Lyutikov 2011 侧向膨胀对余辉的影响

主要内容:
说只有张角特小 theta_j<1/Gamma^2（为什么是平方呢）或者张角大但在中等相对论的时候，才有影响。

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Title:		On the sideways expansion of relativistic non-spherical shocks and GRB afterglows
Authors:		Lyutikov, Maxim
Publication:		eprint arXiv:1106.0025
Publication Date:		05/2011
Origin:		ARXIV
Keywords:		Astrophysics - High Energy Astrophysical Phenomena
Bibliographic Code:		2011arXiv1106.0025L

Abstract

Expansion of non-spherical relativistic blast waves is considered in the Kompaneets (the thin shell) approximation. We find that the relativistic motion effectively "freezes out" the lateral dynamics of the shock front: only extremely strongly collimated shocks, with the opening angles $\Delta \theta \leq 1/\Gamma^2$, show appreciable modification of profiles due to sideways expansion. For less collimated profiles the propagation is nearly ballistic; the sideways expansion of relativistic shock becomes important only when they become mildly relativistic.

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