Self-Similar Evolution of Relativistic Shock Waves Emerging from Plane-Parallel Atmospheres

Abstract

We study the evolution of the ultra-relativistic shock wave in a plane-parallel atmosphere adjacent to a vacuum and the subsequent breakout phenomenon. When the density distribution has a power law with the 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 non-relativistic treatment.

arXiv comment9 pages, 4 figures, To appear in The Astrophysical Journal Corrected typos

References in corpus (10)

• Discovery of the peculiar supernova 1998bw in the error box of GRB980425
• Optical and Long Wavelength Afterglow from Gamma-Ray Bursts
• Discovery of the X-Ray Afterglow of the Gamma-Ray Burst of February 28 1997
• A `Hypernova' model for SN 1998bw associated with gamma-ray burst of 25 April 1998
• The Expulsion of Stellar Envelopes in Core-Collapse Supernovae
• How to Tell a Jet from a Balloon: A Proposed Test for Beaming in Gamma Ray Bursts
• Trans-Relativistic Blast Waves in Supernovae as Gamma-Ray Burst Progenitors
• Production of Lithium, Beryllium, and Boron by Hypernovae
• Roles of Supernova Ejecta in Nucleosynthesis of Light Elements, Li, Be, and B
• A Self-Similar Solution for the Propagation of a Relativistic Shock in an Exponential Atmosphere

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