Non-thermal emission from mildly relativistic dynamical ejecta of neutron star mergers: spectrum and sky image

Binary neutron star mergers are expected to produce fast dynamical ejecta, with mildly relativistic velocities extending to β = v/c > 0.6. In a preceding paper, we derived an analytic description of the time-dependent radio to X-ray synchrotron flux produced by collision-less shocks driven by such fast ejecta into the interstellar medium, 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 ₀β₀ and s = s_ft at γ β > γ ₀β₀ (where γ is the Lorentz factor). Here, we extend our analysis and provide analytic expressions for the self-absorption frequency, the cooling frequency, and the observed angular size of the emitting region (which appears as a ring in the sky). 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 – the analytic results reproduce well (to tens of per cent accuracy) the results of detailed numeric calculations, a significant improvement over earlier order-of-magnitude estimates (based on extrapolations of results valid for γ β ≪ 1).