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 collisionless shocks driven by such fast ejecta into the interstellar medium, for spherical ejecta with broken power-law mass (or energy) distributions, M(>γβ)∝(γβ)⁻ˢ with s=sKN at γβ<γ₀β₀ and s=sft at γβ>γ₀β₀ (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<sKN<3, for the bulk of the ejecta (at γβ≈0.2), and a steep, sft>5, "fast tail" mass distribution -- the analytic results reproduce well (to tens of percent accuracy) the results of detailed numeric calculations, a significant improvement over earlier order-of-magnitude estimates (based on extrapolations of results valid for γβ1).