Non-thermal emission from mildly relativistic dynamical ejecta of neutron star mergers

Abstract

Binary neutron star mergers are expected to produce fast dynamical ejecta, with mildly relativistic velocities extending to $β=v/c>0.6$. We consider the radio to X-ray synchrotron emission produced by collisionless shocks driven by such fast ejecta into the interstellar medium. Analytic expressions are given for spherical ejecta with broken power-law mass (or energy) distributions, $M(>γβ)\propto(γβ)^{-s}$ with $s=s_{\rm KN}$ at $γβ<γ_0β_0$ and $s=s_{\rm ft}$ at $γβ>γ_0β_0$ (where $γ$ is the Lorentz factor). For parameter values characteristic of merger calculation results -- a "shallow" mass distribution, $1 5$, "fast tail" mass distribution -- our model provides an accurate (to 10's of percent) description of the evolution of the flux, including at the phase of deceleration to sub-relativistic expansion. This is a significant improvement over earlier results, based on extrapolations of results valid for $γβ\gg1$ or $\ll1$ to $γβ\approx1$, which overestimate the flux by an order of magnitude for typical parameter values. It will enable a more reliable inference of ejecta parameters from future measurements of the non-thermal emission. For the merger event GW170817, the existence of a "fast tail" is expected to produce detectable radio and X-ray fluxes over a time scale of $\sim10^4$days.