## Abstract

Astrophysical explosions are accompanied by the propagation of a shockwave through an ambient medium. Depending on the mass and energy involved in the explosion, the shock velocity V can be nonrelativistic (V ≪ c, where c is the speed of light), ultrarelativistic (V ≃ c), or moderately relativistic (V ∼ few × 0.1c). While self-similar energy-conserving solutions to the fluid equations that describe the shock propagation are known in the nonrelativistic (the Sedov-Taylor blastwave) and ultrarelativistic (the Blandford-McKee blastwave) regimes, the finite speed of light violates scale invariance and self-similarity when the flow is only mildly relativistic. By treating relativistic terms as perturbations to the fluid equations, here we derive the , energy-conserving corrections to the nonrelativistic Sedov-Taylor solution for the propagation of a strong shock. We show that relativistic terms modify the post-shock fluid velocity, density, pressure, and the shock speed itself, the latter being constrained by global energy conservation. We derive these corrections for a range of post-shock adiabatic indices γ (which we set as a fixed number for the post-shock gas) and ambient power-law indices n, where the density of the ambient medium ρ _{a} into which the shock advances declines with spherical radius r as ρ _{a} ∝ r ^{-n}. For Sedov-Taylor blastwaves that terminate in a contact discontinuity with diverging density, we find that there is no relativistic correction to the Sedov-Taylor solution that simultaneously satisfies the fluid equations and conserves energy. These solutions have implications for relativistic supernovae, the transition from ultra- to subrelativistic velocities in gamma-ray bursts, and other high-energy phenomena.

Original language | English (US) |
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Article number | 108 |

Journal | Astrophysical Journal |

Volume | 880 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1 2019 |

Externally published | Yes |

## Keywords

- gamma-ray burst: general
- hydrodynamics
- methods: analytical
- shock waves

## ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science