Abstract 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 $\sim 30\%$ 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○ ≤ θopen ≤ 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.
Read full abstract