First and second-type self-similar solutions of implosions and explosions containing ultra-relativistic shocks

Details First and second-type self-similar solutions of implosions and explosions containing ultra-relativistic shocks First and second-type self-similar solutions of implosions and explosions containing ultra-relativistic shocks

2005-05-09

arxiv.org/abs/astro-ph/0505174v1

Astronomy and Astrophysics

Astrophysics

Submitted to Physics of Fluids, March 4

Scientific paper

10.1063/1.2174567

We derive self similar solutions for ultra-relativistic shock waves propagating into cold material of powerlaw density profile in radius rho ~ r^-k. We treat both implosions and explosions in three geometries: planar, cylindrical and spherical. For spherical explosions these are the first type solutions of Blandford and McKee for k<4 and the second type solutions found by Best and Sari for k>5-sqrt(3/4). In addition we find new, hollow (with evacuated interior), first type solutions that may be applicable for 4

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