Wu, Shiwei 2011 E_iso函数（随红移的变化）

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Title:		Gamma-Ray Bursts: the Isotropic-Equivalent-Energy Function and the Cosmic Formation Rate
Authors:		Wu, Shiwei; Xu, Dong; Wei, Daming
Publication:		eprint arXiv:1112.2029
Publication Date:		12/2011
Origin:		ARXIV
Keywords:		Astrophysics - High Energy Astrophysical Phenomena
Bibliographic Code:		2011arXiv1112.2029W

Abstract

Gamma-ray bursts (GRBs) are brief but intense emission of soft {\gamma}-rays, mostly lasting from a few seconds to a few thousand seconds. For such kind of high energy transients, their isotropic-equivalent energy ($E_{\rm iso}$) can be reliably measured and may be more scientifically meaningful when compared with GRB isotropic-equivalent luminosity function ($L_{\rm iso}$) as well as cosmic GRB formation rate, as the traditional luminosity function refers to steady emission much longer than a few thousand seconds. In this work we for the first time construct the isotropic-equivalent-energy function for a sample of 95 bursts with measured redshifts (z). Using a {\tau} statistical technique, we find cosmic evolution between $E_{\rm iso}$ and z, i.e., $E_{\rm iso}\propto(1+z)^{1.8^{+0.36}_{-0.63}}$, which is comparable to that between $L_{\rm iso}$ and z, i.e., $L_{\rm iso}\propto(1+z)^{2.30^{+0.56}_{-0.51}}$ (both 1{\sigma}). The local isotropic-equivalent-energy function can be reasonably fitted by a broken power-law, in which the dim and bright segments are $\psi(E_{\rm iso})\propto E_{\rm iso}^{-0.27\pm0.01}$ and $\psi(E_{\rm iso})\propto E_{\rm iso}^{-0.87\pm0.07}$, respectively. For the cosmic GRB formation rate, it increases quickly in the region of $0\leq z \lesssim 1$, and roughly keeps constant for $1\lesssim z \lesssim 4$, and finally falls with a power index of $-3.80\pm2.16$ for $z\gtrsim 4$, in good agreement with the observed cosmic star formation rate so far. In future a larger GRB sample with known redshifts shall better address the consistency/inconsistency between these two formation rates.

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