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

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ABSTRACT Mergers of compact objects [binary neutron stars or neutron star-black hole (NSBH)] with a substantial mass ratio ($q\gt 1.5$) are expected to produce a mildly relativistic ejecta within $\sim 20^\circ$ 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 $\sim 30~{{\ \rm per\ cent}}$ deviations) the observed emission produced by 2D numerical calculations of the full relativistic hydrodynamics. We consider a toroidal ejecta with an opening angle of $15^\circ \le \theta _ \text{open}\le 30^\circ$ and broken power-law mass distribution, $M(\gt \gamma \beta)\propto (\gamma \beta)^{-s}$ with $s=s_{\rm KN}$ at $\gamma \beta \lt \gamma _0\beta _0$ and $s=s_{\rm ft}$ at $\gamma \beta \gt \gamma _0\beta _0$ (where $\gamma$ is the Lorentz factor). The parameter values are chosen to characterize merger calculation results – a ‘shallow’ mass distribution, $1\lt s_{\rm KN}\lt 3$, for the bulk of the ejecta (at $\gamma \beta \approx 0.2$), and a steep, $s_{\rm ft}\gt 5$, ‘fast tail’ mass distribution. While the peak flux is dimmer by a factor of $\sim$2–3, and the peak time remains roughly the same (within 20 per cent), for various viewing angles compared to isotropic equivalent ejecta ($\theta _\text{open}=90^\circ$) considered in preceding papers, the radio maps are significantly different from the spherical case. The semi-analytic method can provide information on the ejecta geometry and viewing angle from future radio map observations and, consequently, constrain the ejection mechanism. For NSBH mergers with a significant mass ejection ($\sim 0.1\,{\rm M}_\odot$), this late non-thermal signal can be observed to distances of $\lesssim 200$ Mpc for typical parameter values.