The distances of short-hard gamma-ray bursts and the soft gamma-ray repeater connection

We present a search for nearby (D less than or similar to 100 Mpc) galaxies in the error boxes of six well-localized short-hard gamma-ray bursts (GRBs). None of the six error boxes reveals the presence of a plausible nearby host galaxy. This allows us to set lower limits on the distances and, hence, the isotropic-equivalent energy of these GRBs. Our lower limits are around 1 x 10(49) ergs (at a 2 sigma confidence level); as a consequence, some of the short-hard GRBs we examine would have been detected by BATSE out to distances greater than 1 Gpc and therefore constitute a bona fide cosmological population. Our search is partially motivated by the 2004 December 27 hypergiant flare from SGR 1806 - 20, and the intriguing possibility that short-hard GRBs are extragalactic events of a similar nature. Such events would be detectable with BATSE to a distance of 50 Mpc, and their detection rate should be comparable to the actual BATSE detection rate of short-hard GRBs. The failure of our search, in contrast, suggests that such flares constitute less than 15% of the short-hard GRBs (< 40% at 95% confidence). We discuss possible resolutions of this discrepancy.