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

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 ($E_{\mathrm{iso}}$) function may be more scientifically meaningful when compared with GRB isotropic-equivalent-luminosity function ($L_{\mathrm{iso}}$), 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 $E_{\mathrm{iso}}\propto (1+z{)}^{1.80_{-0.63}^{+0.36}}$, which is comparable to that between $L_{\mathrm{iso}}$ and $z$, i.e., $L_{\mathrm{iso}}\propto (1+z{)}^{2.30_{-0.51}^{+0.56}}$ (both $1\sigma$). The evolution-removed isotropic-equivalent-energy function can be reasonably fitted by a broken power-law, in which the dim and bright segments are $\psi (E_{\mathrm{iso}})\propto E_{\mathrm{iso}}^{-0.27\pm 0.01}$ and $\psi (E_{\mathrm{iso}})\propto E_{\mathrm{iso}}^{-0.87\pm 0.07}$, respectively ($1\sigma$). For the cosmic GRB formation rate, it increases quickly in the region of $0\le z\lesssim 1$, and roughly keeps constant for $1\lesssim z\lesssim 4$, and finally falls with a power index of $-3.80\pm 2.16$ for $z\gtrsim 4$, in good agreement with the observed cosmic star formation rate so far.

6 pages, 10 figures. Accepted for publication in MNRAS

References in corpus (5)

• The Supernova -- Gamma-Ray Burst Connection
• Low-Luminosity Gamma-Ray Bursts as a Distinct GRB Population:A Firmer Case from Multiple Criteria Constraints
• Revisiting the Long/Soft-Short/Hard Classification of Gamma-Ray Bursts in the Fermi Era
• Peak energy of the prompt emission of long Gamma Ray Bursts vs their fluence and peak flux
• Selection Effects on the Observed Redshift Dependence of GRB Jet Opening Angles

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