GRB isotropic energy function

For short gamma-ray bursts (sGRBs) with duration less than 2 seconds, the isotropic energy (Eiso) function may be more scientifically meaningful and accurately measured than the luminosity (Lp) function. In this work we construct, for the first time, the isotropic energy function of sGRBs and estimate their formation rate.

First, we derive the Lp-Ep correlation using 22 sGRBs with known redshifts and well-measured spectra and estimate the pseduo redshifts of 334 Fermi sGRBs. Then, we adopt the Lynden-Bell c- method to study isotropic energy functions and formation rate of sGRBs without any assumption. A strong evolution of isotropic energy E_iso_{prop.to}(1+z)^5.79^ is found, which is comparable to that between Lp and z.