Constraining double neutron star binary evolution from the spatial distribution of short gamma-ray bursts

Abstract: Short gamma-ray bursts are often observed at large spatial offsets from their host galaxies. Neutron star mergers in double neutron star binaries have also recently been confirmed as a progenitor of short gamma-ray bursts (Abbott et al. 2017). We attempt to constrain uncertainties in the evolution of burst-producing neutron star binaries by generating a distribution of burst offsets from the neutron star natal kick, and then compare to a population of observed offsets in spiral galaxies. In order to do so, we model the dynamical effects of the formation of the second neutron star in a double neutron star binary. We find the resulting binary velocity and the time it takes for the binary to merge. Using the velocity and lifetime, we then integrate the trajectories of the binaries within the environment of a spiral galaxy until they merge. It is found that binaries need to be separated by less than 20 solar radii before the supernova to produce a burst within Hubble time. No constraints were found on exploding star mass or kick strength. We also find that kick strengths much weaker (rms≈50 km/s) than kicks derived from isolated pulsars (rms≈500 km/s) could potentially produce all offsets in the probed population of observed binaries.