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

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.

12 pages, 1 figure, accepted for publication in ApJ

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