Deducing the lifetime of short gamma-ray burst progenitors from host galaxy demography

The frequency of short gamma-ray bursts (GRBs) in galaxies with distinct star formation histories can be used to constrain the lifetime of the progenitor systems. As an illustration, we consider here the constraints that can be derived from separating the host galaxies into early and late types. On average, early-type galaxies have their stars formed earlier than late-type galaxies, and this difference, together with the time delay between progenitor formation and short GRB outburst, leads to different burst rates in the two types of hosts. Presently available data suggest, but do not yet prove, that the local short GRB rate in early-type galaxies may be comparable to that in late-type galaxies. This suggests that, unlike Type Ia supernovae, at least half of the short GRB progenitors that can outburst within a Hubble time have lifetimes greater than about 7 Gyr. Models of the probability distribution of time delays, here parameterized as P(tau) alpha tau(n), with n greater than or similar to - 1 are favored. This apparent long time delay and the fact that early-type galaxies in clusters make a substantial contribution to the local stellar mass inventory can explain the observed preponderance of short GRBs in galaxy clusters.