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Self-similar solutions for the interaction of relativistic ejecta with an ambient medium

Ko Nakamura·Toshikazu Shigeyama
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Abstract

We find self-similar solutions to describe the interaction of spherically symmetric ejecta expanding at relativistic speeds with an ambient medium having a power law density distribution. Using this solution, the time evolution of the Lorentz factor of the outer shock is derived as a function of the explosion energy, the mass of the ejecta, and parameters for the ambient medium. These solutions are an ultra-relativistic version of the solutions for the circumstellar interaction of supernova ejecta obtained by Chevalier and extensions of the relativistic blast wave solutions of Blandford & Mckee.

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Ko Nakamura, Toshikazu Shigeyama. 2006-03-06. Self-similar solutions for the interaction of relativistic ejecta with an ambient medium. https://doi.org/10.1086/504025

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