## Abstract

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 _{0}β_{0} and s = s_{ft} at γ β > γ _{0}β_{0} (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).

Original language | English |
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Pages (from-to) | 3279-3286 |

Number of pages | 8 |

Journal | Monthly notices of the Royal Astronomical Society |

Volume | 531 |

Issue number | 3 |

Early online date | 7 Jun 2024 |

DOIs | |

Publication status | Published - 1 Jul 2024 |

## All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science