV (HDUV) Legacy Survey (Oesch et
al., 2018) has now made it possible to perform direct photometric searches for
LyC leakers at high redshift. Using the HDUV’s deep HST/WFC3 imaging in the
F275W and F336W bands, Naidu et al. (2017) identified six candidate LyC
sources in the GOODS fields at $z\sim 2$, all with $f_{esc}\gtrsim$ 13%.
However, at the redshifts probed by Naidu et al. (2017), the Lyman break sits
squarely in the middle of the F275W bandpass. Since both ionizing and non-
ionizing photons contribute to each object’s F275W photometry, a number of
modeling assumptions are needed to sift out the contribution of just the LyC
to the F275W flux.

However, if one were to push to slightly higher redshifts, say $z\gtrsim 2.4$,
as we did in the GOODS-N in Jones et al. (2018), then the F275W filter becomes
sensitive to LyC photons only. In that work, we identified a raw total of six
sources with spectroscopic redshifts $z\gtrsim 2.4$ that remained bright in
F275W. However, four of these were then shown via optical spectroscopy to be
line-of-sight blends of low- and high-redshift galaxies.

In this paper, we turn our attention to the GOODS-S, using the wealth of
optical/IR spectroscopy in this field in concert with deep F275W imaging from
the HDUV survey, to search for individual candidate LyC-leaking galaxies at
$z>$ 2.35. We place constraints on the mean LyC signal at this redshift using
an averaging analysis and on the contributions to the overall ionizing
luminosity density from SFGs. In Section 2, we describe the data we used to
select and characterize potential high-redshift LyC leakers, including
optical/IR redshift catalogs and spectra, and UV, X-ray, and optical imaging.
We present our search for individual candidate LyC leakers in Section 3 and
discuss the properties of our candidate sources, along with evidence for or
against contamination by foreground galaxies for each. In Section 4, we
perform an averaging analysis of all $z=2.35-3.05$ sources with F275W coverage
in the GOODS-N, in the GOODS-S, and in the two fields combined, from which we
measure their total F275W contributions. In Section 5, we stack the F275W and
F336W images for each GOODS field and for the two fields combined—first for
$z=2.35-3.05$, and then for three redshift bins for the combined images to
look for differences that might arise due to “dilution” from Lyman absorption
along the line-of-sight, which increases with redshift. In Section 6, we
estimate the metagalactic ionizing background at $2.35<z<3.05$ and compare to
the flux required to maintain an ionized IGM at these redshifts. Finally, we
summarize our findings in Section 7.

We assume $\Omega_{M}$ = 0.3, $\Omega_{\Lambda}$ = 0.7, and $H_{0}$ = 70 km
s-1 Mpc-1 throughout this work. All magnitudes are given in the AB system;
magnitude zero-points for the HDUV F275W and F336W observations are given in
Oesch et al. (2018).

##  2 Data

###  2.1 F275W Imaging

The HDUV survey (GO13872; Oesch et al. 2018) is a 132-orbit WFC3 imaging
program centered on the GOODS-North and South fields. Designed to capitalize
on existing WFC3/UVIS imaging from the CANDELS (Grogin et al., 2011; Koekemoer
et al., 2011) and UVUDF (Teplitz et al., 2013; Rafelski et al., 2015)
programs, the HDUV survey imaged both of the GOODS fields in the F275W and
F336W filters around or within the existing CANDELS and UVUDF footprints.

We focused on the HDUV GOODS-N dataset in Jones et al. (2018). Here we focus
on the HDUV GOODS-S dataset, which includes one science image per filter and
corresponding maps of the per-pixel rms, all drizzled to a 60 mas pixel
resolution. The final HDUV images incorporate data from the UVUDF survey,
which substantially deepens this region of the field. We do not include data
from the region of the CDF-S field observed by the Early Release Science (ERS;
Windhorst et al. 2011). This area is almost a magnitude shallower in F275W
than the regions that we use, and it contains significantly more artifacts;
thus, we are unable to construct a high-significance $<26$ magnitude sample
for that region.

When measuring our F275W fluxes (see Section 3.1), we smoothed the F275W and
F336W images using the scipy.ndimage.gaussian_filter function with a standard
deviation of 2 to minimize the impact of residual noise on our measurements,
though as we will show, these residuals still contribute significantly to our
flux uncertainties.

###  2.2 Optical/NIR Spectroscopy

Secure spectroscopic redshifts are required for reliable identification of
LyC-leaking candidates, as photometric redshift estimates and by-eye
inspections are frequently contaminated by galaxies along the line-of-sight
(e.g., Vanzella et al. 2010a; Siana et al. 2015; Jones et al. 2018). We
therefore narrow our search only to those galaxies with robust spectroscopic
redshifts between 2.35 and 3.05. At the lower redshift bound, the Lyman limit
sits at 3055.2 Å, at which point the total throughput of the F275W filter has
declined to 2.3% on the red side. Adopting a slightly stricter redshift
minimum of $z=2.37$, at which point the Lyman limit sits at 3073.4 for a total
F275W throughput of 1%, does not remove any of our candidates, nor does it
substantially change the results of our stacking analyses in Section 4.

Similarly, the upper redshift bound relates to the wavelength at which the
F336W filter probes only the redshifted LyC. Although we considered
F275W-bright candidates with redshifts up to $z=3.55$ in the GOODS-N in Jones
et al. (2018), in this work we use $z=3.05$ as the upper redshift bound in
both the GOODS-N and GOODS-S subsamples for consistency. In principle,
ionizing sources at $z>3.05$ could also be detected in F336W using the methods
described below, though the rapidly increasing opacity of the IGM to LyC
photons at $z=3-4$ would make such a search somewhat more difficult (e.g.,
Inoue et al. 2014). Since the LyC is redshifted fully into the F275W bandpass
at $2.35<z<3.05$, the deep and relatively wide F275W coverage provided by the
HDUV survey enables us to search for potential sources of ionizing radiation
at high redshift.

We consulted spectroscopic catalogs from the literature (Popesso et al. 2009;
Balestra et al. 2010; Cowie et al. 2012; Kurk et al. 2013; Morris et al. 2015;
Bacon et al. 2017; Inami et al. 2017; Pentericci et al. 2018; Barger et al.
2019; Urrutia et al. 2019), along with unpublished spectra that we have
obtained with Keck/DEIMOS, to identify sources in the GOODS-S in the redshift
range of interest. We limited ourselves to objects with redshifts marked as
high-quality/confidence by the respective authors. For example, we only
included spectroscopic redshifts from the MUSE-Deep and MUSE-Wide surveys that
are flagged as confidence level 3, which represent unambiguous, multiple-line
detections (for MUSE-Deep; Bacon et al. 2017 and Inami et al. 2017) or
identifications with “very high certainty” (for MUSE-Wide; Urrutia et al.
2019).

Our final list of candidates (see Section 3.1) has spectroscopic redshifts
from the MUSE-Deep program and from the catalogs of Balestra et al. (2010) and
Kurk et al. (2013).

###  2.3 X-ray Imaging

To identify X-ray counterparts to our F275W sample (see Section 3.1) and to
weed out probable AGN, we used X-ray data and catalogs from the 7 Ms Chandra
X-ray Observatory exposure of the Chandra Deep Field-South (Luo et al., 2017),
which reaches a limiting flux of $f_{0.5-2\mathrm{keV}}\approx 6.4\times
10^{-18}$ erg cm-2 s-1 near the image center. There are 95 F275W sources with
X-ray counterparts within a 1$\farcs$5 search radius. We computed the rest-
frame 2 – 8 keV luminosities, $L_{X}$, of these counterparts from the 0.5 – 2
keV fluxes with an assumed $\Gamma=1.8$ and no absorption correction using

$L_{X}=4\pi
d^{2}_{L}f_{0.5-2\mathrm{keV}}\bigg{(}\frac{1+z}{4}\bigg{)}^{\Gamma-2}\
\mathrm{erg\ s^{-1}.}$ (1)

Of the sources with X-ray counterparts, four have $L_{X}>10^{42}$ erg s-1,
which classifies them as AGN. One of these is a BALQSO. However, none of our
candidate high-redshift LyC-leaking sample (defined below) have X-ray
counterparts.

##  3 Search for Individual $z\sim 3$ Candidate LyC Leakers in the GOODS-S

Figure 1: _Top:_ Spectroscopic redshift vs. HST/ACS F435W magnitude for all
galaxies in the 43.5 arcmin2 footprint of the HDUV GOODS-S with F850LP $<$ 26,
which defines our parent sample. _Bottom:_ Spectroscopic redshift vs. HST/WFC3
F275W magnitude for our primary UV sample of 1115 sources in the GOODS-S with
F275W magnitudes $<$ 26 and total errors fainter than 27.19, corresponding to
a $3\sigma$ detection. Red circles mark sources with an X-ray counterpart in
the Chandra Deep Field South 7 Ms catalog. The purple shaded region shows the
redshift interval where the F275W bandpass straddles the Lyman limit. The four
$>3\sigma$ LyC-leaking candidates lie above this region.

Jones et al. (2018) describes our search for LyC-leaking candidates in the
HDUV GOODS-N field. In the GOODS-S, we begin with all F850LP $<$ 26 galaxies
that are covered by the 43.5 arcmin2 footprint of the HDUV observations. This
area lies entirely within the GOODS-S observations of Giavalisco et al. (2004)
obtained with HST’s Advanced Camera for Surveys (ACS). At $z\sim$ 2.5, the ACS
F850LP filter probes the rest-frame FUV at $\sim$2500 Å, providing a
reasonable selection of star-forming galaxies at these redshifts. In the top
panel of Figure 1, we plot redshift versus F435W magnitude for this area.
Spectroscopic identifications are 97% complete below F435W = 24, 85% from
F435W = 24$-$24.5, and 63% from F435W = 24.5$-$25.

###  3.1 F275W Measurements in the GOODS-S

Using the Python Source Extraction and Photometry (SEP)
library111https://github.com/kbarbary/sep (Barbary, 2016), which is based on
the SExtractor program of Bertin & Arnouts (1996), we measured F275W fluxes in
$2\arcsec$ and $4\arcsec$ diameter apertures at the position of each F850LP
$<$ 26 source with UV coverage. We also estimated the local median background
at each source position in a $4-8\arcsec$ diameter annulus and subtracted this
from the aperture fluxes. Comparing background-subtracted small- and large-
aperture magnitudes (for extended objects with $21<$ F275W $<25$, to avoid
saturated or low S/N sources) reveals a median offset of -0.18 mag, which we
added back to the $2\arcsec$ magnitudes as an aperture correction.

We initially measured magnitude errors in $2\arcsec$ apertures from the
associated rms noise files, with the same -0.18 mag aperture correction
applied. However, this resulted in the selection of objects that, though they
are detected nominally at moderate ($>3\sigma$) significance in F275W,
appeared to be pure noise upon visual inspection.

To estimate the effect of residual noise in the science maps on our flux
measurements, we performed the same aperture photometry methods described
above at $\sim$10,000 random positions across the HDUV field in both the F275W
science and rms images, with the same smoothing applied for consistency with
our source flux measurements. If we were to use only the rms image to
determine uncertainties, we would underestimate the true noise by a factor of
2. This translates to an offset of -0.376 mag, which we added to our initial
magnitude errors.

Our primary UV sample consists of 1115 sources with F275W magnitudes brighter
than 26 and total errors fainter than 27.19, corresponding to a $>3\sigma$
detection. In the bottom panel of Figure 1, we show redshift versus F275W
magnitude for this sample. Spectroscopic identifications are nearly fully
complete to F275W = 24.5 (with only two sources out of 248 missing or
unidentified), 92% complete from F275W $=24.5-25$, and 57% complete from F275W
$=25-26$. The rapid drop-off in spectroscopic completeness at fainter UV
magnitudes is a major motivation for our F275W = 26 cutoff, even though one
might expect the number of candidate $z\sim 2.5-3$ LyC leakers to increase at
very faint UV magnitudes. We have four LyC-leaking candidates in the redshift
range $2.35<z<3.05$ from this selection.

Requiring a $>3\sigma$ detection in F275W at the depth of the HDUV imaging
will necessarily miss UV-fainter sources that otherwise may merit further
consideration as LyC-leaking candidates. We therefore used the following color
selection as a secondary way of selecting potential LyC leakers. We required
(1) F435W $<$ 25; (2) F606W $-$ F850LP $<$ 1 mag; and (3) F275W signal-to-
noise ratio (SNR) $>$ 2\. The first condition ensures that this color-selected
sample remains fairly spectroscopically complete, while the other conditions
select sources with at least marginal F275W detections and relatively flat
rest-frame, non-ionizing UV continua. As shown in Figure 2, this selection
yields four candidates above our minimum redshift threshold, three of which
were already selected directly using our $>3\sigma$ criterion. The remaining
source (enclosed in the green circle in Figure 2) is detected at 2.6$\sigma$
in F275W.

In summary, we have identified five candidate high-redshift LyC leakers in the
redshift range $2.35<z<3.05$ in the GOODS-S, four of which are detected at
$>3\sigma$ significance in F275W. With a total of 46 sources with UV coverage
and secure redshifts in the redshift range, this leads to a $\sim 10.9\%$ raw
success rate in identifying candidate LyC-leaking galaxies. However, after
removing two candidates contaminated by foreground galaxies (see Section 3.2),
this success rate drops to $\sim 6.5\%$.

Figure 2: F275W $-$ F435W color vs. spectroscopic redshift for sources with relatively flat rest-frame UV continua. Red circles mark sources with an X-ray counterpart in the Chandra Deep Field South 7 Ms catalog. Sources with lower limits on F275W $-$ F435W are plotted at their 2$\sigma$ values with blue arrows. The open green circle marks the single $2.35<z<3.05$ source detected at $>2\sigma$ significance in F275W that was not already selected with our $>3\sigma$ significance criterion. The purple hatched region shows the redshift interval where the F275W bandpass straddles the Lyman limit. |  |  |
---|---|---|---
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Figure 3:  Three-color images (_left_ ; red = F160W, green = F850LP, and blue
= F435W) and F275W thumbnails (_right_) of our five candidate LyC leakers.
Cyan contours show regions where the F275W per-pixel SNR exceeds 5$\sigma$,
and the white dashed circle shows the $2^{\prime\prime}$ diameter aperture
used in measuring the magnitudes. Images are $6^{\prime\prime}$ on a side;
North is up and East is to the left. For each source, the redshift (F275W SNR)
is given at the bottom of the left (right) image. Sources 9890 and 20277 were
found to be contaminated by low-redshift interlopers.

###  3.2 Five Candidate LyC Leakers in the GOODS-S

In Table 1, we list the basic properties of our five candidate LyC leakers in
the GOODS-S. This includes an ID number, identical to those given in Table 3
of Guo et al. (2013); decimal coordinates; a spectroscopic redshift from
ground-based observations; the F275W magnitude and error (including the -0.18
mag aperture correction and -0.376 mag noise correction); F435W magnitude; and
F606W – F850LP color. In Figure 3, we show both a three-color thumbnail (left;
red = F160W, green = F850LP, blue = F435W) and the F275W thumbnail (right) of
each source.

Table 1:
Summary of Candidate LyC Leakers IDa | R.A. | Dec. | $z_{spec}^{b}$ | F275W (Error) | F435W | F606W – F850LP
---|---|---|---|---|---|---
98901 | 53.096661 | -27.772339 | 2.483 | 25.50 (27.21) | 24.68 | 0.57
202312 | 53.157532 | -27.798981 | 2.678 | 25.67 (27.54) | 25.49 | 0.33
202773 | 53.157845 | -27.814756 | 2.573 | 25.93 (27.30) | 24.40 | 0.39
246393 | 53.188301 | -27.829344 | 2.571 | 26.00 (27.22) | 24.58 | 0.21
136291 | 53.118439 | -27.805323 | 2.627 | 26.18 (27.24) | 24.59 | 0.16

Although we selected our candidates to have high-quality spectroscopic
redshifts from $2.35<z<3.05$, the optical spectra for two sources (objects
9890 and 20277 in Table 1) show evidence of an intermediate redshift galaxy
along the line-of-sight to the high-redshift galaxy. In source 9890, this is
betrayed by the presence of an [OIII]$\lambda\lambda 4959,5007$/H$\beta$
complex at $z=0.784$. In source 20277, we see a strong [OII]$\lambda\lambda
3727,3729$ doublet at $z=1.094$. At these intermediate redshifts, the F275W
filter probes the rest-frame FUV at $\sim 1300-1500$ Å, well above the Lyman
limit. The UV fluxes for these two sources are almost certainly dominated by
the foreground galaxies and hence cannot be used to measure the ionizing flux
output at $z\sim 2.5$.

We note that these contaminated galaxies, particularly object 9890, reinforce
the need for deep optical and NIR spectroscopy to confirm the nature of any
proposed LyC leakers. In the case of object 9890, the photometric redshift
without HDUV data ($z_{phot}=0.698$; Momcheva et al. 2016) is more consistent
with the spectroscopic redshift of the foreground, low-redshift galaxy. Yet
once the HDUV data are included, the photometric redshift better matches the
spectroscopic redshift of the background galaxy ($z_{phot}=2.36$; Oesch et al.
2018), meaning a selection based only on photometric redshifts would falsely
label this source as a LyC leaker.

We now briefly discuss our remaining three candidate LyC leakers in the
GOODS-S and the foreground contamination rate in our overall candidate sample.
First, three distinct components are seen in the three-color thumbnail for
source 20231 (upper-right of Figure 3): a generally red galaxy with two
clumps, both of which are at almost-identical spectroscopic redshifts (R.
Bacon, private communication), though it is unclear whether they constitute a
single galaxy or an interacting pair. In any case, the F275W flux is not
coincident with the blue clump to the southeast, but instead with the
relatively red knot of emission near the image center.

Second, in source 24639 (middle-right of Figure 3), the F275W emission is
offset from the position of the non-ionizing flux from this galaxy by $\sim
0\farcs 8$, which corresponds to about 6.4 proper kpc at $z=2.571$. Though
regions of LyC escape may not always be fully coincident with the bulk of the
stellar emission, the lack of non-ionizing flux at the position of the F275W
emission in this source is unusual. We do not remove this object from the list
of LyC candidates, but in subsequent sections we note the effects of excluding
it from our calculations.

Third, there is a similar off-center clump of F275W emission to the east of
source 13629. However, unlike the case for source 24639, object 13629 also
shows hints of F275W emission coincident with the position of the non-ionizing
flux from this galaxy.

To estimate the expected level of foreground contamination, we ran Monte Carlo
simulations to randomize the positions of all galaxies in the HDUV GOODS-S
field, regardless of redshift identification or F275W magnitude. This assumes
a spatially uniform foreground F275W population with a surface density of
around 486,900 deg-2 (the number of galaxies within the HDUV GOODS-S footprint
divided by its 43.5 arcmin2 area), similar to the assumptions in Vanzella et
al. (2010a). For a sample size of 5, at least one galaxy is contaminated in
27% of our 500 simulations, with a mean of 0.3 $\pm$ 0.6 contamination events.
This is consistent with expectations from a simple binomial probability
distribution, in which the probability of any single contamination event is
proportional to the source surface density and the aperture size (Nestor et
al., 2013). For the surface density given above and an aperture of radius 1″,
an average of 0.48 $\pm$ 0.66 contamination events are expected in a sample of
size 5.

Finally, we must also be concerned about the limitations of our sample
selection in that we are only using sources with known spectroscopic
redshifts. As we have argued above, it is dangerous to use photometric
redshifts, which may be biased against continuum leakers, and where sources
with incorrect high redshifts may also result in incorrect high fluxes.
However, we have inspected the 185 SFGs that would be placed in the $z$ = 2.35
– 3.05 redshift range by the Straatman et al. (2016) catalog of photometric
redshifts in the field and do not have spectroscopic redshifts. These have
only two $3\sigma$ F275W detections and no significant total signal ($-0.25\pm
0.58~{}\mu$Jy).

Although the apparent offsets between the ionizing and non-ionizing radiation
in some of these sources (particularly object 24639) are peculiar, we retain
all of these objects as candidate LyC leakers. We emphasize that an absence of
evidence for contamination by foreground galaxies does not equate to positive
evidence that such foreground contaminants are absent. For this reason and out
of an abundance of caution, we assert that our three remaining sources in the
GOODS-S should only be considered LyC-leaking candidates.

##  4 Mean ionizing emission from an averaging analysis using both GOODS
fields

In addition to searches for individual LyC leakers, the depth and breadth of
UV coverage offered by the HDUV data enable a robust measurement of the
“typical” ionizing flux output of $z\sim 2.5$ galaxies via averaging.

We select all $2.35<z<3.05$ galaxies with high-quality spectra that lie within
the F275W footprint of the HDUV survey in both GOODS fields. For each field
and band subsample, we applied the same photometric procedure that we used in
our search for individual candidate LyC leakers in Section 3.1 in order to
determine the flux and error for all the sources, including those not detected
individually. In Figure 4, we show F275W flux versus F850LP magnitude for our
F275W subsamples in the GOODS-S and the GOODS-N.

We next excluded sources with X-ray counterparts and sources whose spectra
clearly include emission features from a line-of-sight foreground contaminant.
The X-ray non-detection criterion precludes any major contributions from AGNs
to our stacks. For the GOODS-S, we use the 7 Ms Chandra Deep Field-South
catalog (Luo et al. 2017; see Section 2.3). For the GOODS-N, we use the 2 Ms
Chandra Deep Field-North catalog (Alexander et al. 2003; Xue et al. 2016). We
also searched for any objects with very nearby ($<2\arcsec$) projected
neighbors that might affect our aperture flux measurements, but we did not
find any. Our upper redshift bound is approximately the redshift at which the
F336W filter begins to probe only rest-frame wavelengths $<912$ Å.

We then computed the error-weighted mean flux of all the sources in each
subsample and multiplied that value by the number of sources in the subsample.
Because the flux errors for our sources are very similar to one another, this
is quite similar to computing an unweighted sum. In the GOODS-S, this
selection yielded 38 sources. In the GOODS-N, where the areal coverage in
F275W is wider than in F336W, this yielded 91 sources with F275W coverage and
69 sources with coverage in both bands. In Table 2, we summarize the measured
properties for the individual and combined GOODS fields.

In the GOODS-S, the overwhelming majority of the total contribution at F275W
(0.46 $\mu$Jy of 0.51 $\mu$Jy) comes from the three candidate LyC leakers
listed in Table 1. If we remove individual candidates from the stack
(specifically, source 24639, which appears to have no non-ionizing emission
coincident with its F275W detection), the total F275W flux drops to 0.42
$\mu$Jy, of which 0.32 $\mu$Jy is attributable to the remaining two
candidates. Removing all three candidates from the stack reduces the error-
weighted mean to 0.002 $\pm$ 0.006 $\mu$Jy, giving a total contribution of
only 0.070 $\pm$ 0.21 $\mu$Jy.

Figure 4: F275W flux vs. F850LP magnitude for all $2.35<z<3.05$ galaxies with
high-quality spectra that lie within the F275W footprint of the HDUV survey in
the GOODS-S (top) and GOODS-N (bottom). Sources with X-ray counterparts are
marked in green, while $>3\sigma$ detections, both positive and negative, are
marked in either red or blue (the latter is used to indicate sources
contaminated by foreground galaxies). Note that GN-UVC-6 is a $2.9\sigma$
source and hence not marked in red in the lower panel. GN-UVC-1, the GOODS-N
quasar shown in the lower panel, is marked in green with an upward pointing
arrow, since its measured flux is much higher than the y-axis limit. Table 2:
Properties of the Error-Weighted Summed Fluxes Field | F275W | (SNR) | F336W | (SNR)
---|---|---|---|---
| ($\mu$Jy) |  | ($\mu$Jy) |
GOODS-S | 0.51 | (2.3) | 2.83 | (21)
GOODS-N | 0.52 | (1.5) | 6.74 | (23)
Both | 1.00 | (2.5) | 9.10 | (30)

In order to check the background, we randomized the positions of the GOODS-S
subsample and measured the magnitudes at these positions. We then processed
the sample in the same way as the real sample, i.e., by eliminating low
redshift sources, X-ray sources, or very nearby bright neighbors. We measured
120 random samples and found a mean background of 0.070 $\pm$ 0.023 $\mu$Jy,
which is negligible compared with the measured value in the real sample. 15%
of the random samples had mean backgrounds that exceeded the total
contribution of the real sample, which may suggest that we are slightly
underestimating the true noise. However, it should be emphasized that we did
not carefully curate the random samples in the same way that we did the real
sample, and, thus, we may have a higher degree of unrecognized foreground
contamination, which could result in an overly large dispersion.

Despite the greater number of sources in the GOODS-N, the total contribution
at F275W is similarly small at just 0.52 $\mu$Jy. As with the GOODS-S, a large
fraction of the total contribution comes from just a small number of sources;
here $\sim 40$% (0.21 $\mu$Jy) is attributable to just two sources. These are
GN-UVC-6, a color-selected LyC-leaking candidate at $z=2.439$ that we
discussed in Jones et al. (2018) (a $2.9\sigma$ detection in F275W), and a
$z=2.98$ galaxy with an F275W magnitude of $\sim$26.21 (an $\sim 3\sigma$
detection). The latter object was not discussed in Jones et al. (2018),
because we considered only high-redshift objects detected at $\geq 4\sigma$
significance in constructing our F275W sample, and the source also did not
turn up in our color-selected sample, which probed to lower significance. In
any case, this leaves $\sim$ 0.3 $\mu$Jy of F275W unaccounted for, which must
come from the remaining 89 sources.

Finally, if we combine the two fields, we calculate a total contribution of
1.00 $\pm$ 0.41 $\mu$Jy at F275W, of which about 0.67 $\mu$Jy is directly
attributable to the five LyC-leaking candidates discussed above (3 in the
GOODS-S and 2 in the GOODS-N). Removing an individual candidate from this
calculation (specifically source 24639, for the reasons mentioned in Section
3.2) does not substantially change this result: the remaining 128 galaxies
combined contribute 0.87 $\pm$ 0.39 $\mu$Jy, of which 0.53 is directly
attributable to the remaining candidates. Given the error on the total
contribution, both cases are consistent with the remainder of our sample
contributing little or nothing to the overall ionizing flux output at $z\sim
2.5$.

|
---|---
|
|
Figure 5:  F275W (left) and F336W (right) stacks of spectroscopically
identified sources between $2.35<z<3.05$ with UV coverage from the HDUV
survey. Images from top to bottom show stacks from the GOODS-S, the GOODS-N,
and both fields combined. Images are 6″ on a side and stretched to the same
pixel values for each band (except for the F336W image of the combined GOODS
fields, which saturates at the color scale used for the individual fields).
North is up and East is to the left. The differing number of sources in the
GOODS-N stacks (middle row) are due to wider areal coverage of the field in
F275W than in F336W.

##  5 An Image stacking visualization in both GOODS fields

For visualization purposes, in Figure 5, we show stacked images in each band
for the sample in each GOODS field, as well as for both fields combined.
Bright points more than 1″ away from the image center (for example, the bright
spot to the upper right in the first row of Figure 5) are likely foreground
galaxies with significant F275W flux, though these do not affect our
measurements at $z>2.35$. Most of our candidate LyC leakers across both fields
lie at $z\sim 2.4-2.7$, just above our redshift threshold of 2.35. At higher
redshifts, it is increasingly likely that a Lyman limit system along some
line-of-sight will wipe out any emergent ionizing flux, leading to a greater
number of non-detections (see Section 6). Because of this, it is possible that
including sources at the higher-redshift end of the range we probe here in the
stacks could “dilute” some underlying average signal from sources at the
lower-redshift end.

To test this, we broke apart our stacks for the combined GOODS fields into
three redshift bins, each with equal numbers of galaxies, and performed the
same analysis. At F275W, we found nondetections in all three redshift bins.
This suggests that the “dilution” does not affect our ability to detect
possible LyC-leaking galaxies at the depth of the HDUV F275W data. Meanwhile,
the stacked detection in F336W remains fairly strong in all three redshift
bins, dropping from SNR = 21.6 in the lowest-redshift bin to SNR = 5.7 in the
highest, where most of the band now probes the rest-frame Lyman continuum.

In summary, we are left with (1) a handful of candidate LyC-leaking galaxies
that appear to be individually detected at moderate significance (at the
$\gtrsim 3\sigma$ level), and (2) a general population of galaxies that are
essentially invisible at LyC wavelengths, even in stacked images. This has
some parallels to the results of the LACES program (Fletcher et al., 2019),
which used deep WFC3/UVIS imaging in F336W of the SSA22 field to search for
$z\sim 3.1$ LyC leakers that are also Ly$\alpha$ emitters and Lyman break
galaxies. While they successfully detect significant LyC flux in $\sim 20\%$
of their targets, the majority of their sources (42 of 54) are faint in F336W
(SNR $<$ 4). Stacking these non-detections yielded no net signal, with an
upper limit of F336W = 31.8 (3$\sigma$ in a 0.12″aperture). This led the
authors to conclude that detection of LyC emission in their sample is
dichotomous, occurring either fairly strongly in individual sources or not at
all.

However, we note two important differences in methodology that distinguish
this work from Fletcher et al. (2019). First, their high success rate in
identifying LyC leakers (for comparison, we have a $\sim 6.5\%$ success rate
in the GOODS-S—that is, three candidates out of 46 total sources with robust
redshifts in the $z=2.35-3.05$ range and with UV coverage) can be attributed
largely to (1) the depth of their F336W exposures compared to the typical
depth of an HDUV pointing ($\sim$30 mag at 3$\sigma$ in a 0$\farcs$12 diameter
aperture in LACES vs. $\sim$27.5 mag at 5$\sigma$ in a 0$\farcs$4 diameter
aperture in HDUV), and (2) the higher throughput in F336W compared to F275W,
which partially offsets the rising opacity of the IGM to LyC photons at $z>3$.
Second, their HST/WFC3 followup was highly targeted, focusing on a set of
sources that were already known to have high Ly$\alpha$ equivalent widths and
large O32—both of which may correlate with LyC escape (Nakajima & Ouchi, 2014;
Izotov et al., 2016a, b, 2018; Micheva et al., 2017; Marchi et al., 2018;
Steidel et al., 2018). In contrast, the sample presented here is virtually
blind to such selection effects, since we require only that a source be
reasonably bright in F275W and that it have a spectroscopic redshift.

Figure 6:  F275W flux vs. redshift for the 129 galaxies with high-quality
spectroscopic redshifts and F275W coverage in both GOODS fields. The quasar in
the GOODS-N (GN-UVC-1 from Jones et al. 2018) is marked in green with an
upward pointing arrow, since its measured flux is much higher than the y-axis
limit. The red and blue squares are all the $>3\sigma$ detections, positive or
negative, with the blue denoting contamination by foreground galaxies. Note
that GN-UVC-6 is a $2.9\sigma$ source and hence not marked in red. Thus, there
are five $>3\sigma$ LyC-leaking galaxy candidates in the redshift range
$2.35<z<3.05$. The thick black curve shows the transmission over this redshift
range (right-hand y-axis scale), which drops rapidly as one moves to higher
redshifts. The purple curve shows the F275W filter transmission at the LyC
edge as a function of redshift. The y-axis units are arbitrary. Above
$z=2.35$, we will only have LyC photons within the filter.

##  6 Contributions to the Metagalactic Ionizing Background

Determining the absolute escape fraction for each of our candidate LyC leakers
is challenging, if not impossible, without reliable knowledge of each source’s
intrinsic spectral energy distribution (SED) and degree of reddening. Instead,
we consider the extent to which our candidate sample contributes to the
metagalactic ionizing background. To do so, we combine the GOODS-N and the
GOODS-S data. Excluding the spectroscopically contaminated sources, we have a
total of 129 SFGs together with 9 AGNs based on the X-ray properties. We have
identified six ofthese as candidate LyC leakers. These consist of a single
quasar (the LyC-luminous source GN-UVC-1 from Jones et al. 2018) and the five
SFGs described in Section 4. GN-UVC-1 dominates the flux in the two fields
with a F275W flux of 2 $\mu$Jy, roughly twice the contribution of all of the
SFGs even when including the candidate LyC leakers ($1.00\pm 0.41$ $\mu$Jy).
The remaining AGNs contribute only an insignificant total of 0.096 $\mu$Jy.
Because of the sparseness of the luminous AGNs, the fields are too small to
make an accurate estimate of the AGN contributions, and we focus solely on the
SFGs.

We converted each SFG’s F275W flux density to an ionizing volume emissivity,
$\epsilon_{900}$, defined as the luminosity density at 900 Å per unit
frequency, divided by the comoving survey volume based on (1) the total survey
area in F275W (131 arcmin2) and (2) the redshift bounds $2.35<z<3.05$. We
simplified our calculations by assuming that the entirety of each SFG’s F275W
flux falls at the filter’s effective wavelength of $\sim 2714$ Å, or rest-
frame $\sim$750 Å. We further assumed that the emergent SEDs of these galaxies
are flat in frequency space (i.e., f${}_{\lambda}\propto\lambda^{\beta}$ with
$\beta=-2$) both blueward and redward of 912 Å, albeit with different
amplitudes on each side of the Lyman limit. While a shallower spectral slope
at $\lambda_{rest}<912$ Å may be more plausible, the assumption of a
spectrally flat LyC allows us to use our measured flux densities “as-is”,
without the need for scaling to 900 Å, which would only increase our
calculated values of $\epsilon_{900}$. This assumption thus allows us to
remain as conservative as possible when estimating the ionizing emissivities.

Intergalactic transmission losses are substantial for the higher redshift
galaxies seen in the F275W band, and these losses need to be taken into
account in computing the ionizing emissivity. Below the LyC wavelength, the
opacity is dominated by sources with $N(HI)$ column densities near the Lyman
limit ($\log N(HI)=17.2$ cm-2). Because the number of absorbing systems is
small, there is a wide variation in the mean flux in the F275W filter, after
intergalactic absorption, relative to the galaxy flux at rest-frame 900 Å
(e.g., Inoue et al. 2014 and references therein). The transmission also drops
rapidly with increasing galaxy redshift as the intergalactic path length
increases.

In order to compute the transmission correction, we ran Monte Carlo
simulations, assuming the number of $N(HI)$ systems per unit $N(HI)$ is a
power law with index $-1.7$, and the number of Lyman limit systems with
$\tau>1$ per unit $dz$ is given by the analytic form
$2.8\times((1+z)/4.5)^{1.94}$ of Songaila & Cowie (2010). In Figure 6, we show
the mean flux in the F275W filter relative to the galaxy flux at rest-frame
900 Å versus redshift, which drops from 0.37 at $z=2.35$ to 0.065 at $z=3$.
Because of this rapid drop in the mean transmission, we have chosen to divide
the sample into two redshift intervals in computing the corrected emissivity.
We find a logarithmic value for $\epsilon_{900}$ of $25.0\pm 0.3$ erg s-1 Hz-1
Mpc-3 in the $z=2.35$ – 2.7 interval and $25.2\pm 0.5$ erg s-1 Hz-1 Mpc-3 in
the $z=2.7$ – 3.05 interval. Removing source 24639 from our calculation in the
lower-redshift interval decreases the value of log$(\epsilon_{900})$ by about
0.15 dex.

Figure 7: Ionizing volume emissivity at $z=2.35-2.7$ and $z=2.7-3.05$
estimated from our 5 LyC-leaking candidates together with our stacking
analysis of the remaining $z=2.35-3.05$ galaxies in the combined HDUV-GOODS
fields (filled gold stars). Horizontal error bars on our data points indicate
the redshift range. To compare with literature observations of the ionizing
emissivity from AGN, we show data points from Cowie, Barger, & Trouille (2009)
and Micheva et al. (2017) (red triangles and black squares, respectively) and
best-fit models from Cowie, Barger, & Trouille (2009) and Haardt & Madau
(2012) (red and blue curves, respectively). For the contribution from SFGs, we
show the data point from Steidel et al. (2018) (open green diamond). Cyan
circles show the total inferred metagalactic ionizing luminosity density from
Becker & Bolton (2013).

The bulk of our ionizing flux ($67\%$) comes from the five SFGs, with the
remaining galaxies contributing only a small fraction. This is consistent with
the results of Smith et al. (2018, 2020), who do not detect significant LyC
emission in their own stacking analyses. This bimodality may be caused by
favorable lines-of-sight through the ISM of the host galaxy (e.g., Cen & Kimm
2015) and/or the IGM rather than by the intrinsic galaxy properties, with the
small number of candidate LyC leakers corresponding to lines-of-sight with low
IGM absorption. Even at $z=2.35$, 14% of the lines-of-sight have $<10$%
transmission in the F275W filter, and only 30% of the lines-of-sight have
transmission above 50%, while at $z=2.7$, 48% of the lines-of-sight have
$<10$% transmission in the F275W filter, and only 5% of the lines-of-sight
have transmission above 50%. This is consistent with the redshift distribution
of the candidate LyC leakers (Figure 6), four of which lie in the lower-
redshift interval ($z=2.35-2.7$).

In Figure 7, we summarize the results of our calculations and put them into
context using other $z\sim 3$ measurements of the ionizing background from the
literature. The level of ionizing volume emissivity that we estimate from the
SFGs is roughly consistent with other recent estimates, such as that of
Steidel et al. (2018) at slightly higher redshifts. It is above the AGN
ionizing output measured by Cowie, Barger, & Trouille (2009), Haardt & Madau
(2012), and Micheva et al. (2017) in large samples of quasars and broad-line
AGNs at similar redshifts. Becker & Bolton (2013) used Ly$\alpha$ forest
observations to infer the total ionizing background from $2<z<5$. At $z=3.2$,
they estimated a nominal log$(\epsilon_{900})=24.9$ erg s-1 Hz-1 Mpc-3, which
is comparable to our estimates of $\epsilon_{900}$ for the SFG ionizing
background at these redshifts. However, we emphasize that there may be further
contamination in our sample by intervening sources that we have not
identified. Hence, the present values should be considered as upper limits.

##  7 Summary

We have presented a search for candidate LyC leakers at $z\sim 2.5-3$ in the
GOODS-S field using a combination of deep HST/WFC3 F275W imaging data from the
HDUV survey (Oesch et al., 2018) and extensive optical/NIR spectroscopy. We
found four candidate ionizing sources brighter than F275W $=26$, plus one
additional source just below this cutoff with very blue rest-frame UV colors.
However, two of these five sources are contaminated by foreground lower
redshift galaxies, as seen in their optical spectra, leaving only three
possible candidate LyC leakers.

We performed an averaging analysis of all the sources with spectroscopic
redshifts $2.35<z<3.05$ in the HDUV areas in both the GOODS-S and GOODS-N and
found that the total ionizing output of galaxies at these redshifts is
dominated by just five individual candidate LyC leakers. These include the
three GOODS-S sources described above, and two sources in the GOODS-N (one of
which was presented in Jones et al. 2018). Allowing for the very substantial
effects of intergalactic absorption, we found that the volume ionizing flux
roughly matches that required to ionize the IGM at these redshifts (Becker &
Bolton 2013) and is consistent with other recent estimates.

We thank R. Bacon and the MUSE-Deep team for providing MUSE spectra of some of
our LyC-leaking candidates ahead of publication. Some figures in this work use
colormaps from the Python package CMasher (van der Velden, 2020). We
gratefully acknowledge support from NSF grant AST-1715145, the William F.
Vilas Estate, and the Kellett Mid-Career Award from the University of
Wisconsin-Madison Office of the Vice Chancellor for Research and Graduate
Education with funding from the Wisconsin Alumni Research Foundation (A. J.
B.). Based in part on data obtained at the W. M. Keck Observatory, which is
operated as a scientific partnership among the California Institute of
Technology, the University of California, and NASA and was made possible by
the generous financial support of the W. M. Keck Foundation. The authors wish
to recognize and acknowledge the very significant cultural role and reverence
that the summit of Mauna Kea has always had within the indigenous Hawaiian
community. We are most fortunate to have the opportunity to conduct
observations from this mountain.

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