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Hubble Space Telescope Observations of Short GRB Host Galaxies: Morphologies, Offsets, and Local Environments

[Abridged] We present the first comprehensive analysis of HST observations of short-duration gamma-ray burst (GRB) host galaxies. These observations allow us to characterize the galactic and local environments of short GRBs as a powerful constraint on the nature of their progenitors. Using the HST data for 10 short GRB hosts we determine the host morphological properties, measure precise physical and host-normalized offsets relative to the galaxy centers, and study the locations of short GRBs relative to their host light distributions. We find that most short GRB hosts have exponential disk profiles, characteristic of late-type galaxies, but with a median size that is twice as large as that of long GRB hosts, commensurate with their higher luminosities. The observed distribution of projected physical offsets, supplemented by ground-based measurements, has a median of ~5 kpc, about 5 times larger than for long GRBs, and in good agreement with predicted offset distributions for NS-NS binary mergers. For the short GRB population as a whole we find the following robust constraints: (i) >25% have projected offsets of <10 kpc; and (ii) >5% have projected offsets of >20 kpc. We find no clear systematic trends for the offset distribution of short GRBs with and without extended soft emission. While the physical offsets are larger than for long GRBs, the distribution of host-normalized offsets is nearly identical due to the larger size of short GRB hosts. Finally, unlike long GRBs, which are concentrated in the brightest regions of their host galaxies, short GRBs appear to under-represent the light distribution of their hosts; this is true even in comparison to core-collapse and Type Ia supernovae. Based on these results, we conclude that short GRBs are consistent with a progenitor population of NS-NS binaries.