Late-time non-thermal emission from mildly relativistic tidal ejecta of compact objects merger

Mergers of compact objects (binary neutron stars, BNS, or neutron star-black hole, NSBH) with a substantial mass ratio ($q>1.5$) are expected to produce a mildly relativistic ejecta within ~20^∘ from the equatorial plane. We present a semi-analytic approach to calculate the expected synchrotron emission observed from various viewing angles, along with the corresponding radio maps, that are produced by a collisionless shock driven by such ejecta into the interstellar medium. This method reproduces well (up to ~30% deviations) the observed emission produced by 2D numerical calculations of the full relativistic hydrodynamics. We consider a toroidal ejecta with an opening angle of 15^∘≤θ_ open≤30^∘ and broken power-law mass distribution, M(>γβ)∝(γβ)⁻ˢ with s=sKN at γβ<γ₀β₀ and s=sft at γβ>γ₀β₀ (where γ is the Lorentz factor). The parameter values are chosen to characterize 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. While the peak flux is dimmer by a factor of ~2-3, and the peak time remains roughly the same (within $20%$), for various viewing angles compared to isotropic equivalent ejecta (θₒpen=90^∘) considered in preceding papers, the radio maps are significantly different from the spherical case. The semi-analytic method can provide information on the ejecta geometry and viewing angle from future radio map observations and, consequently, constrain the ejection mechanism. For NSBH mergers with a significant mass ejection (~0.1M_), this late non-thermal signal can be observed to distances of 200Mpc for typical parameter values.