Gamma-Ray Bursts: the Isotropic-Equivalent-Energy Function and the Cosmic Formation Rate

Shi-Wei Wu; Dong Xu; Fu-Wen Zhang; Da-Ming Wei

doi:10.1111/j.1365-2966.2012.21068.x

paper

Gamma-Ray Bursts: the Isotropic-Equivalent-Energy Function and the Cosmic Formation Rate

arXiv:1112.2029 · doi:10.1111/j.1365-2966.2012.21068.x

Abstract

Gamma-ray bursts (GRBs) are brief but intense emission of soft $γ -$ rays, mostly lasting from a few seconds to a few thousand seconds. For such kind of high energy transients, their isotropic-equivalent-energy ( $E_{iso}$ ) function may be more scientifically meaningful when compared with GRB isotropic-equivalent-luminosity function ( $L_{iso}$ ), 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 ( $z$ ) and find an excess of high- $z$ GRBs. Assuming that the excess is caused by a GRB luminosity function evolution in a power-law form, we find a cosmic evolution of $E_{iso} \propto (1 + z)^{1.8 0_{- 0.63}^{+ 0.36}}$ , which is comparable to that between $L_{iso}$ and $z$ , i.e., $L_{iso} \propto (1 + z)^{2.3 0_{- 0.51}^{+ 0.56}}$ (both $1 σ$ ). The evolution-removed isotropic-equivalent-energy function can be reasonably fitted by a broken power-law, in which the dim and bright segments are $ψ (E_{iso}) \propto E_{iso}^{- 0.27 \pm 0.01}$ and $ψ (E_{iso}) \propto E_{iso}^{- 0.87 \pm 0.07}$ , respectively ( $1 σ$ ). For the cosmic GRB formation rate, it increases quickly in the region of $0 \leq z ≲ 1$ , and roughly keeps constant for $1 ≲ z ≲ 4$ , and finally falls with a power index of $- 3.80 \pm 2.16$ for $z ≳ 4$ , in good agreement with the observed cosmic star formation rate so far.

arXiv comment6 pages, 10 figures. Accepted for publication in MNRAS

Gamma-Ray Bursts: the Isotropic-Equivalent-Energy Function and the Cosmic Formation Rate

Abstract

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