Abstract
We examine the stability of self-similar solutions for an accelerating relativistic blast wave that is generated by a point explosion in an external medium with a steep radial density profile of a power-law index greater than 4.134. These accelerating solutions apply, for example, to the breakout of a gamma-ray burst outflow from the boundary of a massive star, as assumed in the popular collapsar model. We show that short wavelength perturbations may grow, but only by a modest factor 10.
Highlights
INTRODUCTIONThe self-similar solutions of relativistic blast waves are of much interest because of their recent applications to the study of gamma-ray bursts (GRBs)
We examine the stability of self-similar solutions for an accelerating relativistic blast wave that is generated by a point explosion in an external medium with a steep radial density profile of a power-law index greater than 4.134
The self-similar solutions of relativistic blast waves are of much interest because of their recent applications to the study of gamma-ray bursts (GRBs)
Summary
The self-similar solutions of relativistic blast waves are of much interest because of their recent applications to the study of gamma-ray bursts (GRBs). The solution describes a shock accelerating with a temporal dependence whose power-law index is uniquely determined by requiring that the self-similar solution cross the sonic line at a singular point. Note that in these second-type self-similar solutions the total energy released in the explosion E is not the determining parameter.. The stability of the WaxmanShvarts self-similar solutions in the nonrelativistic regime was studied by Sari, Waxman, & Shvarts (2000) They found that shocks accelerating at a rate larger than a critical. We study the stability of the selfsimilar solutions of ultrarelativistic blast waves for steep density profiles with a power-law index k > 4.
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