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 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 parametrized as P ( \tau ) \propto \tau ^ { n } , with n \gtrsim - 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 .