The detection of the afterglow emission and host galaxies of short-hard gamma-ray bursts (SHBs) is one of the most exciting recent astronomical discoveries. Indications that SHB progenitors belong to old stellar populations, in contrast to those of the long-soft GRBs, provide a strong clue about their physical nature. Definitive conclusions however are limited by the small number of SHBs with known hosts. Here, we present our investigation of SHBs previously localized by the interplanetary network (IPN) using new and archival optical and X-ray observations. We show that we can likely identify the host galaxies/clusters for additional two bursts, significantly increasing the sample of SHBs with known hosts and/or distances. In particular, we determine that the bright SHB 790613 occurred within the rich galaxy cluster Abell 1892, making it probably the nearest SHB currently known. We show that the brightest galaxy within the error box of SHB 000607, at z=0.14, is most likely the host galaxy of this event. Additionally, we rule out the existence of galaxy overdensities (down to ~21mag) near the locations of two other SHBs, and set a lower limit on their probable redshift. We combine our SHB sample with events discovered recently by the Swift and HETE-2 missions, and investigate the properties of the extended sample. Comparison to SNe Ia shows that the progenitors of SHBs are typically older, implying a typical life time of several Gy. We also show that it is unlikely that there is a significant population of progenitors with life time shorter than 1Gy. This result disfavors the popular model of NS-NS mergers as the progenitors of SHBs.
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