Approximations of the self-similar solution for blastwave in a medium with power-law density variation

TL;DR

This paper reviews and extends approximations of the Sedov self-similar solution for strong explosions in media with power-law density profiles, providing tools for studying adiabatic flows in supernova remnants.

Contribution

It introduces extended and new approximations of the Sedov solution applicable to various geometries and density profiles, enhancing modeling capabilities for astrophysical phenomena.

Findings

Extended Taylor approximation for m≠0 cases

New Lagrangian coordinate approximations for different geometries

Potential applications in supernova remnant ionization studies

Abstract

Approximations of the Sedov self-similar solution for a strong point explosion in a medium with the power-law density distribution \rho^o\propto r^{-m} are reviewed and their accuracy are analyzed. Taylor approximation is extended to cases m\neq 0. Two approximations of the solution are presented in the Lagrangian coordinates for spherical, cylindrical and plane geometry. These approximations may be used for the investigation of the ionization structure of the adiabatic flow, i.e., inside adiabatic supernova remnants.