HUBBLE SPACE TELESCOPE OBSERVATIONS OF SHORT GAMMA-RAY BURST HOST GALAXIES: MORPHOLOGIES, OFFSETS, AND LOCAL ENVIRONMENTS

The galactic and local environments of cosmic explosions provide powerful insight into the nature of their progenitors. For example, past studies of supernova (SN) environments have demonstrated that Type Ia and Type Ib/Ic/II events arise from distinct progenitor systems since the former are located in all types of galaxies, while the latter occur only in star-forming galaxies, pointing to a direct link with massive stars (e.g., van den Bergh et al. 2005). In a similar vein, long-duration gamma-ray bursts (GRBs; duration, T90 ≳ 2 s) have been linked with massive stars through their exclusive association with star-forming galaxies (e.g., Bloom et al. 1998; Djorgovski et al. 1998; Fruchter et al. 1999). Short-duration GRBs, on the other hand, are now known to reside in all types of galaxies (Berger et al. 2005; Fox et al. 2005; Gehrels et al. 2005; Bloom et al. 2006; Berger 2009). Moreover, even the star-forming host galaxies of short GRBs differ from those of long GRBs; they have higher luminosities and metallicities, and lower specific star formation rates (Berger 2009). The difference between long and short GRB host galaxies, along with the lack of SN associations for short GRBs (Berger et al. 2005; Fox et al. 2005; Gehrels et al. 2005; Hjorth et al. 2005; Bloom et al. 2006; Soderberg et al. 2006), demonstrates that they have distinct progenitor populations. In particular, at least some short GRBs are associated with an older progenitor population.

Equally important are the local, sub-galactic environments. In the case of long GRBs, the distribution of their projected physical and host-normalized offsets relative to the host centers matches the overall expected distribution for massive stars in an exponential disk (Bloom et al. 2002). An analysis of the brightness distribution at the locations of long GRBs indicates that they are disproportionately concentrated on the brightest regions of their hosts, primarily in comparison to core-collapse SNe, which follow the overall light distribution of their hosts (Fruchter et al. 2006). Both of these studies have relied on high angular resolution Hubble Space Telescope (HST) imaging observations. Preliminary studies of short GRB offsets (Berger et al. 2005; Fox et al. 2005; Bloom & Prochaska 2006; Soderberg et al. 2006; Troja et al. 2008; D'Avanzo et al. 2009) reveal somewhat larger projected physical offsets than for long GRBs, and have also led to a claimed trend of smaller offsets for short GRBs with extended X-ray emission (Troja et al. 2008). No study of the locations of short GRBs relative to their hosts light distribution has been published so far.

Progenitor models of short GRBs lead to distinct predictions about the distribution of host properties and the local environments of short GRBs (measured by their offsets and location relative to the host light distribution). In particular, the popular model of neutron star and/or black hole (BH) binary mergers (NS–NS/NS–BH; Eichler et al. 1989; Narayan et al. 1992) predicts larger offsets than for the massive star progenitors of long GRBs due to potential systemic velocity kicks. Various authors have employed population synthesis models to predict the distribution of offsets by convolving distributions of kick velocities, merger timescale, and galaxy masses (Bloom et al. 1999; Fryer et al. 1999; Belczynski et al. 2006). For Milky Way mass galaxies, appropriate for short GRB hosts (Berger 2009), the predicted offset distributions have a median of ∼5–10 kpc, with a broad tail extending to tens of kpc. On the other hand, progenitor models that invoke magnetars, either from a young population or through delayed formation in a white dwarf–white dwarf (WD–WD) merger or white dwarf accretion-induced collapse (Levan et al. 2006b; Metzger et al. 2008), are expected to have a modest offset distribution since these systems do not experience kicks. Similarly, any systematic differences in the progenitors of short GRBs with and without extended X-ray emission may be revealed in the offset distribution and specific sub-galactic environments.

To confront these models with observations, we require high angular resolution imaging, best provided by HST. Such observations provide detailed information on the host galaxy morphological properties (e.g., exponential disk versus de Vaucouleurs profile, effective radius), as well as the ability to precisely measure offsets and the distribution of short GRBs relative to their host light. HST observations have served as the backbone for detailed studies of long GRB environments and host galaxy morphologies (Bloom et al. 2002; Fruchter et al. 2006; Wainwright et al. 2007). To date, HST observations of only three short GRBs have been published (050709: Fox et al. 2005; 060121: Levan et al. 2006a; 080503: Perley et al. 2009), and in only one case (050709) was the host morphology addressed.

Here, we present the first comprehensive analysis of all short GRB host galaxies observed with HST to date.³ Using these observations, we determine the host morphologies and structural properties (Section 3), we calculate precise physical and host-normalized offsets using accurate astrometry relative to ground-based afterglow images (Section 4), and we construct the first distribution of short GRB locations relative to their host light (Section 5). We draw conclusions in the context of progenitor models in Section 6. Throughout the paper, we compare and contrast the results of our analysis with similar studies of long GRBs.

We find that: (1) the short GRB hosts have systematically larger effective radii than long GRB hosts, in good agreement with their higher luminosities; (2) the observed short GRB projected physical offset distribution has a median of about 5 kpc, about a factor of 5 times larger than long GRBs, while for the population as a whole ≳25% have projected offsets of ≲10 kpc, and ≳5% have projected offsets of ≳20 kpc; (3) both the observed physical offset distribution and the robust constraints closely match the predicted offset distribution of NS–NS binaries; and (4) short GRBs uniformly trace the light distribution of their hosts, similar to core-collapse SNe, but distinct from long GRBs.

2.1. Sample

We present HST optical observations of ten short GRB host galaxies obtained with the Advanced Camera for Surveys (ACS) and the Wide-Field Planetary Camera 2 (WFPC2). The data were obtained as part of programs 10119, 10624, and 10917 (PI: Fox), as well as 10780 and 11176 (PI: Fruchter). These programs targeted all short GRBs with optical and X-ray (XRT) positions from May 2005 to December 2006, which were visible during HST 2-gyro operations. In this time frame, the only short burst that was not observed was GRB 060801. Thus, the sample in this paper is nearly complete in relation to the short GRBs with optical/X-ray afterglows.⁴ The HST observations of GRBs 050709 and 060121 have been published previously by Fox et al. (2005) and Levan et al. (2006a), respectively, but we re-analyze them here in a uniform fashion and perform a more comprehensive analysis of the host morphology and burst environment. Seven of the 10 bursts have been localized to sub-arcsecond precision from optical afterglow detections, and five have known redshifts (Table 1); we use a constraint of z ≳ 1.4 for GRB 051210 (Berger et al. 2007).

Table 1. HST Observations of Short GRB Host Galaxies

GRB	R.A.	Decl.	Uncert.	OA?	z	Instrument	Filter	Date	Exp. Time	AB Maga	Aλb
	(J2000)	(J2000)	('')					(UT)	(s)		(mag)
050509b	12h36m1406	+28°59'072c	3.4	N	0.226	ACS	F814W	2005 May 14	6870	16.32	0.037
	12h36m1376	+28°59'032	3.3
050709	23h01m2696	−38°58'395	0.2	Y	0.1606	ACS	F814W	2006 Jul 16	6981	21.09	0.02
						WFPC2	F450W	2007 Jul 29	3200	21.43	0.045
050724	16h24m4438	−27°32'275	0.1	Y	0.257	WFPC2	F450W	2008 Apr 7	3200	19.98	2.645
						WFPC2	F814W	2008 May 18	3200	18.74	1.189
051210	22h00m4126	−57°36'465	2.9	N	>1.4	WFPC2	F675W	2007 Apr 3	2800	21.14	0.052
	22h00m4133	−57°36'494	1.7
051221a	21h54m4863	+16°53'274	0.2	Y	0.5465	WFPC2	F555W	2007 Aug 13	3200	21.86	0.227
						WFPC2	F814W	2007 Aug 22	1600	21.42	0.133
060121	09h09m5199	+45°39'456	0.1	Y	⋅⋅⋅	ACS	F606W	2006 Feb 27	4400	26.22	0.047
060313	04h26m2842	−10°50'399	0.2	Y	⋅⋅⋅	ACS	F475W	2006 Oct 13	2088	26.38	0.300
						ACS	F775W	2006 Oct 14	2120	25.61	0.135
060502b	18h35m4553	+52°37'529	3.7	N	⋅⋅⋅	ACS	F814W	2006 May 15–Jul 16	25224	17.88/24.8–27.5d	0.085
	18h35m4528	+52°37'547	5.8
061006	07h24m0778	−79°11'555	0.2	Y	0.4377	ACS	F814W	2006 Oct 14	6054	21.67	0.616
						WFPC2	F555W	2008 May 22	3200	23.90	1.052
061201	22h08m3209	−74°34'471	0.2	Y	0.111/⋅⋅⋅ e	ACS	F606W	2006 Dec 11	2178	18.17/25.34f	0.251
						ACS	F814W	2006 Dec 11	2244	17.82/25.03f	0.147

Notes. Summary of short GRB positions and redshifts, HST observations, and host galaxy magnitudes (calculated using IRAF/ellipse). ^aThese values have been corrected for Galactic extinction. ^bGalactic extinction. ^cIn all cases with Swift/XRT positions, the top and bottom set of coordinates are from the catalogs of Butler (2007) and Evans et al. (2009), respectively. ^dThese magnitudes correspond to galaxy "A" and galaxies "B"–"G" in Figure 8. ^eWe consider two possible host galaxies for this burst (see Appendix B). ^fThe first value is for galaxy "A" and the second is for galaxy "B" in Figure 10.

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Six of the seven short GRBs with sub-arcsecond localization are robustly associated with host galaxies⁵ (we present a host identification for GRB 060313 in this paper; see Appendix A). The sole exception is GRB 061201, for which we explore two possible host galaxy associations based on the HST observations (see Appendix B); previously only one galaxy (at z = 0.111) was considered a potential host (Berger et al. 2007; Stratta et al. 2007). Details of the GRB properties and the HST observations are provided in Table 1.

Throughout the paper, we use the standard cosmological parameters, H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_m = 0.27, and Ω_Λ = 0.73. All reported magnitudes are corrected for Galactic extinction using Schlegel et al. (1998) dust maps.

2.2. HST Data Reduction

We retrieved pre-processed images from the HST archive⁶ for all available short GRBs. We distortion-corrected and combined the individual exposures using the IRAF task multidrizzle (Fruchter & Hook 2002; Koekemoer et al. 2002). For the ACS images, we used pixfrac = 0.8 and pixscale = 0.05 arcsec pixel⁻¹, while for the WFPC2 images, we used pixfrac = 1.0 and pixscale = 0.0498 arcsec pixel⁻¹, half of the native pixel scale. The final drizzled images, flux-calibrated to the AB magnitude system according to the ACS and WFPC2 zero points, are shown in Figures 1–10.

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2.3. Surface Brightness Profile Fitting

We use two methods to fit the surface brightness profiles of the short GRB host galaxies. First, we use the galfit software package (Peng et al. 2007) to construct the best two-dimensional ellipsoidal model of each galaxy image. Second, we use the IRAF task ellipse to produce elliptical intensity isophotes and to construct one-dimensional radial surface brightness profiles. We further use ellipse to measure the integrated AB magnitude for each galaxy (listed in Table 1).

2.3.1. galfit

As an input to galfit, we generate point-spread function (PSF) models for each instrument and filter combination using the tinytim software package. We assume a constant spectrum in F_ν; the difference in the 90% encircled energy width of the PSF for a spectral index ranging from −2 to 0 is only 1%. We additionally correct for distortion in the ACS instrument, and use a sub-sampling factor of 2 for WFPC2 to appropriately account for the reduced pixel scale in the drizzled images.

In each observation, we fit the host galaxy image with a PSF-convolved Sérsic profile:

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

where n is the concentration parameter (n = 1 is equivalent to an exponential disk profile, while n = 4 is the de Vaucouleurs profile), κ_n ≈ 2n − 1/3 + 4/405n + 46/25515n² is a constant that is coupled to the value of n (Ciotti & Bertin 1999), r_e is the effective radius, and Σ_e is the effective surface brightness in flux units. In the subsequent discussion, tables, and figures, we use surface brightness in units of mag arcsec⁻², designated as μ_e.

In all cases, we fit the host galaxies with a single⁷ Sérsic profile and allow the parameters to vary freely. The resulting best-fit values of n, r_e, and μ_e, as well as the integrated AB magnitudes, are provided in Table 2. For host galaxies that are detected at a low signal-to-noise ratio (S/N), we find that a wide range of n values can account for the observed morphology. In these cases, we fit the host galaxies with n fixed at values of 1 and 4, and provide the results of both models in Table 2.

Table 2. Morphological Properties of Short GRB Host Galaxies

GRB	Instrument	Filter	galfit						IRAF/ellipse
			na	re	rec	μeb	AB Magb		n	re	rec	μeb
				('')	(kpc)	(AB mag arcsec−2)				('')	(kpc)	(AB mag arcsec−2)
050509b	ACS	F814W	5.6	5.84	20.98	23.5	16.2		5.6	5.84	20.98	23.4
050709	ACS	F814W	1.1	0.76	2.08	23.0	21.2		0.6	0.64	1.75	22.4
	WFPC2	F450W	1.1	0.71	1.94	23.5	21.9		0.9	0.71	1.94	23.4
050724	WFPC2	F450W	4	1.35	5.34	23.2	19.4		1.3	0.36	1.42	20.8
	WFPC2	F814W	3.0	0.82	3.24	20.5	18.0		2.9	1.01	4.00	20.8
051210	WFPC2	F675W	1	0.70	5.63	23.8	23.7		1.0	0.63	5.07	24.2
			4	2.38	19.14	26.3	22.8
051221a	WFPC2	F555W	0.9	0.36	2.29	23.3	23.1		0.8	0.34	2.17	23.1
	WFPC2	F814W	0.9	0.41	2.61	22.7	22.1		0.9	0.39	2.49	22.7
060121	ACS	F606W	1	0.36	2.89	25.9	27.1		1.4	0.67	5.39	27.2
			4	1.22	9.81	27.4	26.6
060313	ACS	F475W	1	0.14	1.13	23.7	27.3		0.6	0.17	1.37	24.9
			4	0.32	2.57	26.2	26.7
	ACS	F775W	1	0.07	0.56	21.4	26.1		1.3	0.23	1.85	25.0
			4	0.10	0.80	23.6	26.3
061006	ACS	F814W	0.7	0.57	3.22	22.3	22.7		0.7	0.65	3.67	22.9
	WFPC2	F555W	1	0.63	3.55	23.3	23.4		0.8	0.55	3.10	23.6

Notes. Results of morphological analysis performed with galfit and IRAF/ellipse (Section 3). ^aFor the Sérsic index n in galfit, exact values of 1 and 4 indicate a fit with n as a fixed parameter. ^bThese values have been corrected for Galactic extinction. ^cFor the hosts with unknown redshift (GRBs 051210, 060121, and 060313), we assume z = 1.

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The galfit models and residual images for all instrument/filter combinations are shown in Figures 1–9. Objects for which both n = 1 and n = 4 models provide an adequate fit are shown for both cases.

2.3.2. Radial Profiles from IRAF/ellipse

We use ellipse to generate elliptical isophotes for each host galaxy, with the center and ellipticity of each isophote allowed to vary.⁸ The resulting radial surface brightness profiles in units of AB mag arcsec⁻² are shown in Figure 11. We fit each profile with a Sérsic model (Equation (1)) using n, r_e, and μ_e as free parameters. The best-fit values are listed in Table 2, and the resulting models are shown in Figure 11. We find adequate fits in all cases, although some host galaxies clearly exhibit radial complexity due to irregular structure and/or an edge-on orientation.

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2.4. Astrometry

2.5. Host Light Distribution

Using the results of the galfit analysis and the radial surface brightness profiles, we first classify the short GRB hosts in terms of their Sérsic n values. From the galfit analysis, we find that three hosts (GRBs 050709, 051221a, and 061006) are best modeled with n ≈ 1, corresponding to an exponential disk profile, while two hosts (GRBs 050509b and 050724) are best modeled with n ≈ 3 and ≈5.6, respectively, typical of elliptical galaxies. We note that GRB 050724 possibly exhibits weak spiral structure, which may explain the resulting value of n ≈ 3 (see Figure 3 and Malesani et al. 2007), but this putative spiral structure is clearly sub-dominant relative to the elliptical structure. The final three hosts (GRBs 051210, 060121, and 060313) are equally well modeled in galfit with a wide range of n values, and we provide results for both n = 1 and n = 4 in Table 2.

We find identical results using Sérsic model fits to the one-dimensional radial surface brightness profiles generated with ellipse (Figure 11 and Table 2). However, with this approach we find best-fit values of n ∼ 1 for the three host galaxies with ambiguous galfit results, suggesting that they are indeed better modeled as exponential disks. We, therefore, conclude that of the eight short GRB host galaxies studied here only two can be robustly classified as elliptical galaxies based on their morphology. A similar fraction was determined independently from spectroscopic observations (Berger 2009). The distribution of n values is shown in Figure 12.

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As can be seen from the galfit results, the Sérsic models of the two elliptical hosts exhibit significant residuals (Figures 1 and 3). This is a well-known effect for bright elliptical galaxies, which generally require a multi-parameter power law plus Sérsic fit that accounts for a flatter core than expected in the de Vaucouleurs model (Trujillo et al. 2004). Since we are here mainly interested in the distribution of n values and a comparison to long GRB hosts, we retain the simple Sérsic formulation.

We also find significant residuals for a one-component Sérsic fit of the host galaxy of GRB 050709, which has an irregular morphology dominated by an exponential profile (Figure 2). This is the only clearly irregular galaxy in the sample. Finally, we find that the hosts of GRBs 051210, 060121, and 061006 exhibit significant bulges, clearly seen in their radial surface brightness profiles (Figure 11). For the host of GRB 061006, which was observed in two filters, the bulge component is more significant in the F814W filter than in the F555W filter, as expected for an older stellar population; the burst appears to coincide with this bulge component (Figure 9).

The galfit and radial profile fits also yield values of the effective radius, r_e, for each host galaxy. We find a range of ≈02–58, corresponding to physical scales¹¹ of about 1.4–21 kpc. The smallest effective radius is measured for the host of GRB 060313, while the host of GRB 050509b has the largest effective radius. The median value is r_e ≈ 3.5 kpc. We adopt the best-fit values from the radial surface brightness profiles, and plot the resulting distribution, as well as r_e as a function of n, in Figure 12.

Finally, the effective surface brightness values range from μ_e ≈ 21 to ≈27 AB mag arcsec⁻². The galaxy with the highest surface brightness is the host of GRB 050724, while the lowest surface brightness is measured for the host of GRB 060121. The integrated magnitudes range from about 16.3 AB mag (GRB 050509b) to 26.4 AB mag (GRB 060313).

3.1. Comparison to Long GRB Host Galaxies

We next turn to an analysis of short GRB offsets relative to the centers of their host galaxies. Based on the astrometric tie of the HST host observations to ground-based afterglow observations, we find that the projected offsets are in the range of ≈012–177 (Table 3). The corresponding projected physical offsets are about 1–64 kpc, with a median value of about 3 kpc. The largest offsets are measured for GRBs 050509b and 051210, but these are based on Swift/XRT positions with statistical uncertainties of about 12 and 18 kpc, respectively (and possibly larger if we consider systematic uncertainties; Section 2.4). If we consider only the bursts with sub-arcsecond afterglow positions, we find that the largest offset is 3.7 kpc (GRB 050709), and that the median offset for the six bursts is 2.2 kpc. In the case of GRB 061201, the host association remains ambiguous (see Appendix B), but even for the nearest detected galaxy the offset is about 14.2 kpc. The obvious caveat is that an undetected fainter host, with ≳25.5 AB mag, may be located closer to the GRB position.

To investigate the offset distribution in greater detail, we supplement the values measured here with offsets for GRBs 070724, 071227, and 090510 from ground-based observations (Berger et al. 2009; Rau et al. 2009). In the case of GRBs 070724 and 071227, the optical afterglows coincide with the disks of apparent edge-on spiral galaxies (Berger et al. 2009; D'Avanzo et al. 2009). The offsets of the three bursts are 4.8, 14.8, and 5.5 kpc, respectively (Berger et al. 2009; Rau et al. 2009). For GRB 071227, we calculate the relative offset from our Magellan/IMACS observations and find a total (σ_θ,GRB + σ_θ,gal) uncertainty of 65 mas, corresponding to 0.34 kpc at the redshift of the host.¹²

There are seven additional events with optical afterglow identifications. Of these bursts, two (070707 and 070714b) coincide with galaxies (Piranomonte et al. 2008; Graham et al. 2009), but their offsets have not been measured by the respective authors. Based on the claimed coincidence, we conservatively estimate an offset of ≲05, corresponding¹³ to ≲4 kpc. Two additional bursts (070809 and 080503) do not have coincident host galaxies to deep limits, but the nearest galaxies are located about 6.5 and 20 kpc from the afterglow positions, respectively¹⁴ (Perley et al. 2008, 2009). For the final three bursts (080905, 090305, and 090426), no deep host galaxy searches exist in the literature.

In addition to the bursts with sub-arcsecond positions, several hosts have been identified within XRT error circles in follow-up observations (GRBs 060801, 061210, 061217, 070429b, 070729, and 080123; Berger et al. 2007; Berger 2009), but in all of these cases the offsets are consistent with zero, or may be as large as ∼30 kpc (e.g., Berger et al. 2007). For example, the offsets for GRBs 060801, 061210, and 070429b are 19 ± 16 kpc, 11 ± 10 kpc, and 40 ± 48 kpc. We use 30 kpc as a typical upper limit on the offset for these six events. We note that no follow-up observations are available in the literature for most short GRBs with X-ray positions from 2008 to 2009. Finally, about 1/4–1/3 of all short GRBs discovered to date have only been detected in γ-rays, precluding a unique host galaxy association and an offset measurement.

The cumulative distribution of projected physical offsets for the GRBs with HST observations from this work, supplemented by the bursts with offsets or limits based on optical afterglow positions (070707, 070714b, 070724, 070809, 071227, 080503, and 090510) is shown in Figure 13. Also shown is the differential probability distribution, P(δr)d(δr), taking into account the non-Gaussian errors on the radial offsets (see discussion in Appendix B of Bloom et al. 2002). We find that the median for this sample is about 5 kpc.

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As evident from the discussion above, this is not a complete offset distribution; roughly an equal number of short GRBs have only limits or undetermined offsets due to their detection in just the X-rays or γ-rays.¹⁵ Taking these events into account, our most robust inferences about the offset distribution of short GRBs are as follows.

• 1.  
  At least 25% of all short GRBs have projected physical offsets of ≲10 kpc.
• 2.  
  At least 5% of all short GRBs have projected physical offsets of ≳20 kpc.
• 3.  
  At least 50% of all short GRBs have projected physical offsets of ≲30 kpc; this value includes the upper limits for the hosts identified within XRT error circles.

These robust constraints are shown in Figure 13.

Using the observed distribution and the robust constraints outlined above, we now provide a comparison with predicted distributions for NS–NS binaries in Milky Way type galaxies (Bloom et al. 1999; Fryer et al. 1999; Belczynski et al. 2006), appropriate for the observed luminosities of short GRB host galaxies (Berger 2009). We find good agreement between the observed distribution and those predicted by Bloom et al. (1999) and Belczynski et al. (2006). The offset distribution of Fryer et al. (1999), with a median of about 7 kpc, predicts larger offsets and therefore provides a poorer fit to the observed distribution, which has a median of about 5 kpc. However, all three predicted distributions accommodate the offset constraints. In particular, they predict about 60%–75% of the offsets to be ≲10 kpc, about 80%–90% to be ≲30 kpc, and about 10%–25% of the offsets to be ≳20 kpc. Thus, the projected physical offsets of short GRBs are consistent with population synthesis predictions for NS–NS binaries. However, the observations are also consistent with partial contribution from other progenitor systems with no expected progenitor kicks, such as WD–WD binaries.

4.1. Host-normalized Offsets

To compare the offsets in a more uniform manner, we normalize the measured values by r_e for each host galaxy. We use the r_e values measured from the one-dimensional radial surface brightness profiles from ellipse (see Figure 14 and Table 3) and find values ranging from about 0.2 r_e for GRB 060121 to 6.7 ± 2.7 r_e for the Evans et al. (2009) XRT position of GRB 051210. The Butler (2007) position for GRB 051210, however, leads to an offset of 4.65 ± 4.60 r_e, consistent with a negligible offset. For the subset of six bursts with optical afterglow positions and secure host associations, four are located within 1 r_e, while the remaining two bursts are located at about 2 r_e (Figure 14). GRB 050509b, which has the largest physical offset, has a normalized offset of 2–3 r_e, depending on which XRT position is used. Thus, with the exception of the ambiguous case of GRB 061201, we find that all of the available offsets are consistent with ≲2 r_e. The large additional sample of physical offsets that we used above cannot be easily translated to host-normalized offsets at the present since none of the hosts have been observed with HST, thereby precluding a robust morphological analysis. This provides an impetus for future HST observations.

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The differential probability distribution of host-normalized offsets for our HST sample, taking into account the non-Gaussian errors, is shown in Figure 15. We find that the median value for all eight bursts is ≈1 r_e. Moreover, ≲20% of the probability distribution is at large offsets of ≳2.5 r_e.

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4.2. Comparison to Long GRB Host Galaxies

In addition to the offset analysis in the previous section, we study the local environments of short GRBs using a comparison of their local brightness to the host light distribution. This approach is advantageous because it is independent of galaxy morphology, and does not suffer from ambiguity in the definition of the host center (see Fruchter et al. 2006). We note that for the overall regular morphology of short GRB hosts the definition of the host center is generally robust, unlike in the case of long GRBs (Fruchter et al. 2006; Wainwright et al. 2007). On the other hand, this approach has the downside that it requires precise pixel-scale positional accuracy. In our sample, this is the case for only six short bursts.

The fraction of host light in pixels fainter than the afterglow pixel brightness for each host/filter combination is summarized in Table 4. The cumulative light distribution histogram is shown in Figure 16. The shaded histogram represents the range defined by the dual filters for five of the six bursts. We find that the upper bound of the distribution is defined by the blue filters, indicating that short GRBs trace the rest-frame optical light of their hosts better than the rest-frame ultraviolet. This indicates that short GRB progenitors are likely to be associated with a relatively old stellar population, rather than a young and UV bright population.

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The overall distribution has a median value of ≈0.1–0.4 (red); namely, only in about one-quarter of the cases, 50% of the host light is in pixels fainter than at the GRB location. Thus, the overall distribution of short GRB locations under-represents the host galaxies' light distribution. This is also true in comparison to the distribution for core-collapse SNe, which appear to track their host light (Fruchter et al. 2006), and even Type Ia SNe, which have a median of about 0.4 (Kelly et al. 2008). Thus, the progenitors of short GRBs appear to be more diffusely distributed than Type Ia SN progenitors.

5.1. Comparison to Long GRB Host Galaxies

Our extensive analysis of short GRB host galaxy morphologies and the burst local environments has important implications for the progenitor population. We address in particular the popular NS–NS merger model, as well as delayed magnetar formation via WD–WD mergers or WD accretion-induced collapse (Metzger et al. 2008).

6.1. Morphology

6.2. Offsets

6.3. Light Distribution

We presented the first comprehensive analysis of short GRB HST observations, and used these data to extract the morphological properties of the host galaxies, the projected physical and host-normalized GRB offsets, and the brightness at the location of the bursts relative to the overall light distribution of their hosts. The main conclusions of our analysis are as follows.

• 1.  
  The majority of short GRB hosts are consistent with or have exponential surface brightness profiles, typical of late-type galaxies. This conclusion is in good agreement with results from spectroscopic observations that reveal star formation activity in ∼3/4 of short GRB hosts (Berger 2009).
• 2.  
  The host galaxies of short GRBs are on average larger by about a factor of 2 than the hosts of long GRBs.
• 3.  
  The observed short GRB offset distribution extends from ∼1 to 50 kpc, with a median of about 5 kpc. Including the short GRBs with only γ-ray or X-ray positions, we find that ≳25%of all events have offsets of ≲10 kpc, and ≳5%have offsets of ≳20 kpc. A additional, though softer, limit is that ≳50% have offsets of ≲30 kpc.
• 4.  
  The observed physical offset distribution and the robust constraints compare favorably with the predicted distribution for NS–NS binaries. However, they do not rule out at least a partial contribution from other progenitors systems such as WD–WD binaries.
• 5.  
  We find no convincing evidence that short GRBs with extended emission have smaller physical offsets than those without extended emission. In both sub-samples, we find examples of both small offsets (∼few kpc) and possibly large offsets (tens of kpc).
• 6.  
  The distribution of host-normalized offsets for the subset of short GRBs with HST observations is nearly identical to that of long GRBs. This is due to the systematically larger size of short GRB hosts, and indicates that a comparison with long GRBs and progenitor models will benefit from the use of host-normalized (rather than physical) offsets.
• 7.  
  The locations of short GRBs with sub-arcsecond positions and HST imaging under-represent the overall light distribution of their hosts, but less so in the red. This result differs substantially from long GRBs, core-collapse SNe, and even Type Ia SNe.

The results derived in this paper are based mainly on a small sample of short GRBs (10 events) from 2005 to 2006. Seven of these objects have precise positions based on optical afterglow detections. Ten additional events with precise afterglow positions, and a similar number with XRT positions (some of which with identified hosts), are now available for a similar study. It is essential to observe this existing sample, as well as new events from Swift and Fermi, with the refurbished HST using the ACS and WFPC3 instruments. In conjunction with constraints on the progenitor population from the redshift distribution (Berger et al. 2007) and spectroscopic studies of the host galaxies (Berger 2009), the continued use of high angular resolution imaging will provide crucial insight into the nature of the progenitors and the potential for multiple populations.

We present the first host galaxy association for GRB 060313, using HST/ACS observations in the F475W and F775W filters. The offset between the GRB position (determined from Gemini-South observations; Berger et al. 2007) and the galaxy center is about 032 (Table 3). The galaxy brightness is m(F475W) = 26.4 AB mag and m(F775W) = 25.6 AB mag (Table 1). The probability of chance coincidence at this offset and galaxy brightness is only about 3 × 10⁻³ (Beckwith et al. 2006). We thus conclude that this galaxy is the likely host of GRB 060313.

The HST observations of GRB 061201 and its environment are shown in Figure 10. We explore two possibilities for the host galaxy. First, the burst is located 162 (32.5 kpc) from a relatively bright galaxy at z = 0.111 (marked "A" in Figure 10; Berger 2006; Stratta et al. 2007), for which we measure m(F606W) = 18.17 and m(F814W) = 17.82 AB mag. Second, we identify from the HST/ACS observations a second, fainter galaxy (marked "B" in Figure 10) located 18 from the GRB position, and with m(F606W) = 25.34 and m(F814W) = 25.03 AB mag. The redshift of this galaxy is not known, but assuming z ≳ 1 the inferred projected offset is 14.2 kpc. The probability of chance coincidence for both galaxies is about 20% (Beckwith et al. 2006). We therefore do not claim a unique host galaxy association for this burst, and stress that both galaxies should be considered as potential hosts. Deeper HST observations may also uncover an underlying host.

The HST observations of GRB 060502b and its environment are shown in Figure 8. Previously, Bloom et al. (2007) claimed that the host is likely an early type galaxy at z = 0.287 located about 70 kpc away from the burst XRT position. These authors also note the presence of fainter objects within the XRT error circle. A galaxy with R ≈ 25.2 mag was also found by Berger et al. (2007). In the combined HST/ACS/F814W, we find six faint galaxies within the XRT error circles of GRB 060502b (Figure 8). These galaxies have the following AB magnitudes: 27.5 (B), 25.9 (C), 27.2 (D), 26.1 (E), 24.8 (F), and 25.7 (G). The probability of chance coincidence for these galaxies within the XRT error circles is of the order of unity.