The isotropic energy function and formation rate of short gamma-ray bursts

Gamma-ray bursts (GRBs) are brief,intense,gamma-ray flashes in the universe,lasting from a few milliseconds to a few thousand seconds.For short gamma-ray bursts (s GRBs) with duration less than 2 seconds,the isotropic energy (E) function may be more scientifically meaningful and accurately measured than the luminosity (L) function.In this work we construct,for the first time,the isotropic energy function of s GRBs and estimate their formation rate.First,we derive the L-Ecorrelation using22 s GRBs with known redshifts and well-measured spectra and estimate the pseduo redshifts of 334 Fermi s GRBs.Then,we adopt the Lynden-Bell c~-method to study isotropic energy functions and formation rate of s GRBs without any assumption.A strong evolution of isotropic energy E∝(1+z)is found,which is comparable to that between Land z.After removing effect of the cosmic evolution,the isotropic energy function can be reasonably fitted by a broken power law,which isφ(E)∝E,.for dim s GRBs andφ(E)∝E,.for bright s GRBs,with the break energy 4.92×10erg.We obtain the local formation rate of s GRBs is about 17.43 events Gpcyr.If assuming a beaming angle is 6?to 26?,the local formation rate including off-axis s GRBs is estimated asρ=155.79-3202.35 events Gpcyr.