Short gamma-ray burst progenitors have short delay times
Short gamma-ray bursts (SGRBs) are thought to be primarily associated with binary neutron star (BNS) mergers. The SGRB population can therefore be scrutinized for signatures of the delay time between the formation of the progenitor massive star binary and the eventual merger, which could produce an evolution of the cosmic rate density of such events whose shape departs from that of the cosmic star formation history. We therefore studied a large sample of SGRBs within a hierarchical Bayesian framework, with a particular focus on the delay time distribution (DTD) of the population. Following previous studies, we modelled the DTD either as a power-law with a minimum time delay or as a log-normal function. We considered two models for the intrinsic SGRB luminosity distribution: an empirical luminosity function with a doubly broken power-law shape and another based on a quasi-universal structured jet model. Regardless of the chosen parametrization, we found average time delays of $10\lesssim \langle τ_\mathrm{d}\mathrm\rangle/\mathrm{Myr}\lesssim 900$ and a minimum delay time of $τ_\mathrm{d,min}\lesssim 350\,\mathrm{Myr}$, in contrast with previous studies that found long delay times of a few gigayears. We demonstrate that the cause of the longer inferred time delays in past studies most likely resides in an incorrect treatment of selection effects