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Origins of Short Gamma-Ray Bursts Deduced from Offsets to Their Host Galaxies Revisited

The spatial distribution of short Gamma-ray bursts (GRBs) in their host galaxies provide us an opportunity to investigate their origins. Based on the currently observed distribution of short GRBs relative to their host galaxies, we obtain the fraction of the component that traces the mergers of binary compact objects and the one that traces star formation rate (such as massive stars) in early- and late-type host galaxies. We find that the fraction of massive star component is 0.37\pm 0.13 from the analysis of projected offset distribution. This suggests that a good fraction of short GRBs still originate from merger events. From our analysis, we also conclude that the fraction of late-type hosts among the elliptical, starburst and spiral galaxy is 0.82\pm 0.05, which is consistent with the observed early- to late-type number ratio of host galaxies.