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

Binary neutron star mergers are expected to produce fast dynamical ejecta, with mildly relativistic velocities extending $\beta=v/c>0.6$. We consider the radio X-ray synchrotron emission produced by collisionless shocks driven such ejecta into interstellar medium. Analytic expressions given for spherical broken power-law mass (or energy) distributions, $M(>\gamma\beta)\propto(\gamma\beta)^{-s}$ $s=s_{\rm KN}$ at $\gamma\beta<\gamma_0\beta_0$ and ft}$ $\gamma\beta>\gamma_0\beta_0$ (where $\gamma$ is Lorentz factor). For parameter values characteristic of merger calculation results -- a "shallow" distribution, $15$, "fast tail" distribution our model provides an accurate (to 10's percent) description evolution flux, including phase deceleration sub-relativistic expansion. This significant improvement over earlier results, based on extrapolations valid $\gamma\beta\gg1$ or $\ll1$ $\gamma\beta\approx1$, which overestimate flux order magnitude typical values. It will enable more reliable inference parameters from future measurements non-thermal emission. event GW170817, existence detectable fluxes time scale $\sim10^4$days.