THE LOCATIONS OF SHORT GAMMA-RAY BURSTS AS EVIDENCE FOR COMPACT OBJECT BINARY PROGENITORS

We study HST observations of 16 short GRB host galaxies and environments obtained with the Advanced Camera for Surveys (ACS/WFC) and the infrared and ultraviolet-visual channels on the Wide-Field Camera 3 (WFC3/IR and WFC3/UVIS). The data were obtained as part of programs 11669 and 12502 (PI: Fruchter), which targeted all short GRBs with optical positions from 2007 April to 2010 January, and the Director's Discretionary Time program 13497 (PI: Tanvir) for GRB 130603B. We combine these public HST data with ground-based observations of optical afterglows to astrometrically locate the burst positions within the host galaxies.

Of the 16 bursts, 10 have apparent host galaxies based on ground-based imaging (GRBs 070429B, 070707, 070714B, 070724A, 071227, 080905A, 090426A, 090510, 100117A, and 130603B), and all of these except GRB 070707 have spectroscopic redshifts (Cenko et al. 2008; Piranomonte et al. 2008; Berger et al. 2009; D'Avanzo et al. 2009; Graham et al. 2009; Kocevski et al. 2010; Levesque et al. 2010; McBreen et al. 2010; Rowlinson et al. 2010b; Fong et al. 2011; Cucchiara et al. 2013). We note that for GRB 080905A, the host association is less secure (probability of chance coincidence, P_cc(< δR) ≈ 0.01) than the remaining bursts with P_cc(< δR) ≈ 10⁻⁴–10⁻³ (Fong et al. 2013 and Section 3.1), due to the large separation from its claimed host galaxy (Rowlinson et al. 2010b). All of these hosts (except GRB 070429B) have reported near-infrared (NIR) detections or limits (Piranomonte et al. 2008; Berger et al. 2009, 2013; Graham et al. 2009; Leibler & Berger 2010; Levesque et al. 2010; Rowlinson et al. 2010b; Fong et al. 2011; Tanvir et al. 2013).

The remaining six short GRBs have no known coincident host galaxies to optical limits of ≳ 26 mag from previous ground-based or previous HST observations (GRBs 061201, 070809, 080503, 090305A, 090515, and 091109B; Perley et al. 2008, 2009; Berger 2010; Fong et al. 2010; Rowlinson et al. 2010a; Levan et al. 2009). These events have been termed "host-less," but appear to have host galaxies at separations of ≈30–100 kpc with low probability of chance coincidence (Berger 2010).

With the exception of GRB 130603B (Berger et al. 2013; Tanvir et al. 2013), all of the HST observations presented here have not been published in the literature thus far. The results in this work, combined with the HST data from Fong et al. (2010), GRB 080503 (Perley et al. 2009; Berger 2010), and GRB 130603B (Berger et al. 2013; Tanvir et al. 2013), comprise the full available sample of short GRB hosts with HST observations. Details of the GRB properties and the observations are provided in Table 1.

Table 1. HST Observations of Short GRB Host Galaxies

GRB	RA	Dec	Uncert.	z	Instrument	Filter	Date	Exp. Time	AB Maga	Aλ
	(J2000)	(J2000)	('')				(UT)	(s)		(mag)
061201	22h08m3213	−74°34'4705	0.12	0.111?	WFC3/IR	F160W	2012 Jun 11	6397	>26.4/18.63 ± 0.01/24.46 ± 0.03b	0.039
070429B	21h52m0381	−38°49'420	1.5c	0.9023	WFC3/IR	F160W	2010 Apr 26	2797	20.59 ± 0.03	0.012
					WFC3/UVIS	F475W	2010 Apr 26	2797	24.31 ± 0.20	0.096
070707	17h50m5859	−68°55'2759	0.16	<3.6	WFC3/IR	F160W	2010 Jun 24	6397	26.16 ± 0.24	0.035
					ACS	F606W	2010 Jun 30	5644	26.68 ± 0.12	0.177
070714B	03h51m2228	+28°17'5175	0.20	0.923	WFC3/IR	F160W	2009 Aug 16	2798	22.99 ± 0.02	0.069
					WFC3/UVIS	F475W	2009 Aug 16	2698	24.89 ± 0.06	0.467
070724A	01h51m1410	−18°35'3928	0.08	0.4571	WFC3/IR	F160W	2011 Oct 3	2396	19.89 ± 0.02	0.006
070809	13h35m0455	−22°08'308	0.40	0.473?	WFC3/IR	F160W	2010 May 5	5597	>26.2/18.22 ± 0.01d	0.041
					ACS	F606W	2009 Aug 9	5150	>28.1/20.47 ± 0.03d	0.210
071227	03h52m3125	−55°59'0263	0.22	0.381	WC3/IR	F160W	2010 Jun 11	2797	18.73 ± 0.01	0.006
					WFC3/UVIS	F438W	2010 Jun 12	2900	22.35 ± 0.05	0.042
080503	19h06m2877	+68°47'3532	0.14	<4.2	WFC3/IR	F160W	2011 Dec 26	5597	>26.2/25.84 ± 0.07d	0.028
080905A	19h10m4174	−18°52'4744	0.18	0.1218	WFC3/IR	F160W	2011 Oct 16	2397
					WFC3/IR	F160W	2012 Apr 14	2397	25.97 ± 0.11e,f	0.014
					WFC3/UVIS	F814W	2012 Apr 14	2600	>27.5f	0.040
					WFC3/UVIS	F606W	2012 Apr 14	2600	27.29 ± 0.14f	0.066
090305A	16h07m0759	−31°33'2212	0.20	<4.1	WFC3/IR	F160W	2012 Feb 22	5597	25.20 ± 0.10	0.092
090426	12h36m1805	+32°59'0942	0.12	2.609	WFC3/IR	F160W	2011 Oct 28	2397	25.56 ± 0.07	0.008
090510	22h14m1253	−26°34'590	0.20	0.903	WFC3/IR	F160W	2011 Oct 11	2397	21.79 ± 0.01	0.009
090515	10h56m3610	+14°26'2937	0.16	0.403?	WFC3/IR	F160W	2011 Oct 24	5597	>26.1/18.42 ± 0.02d	0.001
091109B	07h30m5661	−54°05'2311	0.16	<4.4	WFC3/IR	F160W	2012 Feb 26	5596	>25.0/19.74 ± 0.03d	0.075
100117A	00h45m0465	−01°35'4199	0.16	0.915	WFC3/IR	F160W	2011 Sep 29	2397	21.37 ± 0.04	0.011
130603B	11h28m4817	+17°04'1803	0.09	0.3564	WFC3/IR	F160W	2013 Jun 13	2612	19.83 ± 0.02	0.012
					ACS	F606W	2013 Jun 13	2216	21.08 ± 0.04	0.057

Notes. ^aCorrected for Galactic extinction, A_λ (Schlafly & Finkbeiner 2011). ^bFor GRB 061201, we report the 3σ limit on a coincident host galaxy, photometry for "G1" and for "G2," respectively. ^c1σ positional error radius from Swift/XRT (Goad et al. 2007; Evans et al. 2009). ^dFor GRBs 070809, 080503, 090515 and 091109B, we report both the 3σ limit on a coincident host galaxy and the magnitude of the galaxy with the lowest probability of chance coincidence. ^eTo attain a higher signal-to-noise ratio, photometry is reported for the 2011 October 16 and 2012 April 14 observations combined. ^fThe position of "G1" is contaminated with saturated stars, so photometry is reported here only for "G2." The F814W limit corresponds to 3σ.

Download table as:  ASCIITypeset image

We retrieved pre-processed images for the 16 short GRBs from the HST archive.¹ We apply distortion corrections and combine the individual exposures using the astrodrizzle package in PyRAF (Gonzaga et al. 2012). For the ACS images we use pixfrac = 1.0 and pixscale = 005 pixel⁻¹. For the WFC3/IR images, we use the recommended values of pixfrac = 1.0 and pixscale = 00642 pixel⁻¹, half of the native pixel scale, while for the WFC3/UVIS images, we use pixscale = 0033 pixel⁻¹. The final drizzled images are shown for 10 events with established host galaxies (Figure 1), multi-band observations of GRB 080905A (Figure 2) and 5 events termed as "host-less" (Figure 3).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We obtained public optical/NIR afterglow discovery images for each burst. These images are from the UV-Optical Telescope (UVOT) on board the Swift satellite, the twin 6.5 m Magellan telescopes, the Gemini-North and -South 8 m telescopes, and the 8 m Very Large Telescope (VLT). The telescope and instrument for each afterglow image is listed in Table 2. For the observations from Magellan, Gemini, and VLT, we use standard IRAF tasks to process the data. For GRBs 070429B and 070714B, which have reported UVOT afterglows (Holland et al. 2007; Landsman et al. 2007), we use the uvotimsum task as part of the HEASOFT package to create co-added images for each of the seven UVOT filters.

We confirm the afterglow detection of GRB 070714B in multiple filters (Landsman et al. 2007). For GRB 070429B, the afterglow is reported to be weak (3.9σ) and detectable only by combining the data from all filters at δt ≈ 600–2660 s. To assess whether this is a real detection, we combine the UVOT observations in the same manner as described in Holland et al. (2007), but we do not detect any source at the reported position, nor within the XRT error circle. We therefore do not consider the reported afterglow to be real, and use the XRT position (Table 1) in our analysis presented here.

We perform aperture photometry for the galaxy with the lowest probability of chance coincidence in each field (see Section 3.1) using standard tasks in IRAF and the tabulated zeropoints for ACS, WFC3/IR and WFC3/UVIS calibrated to the AB magnitude system (Table 1). In addition, for the bursts previously termed as "host-less" (GRBs 061201, 070809, 080503, 090515, and 091109B; Figure 3), we determine the 3σ limit at the afterglow position.

We note that for GRB 080905A, we can only perform photometry for "G2," because "G1," claimed to be the host galaxy by Rowlinson et al. (2010b), is contaminated by foreground saturated stars which we cannot reliably subtract (Figure 2). The position of GRB 090305A, which was previously reported to have no coincident host to r ≳ 25.6 mag (Berger 2010), coincides with an extended NIR source with m_F160W = 25.20  ±  0.10 mag which we consider to be the host galaxy (Figure 1; Section 3.1). For GRB 090426A, we consider the host galaxy to be the source directly coincident with the afterglow position (Figure 1; Section 3.1), previously reported to be a "compact knot" within a multi-component host galaxy complex from ground-based observations (Antonelli et al. 2009; Levesque et al. 2010). For GRB 091109B, for which a host galaxy has not been previously reported, the afterglow position is contaminated by a diffraction spike from a nearby star (Figure 3). We perform photometry at the afterglow position using an aperture radius of 2.5θ_FWHM, and place a 3σ limit of m_F160W ≳ 25 mag on a coincident host galaxy. We note that this NIR limit is substantially shallower than the 3σ limit of the image, ≳ 26 mag. Finally, the F160W observation of GRB 130603B has additional flux from a point source at the optical afterglow position that is not part of the host galaxy (Berger et al. 2013; Tanvir et al. 2013). We perform point-spread function (PSF) subtraction of the point source as described in Berger et al. (2013) and calculate the host photometry from the PSF-subtracted image (Figure 1).

The photometry for all events, as well as 3σ upper limits for "host-less" events are listed in Table 1. All of our values are consistent with those published in the literature from ground-based data except for GRB 070714B, where we calculate m_F160W = 22.99 ± 0.11 mag while the previously published value is H = 23.58 ± 0.20 mag (Graham et al. 2009).

To determine the position of each short GRB afterglow, we perform absolute astrometry using point sources in common between the afterglow discovery images and source catalogs (2MASS, SDSS, or USNO-B depending on availability). If the position of the afterglow is contaminated by host galaxy light in the discovery image, we perform image subtraction using the ISIS package (Alard 2000) relative to late-time observations when the afterglow contribution is negligible. We then use SExtractor² to determine the afterglow position in the subtracted image. To determine the astrometric tie from the ground-based image to the catalog, we use the IRAF astrometry routine ccmap and find that a second-order polynomial with six free parameters corresponding to a shift, scale, and rotation in each coordinate, provides a robust tie in all cases with an average σ_{cat → GRB} ≈ 160 mas. Our afterglow positions are consistent with published positions in all relevant cases, albeit with higher precision. In the cases of GRBs 070809 and 090510, the afterglow discovery images are not available to us so we use the published positions and uncertainties in our analysis (Perley et al. 2007; Nicuesa Guelbenzu et al. 2012). The absolute afterglow positions and uncertainties are listed in Table 1.

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 HST observations to the afterglow discovery images. We consider three sources of uncertainty: the afterglow position (σ_GRB), the astrometric tie uncertainty between the ground-based and HST images (σ_{GB → HST}), and the host galaxy position (σ_gal).

We measure σ_GRB from each afterglow image, where the centroiding accuracy depends on the size of the PSF and the signal-to-noise ratio of the afterglow detection using SExtractor, and find values of σ_GRB ≈ 10–80 mas (Table 2), except in the case of GRB 070429B which has an uncertainty of 15 (1σ) from the Swift/XRT detection of the afterglow. The second source of uncertainty is the astrometric tie between the afterglow and host galaxy HST images (σ_{GB → HST}), which is determined using the same method described in Section 2.4. We use a range of 5–120 common point sources, depending on the depth of the image and source density and find values of σ_{GB → HST} ≈ 20–110 mas. The number of astrometric tie objects and resulting rms values are listed in Table 2. The final source of uncertainty is the centroiding accuracy of the host in the HST images. To determine this uncertainty we again use SExtractor, and find values of σ_gal ≈ 1–13 mas. This is generally the smallest source of uncertainty (Table 2).

For each galaxy/filter combination, we use the afterglow and host position to measure angular offsets, and for the galaxies with known redshifts we also calculate physical offsets (Table 2). We assume z = 1 for host galaxies without known redshift, taking advantage of the relatively flat value of the angular diameter distance at z ≳ 0.5. Finally, we use the effective radii, r_e, determined from surface brightness profile fits (Section 2.6 and Table 3) to calculate host-normalized offsets. The offsets and accompanying combined uncertainties are listed in Table 2. For GRBs 070809 and 090510, where we do not have the afterglow discovery images, we use the published uncertainties of 04 and 02, respectively (Perley et al. 2007; Nicuesa Guelbenzu et al. 2012), which dominate over all other sources of uncertainty.

Table 3. Short GRB Host Galaxy Morphological Properties

GRB	Filter	n	re	re	μe
			('')	(kpc)	(AB mag arcsec−2)
061201/G1	160W	1.03	1.09	2.18	21.86
061201/G2	160W	0.73	0.28	2.25a	25.34
070429B	160W	2.15	0.65	5.08	23.61
	475W	1.54	0.08b	0.62	24.69
070707	160W	0.97	0.36	2.89a	27.01
070714B	160W	0.76	0.34	2.68	24.35
	475W	1.18	0.28	2.20	27.17
070724A	160W	0.92	0.63	3.64	22.16
070809	160W	3.03	0.61	3.59	21.47
	606W	3.38	0.65	3.83	23.64
071227	160W	1.05	0.91	4.72	21.64
080503	160W	0.32	0.26	2.09a	26.81
080905A/G1c	160W	≈1	≈1.8	≈3.9	...
080905A/G2	160W	0.70	0.20	1.60a	25.72
090305A	160W	0.57	0.36	2.89a	25.96
090426A	160W	0.89	0.21	1.70	25.78
090510 (a < 04)	160W	1.27	0.93	7.27	24.92
090510 (a > 04)	160W	0.44	0.74	5.79	24.26
090515 (a < 085)	160W	2.95	0.79	4.24	22.02
090515 (a > 085)	160W	0.73	1.19	6.39	22.47
100117A (a < 06)	160W	0.86	0.28	2.20	22.04
100117A (a > 06)	160W	4.95	0.07	0.55	18.66
130603B (a < 1'')	160W	0.96	0.62	3.07	22.51
130603B (a > 1'')	160W	3.81	3.25	2.02	25.71
130603B (a < 02)	606W	1.98	0.79	3.92	24.97
130603B (a > 02)	606W	1.29	0.68	3.37	24.29

Notes. ^aCalculated assuming z = 1. ^bDue to the low signal-to-noise ratio of this observation, this measurement likely corresponds to a smaller region within the galaxy, and not the entire galaxy itself. ^cAlthough we cannot perform a surface brightness profile fit for GRB 080905A/"G1," these parameters are estimated from the apparent morphology and effective radius of the bulge component.

Download table as:  ASCIITypeset image

We use the IRAF/ellipse routine to generate elliptical intensity isophotes and construct one-dimensional radial surface brightness profiles for each galaxy/filter combination. For each observation, we allow the center, ellipticity, and position angle of each isophote to vary. In two cases (GRB 070707/F606W and GRB 071227/F438W), the isophotal fit does not converge, which can be attributed to the low signal-to-noise ratio of these observations. The surface brightness profiles are displayed in Figure 4.

Zoom In Zoom Out Reset image size

Using a χ²-minimization grid search, we fit each profile with a Sérsic model given by

$$\begin{equation} \Sigma (r)=\Sigma _e\,{\rm exp}\lbrace -\kappa _n[(r/r_e)^{1/n}-1]\rbrace, \end{equation} \tag{ 1 }$$

where n is the concentration parameter (n = 1 is equivalent to an exponential disk profile, while n = 4 is the de Vaucouleurs profile typical of elliptical galaxies), κ_n ≈ 2n − 1/3 + 4/405n + 46/25515n² is a constant that depends on n (Ciotti & Bertin 1999), r_e is the effective radius, and Σ_e is the effective surface brightness in flux units. We convert Σ_e to units of mag arcsec⁻², designated as μ_e. In our grid search, n, r_e, and μ_e are the three free parameters. A single Sérsic component provides an adequate fit ($\chi ^{2}_{\nu } \approx 0.4\hbox{--}1.5$) for most of the host galaxies. In four cases (GRBs 090510, 090515, 100117A, and 130603B) a single component fit yields $\chi ^{2}_{\nu } \gtrsim 2$. To improve the fit for these cases, we use two separate Sérsic components corresponding to the inner and outer regions of each galaxy. The resulting values for n, r_e and μ_e are listed in Table 3. We do not perform a surface brightness fit for GRB 080905A/"G1" since it is contaminated by saturated foreground sources (Figure 2), but given the prominent spiral structure, the morphology of this host is likely characterized by a disk profile with n ∼ 1, and we estimate the size of the bulge component to be ≈18 (≈3.9 kpc). The surface brightness profiles and resulting models are shown in Figure 4.

To determine the brightness of the galaxy at the GRB location relative to the host light distribution, we follow the methodology of Fruchter et al. (2006), Kelly et al. (2008), and Fong et al. (2010), and calculate for each galaxy image the fraction of total light in pixels fainter than the afterglow position ("fractional flux"; Table 4). Eleven bursts have differential astrometric positions of better than one pixel (Table 2). If the afterglow position spans multiple pixels, we take the average brightness among those pixels to be the representative flux of the afterglow position. For each image, we create an intensity histogram of a region centered on the host galaxy and determine a 1σ cut-off level for the host by fitting a Gaussian profile to the sky brightness distribution (equivalent to a signal-to-noise ratio cut-off of 1). We then plot the pixel flux distribution above the appropriate cut-off level for a region surrounding the host, and determine the fraction of light in pixels fainter than the afterglow pixel (see Table 4).

For GRBs 071227/F160W and 130603B/F606W, we mask sources contaminating the position of the galaxy and set these pixels to the brightness level of the surrounding pixels. We note that for GRB 080905A, we are unable to explicitly calculate the fractional flux with respect to "G1" due to the presence of saturated stars, while for GRB 061201 we cannot make a unique host association (Section 3.1). However, both of these bursts have afterglow locations at the level of the sky background, and thus have fractional flux values of zero regardless of their host associations. Table 4 also includes the values for seven bursts from Fong et al. (2010).

To assess the probability that each of the bursts originated from a coincident galaxy or from another galaxy in the field, we perform aperture photometry for galaxies within the HST field of view, discarding noticeably fainter galaxies with increasing distance from the burst since these objects will have a lower probability of being the host galaxy. We then calculate the probability of chance coincidence, P_cc(< δR) for each galaxy based on the distance from the burst position (δR) and apparent magnitude (m) (c.f., Bloom et al. 2002; Berger 2010). For bursts at offsets of <1r_e (GRBs 090426 and 100117A), we use the effective size of the galaxy, δR = r_e, while for the remaining cases, we take δR to be the projected distance between the burst and candidate host center. For the bursts with previously established hosts (Figure 1), we find P_cc(< δR) ≈ 10⁻⁴–10⁻³, consistent with ground-based results (Fong et al. 2013); the next probable hosts have values at least one order of magnitude greater, with P_cc(< δR) ≈ 0.02–0.30. The lowest value of 0.02 is for GRB 090426A, which has two galaxies within 1'' of the optical afterglow position, in addition to the source at the GRB position. From previous ground-based observations, these sources were considered to comprise a single host galaxy complex (Antonelli et al. 2009). However, given the lack of apparent interaction between these sources in the HST image (see Figure 1) and the comparatively low value of P_cc(< δR) ≈ 10⁻⁴ for the source at the afterglow position, we consider the latter to be the host galaxy. For GRB 080905A/"G1" (Figure 2), we are unable to accurately determine the brightness in any of the filters due to the presence of foreground saturated stars, but using R ∼ 18 mag determined from Rowlinson et al. (2010b) and our offset of 83, we find that "G1" has P_cc(< δR) ≈ 0.01, while "G2" has P_cc(< δR) ≈ 0.08. Therefore, "G1" is the more likely host galaxy, although this case is less clear than the other previously established host associations at small offsets.

For bursts with no obvious host galaxy at small offsets from previous ground-based or HST observations (Figure 3), termed "host-less" (GRBs 061201, 070809, 080503, 090305A, 090515: Berger 2010; 091109B: Levan et al. 2009), we calculate a range of probabilities, P_cc(< δR) ≈ 6 × 10⁻³–0.08. The associations are most robust for GRBs 070809 and 090305A with the most probable hosts at offsets of 57 (P_cc(< δR) ≈ 6 × 10⁻³) and 043 (P_cc(< δR) ≈ 7 × 10⁻³), respectively. The host association for GRB 070809 is the same as that made in Berger (2010), although here we calculate a lower probability of chance coincidence by a factor of three. We note that the extended source we associate with GRB 090305A was not detected in ground-based observations to r ≳ 25.6 mag (Berger 2010). Due to the low probability of chance coincidence and the lack of more likely host galaxy candidates in the HST observation, we consider this to be the host galaxy. We calculate moderate probabilities of ≈0.05 for GRBs 080503 and 090515, with the most probable hosts at offsets of 090 and 14'', respectively. These associations are the same as those previously published (Berger 2010; Perley et al. 2009) but the probabilities of chance coincidence are lower by a factor of two in this work.

The associations are more ambiguous for GRBs 061201 and 091109B. For GRB 061201, the two most probable host galaxies ("G1" and "G2"; Figure 3) have offsets of 163 and 18, respectively, and both have P_cc(< δR) ≈ 0.07 so the host association is inconclusive. However, "G1" is at a relatively low redshift of z = 0.111 (Stratta et al. 2007) while "G2" is likely at z ≈ 1; thus the physical offsets are ≳ 15 kpc in both cases (Table 2). For GRB 091109B, the position is contaminated by a diffraction spike, but if there is no coincident host galaxy at ≳ 25 mag, the most probable host has m_F160W ≈ 19.8 mag at an offset of 117, yielding P_cc(< δR) ≈ 0.08. We note that HST imaging at a different rotation angle will be essential in determining whether this burst originates from a host galaxy at ≲ 1'' separation or from a galaxy at a larger offset. Due to the uncertainty of the associations for GRBs 061201 and 091109B, we do not include these bursts in our subsequent offset analysis.

Overall, these probability-of-chance-coincidence results agree with those in the literature (Perley et al. 2009; Berger 2010; Rowlinson et al. 2010b), and provide deep NIR limits of ≳ 26.2 mag for bursts which lack hosts at δR ≲ few arcseconds. We discuss the possibility that such bursts originated from galaxies fainter than the detection threshold of the HST observations (and demonstrate that this is unlikely) in more detail in Section 4.

Using the results from the radial surface brightness profiles (Figure 4), we classify the short GRB hosts in terms of their morphological parameters: Sérsic value, n, and effective size, r_e. We find two elliptical galaxies, the hosts of GRBs 070809 and 090515, with n ≈ 3.0–3.4 while the remaining galaxies have disk-like morphologies with n ≈ 0.3–2.1 (Table 3). We note that GRB 100117A exhibits a complex morphology in the NIR, with Sérsic indices of n ≈ 0.9 and ≈5 for its inner and outer regions, respectively, although it is spectroscopically classified as an early-type galaxy with a stellar population age of ≈1–2 Gyr and no evidence for star formation activity (Fong et al. 2011). GRB 130603B, which is a star-forming galaxy with star formation rate ≳ 1.3 M_☉ yr⁻¹ (Cucchiara et al. 2013), has an inner component in the NIR with n ≈ 1 and a broad outer component with n ≈ 3.8. This host galaxy has an irregular, asymmetric morphology in the optical band with excess flux at radial distances of a ≈ 0.2–04 in the surface brightness profile (Figure 4) and Sérsic components with n ≈ 2 and 1.3.

The effective radii range from ≈0.2–12 with a median size of 036. We note that the signal-to-noise ratio of the GRB 070429B/F475W observation is low and the r_e measurement likely corresponds to a smaller region within the galaxy, and not the entire galaxy. For the host galaxies that require two Sérsic components, we use the radius which encloses half of the flux as the effective size when computing the host-normalized offsets. These values are 095 (GRB 090510), 09 (GRB 090515), 03 (GRB 100117A), 1'' (GRB 130603B/F160W), and 08 (GRB 130603B/F606W). For the short GRBs with known redshifts, the median physical size is about r_e ≈ 3.6 kpc. The smallest hosts are GRBs 070714B and 100117A while the largest are GRBs 090510 and 090515. The median value for this sample is the same as the value of 3.5 kpc reported in Fong et al. (2010) for a preliminary sample of hosts. Compared to the long GRB median host galaxy size of 1.7 kpc (Wainwright et al. 2007), short GRB host galaxies are twice as large. This is consistent with their larger luminosities (Berger 2009) and stellar masses (Leibler & Berger 2010).

To study the locations of short GRBs with respect to their host galaxies, we first consider the distribution of projected angular offsets. The range of angular offsets is ≈0.1–14'' with GRB 090426 as the smallest offset³ and GRB 090515 as the largest. From the angular offsets, we calculate projected physical offsets, assuming z ≈ 1 for bursts without known redshift. We find a range of ≈0.5–75 kpc (Figure 5).

Zoom In Zoom Out Reset image size

We supplement this sample of offsets with six measurements from Fong et al. (2010). In addition, we use offset measurements from ground-based observations of all of the remaining short GRBs with sub-arcsecond positions: GRB 111020A with 6 ± 1 kpc (assuming z ≈ 1, Fong et al. 2012), GRB 111117A with 10.5 ± 1.7 kpc (Margutti et al. 2012; Sakamoto et al. 2013), and GRB 120804A with 2.2 ± 1.2 kpc (Berger et al. 2013). Therefore, the full sample of offsets includes 22 short GRBs (Figure 5) with a resulting median offset of 4.5 kpc. We compare the short GRB physical offset distribution to those determined from HST observations of long GRBs (Bloom et al. 2002), and ground-based observations of core-collapse and Type Ia SNe (Prieto et al. 2008), where the offsets have been calculated in a similar manner as that described in this work. In comparison to the long GRB median offset of 1.3 kpc (Bloom et al. 2002), the short GRB median offset is ≈3.5 times larger. The short GRB median offset is comparable to those for Type Ia and core-collapse SNe of ≈3 kpc (Figure 5; Prieto et al. 2008), but the short GRB offset distribution extends to much larger offsets: only 10% of both SN types have offsets of ≳ 10 kpc, compared to 25% for short GRBs. Furthermore, no SNe have offsets of ≳ 20 kpc, while 10% of short GRBs do.

In Figure 5, we also show a comparison of the short GRB offset distribution to the predicted distributions from independent population synthesis models of NS–NS binary mergers in Milky-Way-type galaxies (Fryer et al. 1999; Bloom et al. 1999; Belczynski et al. 2006). The short GRB distribution is broadly consistent with the NS–NS binary merger predictions, and is in very good agreement with two of the three models (Bloom et al. 1999; Belczynski et al. 2006). The discrepancies between the models themselves can be attributed to uncertainties in their inputs, such as the distribution of kick velocities, orbital separations and details of common envelope evolution. The median offset for the predicted distributions is 5–7 kpc, slightly larger than the observed median of 4.5 kpc. We note that the observed distribution is mainly derived from short GRBs with optical afterglows and may be missing a few bursts with less precise localization from X-ray afterglows (Fong et al. 2013) that may occur outside of their host galaxies. Thus, while the observed distribution of offsets should be fairly representative of the true distribution, accounting for such missing events would only extend the distribution to larger offsets, in even better agreement with the NS–NS merger models.

A study by Troja et al. (2008) suggested that short GRBs with extended emission in the X-rays have smaller offsets than short GRBs with no such emission. Two bursts in our sample, GRBs 070714B and 080503 have reported evidence for extended emission at ≳ 5σ significance (Racusin et al. 2007; Mao et al. 2008; Perley et al. 2009). GRB 070714B has an offset of ≈12.2 kpc while GRB 080503 has an offset of ≈7.2 kpc from its most probable host assuming z ≈ 1. Combining these two bursts with four bursts analyzed in Fong et al. (2010) with sub-arcsecond positions and extended emission (GRBs 050709, 050724, 061006, and 060121), the median offset for the population is 3.2 kpc, with a range of ≈1–12 kpc. For the remaining 16 bursts with no extended emission and precise offset measurements, the median offset is 5.3 kpc. A Kolmogorov–Smirnov (K-S) test comparing the two populations gives a p-value of 0.9, supporting the null hypothesis that the two populations are drawn from the same underlying distribution. Therefore, there is no clear evidence from their locations that short GRBs with and without extended emission require different progenitor systems.

To compare the offset distributions in a more uniform manner, we calculate host-normalized offsets, δR/r_e, using the effective radii as determined from our morphological analysis (Section 2.6). We find a range of host-normalized offsets of ≈0.3–15.5r_e for the bursts with sub-arcsecond positions (Table 2). We supplement this sample with seven measurements from Fong et al. (2010), one of which has only an XRT position and thus a more uncertain offset (GRB 050509B). To account for the varying uncertainty in each offset, we plot a differential distribution of host-normalized offsets following the methodology of Bloom et al. (2002), as well as the resulting cumulative distribution (Figure 6). The total sample of short GRBs with host-normalized offsets is comprised of 20 events, with a median of ≈1.5r_e and only about 25% of the events at ≲ 1r_e. For comparison, the host-normalized offset distributions for long GRBs (Fruchter et al. 2006), core-collapse SNe (Kelly et al. 2008), and Type Ia SNe (Galbany et al. 2012) have median offsets of ≈1r_e. Furthermore, a K-S test comparing the host-normalized offsets for long and short GRBs does not support the null hypothesis that the two populations are drawn from the same underlying distribution (p = 0.03). A K-S test between short GRBs and Type Ia SNe yields p = 10⁻³, indicating that the two populations are drawn from different host-normalized offset distributions. Indeed, ≈20% of short GRBs have offsets of ≳ 5r_e, compared to only ≈5% for Type Ia SNe.

Zoom In Zoom Out Reset image size

To further study the local explosion environments of short GRBs, we utilize the fractional flux method which, unlike the spatial offset method, is independent of host morphology. We divide the fractional flux values into two categories based on the bursts' observed filters and redshifts: rest-frame UV (λ_rest ≲ 0.4 μm) tracking star formation activity and rest-frame optical (λ_rest ≳ 0.4 μm) tracking stellar mass. For bursts with no redshift, we assume fiducial values of z = 1 to determine the proper rest-frame band. For the 14 bursts in this analysis, all have rest-frame optical measurements while only three have rest-frame UV measurements (GRB 070707 assuming z = 1, GRBs 070714B and 071227; Table 4). Despite having coincident host galaxies, these three bursts are located on the lowest level of their hosts' UV light with fractional flux measurements of zero. The rest-frame optical measurements span a range of 0–0.8, with GRB 090426 as the highest measurement (Table 4).

We supplement these data with six additional bursts analyzed in Fong et al. (2010), bringing the total sample size to 20 events. We find that the resulting distributions are strongly skewed to low fractional flux measurements: 45% of short GRBs are located on the lowest optical brightness level of their hosts (fractional flux ≈0), and 55% are on the lowest UV level (Figure 7 and Table 5). The short GRB distributions have very low median fractional flux values of ≈0.15 for the optical and zero for the UV (Table 5). Furthermore, ≈75% of the events are located on the faint end (fractional flux ≲ 0.5) of their hosts' optical and UV regions (Figure 7). A K-S test comparing the observed short GRB distribution to a distribution that is linearly correlated with host galaxy light (diagonal line in Figure 7) yields p-values of 0.04 and 0.01 for the optical and UV, respectively (Table 5). These results demonstrate that short GRBs are not correlated with their hosts' rest-frame UV and optical light, i.e., they do not trace regions of star formation or even stellar mass.

Zoom In Zoom Out Reset image size

The short GRB distribution is particularly striking when compared to long GRBs, which lie on the brightest UV regions of their host galaxies and have a median fractional flux of 0.83 (Figure 7 and Table 5; Fruchter et al. 2006; Svensson et al. 2010). Core-collapse SNe, which have a median value of 0.60, may slightly over-represent their hosts' UV light (Svensson et al. 2010), commensurate with their origin in star-forming regions. Furthermore, at most a few percent of long GRBs and core-collapse SNe lie on the faintest regions of their host galaxies (Table 5).

On the other hand, Type Ia SNe, which result from older stellar progenitor systems, slightly under-represent their hosts' UV and optical light distributions, although K-S test results indicate that this is only marginal (Table 5). In particular, 34% of Type Ia SNe have UV fractional flux values of zero, compared to 55% for short GRBs. The difference is more apparent in the optical, with only 6% of the Type Ia SNe population located on the faintest regions of their hosts, compared to 45% for short GRBs (Table 5). A K-S test comparing the distributions of short GRBs and Type Ia SNe indicates that the populations are not drawn from the same underlying distribution in the optical (p = 0.02).

We cannot completely rule out the remote possibility that the events with less robust host associations (P_cc(< δR) ≳ 0.01) and fractional flux values of zero instead originate from faint host galaxies with m_F160W ≳ 26.2 mag, below the detection threshold of the HST images. In this scenario, the fractional flux values for these events may be greater than zero. Therefore, if we only include events with P_cc(< δR) < 0.01 (thereby excluding GRBs 061201, 080503, 080905A, and 090515 from the distribution), we find that the short GRBs are still uncorrelated with their hosts' optical light (p = 0.07; Table 5), with a median value of ≈0.25 (Figure 7). It is important to note that even in this conservative case, ≈30% of the bursts lie on the lowest optical flux levels of their hosts (Figure 7). The short GRB UV distribution is unaffected since there are no excluded bursts with rest-frame UV measurements.