The Luminosity Function And Formation Rate Of Short Gamma-ray Bursts

Gamma-ray bursts(GRBs)are the most intense explosion phenomenon in the uni-verse.Since they were discovered in 1967,a large number of space satellites and ground-based telescopes have made observations,and the study of GRBs has made great progress.However,the nature of GRBs has not been revealed,and some of the most basic prob-lems have not been resolved,such as:classification,progenitors,central ingine,radiation mechanism,composition of outflow,etc.GRBs can be divided into long GRBs(lGRBs,with a duration greater than 2 seconds)and short GRBs(sGRBs,with a duration less than 2 seconds)according to their duration.In 2017,the association of gravitational wave and short burst was detected for the first time.The result proved that at least part of sGRBs originated from the merger of binary neutron stars,and opened a new window for the study of sGRBs.At the same time,it is urgent to perform a comprehensive analysis of the characteristics of sGRBs.This article focuses on the luminosity function and for-mation rate of short bursts.The full text is divided into five chapters.The first chapter briefly introduces the observational characteristics and theoretical models of GRBs;the second chapter summarizes the various calculation methods of the luminosity function and formation rate of GRBs;the third and fourth chapters focus on the X-ray luminos-ity function of sGRBs,isotropic energy function and formation rate of sGRBs.The last chapter is summary and outlook.The luminosity function and formation rate of sGRBs can directly constrain the nature of their progenitors and distinguish their evolution channels.Some researchers have initially studied the luminosity function of sGRBs using the prompt emission data of sGRBs,but the afterglow luminosity function of sGRBs has not been discussed.We used the sGRBs with the well measured spectra and the X-ray afterglow as sample,and adopted the Lynden-Bell’s c-statistical method to eliminate the redshift evolution ef-fect of luminosity,and analyzed for the first time the luminosity function of the X-ray early afterglow at rest frame 200 seconds of sGRBs.We found that the X-ray afterglow luminosity function can be expressed by a simple broken power-law function,that is,φ(LX,0)∝ LX,0-0.20±0.04 for dim bursts,φ(Lx,o)∝ LX,0-1.05±0.11 for bright burst,the break luminosity is LX,0b=2.57 × 1046 erg s-1.At the same time,it is found that the X-ray af-terglow luminosity of sGRBs has a strong correlation with the isotropic energy/luminosity of the prompt emission,indicating that the X-ray afterglow emission in the early stage of sGRBs is mainly dominated by the prompt emission.Due to the very short durations of sGRBs,even some events have only a few millisec-onds,the isotropic energy of sGRBs can reflect the real physical process than luminosity.We used the all sGRBs with well measured spectra detected by Fermi satellites as samples,and calculated their isotropic energy and luminosity,respectively,and then replaced the traditional luminosity with the isotropic energy to study the isotropic energy function and formation rate of sGRBs.After considering the cosmological evolution effect of isotropic energy,it is found that the isotropic energy function of sGRBs can also be expressed by the cutoff power-law function.For dim bursts,it is φ(Eiso,0)∝ Eiso,0-0.45 for bright burstsφ(Eiso,0)∞ Eiso,0-1.11,The break energy is 4.92 × 1049 erg.Finally,we get the local forma-tion rate of sGRBs is 17.43 Gpc-3 yr-1.If it is assumed that the jet opening angle of the sGRBs is 6° to 26°,when considering the off-axis effect,the local formation rate of the sGRBs is ρ0,all=155.79-3202.35Gpc-3 yr-1.These results are basically consistent with the inferred conclusions of gravitational wave detection,which can predict the merging rate of binary neutron stars and guide future Gravitational wave detection.