Self-similar Evolution of Relativistic Shock Waves Emerging from Plane-parallel Atmospheres

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© 2005. The American Astronomical Society. All rights reserved. Printed in U.S.A.
, , Citation Kazunori Nakayama and Toshikazu Shigeyama 2005 ApJ 627 310 DOI 10.1086/430169

0004-637X/627/1/310

Abstract

We study the evolution of the ultrarelativistic shock wave in a plane-parallel atmosphere adjacent to a vacuum and the subsequent breakout phenomenon. When the density distribution is a power law in distance from the surface, there is a self-similar motion of the fluid before and after the shock emergence. The time evolution of the Lorentz factor of the shock front is assumed to follow a power law when the time is measured from the moment at which the shock front reaches the surface. The power index is found to be determined by the condition for the flow to extend through a critical point. The energy spectrum of the ejected matter as a result of the shock breakout is derived, and its dependence on the strength of the explosion is also deduced. The results are compared with the self-similar solution for the same problem with nonrelativistic treatment.

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10.1086/430169