Most short-hard gamma-ray bursts are not in moderately bright nearby host galaxies

The recent discovery by the Swift and HETE-2 satellites of X-ray afterglows from five short-hard bursts ( SHBs) has lead to a simple picture in which SHBs have a typical isotropic burst energy of around 1050 ergs and in which the bursters are in normal L* host galaxies at nearby distances with redshifts of around 0.2. In this Letter, I compare this simple picture with evidence from five SHBs detected in 1978 - 1979, for which their observed median peak fluxes were similar to 100 times brighter than the 2005 events and for which their positional error regions are empty of galaxies to deeper limits than the associated galaxies for the 2005 events. For example, GRB 790406 had a peak flux of 5 x 10(-5) ergs s(-1), and its error box is empty to 23.29 mag; GRB 050509B had a peak flux of 2 x 10(-7) ergs s(-1), and its associated galaxy is 18.60 mag. Independent of redshift for either set of SHBs, the set from 1978 to 1979 has a ratio of burst luminosity to host galaxy luminosity that differs by almost 2 orders of magnitude when compared with the set from 2005. A Student's t-test produces a probability of less than 2.7% that the two sets are drawn from the same parent population. The explanation for the very different properties of the two sets of SHBs might be due to ( 1) chance coincidence in the 2005 associations, ( 2) two different populations, ( 3) the ejection of the progenitors from their original galaxy, and ( 4) a very broad burst luminosity function. Each of these four explanations has problems, and the true explanation is likely some combination of these.