Introduction

Long-duration gamma-ray bursts (GRBs) have been theoretically (Paczynski 1986;Woosley 1993) and observationally associated with the deaths of massive stars and specifically with Type Ib/c broad-lined (BL) supernovae (SNe). These SNe result from the core collapse of a progenitor star that has completely lost its hydrogen shell and most-to-all of its helium shell, with the "BL" designation in reference to the fast moving SN ejecta resulting in BL emission features (Galama et al. 1998;MacFadyen & Woosley 1999;Hjorth et al. 2003; see Woosley & Bloom 2006;Hjorth & Bloom 2012;Cano et al. 2017 for reviews). 8 There are two main observational components to a GRBthe initial gamma-ray prompt emission is thought to be from dissipation processes within the GRB jet and the multiwavelength afterglow powered by the synchrotron emission originating from the jet's deceleration into the local environment (Chevalier & Li 1999;Miceli & Nava 2022).

GRB follow-up and afterglow studies were revolutionized with the launch of the Neil Gehrels Swift Observatory (Swift; Gehrels et al. 2004). The X-ray Telescope (XRT; Burrows et al. 2005) on board has the ability to localize the GRB afterglow to few arcsecond precision allowing for groundbased observations. As long-duration GRBs are known to occur predominantly within the half-light radius and within the bright, star-forming regions of their host galaxies (Fruchter et al. 2006;Svensson et al. 2010;Blanchard & Berger 2016;Lyman et al. 2017), this precise afterglow-enabled localization often allows for robust host identification. The extreme luminosity (∼10 53 erg s -1 ) of the GRB makes them observable to cosmological distances, with the currently most distant GRB 090429B photometrically estimated to have z = 9.4 (Cucchiara et al. 2011).

High-redshift (z > 3) star-forming galaxies are primarily identified using the Lyman-break technique in which the wavelength of the Lyman break is determined via photometric dropout (Steidel et al. 1996). Studies of star-forming galaxies benefit from large-number statistics and deep observations and, prior to JWST, extend through z ∼ 9 (see, e.g., Stark 2016 for a recent review). Surveys from JWST, including early data release and dedicated programs like the Cosmic Evolution Early Release Science Survey (CEERS; Finkelstein et al. 2023), the GLASS JWST Early Release Science Program (GLASS-JWST; Treu et al. 2022), and the JWST Advanced Deep Extragalactic Survey (JADES; Eisenstein et al. 2023) Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 8 There have been a handful of long GRBs identified to likely be associated with compact object mergers, e.g., GRBs 230307A (Gillanders et al. 2023;Levan et al. 2024), 211211A (Rastinejad et al. 2022;Troja et al. 2022;Gompertz et al. 2023), and 060614 (Fynbo et al. 2006b;Della Valle et al. 2006;Gal-Yam et al. 2006;Gehrels et al. 2006). At early cosmic times, however, the contamination of bright long-GRB samples by merger events is likely to be minimal.

have allowed for analysis of these galaxies to continue to even greater redshift (z ∼ 13). An important characterization of Lyman-break galaxies is the UV luminosity function (LF). This function is a fit to a histogram of these galaxies and allows for an estimate of the percentage of undetectable star formation through extrapolation of the fit to faint magnitudes, whether intrinsic or the consequence of dust obscuration. It is well defined at the bright end (M UV < -15 mag; Finkelstein et al. 2015;Bouwens et al. 2021Bouwens et al. , 2022a;;Finkelstein et al. 2023;Harikane et al. 2023Harikane et al. , 2024) ) with the generally assumed Schechter (1976) function being fit to measurements from thousands of galaxies.

Observations of Lyman-break galaxies, however, only offer a view of the star formation that can be directly observed and are therefore implicitly biased against faint galaxies. Since the ability to detect a GRB is independent of the luminosity of its host galaxy, and the detection of a GRB implies the existence of a galaxy at that location, GRBs offer a way to characterize faint and otherwise unobserved star formation, such as that which is dust obscured or intrinsically faint. Constraining the amount of star formation that would otherwise go undetected, especially at high redshift, is key for determining how large a role this star formation played in reionizing the Universe.

In the low-redshift Universe (z < 2) GRB host galaxies have been shown to have smaller sizes, lower masses, and lower metallicities than the general star-forming galaxy population (Stanek et al. 2006;Kewley et al. 2007;Han et al. 2010;Levesque et al. 2010;Svensson et al. 2010;Graham & Fruchter 2013;Perley et al. 2013;Palmerio et al. 2019). These biases are thought to be a consequence of the preference for a GRB progenitor to form and explode in low-metallicity environments, with low-metallicity star-forming galaxies being smaller and less massive than the general sample (Mannucci et al. 2010;Palmerio et al. 2019). The nature of this preference, both physical and functional, is still actively debated: some studies have theorized multiple metallicity-dependent paths for GRB creation (Trenti et al. 2015;hereafter T15), while some have found evidence for a host galaxy stellar metallicity threshold above which GRBs are rare (i.e., it allows for the possibility of a pocket of lower-Z star formation within a high-Z galaxy). Below this threshold, GRBs seem to trace star formation in an unbiased way (though there is uncertainty on the value of this threshold (Z < Z e : Perley et al. 2016b; Z < 0.7Z e : Palmerio et al. 2019).

The bias of the GRBs in host galaxy mass and size is consistent with being largely a by-product of metal aversion (Perley et al. 2016b), and so, as the average metallicity of the Universe decreases with increasing redshift, the differences in the characteristics of GRB host galaxies as compared to those of actively star-forming galaxies should decrease toward triviality. Indeed, up to z ∼ 4, comparisons of the two galaxy samples have followed this expectation when characterized by the mass-metallicity relation (Levesque et al. 2010;Laskar et al. 2011;Vergani et al. 2017;Graham et al. 2023), the UV LF (Greiner et al. 2015;Schulze et al. 2015), and in direct size and stellar mass measurements (Vergani et al. 2015;Schneider et al. 2022). Comparisons at higher redshift (z ∼ 6) also support these results but are significantly limited in precision due to the small number of localized GRBs with confirmed redshifts at this redshift range (Tanvir et al. 2012a;McGuire et al. 2016).

In this work, we present new Hubble Space Telescope (HST) observations of the largest complete sample of GRB host galaxies at z ∼ 5, to improve significantly these comparisons at the highest possible redshifts with currently available data. In Section 2, we describe our observations and host identification methods. We present our formalism, modeling, and analysis of the UV LF and size-luminosity relation of the GRB host sample and compare to that of Lyman-break galaxies in Section 3. We conclude with a presentation and discussion of our nondetection fraction and its implications toward the amount of undetectable star formation. We use a cosmological model with H 0 = 70 km s -1 Mpc -1 , Ω 0 = 0.3, and Ω Λ = 0.7. Uncertainties are reported as the Gaussian-equivalent 1σ, unless otherwise stated.

Observations

Sample Selection

We define selection criteria for our z ∼ 5 GRB host galaxy sample to minimize selection bias while maximizing completeness. Our initial selection criteria were:

1. the GRB has a spectroscopic or photometric redshift of 4 < z < 6; 2. deep observations at the GRB location were performed with the Spitzer Space Telescope (Spitzer; Werner et al. 2004); 3. the GRB was detected with Swift prior to mid-2015 (the date is a by-product of the Spitzer requirement) and has a localization 2″; and 4. the line of sight along the GRB direction has low Galactic extinction, E(B -V ) < 0.2 mag.

From this first-round sample, we use the following criteria to determine the final sample:

1. the GRB was included in one of the four following uniform samples: The Optically Unbiased GRB Host Survey (TOUGH;

Schulze et al. 2015), A Complete Sample of Bright Swift Long Gamma-Ray Bursts (BAT6; Salvaterra et al. 2012), the X-shooter GRB afterglow legacy sample (XSGRB; Selsing et al. 2019), or the Swift GRB Host Galaxy Legacy Survey (SHOALS; Perley et al. 2016a), or otherwise met the criteria to be included in the SHOALS sample but occurred outside of the project timeline, or 2. the GRB was rapidly observed with a near-infrared (NIR) imager on a >1 m telescope, such as the Palomar 60 inch Telescope (P60; Cenko et al. 2006), the Peters Automated Infrared Imaging Telescope (PAIRITEL; Bloom et al. 2006), or the Gamma-Ray Burst Optical/Near-Infrared Detector (GROND; Greiner et al. 2008) on the MPG/ ESO 2.2 m telescope.

While the Spitzer observations are not used in our analysis, the existence of these Spitzer images helped us to rule out lowredshift interlopers and, in a few cases for which there was not a spectroscopic redshift measurement, allowed us to measure photometric redshifts, though these measurements were already published in samples such as SHOALS (Perley et al. 2016a). Of the 31 host galaxies identified by the redshift and time cuts, only five of these do not have Spitzer imaging. These five sources would have otherwise been excluded from our sample due to our localization, Galactic extinction, and inclusion in a uniform sample criteria.

The typical accuracy of Swift/XRT (with the enhanced analysis) is ∼1 5 (Goad et al. 2007). This is an algorithm update (Goad et al. 2007;Evans et al. 2009) and not a physical update to the instrument, and so this accuracy is applicable to all bursts with observations from Swift/XRT and the Ultraviolet and Optical Telescope (UVOT; Roming et al. 2005) on board Swift; e.g., GRB 050505 was published with a 6″ XRT positional uncertainty (Kennea et al. 2005) in 2005, however, it now has a 1 4 uncertainty listed in the Swift catalog (Evans et al. 2009). This uncertainty is only significantly worse when the afterglow is faint (and thereby sensitive to field and atmospheric conditions) or observations of the afterglow are delayed-properties unrelated to the host environment. If the afterglow is bright, and especially if it is detected with Swift/UVOT, it is not common for observations of the afterglow to be delayed. Typical accuracies for GRB afterglows are 0 1-1″ (optical/NIR from the ground), 0 5-1″ (UVOT; Goad et al. 2007), and ∼1 5 (XRT; Goad et al. 2007). All of these accuracies are less than our required 2″ positional uncertainty, and so this criterion does not substantially limit in size nor bias our host sample.

Our conditional requirement of rapid NIR imaging represents the uniformity of NIR follow up. The programs through which the GRBs were rapidly imaged with NIR instruments were designed to follow up every GRB that was observable with the telescope, such as those listed in criterion 2. The sample of GRB host galaxies with rapid NIR follow up of the burst is therefore uniform in that the criteria for NIR follow up were exclusively based on characteristics unrelated to the properties of the host galaxy, such as the local weather, decl., and Sun angle.

From these criteria, we populate a sample of 19 GRBs for host galaxy follow up. There are four additional GRBs (050505, 060223A, 140304A, and 140311A) that meet our initial selection criteria that also have available HST imaging. After investigating the selection criteria for each of the uniform samples, these four GRBs had been excluded due to a small Sun hour angle separation, too high of a decl., were not observed with XRT within 10 minutes of the Swift Burst Alert Telescope (BAT; Barthelmy et al. 2005) trigger, or had too low a fluence (S 15-150 keV ). These properties, as well as the nonexistence of rapid NIR follow up, have no dependence on the characteristics of the GRB host galaxy and therefore the inclusion of these four GRBs has no effect on the uniformity of our GRB host galaxy sample, and so we include them in our analysis to increase the sample size.

HST Imaging

We present new HST/WFC3 IR imaging for 19 galaxies in our sample (ID: 15644, PI: Perley), while the remaining four (GRBs 050505, 060223A, 140304A, and 140311A) had archival imaging available, which we detail in the following section. The 19 host galaxies from our program were imaged using the F110W filter: galaxies with redshift z < 4.8 were observed over two orbits (average exposure time of 4900 s), while those with z > 4.8 were observed over three orbits (average exposure time of 7400 s). Across our redshift range, the central rest-frame wavelength of F110W converts to 1650-2260 Å, which samples the rest-frame UV emission.

We use archival imaging for four sources which were previously observed by HST. The host galaxies of GRBs 060223, 060522, and 060927 were also imaged using WFC3/F110W (ID: 11734, PI: Levan) with three orbits for the fields of GRBs 060223 and 060522 and five orbits for the field of GRB 060927. The host of GRB 130606A was imaged using WFC3/F140W (ID: 13831, PI: Tanvir) over four orbits. At a redshift of z = 5.913 (Lunnan et al. 2013), the central wavelength of F140W translates to 2014 Å, which is comparable to the observations of the other objects in the sample.

The reduced (i.e., flat-fielded, charge-transfer-efficiency (CTE) corrected, dark-subtracted) and ICRS aligned HST images were downloaded from the Barbara A. Milkulski Archive for Space Telescopes (MAST; see Chapters 2 and 3 of Sahu 2021 for details on this reduction). To drizzle the HST frames and achieve a resolution past the instrument limitation, we use Astrodrizzle (Gonzaga et al. 2012) with final_pixfrac = 0.8 and final_scale = 0.065 for consistency with previous GRB host galaxy HST analyses (e.g., Blanchard & Berger 2016).

Afterglow Localizations

Our analysis requires robust and accurate GRB localizations in order to identify the host galaxy of each GRB, and for that purpose, when possible, we use imaging of the optical afterglow. We were able to use optical afterglow imaging for all but three sources in our sample. For these three sources with no optical/NIR afterglow imaging available, we use their position as reported from Swift-XRT (GRBs 050803 and 050922B; Goad et al. 2007) or from the Karl G. Jansky Very Large Array (VLA; Perley et al. 2011;GRB 140304A;Laskar et al. 2014).

Optical afterglow images were collected from the public archives of the Low Resolution Imaging Spectrometer at the W.M. Keck Observatory (Keck-LRIS; Oke et al. 1995), the Gemini-North/South Multi-Object Spectrograph at the Gemini-North/South Observatory (GMOS-N/S; Hook et al. 2004), the P60 at Palomar Observatory (Cenko et al. 2006), the Very Large Telescope (VLT), the Rapid Eye Mount (REMfoot_1 ) Telescope at La Silla Observatory, the Device Optimized for the LOw RESolution (DOLORES, in short LRSfoot_2 ) at the Telescopio Nazionale Galileo (TNG), and Swift/UVOT. To reduce images from Keck-LRIS, we use the LPIPE pipeline (Perley 2019). When possible, we use the reduction pipelines embedded within the archive services. We otherwise use standard reduction steps such as flat division, bias subtraction, and image stacking. Centroid positions for each afterglow were measured using Source Extractor (Bertin & Arnouts 1996). Imaging and reduction steps for each GRB afterglow are detailed in the Appendix with additional references in Table 1.

Astrometric Alignment

Many of the afterglow images had an initial world coordinate system (WCS) assigned by the data archive. For those that did not, we upload the afterglow image to Astrometry.net (Lang et al. 2010) to get a preliminary WCS assignment. To align the

Table 1 List of GRBs in Our Sample and Their Afterglow Localizations GRB R.A. (ICRS, J2000) Decl. (ICRS, J2000) 1σ Unc. (″) Redshift Imaging Source Filter Date of Imaging References 050502B 9:30:10.0703 +16:59:47.177 0.060 -+ 5.2 0.3 0.3 TNG I 2005 Mar Afonso et al. (2011) 050505 09:27:03.2887 +30:16:23.907 0.050 4.275 Keck/LRIS I 2005 Mar Cenko et al. (2005) 050803 a 23:22:37.84 +05:47:08.4 1.4 -+ 4.3 2.40 0.60 Swift/XRT L L Goad et al. (2007) 050814 17:36:45.3814 +46:20:21.562 0.257 -+ 5.77 0.12 0.12 P60 i 2005 Aug Cenko (2005) 050922B a 00:23:13.37 -05:36:17.3 2 -+ 4.9 0.6 0.3 Swift/XRT L L Goad et al. (2007) 060206 13:31:43.4556 +35:03:03.186 0.067 4.059 P60 Clear 2006 Feb Ofek et al. (2006) 060223 03:40:49.5661 -17:07:48.357 0.077 4.406 Swift/UVOT V 2006 Feb Blustin et al. (2006) 060510B 15:56:29.6236 +78:34:12.102 0.094 4.942 Gemini/GMOS-N i 2006 May Price et al. (2007) 060522 21:31:44.8367 +02:53:09.607 0.054 5.11 TNG R 2006 May D'Avanzo & Cummings (2006) 060927 21:58:11.9907 +05:21:48.355 0.128 5.467 VLT/FORS2 I 2006 Sep Ruiz-Velasco et al. (2007) 071025 23:40:17.0849 +31:46:42.857 0.263 -+ 4.8 0.4 0.4 REM H 2007 Oct Covino et al. (2007) 090516A 09:13:02.5973 -11:51:15.055 0.023 4.111 VLT/FORS2 R 2009 May de Ugarte Postigo et al. (2009) 100219A 10:16:48.4822 -12:34:00.587 0.036 4.667 Gemini/GMOS-S r 2010 Feb Cenko et al. (2010a) 100513A 11:18:26.8480 +03:37:39.899 0.022 4.772 Gemini/GMOS-N i 2010 May Cenko et al. (2010b) 111008A 04:01:48.2508 -32:42:33.260 0.080 4.99 Gemini/GMOS-S R 2011 Oct Levan et al. (2011) 120712A 11:18:21.2254 -20:02:01.292 0.058 4.175 Gemini/GMOS-S R 2012 Jul 12 Tanvir et al. (2012b) 130606A 16:37:35.1301 +29:47:46.538 0.026 5.913 Gemini/GMOS-N i 2013 Jun 07 Chornock et al. (2013) 131117A 22:09:19.3354 -31:45:44.477 0.084 4.042 VLT/X-Shooter R 2013 Nov Hartoog et al. (2013) 140304A a 02:02:34.17 +33:28:26.01 0.02 5.283 VLA L L Laskar et al. (2014) 140311A 13:57:13.2771 +00:38:31.388 0.060 4.954 Gemini/GMOS-N i 2014 Mar Chornock et al. (2014b) 140428A 12:57:28.4075 +28:23:06.280 0.066 -+ 4.68 0.18 0.52 Keck/LRIS I 2014 Apr Perley (2014) 140518A 15:09:00.6009 +42:25:05.886 0.046 4.7055 Gemini/GMOS-N i 2014 May Chornock et al. (2014a) 140614A 15:24:40.4961 -79:07:43.255 0.349 4.233 VLT/X-Shooter i' 2014 Jun 14 Kruehler et al. (2014) Notes. From left to right: GRB name, position and uncertainty of the afterglow (as measured from afterglow imaging or reported in the literature), redshift of the afterglow, filter of the afterglow imaging, and references for the afterglow images (or reported position). Afterglow redshift citations are in the Appendix. a Positions for these afterglows are reported from the literature.

afterglow images to the HST images, we used TweakReg (Gonzaga et al. 2012). In the first alignment attempt, we use a catalog of Gaia sources within ¢ 2 of the afterglow position. If this failed or if there were fewer than six catalog sources in the HST image, we instead used a catalog of at least six, but often >10, matching sources (all of the bright and unsaturated stars and sometimes bright galaxies) between each afterglow and HST image pair. These sources were selected from visual inspection in SAOImageDS9 (DS9; Joye & Mandel 2003). The alignment was deemed successful when common sources were aligned to within approximately 1 HST pixel = 0 065. In the case of GRB 060223, there was only one source (a saturated star) in common between the two images, and so we instead aligned each image separately to the Gaia DR2 catalog. Details on alignment steps for each source are in the Appendix.

The afterglow positions found by Source Extractor were then converted from pixel to WCS coordinates for use in host galaxy identification in the corresponding HST image. To quantify the uncertainty on the position of the afterglow, reported in Table 1, we add in quadrature the uncertainty in the afterglow centroid from Source Extractor and the rms of the astrometric match to the HST image of the host. When optical afterglow imaging was unavailable, we list the uncertainty reported in the literature (GRB 140304A; Laskar et al. 2014) or the Swift-XRT catalog (GRBs 050803 and 050922B; Goad et al. 2007). All but two afterglows (GRBs 050803 and 050922B, for which only Swift-XRT imaging was available) were localized to better than 0 5, with a median localization uncertainty ∼ 0 06.

For all but one case (GRB 050922B), if there was a galaxy coincident within the afterglow uncertainty region, we designate that as the host of the GRB, as lower-redshift GRB afterglows are found near the centers of their host galaxy (Blanchard & Berger 2016). Within the afterglow uncertainty region of GRB 050922B, there are two galaxies: a compact source and a merging system. In agreement with Perley et al. (2016a), we designate the merging system as the host of this GRB. The identification of this galaxy as the host is elaborated upon in the next section. If there was no galaxy within the region, we classified this as a nondetection for the host galaxy. Details on the detection classification for each host are in the Appendix, and excerpts of the HST imaging with afterglow positions, their 3σ uncertainty regions, and host galaxy identifications are shown in Figure 1.

P cc Calculations

We consider the false alarm probability for our claimed host galaxies and nearby sources to our claimed nondetections. The false alarm probability is the chance of an unrelated galaxy being within the measured proximity to the line of sight to the GRB. When the afterglow is well localized, this probability is largely dependent on the offset from the afterglow and the apparent magnitude of the putative host. We calculate the probability of chance coincidence (P cc ) following the methods in Bloom et al. (2002) and using

R e is taken to be the maximum of

, where σ TIE is the uncertainty in the astrometric tie between the afterglow and galaxy positions and σ AG is the uncertainty in the afterglow position. R is the offset of the considered galaxy from the center of the afterglow, and R eff is the half-light radius of this considered galaxy. σ(m) is calculated from summing the galaxy number densities below the measured m F110W in Tables 3 and 4 in Metcalfe et al. (2006).

For our detections, we calculate the P cc for the putative host. Only four of the 16 putative host galaxies had P cc > 0.1. These were the host galaxies of GRBs 050803 (P cc = 0.98), 050922B (P cc = 0.99), 071025 (P cc = 0.12), and 140614A (P cc = 0.21). These four cases include our two GRBs with only Swift-XRT positions available (GRBs 050803 and 050922B) and two sources with the next largest afterglow positional uncertainty. In the cases of GRBs 050803 and 050922B, these GRBs were included in our sample due to the photometric redshifts of the claimed host galaxies (Perley et al. 2016a), and so we continue analysis with the assumption that these are the host galaxies of these GRBs. We repeated our analysis in Section 3 treating these hosts as nondetections, and found that the best-fit LF parameters are consistent to within 1σ, so our results are not strongly sensitive to the uncertainty in these host associations. In the other two cases, these were the only sources within the afterglow uncertainty region, and so we classify them as the host galaxy of their respective GRB. Details on each P cc are in the Appendix.

For our nondetections, we calculate the P cc for all sources detected by Source Extractor within a 5″ × 5″ box centered on the afterglow position reported in Table 1. Only two of the 21 nearby sources in the 5″ fields of our nondetections had P cc < 0.1. These two sources (one each in the fields of GRBs 060927 and 100219A) were confirmed to have a lower redshift than each respective GRB and are therefore not the host galaxies. The galaxy in the field of GRB 060927 was detected in R-band VLT imaging (Basa et al. 2012) and has a redshift z < 4, which is incompatible with the spectroscopic afterglow redshift of z = 5.467 reported in Ruiz-Velasco et al. (2007). The galaxy in the field of GRB 100219A was spectroscopically confirmed to have z = 0.217 in Cenko et al. (2010a), which is incompatible with the spectroscopic afterglow redshift of z = 4.667 for GRB 100219A (Selsing et al. 2019). Because all other detected candidate host galaxies have P cc > 0.1, we report the host galaxies of these seven GRBs as nondetections. Details on each P cc are in Appendix.

HST Photometry

We measure apparent magnitudes of all detected GRB host galaxies with Source Extractor using MAG_AUTO with PHOT_AUTOPARAMS set to the default values of 2.5 and 3.5. This parameter couplet sets the multiplicative factor and minimum Kron radius used in the "auto" measurement and is explained in greater detail in the Source Extractor documentation.foot_4 These measurements are reported in Table 2. We convert these apparent magnitudes to absolute UV magnitudes at 1600 Å using the distance modulus and a K-correction, as detailed below. We first aperture correct the apparent magnitudes using the Encircled Energy (EE) tables from STScI. 12 We interpolate the table values for F110W and F140W with a cubic spline to determine the appropriate EE term for the precise KRON_RADIUS used by Source Extractor for each galaxy. We then correct these aperture-corrected magnitudes for Galactic dust absorption as reported in the NASA/IPAC Extragalactic Database (NED;

Schlafly & Finkbeiner 2011) at the location of the afterglow. We assume a UV spectral slope of β = -2 (see Figure 2 in Wilkins et al. 2013), where f ν ∝ ν -β and then apply a K-correction of ( ) -+ z 2.5 log 1 10 . The component of the K-correction for the spectral shape is proportional to (2 + β), and therefore vanishes since we assume β = -2. In summary:

5 log 5 5 log 2.5 log 1 , L 1600 F110W 10 frac MW 10 10

where D L is the luminosity distance. We report in Table 2 absolute magnitude, M 1600Å , uncertainties as the uncertainty on the apparent magnitude as reported by Source Extractor with propagation of the redshift uncertainty, when reported.

We report 3σ lower limits on the observed magnitude for sources that are not detected in our images. In each HST image of a nondetected galaxy, we measure the flux within randomly placed 0 37 radius apertures within 6″ of position of the afterglow. This aperture size was chosen as it is the average 1 and 2, respectively. North is up and east is to the left. radius used for the detections. We calculate the median flux within these regions, and we clip any flux measurements with a >3σ divergence from this value and then recalculate the median. We repeat this 3σ median-clipping procedure until convergence of the median. Three standard deviations above this median value is used as an upper limit for the magnitude of the host galaxy. We then aperture correct these limits using the same methods as were used for the detections and report these final upper limits in Table 3. These galaxy magnitudes, both detections and upper limits, were derived in this way for modeling and comparison of the UV LF of our sample, which we detail in Section 3.

Discussion

Lyman-break Galaxy Ultraviolet Luminosity Functions

We derive the luminosity distribution of our GRB host galaxy sample from Tables 2 and 3. We compare these results to samples of Lyman-break galaxies at z ∼ 5 from Bouwens et al. (2021;hereafter B21a) and Finkelstein et al. (2015;hereafter F15). These LFs are based on the largest and most complete samples of these galaxies in the relevant redshift range. As such, they provide a good representation of the state of knowledge of the Lyman-break galaxy LF at z ∼ 5 and provide some indication of systematic variations that may be due to the different approaches of the these independent teams. We elected to not use results from the more recent Bouwens et al. (2022a) due to their choice of functional form for the LF, which deviates from the standard Schechter function by including an additional parameter, δ, that allows for curvature at the faint end (M UV > -16 mag) of the LF. Their formula and best-fit parameters result in a divergent LF whose CDF is inherently highly sensitive to the choice of the lower integration limit. Furthermore, since our faintest detected GRB host galaxy is at M UV = -18.1 mag and even the upper limits for our nondetections are not much fainter than this, our data are insensitive to the shape of the faint-end LF and could not place any meaningful limitations on this additional parameter. Indeed, even with their larger sample of 59 z ∼ 5 Lyman-break galaxies, they find δ = 0.07 ± 0.2, to an uncertainty 5× greater than that they find for their α (0.04). The Schechter function parameters from both B21a and F15 are reported in Table 4.

To compare the Lyman-break galaxy LFs of B21a and F15 meaningfully to that of our GRB host galaxies (detailed in the following sections), we must first account for the GRBproduction rate. To do so, it is necessary to weight the Lymanbreak galaxy LFs by the instantaneous SFR, as the GRBproduction rate is expected to be proportional to the SFR. The SFR is proportional to the intrinsic UV luminosity (Kennicutt 1998), and so we can effectively account for GRB selection effects by multiplying the Lyman-break galaxy LF by the intrinsic luminosity of the Lyman-break galaxy. We consider two conversions of the intrinsic to the observed UV luminosity, as the LFs are functions of the observed luminosity. In both cases, we construct the base SFR-weighted Schechter Notes. From left to right: name of the GRB, host centroid position in ICRS, apparent magnitude of the host galaxy as reported from Source Extractor, Galactic extinction from NED (Schlafly & Finkbeiner 2011), and the absolute UV magnitude of the host galaxy as converted using the methods described in Section 2. The uncertainty on the absolute magnitude also accounts for that in redshift. a Galactic extinction for GRB 130606A is A F140W . Note. From left to right, apparent magnitudes (as 3σ above sky and EE corrected), Galactic extinction from NED (Schlafly & Finkbeiner 2011), and extinction-corrected absolute magnitudes as converted using the methods described in Section 2. When applicable, the redshift uncertainty was propagated, and the brighter limit was chosen.

LF (i.e., a predicted GRB host LF) as below:

where L * is the characteristic luminosity, L int is the intrinsic luminosity, L obs is the observed luminosity, f * is a normalization parameter, and α is the faint-end slope, as is standard in the Schechter function. In magnitude space, this can be restated as:

where f (M obs ) = 0.4 × (M * -M obs ), M int is the intrinsic magnitude, M obs is the observed magnitude, f ** is a normalization parameter, and α is still the faint-end slope. M * is the characteristic magnitude and is defined as

, where L 0 is the luminosity of a source with an absolute magnitude of 0.

1. In our first formalism, we assume a luminosity-independent dust contribution where the intrinsic luminosity, L int , is linearly proportional to the observed luminosity, L obs .

Here, µµ -Ĺ L 10 M int obs 0.4 obs . 2. Our second formalism is one where we assume a nonlinear luminosity-dependent dust contribution. We make this assumption because we expect more massive galaxies to have more dust. We construct this formalism from the following two relations from O11 13 and Bouwens et al. (2014), respectively:

where A 1600 is the extinction at 1600 Å and β is defined as:

91 0.14 19.5 . 4 UV Since A 1600 cannot be negative, this results in a piecewise LF of the form of Equation (1) where now ( ) µ> --Ĺ M 10 for 17.3 5 M int 0.4 obs obs and ( ) ( ) µ -´´+  L M 10 for 17.3 6 M int 0.4 1.25 4.39 obs obs 3. Our third formalism is one where we again assume a nonlinear luminosity-dependent dust contribution, however we substitute for Equation (3) an estimation of the same relation from M99: ( ) b =+ A 1.99 4.43 7 1600

We refer to our second and third formalisms as "O11" and "M99," respectively, in reference to the choice of the A 1600 (β) formulation (i.e., the choice of Equations (3) or (7)).

Gamma-Ray Burst Host Ultraviolet Luminosity Function

We use Bayesian hierarchical modeling to constrain the parameters of the luminosity distribution of the GRB host galaxies. We assume the galaxies follow a SFR-weighted Schechter function (see Equation (1)) with a faint-end magnitude limit of M UV = -14.1 mag (this arbitrary magnitude choice converts to a convenient value in our luminosity units and is well below our detection threshold in all cases, although we find that our results are not statistically sensitive to this precise choice). We used weakly informative Gaussian priors of μ α = -1.6, σ α = 1.0 and m s == 10, 1

for the α and L log parameters, respectively. The model self-consistently included both the detections and the seven upper limits: the luminosity for each of these 23 objects was a free parameter in the model, and hence each has a corresponding posterior distribution. We symmetrized the uncertainties for each measurement, conservatively selecting the greater of the two, though we find that our results are also not sensitive to this choice. Four chains were run per model with at least 100,000 samples per chain after warm-up, which ensured negligible MCMC standard errors for all parameters of interest. In the final model runs, there were no divergences, and the chains for all parameters mixed well, with the convergence diagnostic =  R 1. We complete this process three times, once each for our different considerations of the SFR-weight on the Lyman-break galaxy LF as described in the previous section. To model these luminosity distributions of the GRB host galaxies, we use the Stan software as implemented in version 2.26.13 of the RStan package (Stan Development Team 2024).

We show the posteriors and best-fit SFR-weighted Schechter functions for the L-independent and O11 weightings in Figure 2. These best-fit α and M * parameters, along with their 1σ uncertainties, are provided in Table 4 as well as the same parameters for the M99 weighting. The Schechter parameters from B21a (α = -1.74 ± 0.06 and M * = -21.10 ± 0.11 mag) are consistent to within 2σ to our O11 best-fit parameters (α = -1.47 ± 0.27 and M * = -20.25 ± 0.47 mag). The same is true for the parameters from F15 as well as for those from other z ∼ 5 Lyman-break galaxy LF studies (e.g., van der Burg et al. 2010;Ono et al. 2018;Harikane et al. 2022). These Lyman-break galaxy fits are consistent to within 2σ to our Lindependent weighting as well. The slightly better agreement of the Lyman-break galaxy LFs to the O11 formalism is expected, as this formalism offers a more realistic estimate of the intrinsic extinction at z ∼ 5. Along this parametric comparison, there is Note. The fits to the GRB hosts were measured from our RStan program, while fits to the Lyman-break galaxies were copied from the listed citations. 13 The amount of host UV extinction due to dust at z ∼ 5 is an active area of research. The choice for this correction has often been that from M99, A 1600 = 4.43 + 1.99β. However, there have been several updates to this relation (e.g., O11; Takeuchi et al. 2012;Bouwens et al. 2014;Casey et al. 2014). Here, we elect to use the relation from O11 (as stated in Equation (3)), as it is measured from Lyman-break analog galaxies, which offers the closest comparison to our GRB hosts.

no evidence of disagreement between the GRB host galaxy sample and the Lyman-break galaxy samples. While the differences between the galaxy samples are not statistically significant, the best fits to the GRB host galaxies have a shallower α and a fainter M * . With a larger GRB host galaxy sample, if these parameter differences were to become statistically significant, the move toward a shallower α and a fainter M * would indicate that Lyman-break galaxy LFs overpredict the amount of faint star formation.

We construct a CDF of the GRB host galaxy LF by using Kaplan-Meier estimation (Kaplan & Meier 1958) on our observed magnitudes and upper limits. We plot this CDF in Figures 2 and 3. We qualify the uncertainty on this CDF by plotting also a subset of the CDFs created from random draws of the modeled magnitude sets. In this figure we also show the CDFs of the UV LFs from B21a and F15 with the different extinction assumptions.

To measure the likelihood of inconsistency between the Lyman-break galaxy and metallicity-biased GRB host galaxy luminosity distributions to that of the observed z ∼ 5 GRB host galaxy distribution, we use a log-rank test. This test was chosen because for its applicability to distributions including censored data (i.e., our upper limits), unlike commonly used statistical tests, like a Kolmogorov-Smirnov (Massey 1951) or an Anderson-Darling test (Stephens 1974). We report the p-value corresponding to the calculated χ 2 statistic for each test in Table 5. This p-value is the probability of achieving the χ 2 test statistic, and so since we consider a 2σ threshold, we accept p < 0.05 as confirmation for the null hypothesis that the compared samples are pulled from different distributions. To complete these tests, we use survdiff within the survival package in R (Terry & Patricia 2000; R Core Team 2023; Therneau 2024).

With p-values all above p = 0.05, we find no evidence for inconsistency between our O11 and M99 SFR-weighted Lyman-break galaxy luminosity distributions and our derived GRB host galaxy luminosity distribution. We do, however, find 2σ disagreement (though 3σ agreement) between our Lindependent SFR weighting for both the B21a and F15 Lyman-break galaxy luminosity distributions and that of our GRB host galaxies. These results imply that if GRBs are to trace star formation, either the L-independent extinction correction is an incorrect assumption for the distribution of dust in z ∼ 5 star-forming galaxies or additional parameters are necessary, perhaps the faint-end slope curvature parameter δ presented in Bouwens et al. (2022a).

Investigating the Metallicity Bias

Lastly, we consider the influence of metallicity in our LF fits. To quantify GRB-production metallicity sensitivity, we consider the UV LF predictions at z = 4.75 from T15). Those authors developed a model that considers two GRB progenitor pathways: one that is metallicity dependent and one that is metallicity independent, which they refer to as "metallicity sensitive" (MS) and "metallicity insensitive" (MI) channels. They quantify the percentage of GRBs originating from a MI pathway with their "GRB efficiency" function, κ(Z). This is . Right: a similar plot to that on the left, with the same GRB host galaxy LF, but using as comparison now the z ∼ 5 SFR-weighted UV LF from F15. The pink LF again contains the assumption that galaxy extinction is luminosity independent, while the LF in dark blue (light blue) assumes the O11 (M99) extinction correction. defined as:

where κ 0 , a, and b are piecewise defined based on galaxy metallicity and take on the same values as in T15. In this context, p is what they refer to as the "plateau" parameter and can take on any nonnegative value.

In the low-metallicity (and therefore high-z) limit, this MI efficiency function, κ(Z), asymptotically "plateaus" to the value p/(1 + p). While p is explicitly not a probability (and can take on any nonnegative value), it is correlated with the percentage of GRBs originating from the MI channel. Across all metallicities and redshifts, when p = 0, it is assumed that GRBs originate exclusively from the MS channel, and when p = ∞, it is assumed GRBs originate exclusively from the MI channel. Positive and finite values of p assume a split of GRB progenitor paths. Trenti et al. (2015) applied their models to the Swift GRB catalog and to other GRB host galaxy samples (Savaglio et al. 2009;Cucchiara et al. 2015) and found that p = 0.2 best replicates the redshift evolution of the GRB rate to z ∼ 6. At z ∼ 5, the majority of galaxies have metallicities below the threshold values found in the local Universe, so we expect the host galaxy LF to be more consistent with the MI parameterization, p = ∞.

We show in Figure 4 the four z = 4.75 LFs predicted by Trenti et al. (2015) for different values of p overlaid on our GRB host galaxy LF, and we report the results of log-rank tests between these relations in Table 5. We find only the p = 1000 case to be consistent with our LF to within the Gaussian-equivalent 2σ. Specifically, we find disagreement with our observations and the p = 0.2 model favored by Trenti et al. (2015). The disagreement of the p = 0.2 model with the high-redshift host galaxy LFs (ours at z ∼ 5 and that at z ∼ 3.5 from Greiner et al. 2015) implies that a different metallicity parameterization for GRB production is necessary.

Gamma-Ray Burst Host Size Distribution

Observations of Lyman-break galaxies have shown a correlation between UV luminosity and half-light radius (Kawamata et al. 2015;Shibuya et al. 2015;Bouwens et al. 2022b). Studies of the sizes of GRB host galaxies have shown that they are, on average, smaller than the general population at z < 1 but by z ∼ 3 they have comparable sizes (Conselice et al. 2005;Kelly et al. 2014;Lyman et al. 2017;Schneider et al. 2022). Additionally, Wainwright et al. (2007) showed evidence for a size-luminosity relation for GRB host galaxies at 0 < z < 3, with 〈z〉 ∼ 1. We investigate this relation and how it compares to that of field galaxies of our sample of GRB host galaxies at z ∼ 5. We present half-light radii (R eff ) for our 16 detected host galaxies in Table 6 and Figure 5. We first constructed point-spread functions (PSFs) for each of our two filters, F110W and F140W. Schneider et al. (2022) found that for a sample of the fields of 42 GRB host galaxies at z ∼ 2 imaged with WFC3/F160W, the constructed PSF had a radius profile stable against the choice of field in which to select stars for the star catalog but had a signal-to-noise ratio that was dependent on the number of stars selected, increasing with the size of the star catalog. In their study of GRB host half-light radii at z ∼ 2, Schneider et al. (2022) find that N ∼ 30 is a sufficient size for the catalog. We apply this finding to our sample and use 33 stars from the fields of GRBs 050814 and 050922B to construct the PSF for F110W. The choice of these fields was mostly arbitrary, however we chose not to use fields crowded with several saturated stars (such as that of GRB 140614A). We had only one GRB field imaged in F140W, and so we select 26 stars from the field of GRB 130606A to construct the PSF for this filter. We use the astropy package EPSFBuilder (Bradley et al. 2023) to generate the two PSFs from these star catalogs. (2015). Described in detail in Section 3.3, the p-parameter is tied to the influence of metallicity on the GRB progenitor path. Across all redshifts, when p = 0, there is a metallicity bias where GRBs cannot be produced in environments with Z > Z e , and when p tends to infinity, GRB creation is MI. In Trenti et al. (2015), they report Schechter function LF parameters for four choices of p, which we plot here. The results from log-rank tests between the black, median LF for our GRB host sample, and the four metallicity-biased LFs are shown in Table 5. Note. From left to right the columns are the name of the GRB, the half-light radius (R eff ) in pixels, and R eff in parsecs. When applicable, the redshift uncertainty was propagated.

We measure the half-light radii of our detected GRB host galaxies by fitting a Sérsic light profile with GALFIT (Peng et al. 2010). On our first measurement attempt, we use as guesses the results from Source Extractor with GALFIT able to fit all parameters. If the program was not able to converge all parameters, we try again holding R eff constant but all other parameters open. If the other parameters converge on this run, we fix the parameters to these new values and allow for GALFIT to fit for R eff on the next run. If the parameters do not converge, or if R eff does not converge as the only free parameter, we instead try fixing all parameters to the Source Extractor guesses and allowing the program to fit for only R eff . If there still was no convergence, and there was a second source within 20 pixels of the host, we rerun the program with a second Sérsic profile for the second source. We use the same methods to attempt convergence for both sources. In all cases, if there was sufficient convergence, the residual was visually checked for confirmation of a good fit. We record R eff and its uncertainty reported by GALFIT in Table 6.

For three of our sources (the host galaxies of GRBs 050814, 111008A, and 140311A), no runs were successful following this procedure, meaning either no convergence of R eff or a visually bad residual. For the host galaxies of GRBs 111008A and 140311A, we adopt R eff upper limits as those reported by Source Extractor. For the host galaxy of GRB 050814, we updated the Source Extractor guesses to our best guesses, with our only change being updating the position angle (PA) from -61°to 40°. With this update, GALFIT converged all parameters. This fit is elaborated upon in the Appendix entry for GRB 050814.

We compare this sample of GRB host galaxy sizes to Lyman-break galaxy sizes at z ∼ 4 and z ∼ 6-8 (Bouwens et al. 2022b) in the form of a size-luminosity relation in Figure 5. Under the assumption that GRBs unbiasedly trace star formation, we expect z ∼ 5 GRB host galaxies to fall in between the z ∼ 4 and z ∼ 7 relations. Since our smaller sample has an average z = 4.6, if this assumption is to be true, we would expect the GRB host sample to be weighted closer to the z ∼ 4 relation. We find that ∼68% (11/16) of our GRB host galaxies fall within or below the 1σ scatter of the z ∼ 4 relation. This supports our claim that at z ∼ 5, Lyman-break and GRB host galaxies trace the same stellar populations.

Gamma-Ray Burst Host Galaxy Nondetection Fraction and Implications of Hidden Star Formation

The source of the UV photons needed to reionize the intergalactic medium in the early Universe has been and continues to be an area of very active research (Furlanetto & Mesinger 2009;Robertson et al. 2015;Endsley et al. 2023). One explanation for this process is the UV radiation from massive stars in star-forming galaxies (Madau et al. 1999;Ciardi et al. 2000;Bunker et al. 2004Bunker et al. , 2010;;Finkelstein et al. 2010Finkelstein et al. , 2012)). Until recently, with the launch of JWST, investigations of the feasibility of this explanation have mostly stopped at z ∼ 8 or have relied on the extrapolation of the characterizations of lower-redshift observations of Lymanbreak galaxies to higher redshifts and fainter magnitudes (Oesch et al. 2010;Bouwens et al. 2012). Recent JWST-based studies have found discrepancies from lower-z expectations and models, namely the detection of more massive, bright galaxies than expected (Harikane et al. 2023;Finkelstein et al. 2023). There have been many offered explanations for these discrepancies, including stochastic star formation (Furlanetto & Mirocha 2022;Mirocha & Furlanetto 2023;Shen et al. 2023) and high-efficiency star formation (Dekel et al. 2023).

While using GRBs to test the feasibility of massive star reionization of the Universe is not new (e.g., Tanvir et al. 2019), our complete GRB sample offers the first opportunity to test this feasibility with statistical robustness at a redshift just outside the "Epoch of Reionization." From our nondetection fraction, we can estimate the percentage of star formation that is occurring in galaxies fainter than our detection limit (i.e., galaxies that are intrinsically faint and galaxies that would otherwise be detected but are dust obscured). These are galaxies that are inherently often missed in star-forming galaxy samples as they are not directly observable. Comparing the direct measurement of the percentage of faint star formation to expectations from Lyman-break galaxy LFs is critical, as faint star-forming galaxies are thought to be important contributors of ionizing photons (McLure et al. 2010).

Under the assumption that GRBs unbiasedly trace star formation at this redshift, using binomial statistics, our nondetection fraction of 7/23 is consistent at the 95% confidence level with 13%-53% of star formation occurring in galaxies fainter than our detection limit of M UV ≈ -18.3 mag. This measurement is unique in that it is independent of the functional form of the LF and offers a nonparametric way to test the consistency of an assumed functional form to an observed quantity. It is shown in Figure 3, that the percentage of undetectable star formation predicted by the SFR-weighted Schechter function Lyman-break galaxy LFs is ∼40% ± 5% and ∼25% ± 5% when considering L-independent and Ldependent (O11 and M99) host extinction, respectively. The lack of disagreement between all of the Lyman-break galaxy predictions and the GRB host galaxy measurement offers support for the hypothesis that star-forming galaxies are large contributors of ionizing photons in the early Universe.

Conclusions

We present new rest-frame UV HST imaging of a complete sample of 23 long-GRB host galaxies at z ∼ 5. From our imaging, we measure UV magnitudes and galaxy sizes. We detect 16 GRB host galaxies and place upper limits on the magnitudes of the remaining seven. Of the 16 detections, we are able to spatially resolve 14 and place upper limits on the sizes of the remaining two. Through the construction of a UV LF, we find that our GRB host sample is statistically consistent (log-rank test p > 0.05) with that of the star-forming galaxy population at the same redshift, when using reasonable corrections for the intrinsic extinction in star-forming galaxies. When investigating the feasibility of the metallicity-bias model of GRBs from Trenti et al. (2015), we find that our host sample is inconsistent with this model. Assuming a SFR-weighted Schechter function formalism and a GRB rate proportional to the dust-corrected UV luminosity, we find parametric agreement between both α and M * of our best fits and those from B21a and F15, again regardless of our choice of galaxy extinction. We find that 11 of our 16 (∼68%) host galaxies fall within or below the 1σ scatter of the size-luminosity relation of z ∼ 4 star-forming galaxies from Bouwens et al. (2014). The lack of disagreement between the luminosity-dependent UV LFs and the size-luminosity relations between the Lymanbreak and GRB host galaxy samples implies that at z ∼ 5, GRBs are unbiased tracers of star formation.

Under this well-supported assumption that GRBs are unbiased tracers of star formation at this redshift, we use our nondetection fraction of 7/23 and binomial statistics to estimate that, at 95% confidence, 13%-53% of star formation is undetected in observations of these depths. In other words, we find that up to ∼50% (or alternatively, only ∼10%) of star formation could be occurring in galaxies with M UV > -18.3 mag. This measurement is complementary to and unique from similar measurements from Lyman-break galaxy surveys since it is insensitive to the parameterization of the LF. This solidifies the importance of GRB afterglow and host galaxy observations as a tool for studies of high-z star formation.

The sample presented here is the largest and most complete sample of GRB host galaxies at this redshift. It is unlikely that this sample will be surpassed in statistical sensitivity in the near future, due to our bias-minimizing selection cuts. One of the selection criteria was a detection cut pre-2015. Since then, there have been 12 additional Swift-detected GRBs with z > 4. If all of these sources were to meet our sample criteria and followed our detection distribution, the addition of these 12 sources would improve our sensitivity by ∼40% (i.e., our uncertainty on the Schechter parameters would be reduced by ∼40%). While an improvement, this precision is still not better than that from Lyman-break galaxy samples and therefore the inclusion would not result in a significant statistical advance from the analysis performed here. What is needed to improve this analysis is, simply, the detection and follow up of many more high-redshift GRBs. There are missions, like the Space-based multiband astronomical Variable Objects Monitor (SVOM; Wei et al. 2016), Gamow Explorer (White et al. 2021), and The Transient High-Energy Sky and Early Universe Surveyor (THESEUS; Tanvir et al. 2021) planned expressly for such follow up. The analysis presented here shows directly how results from such missions can be interdisciplinary, improving not GRB science but our understanding of star-forming galaxies as well.

Swift-XRT error circle. The centroid of the afterglow was measured to an uncertainty of 0 041 using Source Extractor, and the astrometric alignment to the HST image had a measured rms uncertainty of 0 043 using TweakReg. These uncertainties are added in quadrature for a total positional uncertainty on the afterglow of 0 060. Within a 3σ (0 18) radius region in the HST image at the position of the afterglow, there is no source detected with Source Extractor. We find two sources within a 5″ box centered at the position of the afterglow, and we calculate P cc values for both above 0.6. For this reason we consider the host of this GRB to be a nondetection. Following the prescription in Section 2, we estimate a limiting magnitude of m F110W > 27.55 mag at 3σ above background in a 0 37 radius aperture.

A.2. GRB 050505

GRB 050505 has a spectroscopic redshift of z = 4.275 from Keck/LRIS afterglow spectroscopy analyzed in Cenko et al. (2005). With Keck/LRIS I-band imaging from 2005 May 6, we identify a source within the Swift-XRT error region. We estimate an uncertainty on the centroid of 0 0024 and an uncertainty on the astrometric alignment to the HST image of 0 050. These uncertainties are added in quadrature for a total afterglow positional uncertainty of 0 050. The afterglow and its 3σ uncertainty region are coincident with a source in the HST image. We calculate P cc = 0.02 for this source, and we identify it as the host of this GRB. We report a measured apparent magnitude of m F110W = 25.95 ± 0.10 mag.

A.3. GRB 050803

GRB 050803 has a photometric host galaxy redshift of = -+ z 4.3 2.40 0.60 as detailed in Perley et al. (2016a). All optical afterglow imaging referenced in the General Coordinates Network (GCN) circulars for this source was for a misidentified source at z = 0.4, and consequently the afterglow position we report is the enhanced Swift-XRT position with its 1 4 uncertainty. The MAST-assigned WCS for the WFC3/ F110W image was incorrect by several arcseconds, however, we were able to correct this with alignment to a WFC3/F160W image (ID: 12307, PI: Levan) of the same field. This alignment has an uncertainty of 0 094. Within the Swift-XRT region in the HST image, we detect only one source. This source is consistent with that reported in Perley et al. (2016a) used to identify the photometric host galaxy redshift, and we therefore classify it as the host galaxy of this GRB. Using Source Extractor, we measure an apparent magnitude of this host galaxy of m F110W = 26.08 ± 0.11 mag. We calculate P cc = 0.35 for this source when using the 90% confidence Swift-XRT uncertainty as R e . This percent chance coincidence is well above our 10% threshold. When estimating the impact of false host-association contamination in our sample, we also consider the possibility that this is a nondetection with a measured limiting magnitude of m F110W > 27.16 mag.

A.4. GRB 050814

GRB 050814 has a photometric afterglow redshift of z = 5.77 as reported in Curran et al. (2008). We detect the afterglow in stacked P60 i-band imaging from 2005 August 15. We report an uncertainty on the centroid of the afterglow of 0 16, and an uncertainty on the astrometric alignment to the HST image of 0 20, for a total positional uncertainty of 0 257. Within a 0 78 radius region centered at the afterglow position in the HST image, we detect a single source for which we calculate P cc = 0.08. We identify this source as the host galaxy of GRB 050814 and measure an apparent magnitude of this galaxy of m F110W = 25.46 ± 0.03 mag.

GALFIT was unable to converge on a single Sérsic profile, following our standard methods of using the Source Extractor parameter results as input. We were able to achieve converge after modifying the PA guess from -61°to 40°, our estimate of the PA of the galaxy. While all parameters converged and the residual image of this solution passed our visual check, the Sérsic index, N, converged to N = 9.97 ± 3.03, which is much larger than expected. We also attempted to fit the galaxy with two Sérsic components and achieved convergence for both profiles, but the residual did not pass our visual check. We chose to complete the analysis with the R eff from the single component solution, R eff = 1.00 ± 0.11 pixel.

A.5. GRB 050922B

GRB 050922B has no afterglow detections reported in the literature but has a photometric host redshift of = -+ z 4.9 0.6 0.3 as detailed in Perley et al. (2016a) from i-and z-band Gran Telescopio CANARIAS (GTC)/OSIRIS imaging. We detect three sources within the Swift-XRT error circle including the source identified in Perley et al. (2016a). We measure an apparent magnitude of this source of m F110W = 25.37 ± 0.08 mag. We calculate P cc = 0.44 for this source when using the 90% confidence Swift-XRT uncertainty as R e . This percent chance coincidence is well above our 10% threshold. When estimating the impact of false host-association contamination in our sample, we also consider the possibility that this is a nondetection with a measured limiting magnitude of m F110W > 27.85 mag.

A.6. GRB 060206

GRB 060206 is located at z = 4.048 as reported in Fynbo et al. (2006a). We were unable to use TweakReg to align the P60 R-band imaging of the afterglow from 2006 February 6 (Ofek et al. 2006) to our HST image due to there being only one sufficiently bright source in common between the two images. We instead align each image separately to the Gaia DR2 catalog. For this alignment, we consider an uncertainty of approximately 1 HST pixel = 0 065. We detect the afterglow with Source Extractor with a positional uncertainty on the centroid of 0 016 for a total positional uncertainty of 0 067. Within a 0 20 radius region at the position of the afterglow, we detect a source in our HST image. We calculate P cc = 0.02 for this galaxy, and we therefore identify it as the host galaxy of this GRB. We measure an apparent magnitude of m F110W = 27.56 ± 0.22 mag.

A.7. GRB 060223

GRB 060223 has a spectroscopic afterglow redshift of z = 4.406 as reported by Chary et al. (2007). The only afterglow imaging provided in the literature is V-band Swift-UVOT imaging from 2006 February 23 (Blustin et al. 2006). There was only one source (a saturated star) in common between the HST and UVOT images, so we were unable to complete image alignment using TweakReg. Since each image was aligned to Gaia DR2 upon download from their respective archives, we consider the alignment uncertainty to be within 1 HST pixel = 0 065. We add this in quadrature to the afterglow centroid uncertainty measured with Source Extractor of 0 042 to get a total afterglow positional uncertainty of 0 077. The afterglow position and its 3σ (0 23) uncertainty region are coincident with a source in the HST image. We calculate P cc = 0.06 for this source and identify it as the host galaxy of GRB 060223. We measure an apparent magnitude of this galaxy of m F110W = 26.63 ± 0.07 mag. For this host galaxy, Blanchard & Berger (2016) report a Galacticextinction-corrected magnitude of m F110W = 26.534 ± 0.069 mag, which is consistent with our measurement of m F110W = 26.53 ± 0.07 mag.

A.8. GRB 060510B

GRB 060510B has a spectroscopic afterglow redshift, z = 4.941, as measured in Price et al. (2007). We align i-band GMOS-N imaging of the afterglow from 2006 May 10 ( Price et al. 2006) to the HST image. We measure an rms alignment uncertainty of 0 09, and we add this in quadrature to the afterglow centroid uncertainty of 0 0062 measured with Source Extractor for a total afterglow positional uncertainty of 0 09. The afterglow position and its 3σ (0 27) uncertainty region are coincident with a source in the HST image. We calculate P cc = 0.04 for this source and identify it as the host galaxy of this GRB. We measure an apparent magnitude of this source of m F110W = 26.05 ± 0.06.

A.9. GRB 060522

GRB 060522 has a spectroscopic afterglow redshift of z = 5.110 as reported in Chary et al. (2007). We reduced Rband TNG imaging of the afterglow from 2006 May 22 and report a 0 028 uncertainty on the centroid of the afterglow. We align this reduced image to the HST image and report an uncertainty of 0 05 on this astrometric alignment. We sum these uncertainties in quadrature and report a total positional uncertainty of 0 05. We do not detect a source within a 0 15 radius region centered at this afterglow position in the HST image. We find three sources within a 5″ box centered at the position of the afterglow, and we calculate P cc values for all above 0.2. For this reason we consider the host of this GRB to be a nondetection. We report a limiting magnitude of m F110W > 27.83 mag. For this source, Blanchard & Berger (2016) report a nondetection and an upper limit of m F110W > 28.9 mag, and Tanvir et al. (2012a) report a nondetection and an upper limit of m F110W > 28.13 mag. Blanchard & Berger (2016) define their 3σ upper limits as the magnitude at which sources are detected at 3σ significance. The result from Tanvir et al. (2012a) is inconsistent with our upper limit, however they perform forced photometry in a 0 4 radius aperture at the afterglow location and also use a 2σ detection threshold. When we apply the same methods, we are able to reproduce their limit. For consistency of our GRB host galaxy sample, we continue with our limit of m F110W > 27.83 mag.

A.10. GRB 060927

GRB 060927 has a spectroscopic afterglow redshift of z = 5.467 as detailed in Ruiz-Velasco et al. (2007) from VLT/FORS1 spectroscopy. We are unable to find the centroid of the afterglow with Source Extractor due to blending with a nearby galaxy in I-band VLT imaging at 2.6 days posttrigger (Ruiz-Velasco et al. 2007), but the afterglow is visible in DS9 after adjusting the scale and smoothing parameters. We are able to estimate the center of the afterglow to within 0.5 VLT pixels (0 126), and we also report a 0 023 astrometric uncertainty, resulting in a total positional uncertainty of 0 128 for the afterglow. There are no sources detected within 0 385 of this position. Within a 5″ box centered at the position of the afterglow, we find three sources and calculate P cc values for two of them above 0.8. The third source (the only one visible with our scaling choice in Figure 1 and is the blended source in the VLT imaging) had P cc = 0.11. This nearby source was detected in VLT R-band imaging (Basa et al. 2012) and therefore is at z < 4, and we therefore exclude this source as the possible host galaxy for GRB 060927. For these reasons, we consider the host of this GRB to be a nondetection. We report a limiting magnitude of m F110W > 27.84 mag. Tanvir et al. (2012a) report a limiting magnitude m F110W > 28.57, however they perform forced photometry in a 0 4 radius aperture at the afterglow location and also use a 2σ detection threshold. When we apply the same methods, we are able to reproduce their limit. For consistency of our GRB host galaxy sample, we continue with our limit of m F110W > 27.84 mag.

A.11. GRB 071025

GRB 071025 has a photometric afterglow redshift of z = 4.8 ± 0.4 as presented in Perley et al. (2010). To identify the host galaxy of this GRB, we use H-band REM imaging of the afterglow from 2007 August 25. We were successful in using TweakReg to align the afterglow and HST images, despite there being few sources (many of them saturated stars) in common between the fields. We report an alignment rms uncertainty of 0 22 and an afterglow centroid uncertainty of 0 14 for a total positional uncertainty on the afterglow of 0 26. We detect one source within 0 78 of the afterglow position in the HST image, though this source has a calculated P cc = 0.12. We identify only one other source within 5″ of the afterglow position: the bright source in the upper left corner in Figure 1. We measure an apparent magnitude of m F110W = 23.6573 mag and P cc = 0.24 for this source. Because of the bright magnitude and higher P cc , we elect to identify the first source as the host galaxy of GRB 071025. We report an apparent magnitude of m F110W = 26.06 ± 0.10 mag for this galaxy.

A.12. GRB 090516A GRB 090516A has a spectroscopic afterglow redshift of z = 4.111 as reported in de Ugarte Postigo et al. (2012). We identify the afterglow in VLT/FORS2 R-band imaging from 2009 May 17 and align this imaging to the HST image of the field of the GRB. We report an astrometric alignment uncertainty of 0 022 and a centroid positional uncertainty of 0 0058 for a total positional uncertainty on the afterglow of 0 023. This position and its 3σ uncertainty region are directly on a galaxy in the HST image. We calculate P cc = 0.08 for this source and identity it as the host galaxy of GRB 090516A. We report an apparent magnitude of m F110W = 25.04 ± 0.07 for this galaxy. This source was also identified by Greiner et al. (2015) and has a reported M UV = -20.99 ± 0.4 mag, which is consistent with our absolute magnitude of M UV = -21.24 ± 0.07 mag. 3σ of this afterglow position in the HST image. We find four sources within a 5″ box centered at the position of the afterglow, and we calculate P cc values for all above 0.4. For these reasons, we consider the host of this GRB to be a nondetection. We measure a limiting magnitude for this galaxy of m F110W > 27.49 mag.

A.20. GRB 140311A

GRB 140311A has a redshift of z = 4.954 as measured from Gemini/GMOS-N spectroscopy of the afterglow (Chornock et al. 2014b). From i-band GMOS-N imaging from 2014 March 12 from the same reference, we measure an uncertainty of 0 058 on the astrometric alignment to the HST image and an uncertainty on the centroid of the afterglow of 0 016. This results in a total afterglow positional uncertainty of 0 060. At the location of the afterglow, we detect a source in our HST image with P cc = 0.03, and we classify it as the host of GRB 140311A. We measure an apparent magnitudes of m F110W = 28.38 ± 0.35 mag.

A.21. GRB 140428A

GRB 140428A is located at a redshift = -+ z 4.68 0.18 0.52 as measured from afterglow photometry reported in Bolmer et al. (2018). We reduced and aligned I-band Keck/LRIS imaging from 2014 April 29 (Perley 2014) to our HST image and report an astrometric tie uncertainty of 0 061. We measure an uncertainty on the centroid of the afterglow of 0 026 for a total afterglow positional uncertainty of 0 066. We find no sources in the HST image within 0 18 of the afterglow position. We find four sources within a 5″ box centered at the position of the afterglow, and we calculate P cc values for all above 0.2. For this reason, we consider the host galaxy of GRB 140428A to be a nondetection, and we report a limiting magnitude of m f110w > 27.66 mag.

A.22. GRB 140518A

GRB 140518A is at a redshift of z = 4.7055 as reported in Cucchiara et al. (2015) from GMOS-N afterglow spectroscopy. We align i-band GMOS-N imaging from 2014 May 18 (Chornock et al. 2014a) to our HST image, and we report an astrometric tie uncertainty of 0 047. We also report an uncertainty of 0 002 on the centroid of the afterglow for a total positional uncertainty on the afterglow position of 0 047. The afterglow position is coincident with a source in the HST image, and we calculate P cc = 0.05 for this source. We therefore classify this galaxy as the host of this GRB. We report an apparent magnitude of m F110W = 27.22 ± 0.13 mag.

A.23. GRB 140614A

GRB 140614A has a redshift of z = 4.233 as reported in GCN 16401 (Kruehler et al. 2014) from VLT/X-shooter afterglow spectroscopy. We reduce and align i'-band VLT/Xshooter imaging of the afterglow from 2014 June 14 (Kruehler et al. 2014) to our HST image and report an uncertainty on this astrometric alignment of 0 35. We measure an uncertainty of 0 045 on the centroid of the afterglow with Source Extractor for a total positional uncertainty on the afterglow of 0 349. We detect a source in the HST image within the 3σ uncertainty region. We calculate P cc = 0.21. While this is above our threshold of P cc = 0.1, we identify this source as the host of this GRB because the source is close to the center of the uncertainty region. We report an apparent magnitude for this galaxy of m F110W = 26.14 ± 0.09 mag.