Narayan 2008 Turbulent Model

主要内容:
主要是想抛弃 delta t = R/Gamma^2 c这个关系. 这个关系的限制太大, 导致和很多观测不符.

想法是在shell里有一个eddy, 也就是一个小的球体的样子, 在shell里辐射, 我们看到的delta t = R/Gamma^2/gamma_t^2/c, 其中gamma_t是eddy的LF.

但是我觉得可能不是很对. 其中(4)式的n_e的估算可能有问题. 如果eddy在自己系里是球形的, 那么在shell系里就不是. n_e~(r/r_e)^3就是不对的. 另外, 感觉整个模型貌似没什么意义 :P.

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Title:		A Turbulent Model of Gamma-Ray Burst Variability
Authors:		Narayan, Ramesh; Kumar, Pawan
Publication:		eprint arXiv:0812.0018
Publication Date:		11/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		Submitted to MNRAS
Bibliographic Code:		2008arXiv0812.0018N

Abstract

A popular paradigm to explain the rapid temporal variability observed in gamma-ray burst (GRB) lightcurves is the internal shock model. We propose an alternative model in which the radiating fluid in the GRB shell is relativistically turbulent with a typical eddy Lorentz factor $\gamma_t$. In this model, all pulses in the gamma-ray lightcurve are produced at roughly the same distance $R$ from the center of the explosion. The burst duration is $\sim R/c\Gamma^2$, where $\Gamma$ is the bulk Lorentz factor of the expanding shell, and the duration of individual pulses in the lightcurve is $\sim R/c\Gamma^2\gamma_t^2$. The model naturally produces highly variable lightcurves with $\sim\gamma_t^2$ individual pulses. Even though the model assumes highly inhomogeneous conditions, nevertheless the efficiency for converting jet energy to radiation is high.

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