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 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. Analytical expressions are given for spherical ejecta with broken power-law mass (or energy) distributions, M(> γ β) ∝ (γ β)^−s with s = s_KN at γ β < γ ₀ β₀ and s = s_ft at γ β > γ ₀ β₀ (where γ is the Lorentz factor). For parameter values characteristic of merger calculation results – a ‘shallow’ mass distribution, 1 < s_KN < 3, for the bulk of the ejecta (at γ β ≈ 0.2), and a steep, s_ft > 5, ‘fast tail’ mass distribution – our model provides an accurate (to tens of per cent) description of the evolution of the flux, including at the phase of deceleration to subrelativistic expansion. This is a significant improvement over earlier results, based on extrapolations of results valid for γ β ≫ 1 or ≪1 to γ β ≈ 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 ∼10⁴ d.