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 $\beta =v/c>0.6$. 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, $M(>\gamma \beta )\propto (\gamma \beta {)}^{-s}$ with $s=s_{\mathrm{KN}}$ at $\gamma \beta <{\gamma }_0{\beta }_0$ and $s=s_{\mathrm{ft}}$ at $\gamma \beta >{\gamma }_0{\beta }_0$ (where $\gamma$ is the Lorentz factor). For parameter values characteristic of merger calculation results -- a "shallow" mass distribution, $1<s_{\mathrm{KN}}<3$, for the bulk of the ejecta (at $\gamma \beta \approx 0.2$), and a steep, $s_{\mathrm{ft}}>5$, "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 $\gamma \beta \gg 1$ or $\ll 1$ to $\gamma \beta \approx 1$, 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 $\sim 10^4$days.

arXiv comment11 pages, 12 figures. Minor revisions following referee's report, accepted to MNRAS

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