Constraints on the circumburst environments of short gamma-ray bursts

Observational follow up of well localized short gamma-ray bursts (SGRBs) has left 20-30 per cent of the population without a coincident host galaxy association to deep optical and NIR limits (greater than or similar to 26 mag). These SGRBs have been classified as observationally hostless due to their lack of strong host associations. It has been argued that these hostless SGRBs could be an indication of the large distances traversed by the binary neutron star system (due to natal kicks) between its formation and its merger (leading to an SGRB). The distances of GRBs from their host galaxies can be indirectly probed by the surrounding circumburst densities. We show that a lower limit on those densities can be obtained from early afterglow light curves. We find that less than or similar to 16 per cent of short GRBs in our sample took place at densities less than or similar to 10(-4) cm(-3). These densities represent the expected range of values at distances greater than the host galaxy's virial radii. We find that out of the five SGRBs in our sample that have been found to be observationally hostless, none are consistent with having occurred beyond the virial radius of their birth galaxies. This implies one of two scenarios. Either these observationally hostless SGRBs occurred outside of the half-light radius of their host galaxy, but well within the galactic halo, or in host galaxies at moderate to high redshifts (z greater than or similar to 2) that were missed by follow-up observations.