Short GRB Host Galaxies. I. Photometric and Spectroscopic Catalogs, Host Associations, and Galactocentric Offsets

We first present new ground-based data for events in our sample that were discovered since the launch of Swift in 2004 until 2021 December. We attempted a photometric host galaxy search for every short GRB discovered during these years, except for those that have already published identified hosts, are difficult to access with our telescope resources, or have observing constraints that would prevent a meaningful search. In some cases for bursts with published hosts, we obtained imaging in complementary filters to characterize the host SEDs.

To search for host galaxies, we initiated an initial round of deep ground-based imaging for 58 bursts. In general, we obtained optical imaging centered on the most precise available afterglow position in the r or i band. If this imaging did not yield a plausible host galaxy candidate at or proximal to the afterglow position, we obtained NIR imaging in the J or K bands to search for a reddened host (potentially due to a dusty or higher-redshift origin). If either set of optical or NIR initial imaging revealed a plausible host galaxy (see Section 4.2), we obtained 1–10 bands of additional multi-band observations in any of the ugriz, UVRI, RG850, YJHK, or K_s filters to characterize the putative host galaxy SED. If neither our optical nor NIR imaging yielded a plausible host galaxy, we used these ground-based limits to place constraints on the luminosity and redshift of spatially coincident hosts. For five of these events, we obtained follow-up HST observations to perform a more sensitive search for spatially coincident hosts (Section 3.3).

We obtained these observations with the twin 6.5 m Magellan/Baade and Clay telescopes (PIs: Berger, Blanchard), 8 m Gemini-North and Gemini-South telescopes (PIs: Fong, Cucchiara), 6.5 m MMT (PIs: Fong, Nugent), twin 10 m Keck I and II telescopes (PIs: Paterson, Fong, Terreran, and Miller), the 3.8 m United Kingdom InfraRed Telescope (UKIRT; PI: Fong), and the twin 8.4 m Large Binocular Telescopes (LBT; PI: Fong, Smith). We used 18 distinct instruments across these facilities for imaging. The telescopes, instruments, and filters used for our catalog are listed in Table 1. This imaging typically reaches 3σ limits of m_AB,opt ≳ 24–26 mag and m_AB,NIR ≳ 22–23.5 mag.

For data reduction and co-addition, we use a combination of standard tasks in the IRAF/ccdred package (Tody 1986; for Magellan, LBT, MMT/MMTCam data), observatory-specific pipelines (for Gemini data), and the POTPyRI software ¹⁹ (for Keck, MMT/Binospec and MMIRS data). For optical data, we apply bias corrections, flat-field corrections using either dome or twilight flats, and dark current corrections when relevant. For NIR data, we additionally apply sky subtraction using coeval on-sky frames. For UKIRT/WFCAM data, we obtain preprocessed images from the WFCAM Science Archive (Hamly et al. 2008), which are already corrected for bias, flat field, and dark current by the Cambridge Astronomical Survey Unit. ²⁰ For each epoch and filter, we co-add the images and perform astrometry relative to Two Micron All Sky Survey (2MASS) using a combination of tasks in Starlink ²¹ and IRAF. The full listing is available in Appendix A and the BRIGHT website. ²² The images are shown in Figures 2 and 3.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

View figure set (90 panels)

Tarball of figure set images

Zoom In Zoom Out Reset image size

We supplement the ground-based imaging with HST observations for 10 events, consisting of events that we have not yet analyzed in our previous works. Six GRBs were imaged in a single band with the F110W filter using the infrared channel on the Wide-Field Camera 3 (WFC3/IR) under Program 14685 (PI: Fong). The purpose of this program was to search for redder host galaxies that may have gone undetected from ground-based optical observations. Indeed, at the time of observation, five of these events had no reported or detected host galaxy at their subarcsecond optical afterglow positions to the limits of ground-based imaging (GRBs 091109B, 110112A, 130912A, 131004A, and 150423A). We recover plausible host galaxies for three of these events (Section 4.2). The sixth event observed in F110W, GRB 160303A, had a ground-based GTC detection of a possible host galaxy (Cano et al. 2016), and this is well detected in our HST imaging (Figure 2). These HST data also newly appear in O'Connor et al. (2022).

The four additional events have multiple epochs and filters (GRBs 060614, 150424A, 160624A, and 160821B) under Programs 10917 (PI: Fox), 13830, 14237 (PI: Tanvir), and 14357 (PI: Troja), and were previously published (Gal-Yam et al. 2006; Knust et al. 2017; Jin et al. 2018; Lamb et al. 2019a; Troja et al. 2019; O'Connor et al. 2021; Rastinejad et al.2021). For each of these latter events, we select the filter that yields the highest signal-to-noise ratio (S/N) for sources in the image to perform our subsequent analysis.

For data reduction, we retrieved preprocessed images from the HST archive ²³ for observations of these nine short GRBs. We used the astrodrizzle routine as part of the drizzlepac package in PyRAF to apply standard distortion corrections and combine the exposures for each event and filter. For WFC3/IR imaging, we use pixfrac = 0.8 and pixscale = 00642 pixel⁻¹, half of the native pixel scale. For WFC3/UVIS images, we first apply a charge transfer efficiency (CTE) correction using the stand-alone Fortran program, ²⁴ and then use astrodrizzle to combine the CTE-corrected exposures using pixscale = 0033 pixel⁻¹. For the ACS images, we use pixfrac = 1.0 and pixscale = 005 pixel⁻¹. The images are shown in Figure 2.

We also compile available photometric data and reduced imaging for all remaining short GRBs with HST observations from our previous works. This results in the addition of 26 short GRBs with HST data. These bursts and their references are listed in Table 2 and Table A1.

Table 2. Short Gamma-Ray Burst Host Galaxy Sample

GRB	R.A.	Decl.	Redshift	Filter	mAB	Pcc	Class	References
	(J2000)	(J2000)			(AB mag)
050509B	12h36m12875	$+28^\circ 58^{\prime}$ 5884	0.2248 ± 0.0002	r	17.123 ± 0.01	5 × 10−3	Gold	1–4
050709	23h01m26765	$-38^\circ 58^{\prime}$ 40422	0.1607 ± 0.0004	R	21.258 ± 0.07	3 × 10−3	Gold	2, 5–8
050724	16h24m44410	$-27^\circ 32^{\prime}$ 26393	0.254 ± 0.001	R	19.829 ± 0.03	2 × 10−5	Gold	2, 9–10
050813	16h07m57200	$+11^\circ 14^{\prime}$ 5309	0.719 ± 0.001	R	23.43 ± 0.07	0.2	Bronze	11–13
051210	22h00m40942	$-57^\circ 36^{\prime}$ 47063	${2.58}_{-0.17}^{+0.11}$	r	24.043 ± 0.15	0.04	Silver	2, 8, This work
051221A	21h54m48653	$+16^\circ 53^{\prime}$ 27335	0.5464 ± 0.0001	r	22.178 ± 0.09	5 × 10−5	Gold	2, 8, 14
060121	09h09m52026	$+45^\circ 39^{\prime}$ 45538	⋯	F606W	26.27	2 × 10−3	Gold	2
060313	04h26m28402	$-10^\circ 50^{\prime}$ 39901	⋯	F475W	26.68	3 × 10−3	Gold	2
060614 c	21h23m32102	$-53^\circ 01^{\prime}$ 36436	0.125 ± 0.002	F814W	21.92 ± 0.1	3 × 10−4	Gold	15
060801	14h12m01262	$+16^\circ 58^{\prime}$ 5597	1.131 ± 0.001	r	23.202 ± 0.11	0.02	Gold	8, 16
061006	07h24m07808	$-79^\circ 11^{\prime}$ 55188	0.461 ± 0.0007	r	24.153 ± 0.09	4 × 10−4	Gold	2, 8, 17, This work
061201	⋯	⋯	⋯	F160W	≳26.4	⋯	Inconclusive	18
061210	09h38m05362	$+15^\circ 37^{\prime}$ 18877	0.4095 ± 0.0001	r	21.396 ± 0.05	0.02	Gold	8, 16
070429B	21h52m03691	$-38^\circ 49^{\prime}$ 4282	0.902 ± 0.001	r	23.283 ± 0.04	3 × 10−3	Gold	8, 19
070707	17h50m58555	$-68^\circ 55^{\prime}$ 2760	⋯	F606W	26.857 ± 0.12	7.0 × 10−3	Gold	18
070714B	03h51m22272	$+28^\circ 17^{\prime}$ 50943	0.923 ± 0.001	r	24.889 ± 0.21	5 × 10−3	Gold	18–20
070724	01h51m14068	$-18^\circ 35^{\prime}$ 3847	0.457 ± 0.0007	r	20.776 ± 0.03	8 × 10−4	Gold	8, 18, This work
070729	3h45m15808	$-39^\circ 19^{\prime}$ 18590	${0.52}_{-0.28}^{+1.17}$	r	23.019 ± 0.263	0.036	Silver	This work
070809	13h35m04177	$-22^\circ 08^{\prime}$ 3301	0.473	r	20.142 ± 0.02	6 × 10−3	Gold	8, 18, 21
071227	3h52m31026	$-55^\circ 59^{\prime}$ 0089	0.381	r	20.635 ± 0.05	0.01	Gold	8, 17–18
080123	22h35m46943	$-64^\circ 53^{\prime}$ 54973	0.495	r	20.96 ± 0.05	0.11	Bronze	8
080503	19h06m28901	$+68^\circ 47^{\prime}$ 3478	⋯	F606W	27.151 ± 0.2	0.05	Silver	18, 22
080905A	19h10m42045	$-18^\circ 52^{\prime}$ 5451	0.1218 ± 0.0003	R	18.0 ± 0.5	0.01	Gold	18, 23
081226A	08h22m0045	$-69^\circ 01^{\prime}$ 495	⋯	r	26.029 ± 0.34	0.01	Gold	24
090305A	16h07m07596	$-31^\circ 33^{\prime}$ 2254	⋯	F160W	25.292 ± 0.10	7 × 10−3	Gold	18
090426A	12h36m18047	$+32^\circ 59^{\prime}$ 0946	2.609 b	F160W	25.57 ± 0.07	1.5 × 10−4	Gold	18, 25
090510	22h14m12623	$-26^\circ 34^{\prime}$ 5855	0.903 ± 0.001	i	22.452 ± 0.14	8 × 10−3	Gold	8, 18, 26
090515	10h56m35847	$+14^\circ 26^{\prime}$ 4284	0.403	r	20.268 ± 0.05	0.05	Silver	8, 18, 21
091109B	07h30m5655	$-54^\circ 05^{\prime}$ 2322	⋯	F110W	27.808 ± 0.24	0.11	Bronze	This work
100117A	00h45m04661	$-01^\circ 35^{\prime}$ 4202	0.914 ± 0.0004	r	24.40 ± 0.10	7 × 10−5	Gold	18, 27
100206A	3h08m39142	$+13^\circ 09^{\prime}$ 2934	0.407 ± 0.002	R	21.53 ± 0.09	0.02	Gold	28, 29
100625A	1h03m10918	$-39^\circ 05^{\prime}$ 1844	0.452 ± 0.002	r	22.659 ± 0.09	0.04	Silver	30
101219A	4h58m20497	$-02^\circ 32^{\prime}$ 2245	0.7179 ± 0.0008	r	24.083 ± 0.05	0.06	Silver	30
101224A	19h03m41919	$45^\circ 42^{\prime}$ 4886	0.454 ± 0.0007	r	22.071 ± 0.052	0.015	Gold	This work
110112A	⋯	⋯	⋯	F110W	≳28.0	0.44	Inconclusive	This work
111117A	0h50m46268	$+23^\circ 00^{\prime}$ 4141	2.211 ± 0.001	r	23.789 ± 0.11	0.024	Silver	31–32
120305A	03h10m08754	$28^\circ 29^{\prime}$ 3587	0.225 ± 0.001	r	22.398 ± 0.050	0.053	Silver	This work
120804A	15h35m47510	$-28^\circ 46^{\prime}$ 5611	${1.05}_{-0.09}^{+0.23}$	r	26.406 ± 0.200	0.02	Gold	33, This work
121226A	11h14m34121	$-30^\circ 24^{\prime}$ 2284	${1.37}_{-0.06}^{+0.05}$	r	24.309 ± 0.06	0.019	Gold	This work
130515A	18h53m45021	$-54^\circ 16^{\prime}$ 5072	0.80 ± 0.01	r	22.651 ± 0.040	0.081	Silver	This work
130603B	11h28m48231	$+17^\circ 04^{\prime}$ 1861	0.3568 ± 0.0005	r	21.06 ± 0.06	2 × 10−3	Gold	18, 34-35
130716A	11h58m17862	$+63^\circ 03^{\prime}$ 1535	${2.2}_{-0.37}^{+0.35}$	r	24.894 ± 0.344	0.36	Bronze	This work
130822A	1h51m42708	$-3^\circ 12^{\prime}$ 25447	0.154 ± 0.001	r	18.248 ± 0.063	0.086	Silver	This work
130912A	03h10m222	$13^\circ 59^{\prime}$ 4874	⋯	F110W	27.471 ± 0.23	0.12	Bronze	This work
131004A	19h44m27064	$-2^\circ 57^{\prime}$ 30429	0.717 b	F110W	25.464 ± 0.09	0.055	Silver	36, This work
140129B	21h47m01649	$26^\circ 12^{\prime}$ 23270	0.43 ± 0.003	r	23.55 ± 0.07	8.7 × 10−4	Gold	This work
140516A	⋯	⋯	⋯	i	≳26.1	⋯	Inconclusive	This work
				K	≳23.6	⋯		This work
140622A	21h08m41744	$-14^\circ 25^{\prime}$ 06166	0.959 ± 0.001	r	22.703 ± 0.042	0.10	Bronze	This work
140903A	15h52m03265	$+27^\circ 36^{\prime}$ 1071	0.3529 ± 0.0002	r	21.367 ± 0.194	6.2 × 10−5	Gold	37, This work
140930B	0h25m23473	$+24^\circ 17^{\prime}$ 3793	1.465 ± 0.001	r	24.206 ± 0.248	0.021	Silver	This work
141212A	2h36m29957	$+18^\circ 08^{\prime}$ 47228	0.596 ± 0.001	r	22.945 ± 0.056	2.9 × 10−4	Gold	This work
150101B	12h32m04973	$-10^\circ 56^{\prime}$ 0050	0.134 ± 0.003	r	16.604 ± 0.04	4.8 × 10−4	Gold	38
150120A	0h41m16563	$+33^\circ 59^{\prime}$ 42598	0.4604 ± 0.0004	r	22.051 ± 0.063	1.9 × 10−3	Gold	This work
150423A	⋯	⋯	1.394 b	F110W	≳28.1	⋯	Inconclusive	39, This work
150424A	10h09m13406	$-26^\circ 37^{\prime}$ 51745	⋯	F125W	26.293 ± 0.15	0.06	Bronze a	This work
150728A	19h28m54808	$+33^\circ 54^{\prime}$ 5822	0.461 ± 0.0005	i	21.420 ± 0.054	0.018	Gold	This work
150831A	14h44m05939	$-25^\circ 38^{\prime}$ 0578	1.180 ± 0.001	r	24.434 ± 0.446	0.037	Silver	This work
151229A	21h57m28701	$-20^\circ 43^{\prime}$ 5480	${0.63}_{-0.35}^{+0.49}$	i	24.924 ± 0.134	0.040	Silver	This work
160303A	11h14m48119	$+22^\circ 44^{\prime}$ 33420	${1.01}_{-0.23}^{+0.18}$	F110W	23.774 ± 0.02	0.096	Silver	40, This work
160408A	8h10m29580	$+71^\circ 07^{\prime}$ 4503	${1.90}_{-0.53}^{+0.38}$	r	25.736 ± 0.162	0.14	Bronze	This work
160410A	⋯	⋯	1.7177 ± 0.0001 b	r	>27.2	⋯	Inconclusive	41, This work
160411A	23h17m25355	$-40^\circ 14^{\prime}$ 3056	${0.82}_{-0.45}^{+0.64}$	r	24.532 ± 0.134	7.2 × 10−4	Gold	This work
160525B	9h57m32246	$+51^\circ 12^{\prime}$ 2460	${0.64}_{-0.14}^{+2.03}$	r	23.29 ± 0.09	0.001	Gold	42, This work
160601A	15h39m43949	$+64^\circ 32^{\prime}$ 30604	⋯	z	24.947 ± 0.344	8.9 × 10−4	Gold	This work
160624A	22h00m46145	$+29^\circ 38^{\prime}$ 39336	0.4842 ± 0.0005	r	21.960 ± 0.047	0.037	Silver	This work
160821B	18h39m53994	$+62^\circ 23^{\prime}$ 34427	0.1619 ± 0.0002	r	19.548 ± 0.004	0.044	Silver	This work
160927A	⋯	⋯	⋯	G	≳25.7	⋯	Inconclusive	This work
				J	≳24.4	⋯		This work
161001A	4h47m40530	$-57^\circ 15^{\prime}$ 39184	0.67 ± 0.02	r	22.968 ± 0.046	0.045	Silver	39, This work
161104A	05h11m3437	$-51^\circ 27^{\prime}$ 3629	0.793 ± 0.003	r	23.847 ± 0.10	0.06	Bronze a	43
170127B	1h19m54415	$-30^\circ 21^{\prime}$ 29615	2.28 ± 0.14	r	25.320 ± 0.290	0.098	Silver	This work
170428A	22h00m18710	$+26^\circ 54^{\prime}$ 56280	0.453 ± 0.001	r	22.346 ± 0.100	6.7 × 10−3	Gold	This work
170728A	3h55m33116	$+12^\circ 10^{\prime}$ 5104	1.493 ± 0.009	R	24.735 ± 0.136	0.22	Bronze	This work
170728B	15h51m55529	$+70^\circ 07^{\prime}$ 22038	1.272 ± 0.002	r	23.313 ± 0.096	8.3 × 10−3	Gold	This work
180418A	11h20m2921	$24^\circ 55^{\prime}$ 58734	${1.56}_{-0.43}^{+0.21}$	r	25.729 ± 0.21	1.5 × 10−3	Gold	44, This work
180618A	11h19m45801	$+73^\circ 50^{\prime}$ 1503	${0.52}_{-0.11}^{+0.09}$	i	22.183 ± 0.081	8.2 × 10−3	Gold	This work
180727A	23h06m40038	$-63^\circ 03^{\prime}$ 07088	${1.95}_{-0.58}^{+0.5}$	r	26.486 ± 0.277	8.6 × 10−3	Gold	This work
180805B	1h43m07655	$-17^\circ 29^{\prime}$ 33091	0.6612 ± 0.002	r	22.153 ± 0.063	0.042	Silver	This work
181123B	12h17m2791	$+14^\circ 35^{\prime}$ 5227	1.754 ± 0.001	r	23.92 ± 0.19	4.4 × 10−3	Gold	45
191031D	18h53m09522	$+47^\circ 38^{\prime}$ 4013	${1.93}_{-1.44}^{+0.22}$	r	24.462 ± 0.263	0.043	Silver	This work
200219A	22h50m33108	$-59^\circ 07^{\prime}$ 11579	0.48 ± 0.02	r	20.661 ± 0.05	2.2 × 10−3	Gold	13, This work
200411A	03h10m39135	$-52^\circ 18^{\prime}$ 59545	${0.82}_{-0.17}^{+0.18}$	r	22.564 ± 0.042	0.11	Bronze	13, This work
200522A	00h22m43717	$-00^\circ 16^{\prime}$ 57466	0.5536 ± 0.0003	r	21.196 ± 0.02	3.5 × 10−5	Gold	46-47
200907B	05h56m06951	$+6^\circ 54^{\prime}$ 22637	${0.56}_{-0.32}^{+1.39}$	i	23.936 ± 0.108	9 × 10−3	Gold	This work
201006A d	⋯	⋯	⋯	K	≳23.6	⋯	Constraint	This work
201221D	11h24m14064	$+42^\circ 08^{\prime}$ 40047	1.055 ± 0.001	r	23.418 ± 0.076	0.12	Bronze	48, This work
210323A	21h11m47320	$+25^\circ 22^{\prime}$ 09989	0.733 ± 0.001	r	24.972 ± 0.252	0.013	Gold	This work
210726A	12h53m09820	$+19^\circ 11^{\prime}$ 25032	${0.37}_{-0.17}^{+0.32}$	i	25.211 ± 0.289	7.3 × 10−5	Gold	13, This work
210919A	05h21m01954	$+1^\circ 18^{\prime}$ 40022	0.2415 ± 0.001	r	20.50 ± 0.05	0.13	Bronze	13, This work
211023B	11h21m14311	$+39^\circ 08^{\prime}$ 0836	0.862 ± 0.001	r	24.361 ± 0.377	4.7 × 10−3	Gold	13, This work
211106A	22h54m20541	$-53^\circ 13^{\prime}$ 50548	⋯	F814W	25.791 ± 0.069	5.5 × 10−4	Gold	This work, 49
211211A c	14h09m10467	$+27^\circ 53^{\prime}$ 21050	0.0763 ± 0.0002	F606W	19.57 ± 0.01	0.0136	Gold	50
170817A e	13h09m4770	$-23^\circ 23^{\prime}$ 020	0.009787 ± 0.000057	r	12.44 ± 0.01	4.9 × 10−4	⋯	51-52

Notes. Magnitudes m_λ are not corrected for Galactic extinction, A_λ , in the direction of the burst. Photometric redshift uncertainties correspond to 68% confidence and the methods to determine them are described in Nugent et al. (2022).

^a Hosts reclassified as Bronze due to at least one other galaxy with comparably low P_cc value in the field. ^b Redshift determined from afterglow. ^c Long-duration GRBs thought to be associated with NS merger origins. ^d This burst has a high Galactic extinction of A_V = 3.5 mag and is therefore considered an observing constraint burst with a sightline that precludes a meaningful host galaxy search in the optical bands. However, we report a K-band limit here on a galaxy within the XRT position for completeness. ^e This host is only considered as a point of comparison to the cosmological short GRB sample.

References. (1) Bloom et al. (2006), (2) Fong et al. (2010), (3) Albareti et al. (2017), (4) Skrutskie et al. (2006), (5) Covino et al. (2006), (6) Fox et al. (2005), (7) Hjorth et al. (2005), (8) Leibler & Berger (2010), (9) Berger et al. (2005), (10) Gorosabel et al. (2006), (11) Ferrero et al. (2007), (12) Prochaska et al. (2006), (13) Schlegel et al. (2021), (14) Soderberg et al. (2006), (15) Gal-Yam et al. (2006), (16) Berger et al. (2007), (17) D'Avanzo et al. (2009), (18) Fong & Berger (2013), (19) Cenko et al. (2008), (20) Graham et al. (2009), (21) Berger (2010), (22) Perley et al. (2009), (23) Rowlinson et al. (2010), (24) Nicuesa Guelbenzu et al. (2012), (25) Levesque et al. (2010), (26) McBreen et al. (2010), (27) Fong et al. (2011), (28) Perley et al. (2012), (29) Wright et al. (2010), (30) Fong et al. (2013), (31) Margutti et al. (2012), (32) Selsing et al. (2018), (33) Berger et al. (2013), (34) de Ugarte Postigo et al. (2014), (35) Cucchiara et al. (2013), (36) Chornock et al. (2013), (37) Troja et al. (2016), (38) Fong et al. (2016), (39) Selsing et al. (2019), (40) Cano et al. (2016), (41) Agüí Fernández et al. (2021), (42) O'Connor et al. (2022), (43) Nugent et al. (2020), (44) Rouco Escorial et al. (2021), (45) Paterson et al. (2020), (46) Chambers et al. (2016) (47) Fong et al. (2021), (48) Kilpatrick et al. (2020), (49) Laskar et al. (2022), (50) Rastinejad et al. (2022), (51) Blanchard et al. (2017), (52) Wenger et al. (2000).

A machine-readable version of the table is available.

Download table as:  DataTypeset images: 1 2

Observations from IRAC (Fazio et al. 2004) on the Spitzer Space Telescope (Werner et al. 2004) were available for 13 of the GRB host galaxies in our sample taken during 2006–2017 ²⁵ (PIs: Perley, Savaglio, Gladders). We obtained the Level 2 PBCD mosaic images from the Spitzer Heritage archive for these fields and deblended the GRB host from its (apparent) companions using the interactive Galfit-based modeling method detailed in Perley et al. (2016c). For host galaxies smaller than 1'' we measure the host galaxy magnitude on the companion-subtracted image using a custom IDL aperture photometry routine using a 24 aperture and a 36–48 background annulus fixed at the GRB host location from Table 2, with a custom aperture correction calculated using the Spitzer-supplied point-response function model. (The photometric scale is taken from the PBCD images, which have already been flux calibrated.) For two cases (GRBs 050509B and 050724A), we use a larger source aperture of 48 as the smaller aperture does not adequately encompass the source flux. The results are presented in Table A1. In the case of a non-detection, the quoted limit corresponds to 5σ confidence.

To supplement these observations, we draw from published ground-based data in the literature, focusing on (i) previously published, well-characterized hosts, or (ii) hosts that lack imaging in a given filter in our catalog. In this vein, we collect literature photometry for 44 bursts. We list the references for all of these data in Table 2. When made available by corresponding authors, we also provide the reduced stacks from these works on the BRIGHT website. We emphasize that the literature data set is comprehensive for a given host in that we attempt to fill out the SED, but does not include all literature photometry that exists for every host galaxy.

Finally, for 10 bursts, we include archival photometric survey data. We draw from Two Micron All Sky Survey All-Sky (2MASS; Skrutskie et al. 2006), Legacy Surveys Data Release 9 (DR 9; Dey et al. 2019), Pan-STARRS Data Release (DR2; Flewelling et al. 2020), Sloan Digital Sky Survey Data Release 12 (SDSS DR12; Alam et al. 2015), SDSS DR13, (Albareti et al. 2017), Spitzer (Papovich et al. 2016; Timlin et al. 2016), and Wide-field Infrared Survey Explorer (WISE; Lang et al. 2016).

To obtain afterglow positions and thus burst locations with respect to putative host galaxies, we first use ground-based optical discovery images when available. In particular, we utilize a combination of our Target-of-Opportunity programs on the twin 6.5 m Magellan telescopes, the 6.5 m MMT, the twin Gemini telescopes, and the 60 in Palomar Observatory P60 telescope (PIs: Berger, Fong, Cenko, Cucchiara), as well as publicly available ground-based imaging from the 4.2 m William Herschel Telescope and the 8.2 m Very Large Telescope (VLT). For all ground-based observations, we use the same procedures for data reduction as for our host galaxy imaging, described in Section 3.

For the subset of bursts for which there exists HST afterglow discovery imaging, we retrieve and process the images as described in Section 3.3. For both ground-based and HST imaging, if the position of the afterglow is contaminated by host galaxy light in the discovery image, we use the HOTPANTS software package (Becker 2015) to perform image subtraction between the afterglow images and late-time templates to produce residual images for accurate afterglow centroiding. We use Source Extractor (SExtractor; Bertin & Arnouts 1996) to determine the positional uncertainties of the afterglows, σ_GRB. We calculate a range of σ_GRB ≈ 10–120 mas for ground-based discoveries, and σ_GRB ≈ 1–4 mas for bursts with HST-detected afterglows.

For bursts for which the most precise afterglow localization is from the CXO, we retrieve Level II files from the Chandra archive, and we use CIAO/wavdetect to determine their positions and uncertainties. We describe how relative astrometry is performed to the host galaxy images in Section 4.1. For afterglows detected with the Karl G. Jansky Very Large Array (VLA) or Atacama Large Millimeter Array, we use CASA/jmfit to fit a 2D Gaussian to the afterglow. Finally, for 33 bursts, the most precise afterglow localization is from Swift/XRT. In these cases, we use the published positions and uncertainties, ²⁶ with the methods described in Evans et al. (2009).

For each host galaxy stack, we perform absolute astrometry using common sources between the host galaxy imaging and available source catalogs: Gaia DR2 (Gaia Collaboration et al. 2018), Pan-STARRS (PS1; Chambers et al. 2016), SDSS DR12 (Alam et al. 2015), or 2MASS. We use SExtractor to determine the centroids of common sources, and IRAF/ccred and ccsetwcs to determine the astrometric solution from each image to the catalog. We find that a fourth-order polynomial with six free parameters corresponding to a shift, scale, and rotation in each coordinate provides robust solutions. The 1σ absolute astrometric uncertainties have a range of σ_abs ≈ 01–03. We report the host galaxy positions in Table A1.

In order to make host galaxy identifications, it is necessary to align the afterglow and host galaxy imaging to the same frame. Thus, we additionally perform relative astrometry from the available afterglow imaging (from ground-based facilities, HST, or CXO) to the host galaxy images, which themselves are tied to an absolute astrometric system. We again use a combination of SExtractor and IRAF using common sources. The 1σ uncertainty on the afterglow position includes the afterglow positional uncertainty (see Section 3.5) and the relative astrometric tie uncertainty (σ_rel ≈ 10–100 mas) added in quadrature. If we do not have access to afterglow discovery images, we use published positions from the literature or GCNs. If uncertainties are not provided with those positions, we assume a conservative 1σ uncertainty of 05. For the 33 bursts with no subarcsecond localization, and X-ray positions only from Swift/XRT, we use the published XRT positions directly (typically ≈15–5''; Evans et al. 2009). For 89 of the 90 fields, we show a representative, deep optical or NIR image centered on the most precise afterglow position for each burst in Figures 2 and 3. ²⁷

We use the available imaging data to determine the most probable host galaxy for each burst by calculating the probability of chance coincidence (P_cc) for nearby galaxies in the field of view. The fields of view are typically >25 in radius, corresponding to ≈1 Mpc at z = 0.5. For context, the largest observed projected physical offsets for short GRBs are only ≲100 kpc (Berger 2010; Tunnicliffe et al. 2014). The P_cc method requires two ingredients: angular offsets between a host galaxy candidate and burst location, δ R, and putative host galaxy magnitudes, m_i . The methods to calculate δ R are described in Section 6.

Using our deepest available image for each burst, which is typically in the r band or JH bands, we start with the extended source that has the smallest angular offset to the most precise afterglow position. For this source, we perform aperture photometry using the IRAF/apphot package. We begin with default apertures of 2.5θ_FWHM, but often use larger apertures to fully encompass the galaxy light. For background regions, we use annuli immediately surrounding the putative hosts, and adjust the radii as needed to avoid any contaminating sources. We determine zero points either by using stars with cataloged magnitudes in the field of the host galaxy, or by using standard star fields taken on the same night at similar airmasses. For the determination of optical zero points, we use SDSS DR12, Pan-STARRS (applying transformations to the SDSS system; Tonry et al. 2012), or the USNO-B catalogs. For NIR zero points, we use the 2MASS catalog. When relevant, we convert from the Vega to the AB system, using standard transformations or instrument-specific conversions. For HST data, we use the relevant tabulated zero point for each instrument and filter, ²⁸ again varying the apertures and background regions based on the size of each galaxy.

We follow the methodology of Bloom et al. (2002) to calculate P_cc based on the surface density of galaxies brighter than a given magnitude, σ( ≤ m_i ) within a radius, R_i . To determine σ( ≤ m_i ), we interpolate r-band or H-band number counts from galaxy surveys (compiled in Hogg et al. 1997; Beckwith et al. 2006 and Metcalfe et al. 2006) and integrate the relevant function for m ≤ m_i depending on the filter of the observation. For the value of R_i , we use the maximum of δ R or σ_GRB, which is an approximation of the methods described in Bloom et al. (2002) and Blanchard et al. (2016), in the absence of effective radii measurements for all putative GRB hosts. If the most proximal extended source has P_cc ≲ 0.01, we consider it to be the host galaxy of that burst.

If the most proximal source to the GRB has P_cc ≳ 0.01, we continue to perform photometry of all extended sources in the image using the IRAF/apphot package. We discard noticeably fainter galaxies with increasing angular distance δ R from the burst since these objects will have a lower probability of being the host galaxy based on chance alignment arguments. We then calculate P_cc for each of these sources. For each burst, the minimum in the probability function, ${P}_{\mathrm{cc},\min }$, corresponds to the most probable host galaxy. In many cases, this still ends up being the most proximal host galaxy, although in some cases a galaxy at a larger separation is favored as the host.

In general, the P_cc method can recover clear host galaxies for most bursts. However, it favors apparently brighter galaxies at a given angular separation, and it is difficult to interpret if two putative hosts for a given burst have similarly low P_cc values. To reflect the varying robustness of associations and the nuances of the method, we divide our sample into four categories based on the minimum probability of chance coincidence value, ${P}_{\mathrm{cc},\min }$ as follows:

• 1.  
  Gold: Bursts with putative hosts that have ${P}_{\mathrm{cc},\min }\leqslant 0.02$. There are 50 events in the Gold sample. These represent short GRBs with the most robust host associations, although they are likely to be biased toward bursts with subarcsecond localizations (e.g., optical afterglows), smaller offsets, and apparently brighter hosts.
• 2.  
  Silver: Bursts with putative hosts that have $0.02\lt {P}_{\mathrm{cc},\min }\leqslant 0.10$. There are 21 events in the Silver sample. These represent short GRBs with moderately robust host associations. This sample is subject to less of the biases outlined for the Gold sample.
• 3.  
  Bronze: Bursts with putative hosts that have $0.10\lt {P}_{\mathrm{cc},\min }\leqslant 0.20$. There are 13 events in the Bronze sample. These represent short GRBs with the least robust host associations, but for which more probable alternatives do not exist. There is likely a small loss of integrity in individual host assignments (addressed in Section 7). However, this is an important sample to include as it is least subject to the biases of the P_cc assignment method.
• 4.  
  Inconclusive: Bursts for which the lowest value for an extended source in the field is ${P}_{\mathrm{cc},\min }\gt 0.20$. There are six events in the Inconclusive sample. In all cases, there are deep optical or NIR limits on a coincident host galaxy to ≳26–28 mag.

In general, we follow the above guidelines to associate each short GRB with its host galaxy. However, we make three exceptions and modifications to the above scheme based on information from their afterglows, or an analysis that yields multiple putative hosts with similarly low P_cc values.

For GRB 150424A, the first and second closest galaxies (in angular separation) have similar values of P_cc = 0.06 and 0.04, respectively, both of which would place the burst in the Silver sample. The second closest galaxy has a spectroscopic redshift of z = 0.3, but this is at odds with the inferred value from the afterglow SED, which implies $z={1.0}_{-0.2}^{+0.3}$ (Castro-Tirado et al. 2015; Knust et al. 2017). Instead, the closest galaxy, which was first reported in early HST imaging (Tanvir et al. 2015), has a probable redshift range of z ≈ 0.9–1.6 based on the likely location of the 4000 Å break (Jin et al. 2018). Thus, despite having a slightly higher P_cc value, we conclude that the closest galaxy is the most likely host of GRB 150424A. We downgrade this burst to the Bronze sample given the more ambiguous nature of this association.

For GRB 161104A, the galaxies with the two lowest P_cc values have P_cc = 0.06 and 0.08 (Nugent et al. 2020), which would nominally place this burst in the Silver sample. The closest galaxy, with P_cc = 0.06, is fully encompassed in the XRT position and is part of a galaxy cluster at z ≈ 0.79. We consider this to be the host galaxy, but we also demote this burst to the Bronze sample.

Finally, for GRB 061201, there are two galaxies at very different offsets that have identical P_cc values of 0.07, which would be a Silver sample burst. While one of the putative hosts is at z = 0.111 and has previously been considered as a tentative association (Stratta et al. 2007; Fong & Berger 2013), we cannot conclude on an individual host association and consider this to be an Inconclusive burst.

Overall, we make associations for 84 events. The resulting minimum P_cc value, corresponding to the most probable host galaxy, for each short GRB is listed in Table 2. We also list the optical or NIR magnitude, and the host classification (Gold, Silver, Bronze, Inconclusive). We confirm many associations that were previously made in the literature, as well as make 26 new identifications. ²⁹ We also revise associations for three bursts: GRBs 070729, 161001A, and 191031D. For GRB 070729, the XRT position shifted significantly compared to the initial published position on which the host association was made. The updated position coincides with a faint source on the edge of the XRT position (90% confidence) while the original host published in Leibler & Berger (2010) now has a substantially larger value of P_cc. For GRB 161001A, Selsing et al. (2019) note a faint extended source in the wings of an M star that overlaps with the XRT position with z = 0.891, which is taken to be the host galaxy. However, this galaxy is not apparent in our imaging and instead we find a (presumably) brighter r ≈ 22.9 mag galaxy coincident with the XRT position (Figure 2). We consider this to be the host galaxy and determine a photometric redshift of z ≈ 0.67. Finally, for GRB 191031D, O'Connor et al. (2022) identified a galaxy outside of the XRT position at z ≈ 0.5 as the host. However, our deep Keck NIR imaging reveals a red, extended source within the XRT position with P_cc = 0.04 (compared to the larger value of P_cc ≈ 0.1 for the galaxy identified by O'Connor et al. 2022). Thus, we revise this host identification and photometric redshift to z ≈ 1.9. We use the categories in our downstream analysis and in Nugent et al. (2022).

We show the fields of the six bursts in the Inconclusive host association class in Figure 3. We also show a seventh burst, GRB 201006A, which has a high-extinction sightline through the galaxy of A_V = 3.5 mag but for which we have deep K-band imaging in which the extinction is less severe. Thus, we consider this burst to have meaningful information at NIR wavelengths only. Five have subarcsecond localizations from optical afterglows while two (GRBs 140516A and 201006A) only have XRT positions.

This class of bursts was formerly termed host-less (Berger 2010). The fields of GRBs 061201, 110112A, and 160410A were previously studied and classified as such (Berger 2010; Fong & Berger 2013; Agüí Fernández et al. 2021) (although deeper HST imaging for GRB 110112A is presented here). We introduce four new cases. Both GRB 140516A ³⁰ and 201006A have faint extended sources in the vicinity of their XRT positions (90% confidence) although no galaxy reaches the threshold of ${P}_{\mathrm{cc},\min }\leqslant 0.2$.

Two of these bursts, GRBs 150423A and 160410A, have known redshifts from their afterglows (Selsing et al. 2019; Agüí Fernández et al. 2021; Table 2). From HST imaging, we find that GRB 150423A has no host to m_F110W ≳ 28.1 mag at the position of its optical afterglow, constraining any spatially coincident galaxy to L_r ≲ 3 × 10⁸ L_⊙ at z = 1.394. The most probable host galaxy using the P_cc method has z = 0.456 (Perley 2015) with P_cc ≈ 0.2, but is inconsistent with the afterglow redshift. Meanwhile, the next most probable host galaxy (and the one at the smallest angular separation to the afterglow) has P_cc = 0.23, too high to meet the Bronze class threshold. For GRB 160410A at z = 1.7177, the reported limit is r ≳ 27.2 mag (Agüí Fernández et al. 2021), which constrains any coincident host to L_r ≲ 1.6 × 10⁹ L_⊙.

Overall, while this population may represent bursts with the largest offsets, and is thus an important population to include, it comprises only a small fraction of the total short GRBs in this sample. We also note that several formerly host-less bursts have associations that meet the threshold to fall in one of the Gold, Silver, or Bronze categories, thus highlighting the importance of using a uniform method across all bursts for association.

We obtained spectroscopic observations for 22 short GRB hosts with unpublished spectra: GRBs 101224A, 120305A, 130822A, 140129B, 140622A, 140930B, 141212A, 150120A, 150728A, 150831A, 151229A, 161001A, 160411A, 170428A 170728A, 170728B, 180618A, 180805B, 201221D, 210323A, 210919A, and 211023B. For these observations, we used the twin 6.5 m Magellan/Baade and Clay telescopes, 8 m Gemini-North and Gemini-South telescopes, 6.5 m MMT, twin 10 m Keck I and II telescopes, and the twin 8.4 m LBT. Additionally, we obtained our own spectroscopic observations for four short GRBs which have previously published spectra from other telescopes and have known redshifts: GRBs 070724A (Leibler & Berger 2010), 140903A (Troja et al. 2016), 160624A (O'Connor et al. 2021), and 160821B (Kasliwal et al. 2017). We list the telescope and instruments used for these new observations in Table 1, as well as the details of the spectra in Table 3.

We also draw from archival and literature sources to obtain spectroscopy for the remaining host galaxies. Our aim is to build as complete a spectroscopic catalog as possible to enable the uniform stellar population modeling analysis in Nugent et al. (2022). Thus, we first retrieved the raw 2D spectra and calibration files of 10 short GRB hosts from observatory archives for re-reduction and analysis. We note that these same spectra were previously published in the following works: GRBs 050509B (Bloom et al. 2006), 050709 (Fox et al. 2005), 050724 (Berger et al. 2005), 051221A (Soderberg et al. 2006), 060614 (Niino et al. 2017), 060801 (Berger et al. 2007), 061006 (Berger et al. 2007), 070429B (Cenko et al. 2008), 070714B (Cenko et al. 2008), and 090510 (McBreen et al. 2010). From the literature, we also obtained reduced 1D object and error spectra for 10 events from the corresponding authors: GRBs 100117A (Fong et al. 2011), 100206A (Perley et al. 2012), 100625A, 101219A (Fong et al. 2013), 130603B (Cucchiara et al. 2013), 150101B (Fong et al. 2016), 161104A (Nugent et al. 2020), 181123B (Paterson et al. 2020), 200522A (Fong et al. 2021), and 211211A (Rastinejad et al. 2022). This archival and literature sample uses Magellan, Gemini, Keck, and the VLT. We list the details of these spectra, when available, in Table 3.

We use a combination of reduction tasks and methods depending on the origin of the spectra. For the subset of 10 host galaxies with spectra taken with LBT/MODS, Magellan (IMACS and LDSS), and Keck/LRIS (GRBs 101224A, 120305A, 130515A, 130822A, 140622A, 140903A, 140930B, 160411A, 160624A, and 201221D), we use standard IRAF tasks in the ccdred, longslit, and immatch packages to process and co-add the data (Tody 1986, 1993). For each set of data, we subtract the overscan regions or apply bias corrections, apply flat-field corrections, model the sky background, and subtract this background from the individual frames. We co-add individual background-subtracted 2D frames and then use IRAF/apall to extract the 1D spectra. We perform wavelength calibration using standard arc lamp spectra (HgNeArKrXe for MODS, HeNeAr for LDSS, NeArKrXe for IMACS, and HgNeArCdZn for LRIS). We apply spectrophotometric flux calibration using standard stars taken at a similar airmass on the same night in the same spectral setup as the host spectra. We determine the error spectrum by performing the aforementioned reduction steps, but on the 2D spectra without sky subtraction. We perform standard error propagation in the combination. The spectra for six of these short GRB hosts are shown in Figure 4.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

For five hosts (GRBs 050709, 050724, 051221A, 060801, and 061006) with Gemini/GMOS (EEV detector) observations, we use the gemini/gmos IRAF package. We apply bias subtraction, flat-field corrections, and model the sky background. We determine the wavelength solutions using CuAr arc lamps and calibrate the individual 2D science frames with the gswavelength and gssubtract tasks. We apply flux calibration to the spectra with a standard star taken within the same observing semester. We extract the 1D spectra with gsextract and combine these with gscombine. The Gemini IRAF package propagates variance in traces through each task, which we use to determine the final error spectra.

For three hosts (GRB 170428A, 170728B, and 180618A), we obtain 1D, co-added, flux and wavelength-calibrated spectra from the MMT/Binospec observatory products. This data was reduced with the instrument's spectroscopic reduction software, which is based on IDL. ³¹ The software automatically applies a flat-field and sky background correction. It uses a barycentric wavelength calibration and flux calibrates based on the spectrophotometric standard taken on the same night at a similar airmass. It extracts a 1D spectrum from co-added 2D frames, using a 1'' radius, and provides an uncertainty, which we use as the error spectrum.

Finally, for 19 hosts with data from Keck (DEIMOS and LRIS), Gemini/GMOS (E2V and Hamamatsu detectors), and VLT/FORS2, we used the Python Spectroscopic Data Reduction Pipeline (PypeIt; Prochaska et al. 2020) for data processing and spectral extraction. These hosts are GRBs 050509B, 060614, 070429B, 070714B, 070724A, 090510, 140129B, 141212A, 150120A, 150728A, 150831A, 151229A, 160821B, 170728A, 180805B, 191031D, 210323A, 210919A, and 211023B (Table 3). In PypeIt, we apply an overscan and/or bias subtraction, flat-field correction and perform wavelength calibration and spectral extraction (using the boxcar method with a 15–25 radius, in order to include all of the emission line flux). We apply flux calibrations using appropriate spectrophotometric standards. We co-add the flux-calibrated 1D spectra and apply a telluric correction using an atmospheric model. PypeIt determines the variance on each trace, which we use to determine the error spectra.

For all 26 new and unpublished spectra in our sample as well as the 10 re-reduced spectra, we use the Cardelli et al. (1989) extinction law and the A_V in the direction of each burst (Schlafly & Finkbeiner 2011) to correct for Galactic extinction. We then normalize the host spectra to their extinction-corrected photometry. The final 1D spectra of 18 hosts with determined redshifts and their spectral line identifications are displayed in Figure 4. Not shown are the four new spectra which have consistent results with previous works.

For 22 hosts of the 24 hosts with new, unpublished spectroscopic observations, we determine redshifts through feature identification. The most common features in our spectra are [O ii]λ3727, Hβ, [O iii]λ4959, [O iii]λ5007, and Hα for star-forming galaxies, and the Ca ii H&K for quiescent or transitioning galaxies. We search for high S/N spectral lines (S/N > 5) with Gaussian-like structures in both the 1D and 2D frames. When multiple spectral lines are found, we use the mean of the Gaussian lines to determine ratios between each pair of lines. We compare these ratios to those of the rest-frame wavelengths of spectral lines at redshifts between 0 ≤ z ≤ 3.0. We require that the ratios of observed lines are within 0.1% of the rest-frame spectral line ratios to maintain accuracy in line determination. From there, we can determine what each observed line is and the redshift. We determine error on the redshift by fitting the spectral lines and their direct background (∼ ±100 Å) with a Gaussian profile and determining the mean of 1σ uncertainties on each line.

For 16 hosts, we have at least two spectral lines with S/N > 5 above the continuum from which we can determine a common redshift. Out of these 16, 6 are completely new redshifts, unconfirmed in GCNs or other works. The redshifts of GRBs 101224A, 130822A, 140622A, 170428A, and 180805B are consistent with those reported in O'Connor et al. (2022). A few redshifts were reported in GCNs and are also consistent with our findings: GRBs 141212A (Chornock et al. 2014) and 210919A (Rossi et al. 2022). The GCN redshift of 211023B (Rossi et al. 2021) is slightly inconsistent with our result and only based on one detected emission line; thus we consider this a new redshift.

For five hosts (GRBs 140930B, 150831A, ³² 170728A, 170728B, 201221D), we can only identify a single emission line. However, in all cases the width of this line is double-peaked in nature, suggesting it is likely a doublet, specifically the [O ii]λ λ 3727, 3729 doublet. In addition, these lines were all found at higher wavelengths (>9100 Å for GRBs 140930B and 170728A, >8100 Å for GRBs 150831A and 170728B, and ≈7659 Å for GRB 201221D). If these lines were instead Hβ or [O iii], we would expect to detect the [O ii], Hβ, and [O iii] in all five spectra, or if these lines were Hα, we would be able to detect all the common emission lines in the spectra of GRBs 140930B, 150831A, 170728B, and 201221D, and everything but [O ii] in the spectrum of 170728A. Given that these additional lines are not detected, despite the wavelength coverage of these spectra, it is most likely that the identified lines are [O ii]. Therefore, in all three cases, we identify the line as the [O ii]λ3727 doublet. GRBs 140930B, 150831A, 170728A, and 170728B do not have published spectroscopy or redshifts so we report these redshifts for the first time. Our redshift of z = 1.055 ± 0.001 is close, although not formally consistent with, the previously reported redshift in the GCNs (z = 1.045; de Ugarte Postigo et al. 2020). We present all spectroscopic redshifts and uncertainties in Table 2.

For short GRBs with photometric data only, we use the stellar population inference code Prospector (Leja et al. 2017; Johnson et al. 2021) to model their SEDs and determine their photometric redshifts. The full stellar population modeling methods and analysis are described in Nugent et al. (2022). We report 20 new photometric redshifts (see Nugent et al. 2022, Appendix for fits). We note that our photometric redshifts for five GRBs (070729, 120804A, 151229A, 191031D, and 200411A) differ from the literature, due to a combination of modeling assumptions (such as truncated redshift priors in other works), less complete data sets, or incorrect host associations. Combined with the literature sample, we find a median redshift for the full population of 0.64 with a 68% credible interval on the distribution of [−0.32, +0.83], and a higher median and credible interval of 0.93 [−0.46, +1.16] for the photometric redshift population; this is discussed and explored in more detail in Nugent et al. (2022).

With imaging, host identifications, and redshifts in hand, we now turn to the locations of short GRBs with respect to their hosts. In the context of their NS merger progenitors, offsets are an observable diagnostic for a combination of progenitor kicks and delay times (e.g., Zevin et al. 2020. To determine the position of each GRB relative to its host galaxy, and thus measure precise offsets, we perform relative astrometry by aligning each of the afterglow discovery images to the host galaxy imaging. We consider three sources of uncertainty in the offsets: the afterglow centroid (σ_GRB), the astrometric tie uncertainty between the afterglow discovery and the host images (σ_GRB→host), and the host galaxy centroid uncertainty (σ_host). We perform the astrometric tie in the same manner as described in Section 4.1. To determine the host centroid uncertainty, we again use SExtractor, and find a range of values, σ_gal ≈ 1–50 mas. This is generally the smallest source of uncertainty.

For each galaxy/filter combination, we first use the afterglow and host position to measure angular offsets (δ R). The offsets and accompanying combined uncertainties are listed in Table 4. To convert to physical offsets, we use the redshifts in Table 2. The values of angular and physical offsets for 84 short GRBs are listed in Table 4. For bursts with unknown redshift or no redshift information, we assume z = 1. While the median redshift for the entire population is lower (z ≈ 0.6), we assume that host galaxies that lack redshift information are at higher redshifts than the median. We also note that the angular diameter distance at z ≳ 0.5 is relatively flat, so the exact choice of redshift beyond this value will not have a large effect on the physical offset distribution.

Table 4. Short GRB Angular, Physical, and Host-normalized Offsets

GRB	z	Afterglow a	Offset	σ	Offset b	σ	Offset	σ	Reference c
			('')	('')	(kpc)	(kpc)	(re )	(re )
050509B	0.2248	X	15.10	3.40	55.19	12.43	2.59	0.58	1
050709	0.1607	X	1.35	0.020	3.76	0.056	2.00	0.030	1
050724A	0.254	O	0.68	0.020	2.74	0.080	0.67	0.020	1
050813	0.719	X	5.96	2.34	43.57	17.37	⋯	⋯	This work
051210	2.58	X	3.56	2.00	29.08	16.34	5.65	3.17	1
051221A	0.5464	O	0.32	0.030	2.08	0.19	0.89	0.083	1
060121	⋯	O	0.119	0.046	0.97	0.37	0.18	0.069	1
060313	⋯	O	0.32	0.068	2.60	0.55	1.39	0.30	1
060614	0.125	O	0.31	0.35	0.70	0.79	0.86	0.97	This work
060801	1.131	X	1.23	1.31	10.25	10.92	⋯	⋯	2
061006	0.461	O	0.24	0.05	1.39	0.29	0.37	0.077	1
061210	0.4095	X	2.82	2.61	15.51	14.36	⋯	⋯	3
070429B	0.902	X	0.76	1.7	6.00	13.44	1.17	2.62	3
070707	⋯	O	0.4	0.03	3.25	0.24	1.11	0.083	3
070714B	0.923	O	1.55	0.11	12.33	0.87	5.17	0.37	3
070724A	0.457	O	0.94	0.03	5.52	0.18	1.49	0.048	3
070729	0.52	X	3.13	2.3	19.72	14.49	⋯	⋯	This work
070809	0.473	O	5.70	0.46	34.11	2.75	9.34	0.75	3
071227A	0.381	O	2.80	0.05	14.74	0.26	3.08	0.055	3
080123	0.495	X	8.74	1.25	53.63	7.67	⋯	⋯	This work
080503	⋯	O	0.9	0.03	7.31	0.24	3.46	0.12	3
080905	0.1218	O	8.29	0.08	18.30	0.18	4.61	0.044	3
081226A d	⋯	O	<0.5	⋯	<4.06	⋯	⋯	⋯	4
090305A	⋯	O	0.43	0.030	3.49	0.24	1.19	0.083	3
090426A	2.609	O	0.060	0.030	0.49	0.24	0.29	0.14	3
090510	0.903	O	1.33	0.37	10.51	2.92	1.66	0.46	3
090515	0.403	O	13.98	0.03	76.19	0.16	13.98	0.03	3
091109B	⋯	O	0.52	0.05	4.22	0.41	1.93	0.19	This work
100117A	0.914	O	0.17	0.04	1.35	0.32	0.61	0.14	2
100206A	0.407	X	4.59	2.37	25.28	13.05	⋯	⋯	This work
100625A	0.452	X	0.45	1.16	2.63	6.77	⋯	⋯	This work
101219A	0.718	X	0.75	0.91	5.48	6.65	⋯	⋯	This work
101224A	0.454	X	2.18	2.31	12.75	13.51	⋯	⋯	This work
111117A	2.211	X	1.25	0.2	10.52	1.68	⋯	⋯	This work
120305A	0.225	X	4.967	1.44	18.09	5.25	⋯	⋯	This work
120804A	1.05	O	0.27	0.15	2.22	1.23	⋯	⋯	This work
121226A	1.37	X	0.27	1.07	2.31	9.15	⋯	⋯	This work
130515A	0.8	X	8.05	1.81	61.22	13.77	⋯	⋯	This work
130603B	0.3568	O	1.07	0.04	5.40	0.20	0.71	0.027	3
130716A	2.2	X	3.93	1.69	33.08	14.23	⋯	⋯	This work
130822A	0.154	X	22.32	1.82	60.09	4.90	⋯	⋯	This work
130912A	⋯	O	0.48	0.13	3.90	1.06	1.41	0.38	This work
131004A	0.717	O	0.11	0.030	0.80	0.22	0.25	0.068	This work
140129B	0.43	O	0.31	0.31	1.76	1.76	⋯	⋯	This work
140622A	0.959	X	4.1	1.4	32.95	11.25	⋯	⋯	This work
140903A	0.351	O	0.18	0.02	0.90	0.10	⋯	⋯	This work
140930B	1.465	O	1.12	0.5	9.62	4.30	⋯	⋯	This work
141212A	0.596	R	2.782	1.823	18.75	12.29	⋯	⋯	This work
150101B	0.134	O	3.07	0.030	7.36	0.072	0.78	0.0076	5, This work
150120A	0.46	X	0.81	1.094	4.77	6.44	⋯	⋯	This work
150424A	⋯	O	0.42	0.04	3.41	0.32	1.5	0.14	This work
150728A	0.461	X	1.28	3.44	7.52	20.29	⋯	⋯	This work
150831A	1.18	X	1.48	1.18	12.43	9.90	⋯	⋯	This work
151229A	0.63	X	1.18	0.88	8.16	6.05	⋯	⋯	This work
160303A	1.01	O	1.88	0.11	15.31	0.90	3.42	0.2	This work
160408A	1.9	O	1.65	0.15	14.13	1.25	⋯	⋯	This work
160411A	0.82	O	0.18	0.3	1.40	2.30	⋯	⋯	This work
160525B	0.64	X	0.79	1.06	5.50	7.38	⋯	⋯	This work
160601A	⋯	O	0.17	0.5	1.38	4.06	⋯	⋯	This work
160624A	0.4842	X	1.59	1.03	9.63	6.24	2.37	1.54	This work
160821B	0.1619	O	5.61	0.01	15.74	0.03	4.24	0.008	This work
161001A	0.67	X	2.61	0.88	18.54	6.22	⋯	⋯	This work
161104A	0.793	X	0.219	2.19	1.66	16.60	⋯	⋯	6
170127B	2.28	X	1.24	1.63	10.37	13.60	⋯	⋯	This work
170428A	0.453	O	1.32	0.58	7.72	3.39	⋯	⋯	This work
170728A	1.493	O	3.75	0.35	32.25	3.01	⋯	⋯	This work
170728B	1.272	O	0.99	0.30	8.40	2.55	⋯	⋯	This work
180418A	1.56	O	0.16	0.04	1.30	0.32	⋯	⋯	7
180618A	0.52	O	1.54	0.27	9.70	1.69	⋯	⋯	This work
180727A	1.95	X	0.3	0.6	2.56	5.13	⋯	⋯	This work
180805B	0.6612	X	3.44	1.06	24.30	7.49	⋯	⋯	This work
181123B	1.754	O	0.59	0.16	5.08	1.38	⋯	⋯	8
191031D	1.93	X	1.53	1.25	13.08	10.69	⋯	⋯	This work
200219A	0.48	X	1.38	0.88	8.30	5.28	⋯	⋯	This work
200411A	0.82	X	4.91	0.88	37.66	6.75	⋯	⋯	This work
200522A	0.5536	O	0.143	0.029	0.93	0.19	0.24	0.048	9
200907B	0.56	X	0.37	1.19	2.41	7.78	⋯	⋯	This work
201221D	1.055	X	3.57	2.93	29.35	24.09	⋯	⋯	This work
210323A	0.733	O	0.8	0.5	5.89	3.68	⋯	⋯	This work
210726A	0.37	R	0.044	0.15	0.23	0.78	⋯	⋯	This work
210919A	0.2415	O	13.28	0.5	51.05	1.92	⋯	⋯	This work
211023B	0.862	O	0.49	0.33	3.84	2.57	⋯	⋯	This work
211106A	⋯	R	0.097	0.036	0.79	0.29	0.49	0.18	10, This work
211211A	0.0763	O	5.44	0.02	7.92	0.029	3.20	0.01	11, This work

Notes. Galactocentric offsets for 84 bursts, and one upper limit on the offset (for GRB 081226A). Physical offsets are calculated using the same cosmological parameters across all bursts. For bursts with optical afterglow detections and no publicly available afterglow imaging, we assume an astrometric tie error of 05 in our calculation of the offset uncertainty. The positions for bursts with only XRT positions are based on the enhanced XRT positions as of 2022 May (Evans et al. 2009).

^a Wave band of afterglow used to calculate the offset: X = X-ray, O = Optical, and R = Radio. ^b For bursts with unknown redshift, physical offsets are calculated for an assumed z = 1. ^c Angular offset measurement references: (1) Fong et al. (2010), (2) Berger et al. (2007), (3) Fong & Berger (2013), (4) Nicuesa Guelbenzu et al. (2012), (5) Fong et al. (2016), (6) Nugent et al. (2020), (7) Rouco Escorial et al. (2021), (8) Paterson et al. (2020), (9) Fong et al. (2021), (10) Laskar et al. (2022), (11) Rastinejad et al. (2022). ^d An angular offset of <05 is reported in Nicuesa Guelbenzu et al. (2012), but an afterglow position is not.

Download table as:  ASCIITypeset images: 1 2

The high angular resolution of HST data enables us to calculate the effective radii, r_e , and thus host-normalized offsets, which we determine from surface brightness profile fitting. When given the choice, we select the filter that corresponds to the rest-frame optical band of the host, as there can be small size differences between filters. We use the IRAF/ellipse routine to generate elliptical intensity isophotes and construct one-dimensional radial surface brightness profiles for the most probable host galaxy for each burst. For each observation, we allow the center, ellipticity, and position angle of each isophote to vary. Using a χ²-minimization grid search, we fit each profile with a Sérsic model with three free parameters: Sérsic index n (Ciotti & Bertin 1999), the effective radius (r_e , also known as the half-light radius), and the effective surface brightness (Σ_e ). A single Sérsic component provides an adequate fit (${\chi }_{\nu }^{2}\approx 0.4\mbox{--}1.5$) for most of the host galaxies. We perform this analysis for the hosts of 10 short GRBs with HST data that do not already have half-light radii measurements determined in this same manner.

Finally, we compile offset measurements for 32 short GRBs with ground-based or HST data (Bloom et al. 2007; Fong et al. 2010, 2016, 2021; Nicuesa Guelbenzu et al. 2012; Fong & Berger 2013; Nugent et al. 2020; Paterson et al. 2020; Rouco Escorial et al. 2021; Laskar et al. 2022; Rastinejad et al. 2022). We recalculate the physical and host-normalized offsets and uncertainties using the best-fit redshifts and the same cosmological parameters as used in this work. We also assume z = 1 for bursts with unknown redshift, and use updated, enhanced XRT positions for bursts in which the most precise position comes from the X-ray afterglow (Goad et al. 2007; Evans et al. 2009). These combined corrections result in minor revisions to the originally published values and are listed in Table 4.

We show all of the physical offsets of 84 short GRBs in Figure 5, with each short GRB's host galaxy center represented by the origin. While the majority of short GRBs occur at ≲10 kpc and drive the median of ≈7.7 kpc (Section 6.2), a substantial fraction occur outside of this galactocentric radius.

Zoom In Zoom Out Reset image size

We now combine the distribution for 84 short GRBs, which are all events for which offset measurements are available. This sample includes 34 short GRBs that have enough information for host-normalized offsets. Due to the inclusion of both XRT-localized and subarcsecond localized bursts, the measurement uncertainties vary significantly across the population and have an impact on the offset distribution. Thus, it is imperative to take these uncertainties into account in the final distribution. Indeed, driven largely by the few arcsecond-size XRT positions, 15 short GRBs are in the regime in which the measurement uncertainty is larger than the offset.

To account for these uncertainties and the fact that offsets must be a positive definite value, we use the Rice distribution for each short GRB given their offset and 1σ uncertainty. We randomly sample from the resulting distributions 500 times, using the method described in Blanchard et al. (2016). In particular, we use Equation (2) in Blanchard et al. (2016) for the Rice distribution, and note that when δ R/σ_{δ R} > 5, the Rice distribution is the same as a Gaussian distribution. We then build 500 cumulative distribution functions (CDFs) and compare them against the observed offsets. Since the CDFs are built from the random samples, the sampled distributions overall have larger physical offsets than the observed distribution since they are driven by the larger uncertainties. We show the distributions of angular, physical, and host-normalized offsets in Figures 6 and 7.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

For the observed distribution, we calculate a median of 123 [−096, +330] (16th and 84th percentiles on the full distribution) or 143 [−111, +401] for the sampled distributions. For the physical offset distribution, we find an observed median of 7.72 kpc with an interval on the full distribution of [−6.05, +20.91] kpc, or 9.57[−7.48, +22.82] kpc for the sampled distributions. We note that the physical offset distribution includes 11 events with an assumed z = 1, although the distribution and median minimally change when excluding these events. We find that the short GRBs in the Bronze sample are overall farther from their host galaxies than the Gold or Silver samples (Figure 6); this is to be expected given their less robust associations. Thus, the Gold sample median of ≈4.77 kpc can be interpreted as a minimum on the short GRB median offset.

Finally, for 34 short GRBs with effective radii measurements, we find medians of 1.45r_e [−0.93r_e , +2.57r_e ] (1.55r_e [−1.07r_e , +2.71r_e ]) for the observed (sampled) distributions. Overall, we find that the observed physical offset distribution here is more extended than determined in previous literature, with a median that is ≈2–3 kpc higher (Fong et al. 2010; Fong & Berger 2013; O'Connor et al. 2022).

We compare the observed distributions of short GRBs to those of long GRBs (Blanchard et al. 2016), the predicted distributions of field BNS mergers for solar and subsolar metallicities (Wiggins et al. 2018; Figure 6), and the observed distributions of globular clusters in the elliptical galaxy NGC821 (Spitler et al. 2008; Figures 6 and 7). Overall, short GRBs occur at larger offsets than long GRBs, are in reasonable agreement with the expected locations of BNS mergers, and are occur closer to their host galaxies than the observed distributions of globular clusters, in terms of both physical and host-normalized offsets. We further explore the relationship between offset and host galaxy type in Nugent et al.(2022).

We first address the effects of our methods in defining host galaxy associations. Here, we have adopted a uniform, generous criteria of association, in which every burst with a galaxy in the field that has ${P}_{\mathrm{cc},\min }\lesssim 0.2$ is assigned to a host. Realistically, with this method we inevitably inherit some incorrect host assignments when imposing a high P_cc threshold of 20% for any given association. In particular, we expect ≲2% of Gold, ≲10% of Silver, and ≲20% of Bronze associations to be spurious. This results in an expected total of ≲5.7 incorrect identifications, which is only ≈6.3% of our total sample of associations. On the other hand, by only including the most robust associations (Gold sample, ${P}_{\mathrm{cc},\min }\leqslant 0.02$) in short GRB studies, we subject the sample to biases and draw conclusions that may not be reflective of the entire population. Moreover, since the compact object binary progenitors of short GRBs experience natal kicks and thus systemic velocities from their birth sites (e.g., Fryer & Kalogera 1997; Fryer et al. 1999; Belczynski et al. 2006; Vigna-Gómez et al. 2018), it is inevitable that a fraction of events will explode far from their host galaxies, largely irrespective of host brightness. Thus, it is expected that due to the nature of their progenitors and the nature of the P_cc method, some short GRBs will still have correctly assigned host galaxies with relatively high P_cc values.

Indeed, we find that by including the less robust host associations (Silver and Bronze), we capture a substantial number of bursts at z ≳ 1 (Figure 8). Similarly, we find that the inclusion of the Silver and Bronze hosts results in additional lower-luminosity hosts with L_R ≲ 10¹⁰ L_⊙ (Figure 9). Finally, the locations of the most robustly associated short GRBs (Gold) are on average 3 kpc closer to their host galaxies than the sample including all associations (≈4.8 kpc versus ≈7.7 kpc; Figure 6). To summarize, we find that establishing a generous association criteria helps to capture more bursts at larger offsets, as well as higher-redshift (z ≳ 1) and lower-luminosity hosts. While this may come at a cost of incorrect host assignments at the level of ≲7%, we note that the Gold sample still comprises over half of the host associations. It is also the subsample with the most information (e.g., redshifts, host-normalized offsets) so these bursts still dominate the distributions in every property. Overall, it is clear that including more associations results in a diversification of the known population of short GRB hosts. In terms of drawing physical conclusions for their progenitors, we further explore the effect of host associations on stellar population properties in Nugent et al. (2022).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We next explore the effects of including photometric redshifts (the full modeling methods go hand in hand with the stellar population properties, and are thus described in detail in Nugent et al. 2022). Figure 8 shows that the inclusion of a large sample of photometric redshifts also captures higher-redshift events. Indeed, for z ≳ 1, we find that there is a steep drop-off in spectroscopic redshifts, and in turn, a higher frequency of bursts with photometric redshifts (Figure 8). This is in part due to the so-called redshift desert in which the most prevalent optical spectral features for redshift identification are shifted into the NIR band where ground-based spectroscopy is less sensitive. At these redshifts, the apparent faintness of the host galaxies also precludes high S/N spectroscopy and only photometric redshifts are possible. In short, including short GRB hosts with photometric redshifts helps fill out the short GRB redshift distribution at z ≳ 1.

This population is particularly important for constraining the functional form of the delay time distribution (DTD). Indeed, Wanderman & Piran (2015) and Paterson et al. (2020) found that even a few short GRBs at z ≳ 1.5 could rule out log-normal DTD models to high confidence, whereas power-law DTD models could accommodate tens of events within the Swift short GRB population at z ≳ 1. Here, we find that ≈23% of bursts with known redshift have z ≳ 1, while ≈12% have z ≳ 1.5. As not all bursts have associations or redshifts, these likely represent lower limits on the fractions. Indeed, 10 bursts with identified hosts are too faint to have determined redshifts, while six events have inconclusive host associations. In the extreme case that all 16 of these events are at z > 1 or z > 1.5 in similar proportions to the sample with known redshifts, then as many as ≈41% (22%) could reside at z > 1 (z > 1.5). In summary, we find that ≈23%–41% of short GRBs originate at z > 1 whereas ≈12%–22% originate at z > 1.5. Our results are in broad agreement with the finding that ≈20%–50% of short GRBs could reside at z > 1 based on bursts with no identified host galaxies (O'Connor et al. 2022). In Zevin et al. (2022), we use the full sample of host galaxies with star formation histories, stellar population ages, and stellar masses derived in Nugent et al. (2022) to calculate a power-law DTD with a fairly steep slope of ∝ t^−1.8 (e.g., more short delay-time systems compared to a canonical ∝t⁻¹ model), commensurate with the larger fraction of bursts at higher redshift reported here.

Using optical magnitudes and redshifts for 73 short GRBs, we find a range of host optical luminosities, L_r ≈ 1.4 × 10⁸ L_⊙ to ≈1.2 × 10¹¹ L_⊙ with a median of 〈L_r 〉 ≈ 8 × 10⁹ L_⊙ (Figure 9). This is a factor of ≈2 lower than the previous medians based on smaller samples of events (Berger 2009, 2014; Fong et al. 2017). This difference can naturally be explained by the inclusion of a larger number of lower-luminosity hosts, some of which are less robust associations compared to the focus of earlier works. The short GRB photometric catalog presented here generally reaches ${m}_{\mathrm{lim}}\approx 26$ mag (3σ), which is sensitive enough to detect L_r ≲ 10⁹ L_⊙ galaxies out to z ≈ 1. Despite this, there is a lack of short GRB hosts with L_r ≲ 10⁹ L_⊙ when compared to the field galaxy sample from the COSMOS2015 survey (Laigle et al. 2016). Although such galaxies are more common in the universe, this is likely due to the fewer numbers of stars, and thus BNS progenitors, in these galaxies, and goes hand in hand with the lack of low-mass short GRB hosts (Nugent et al. 2022).

We also compare the short GRB population to a sample of 85 long GRB hosts at z ≲ 3 (Savaglio et al. 2009; Svensson et al. 2010; Hjorth et al. 2012; Vergani et al. 2015; Blanchard et al. 2016). Long GRBs are known to originate from massive star progenitors and overall explode in lower-luminosity host galaxies (Savaglio et al. 2009; Svensson et al. 2010). Figure 9 shows that while there is substantial overlap in the observed host luminosity functions, there are more long GRB hosts with L_r ≲ 10⁹ L_⊙ compared to almost none for the short GRB host population. Indeed, there are only two short GRB hosts with L_r ≲ 10⁹ L_⊙ compared to 10 long GRB hosts. When compared to the short GRB host population, the host galaxies of long-duration GRB 211211A and the possible short GRB-EE GRB 060614 are among the least luminous galaxies compared to the short GRB host sample. On the other hand, NGC4993 (the host galaxy of GW170817) is more typical of short GRB hosts, albeit older and more quiescent (see, Nugent et al. 2022).

For the six hosts with Inconclusive associations, two have known redshifts from their afterglows (GRBs 150423A and 160410A). The limits on coincident hosts for these bursts are deep enough to rule out hosts down to L_r ≈ 10^8.5–10⁹ L_⊙ (Figure 9). For the remaining four Inconclusive bursts, the limits are deep enough to detect the faintest known short GRB hosts to z ≈ 2.5. Thus, these bursts either originate from hosts with particularly low luminosities or are highly offset from hosts that are closer to the median.

In terms of galactocentric offsets, the hosts with the most robust associations can be taken as a minimum distribution. Compared to other studies that determined a median of ≈5–6 kpc (Fong et al. 2010; Fong & Berger 2013; O'Connor et al. 2022), our median value for the entire population is larger, with ≈7.7 kpc. This is largely because previous studies focused on the most robust associations (e.g., the Gold sample); indeed, we find a smaller median of ≈4.8 kpc for this sample alone. In keeping with previous work, we find that short GRBs are also ≈6 times larger in physical offsets than long GRBs, and ≈2.5 times larger in host-normalized offsets. This is consistent with the migratory ability of short GRB progenitors and their long delay times, compared to the young and relatively stationary massive star progenitors of long GRBs. Compared to NS merger models, we also find a dearth of observed highly offset (≳30 kpc) SGRBs (Figure 6). This can be reconciled if most of the Inconclusive associations originate from hosts at large offsets (as opposed to from low-luminosity, spatially coincident hosts).

Early work suggested that dynamical channels in globular clusters could form BNS mergers and be responsible for ≈30% of observed short GRBs (Grindlay et al. 2006). However, more recent globular cluster simulations have shown the rate of BNS and NSBH mergers to be negligible in clusters compared to the field (Ye et al. 2020). This is corroborated by the lack of a globular cluster to deep limits at or proximal to the position of the BNS merger GW170817 (Lamb et al. 2019b; Fong et al. 2019; Kilpatrick et al. 2022). Indeed, when we compare to the globular cluster distributions, we find that at most ≲10% of observed short GRBs could originate from globular clusters in situ.

We finally examine whether or not short GRB-EE or possible short GRB-EE events are distinct in their properties. The mechanism powering the extended emission is uncertain, although has been proposed to be linked to protomagnetar winds (Bucciantini et al. 2012), two-component jets (Barkov & Pozanenko 2011), or a progenitor-specific phenomenon such as NS-BH merger origins (Troja et al. 2008; Gompertz et al. 2020). Equipped with a large sample of short GRBs, we now examine this question in further detail, here and in Nugent et al. (2022). For the 14 short GRB-EE bursts with optical luminosities and magnitudes, we find that these bursts span the full range in host luminosity with a median of 〈L_r,EE〉 ≈ 1.0 × 10¹⁰ L_⊙, virtually indistinguishable from the classical short GRB sample. We also find a clear lack of correlation with any galaxy-scale environmental property (e.g., stellar population age, stellar mass; Nugent et al. 2022). In terms of locations, Troja et al. (2008) claimed that short GRB-EE events lie closer to their host galaxies than classical short GRBs, and likely arise from NS-BH mergers; this was tentatively supported in Gompertz et al. (2020) although the latter works find their host-normalized offsets to be indistinguishable. Here, we perform an Anderson–Darling (AD) test between these two populations to test the null hypothesis that their projected physical (host-normalized) offsets are drawn from the same underlying distribution. We calculate a p-value of p = 0.25 (p = 0.25). Thus, we cannot rule out the null hypothesis in both cases, and find that these two populations are statistically indistinguishable in terms of the locations with respect to their hosts. We note that if the observed population of short GRB-EE events arise from different progenitors than classical short GRBs, these differences are not manifested as a distinct set of environmental properties.

Here, we address the selection effects of our sample born out of the required inclusion criteria, and assess the potential contamination from events that originate from collapsars (e.g., traditional long GRBs). First and foremost, robust host galaxy identifications require localization via the detection of afterglows. The brightness of the afterglow depends on a combination of kinetic energy and circumburst density (e.g., Granot & Sari 2002). Thus, the requirement of a detected afterglow might translate to a missing population of bursts at large offsets in the galaxy halos or IGM, or in quiescent galaxies for which the average ISM densities are lower (Perna et al. 2022). Indeed, Figure 6 shows that the predicted spatial distributions of BNS mergers expect ≈20% of the population to reside at ≳50 kpc (Wiggins et al. 2018). We briefly quantify how many bursts we could be missing at larger offsets. In our study, the requirement for the detection of an afterglow reduces the total available sample by ≈28%. However, the majority (≈70%) of the events that lack X-ray afterglows have delayed XRT follow-up observations, either due to observatory constraints or discoveries in BAT ground analysis, whereas only a couple of events in our well-localized sample had delayed X-ray follow-up. Thus, most of the events which lack X-ray afterglows are not likely to have systematically fainter X-ray afterglows than the rest of the population. This leaves ≈12 events with presumably fainter X-ray afterglows that resulted in afterglow non-detections. If these events indeed went undetected as a result of lower circumburst densities and larger offsets, their inclusion in this sample would have an effect of ≲10%. While the optical afterglows of highly offset bursts have been found to be fainter (Berger 2010), a more recent study exploring the X-ray afterglows did not find any correlation between offset and X-ray afterglow brightness (O'Connor et al. 2022). In summary, we do not expect the population missing at large offsets to be substantial.

Our second major criteria for selection is based on the observed gamma-ray duration (T₉₀). The duration-based classification has been shown to be a detector-specific and imperfect delineation between NS merger and collapsar events (Bromberg et al. 2013; Jespersen et al. 2020), and thus we expect to inherit some contamination in our sample. This is rooted in a few examples in which the duration does not provide a one-to-one mapping to the progenitor. For instance, the Fermi short GRB 200826A had a duration of ≈1.1 s (30–500 keV), but has a photometric excess fully consistent with an associated SN, indicative of a massive star (non-NS merger) origin (Ahumada et al. 2021). Similarly, the Swift and Fermi long GRB 211211A was found to have a photometrically identified kilonova, consistent with an NS merger origin (Rastinejad et al. 2022). To assess the degree of potential contamination by true collapsar events, we apply both the Bromberg et al. (2013) and Jespersen et al. (2020) criteria to our sample, and subsequently search for any systematic variations between bursts classified as collapsars via the various schemes. Bromberg et al. (2013) determine the probability of a given burst arising from a collapsar based on the number counts of bursts at a given duration, and the expectation of a plateau in durations corresponding to the breakout time from a collapsar. They critically conclude that spectral hardness is, if anything, a more important tool for distinction than duration. They subsequently provide a route for the determination of the collapsar probability as a function of duration, as well as in different spectral hardness bins (f_NC). Since the fit parameters for the spectral hardness bins are not provided directly in Bromberg et al. (2013) we recalculate them based on the provided distributions. Furthermore, we calculate the probabilities based on single power-law spectral fits to the bursts in our sample from the more recent BAT catalog, resulting in some small (typically not important) discrepancies between our values and those in Bromberg et al. (2013). For Jespersen et al. (2020) we directly determine bursts that are either in the short or long category. In this case, Jespersen et al. (2020) used a machine-learning approach to identify features that distinguish short and long GRBs, and these appear to provide a cleaner separation than duration alone. However, they also cannot perform this analysis on bursts of very short duration, and thus we assign these bursts to the short class. It should also be noted that this classification scheme places some short GRB-EE in the long category, perhaps most notably GRB 060614. Our results are listed in Appendix B.

We can then confront the outcomes of these classification schemes based on gamma-ray properties and examine trends with offsets. The baseline expectation is that true NS merger events will have larger offsets than collapsar contaminants. Bromberg et al. (2013) found that ≈35% of Swift GRBs with T₉₀ ≤ 2 s could be true collapsars. If these probabilities provide an accurate indication of progenitor, we would overall expect that bursts with larger values of f_NC would have larger offsets. However, we find that both the potential contaminants and the pure NS merger populations under this scheme have indistinguishable offset distributions and span the full range.

In addition to offsets, we can test if the populations of bursts identified as likely collapsars differ from those identified as mergers (shorts) in other properties. Perhaps most notably these include the redshift and the host-specific star formation rate (the latter of which are reported in Nugent et al. 2022). Since the long GRB population is typically found at higher redshift than the short burst population, we may expect that the collapsar contamination may give rise to the apparent high-redshift short GRBs. Similarly, while short GRBs do arise predominantly from star-forming host galaxies, their specific star formation rates are lower. However, AD tests do not reveal any significant differences between the redshifts or specific star formation rates between our sample split according to the two alternative schemes. Moreover, the classification of Bromberg et al. (2013) predicts that ≈1/3 of z < 0.5 events in our sample are contaminated by true collapsars but this is at odds with the fact that the large majority of events at these redshifts have strong constraints on associated SN emission. We further find that the distributions between our sample and the classical long GRB sample are quite distinct in several properties, including host luminosities, physical offsets (this work), stellar masses, and star formation rates (Nugent et al. 2022). These vastly different distributions are also at odds with a large contamination fraction by true collapsars, and if true, would require extreme host properties in the contaminating population to reconcile the differences.

Zhang et al. (2009) suggest that a full characterization of the population should include the consideration of multiple physical criteria, including host type, offset, location in high energy correlations, and the presence of SNe as a route of distinction between the two classes of burst which they term type I (mergers) and type II (collapsars). Not all of the ideal information is available for each burst. However, based on the available information, the majority of our sample would be classed as type I, or would be inconclusive.

The lack of apparent differences between the samples when employing different inclusion criteria demonstrates that our duration cut is as efficient as others in identifying true, merger-driven short GRBs. While it is impossible to precisely quantify the contamination, since alternative cuts do not result in significantly different distributions in the core parameters, our physical conclusions are not sensitive to our choice of method of determining what constitutes a short GRB.