The Intrinsic Statistical Properties and Correlations of Short Gamma-Ray Bursts

Abstract

The intrinsic statistical properties and correlations of short gamma-ray bursts (SGRBs) have not been fully determined, due to the limitations of observations. In this paper, we compile a more extensive sample of 82 SGRBs with measured redshifts and present a comprehensive study of their intrinsic characteristics. We obtain the median values of the intrinsic duration (T 90,z), peak energy (E p,z), isotropic energy (E iso), and peak luminosity (L iso) as 0.47 s, 466 keV, 8.21 ×1050 erg, and 3.22 × 1051 erg s−1, respectively. We update the spectrum–energy correlations, and report and , which further confirm the previous results that the E p,z–E iso correlations of SGRBs and long gamma-ray bursts (LGRBs) are different and that this correlation can be used to distinguish GRB types. We report for the first time that there is a tighter correlation between the isotropic energy of the prompt emission of SGRBs and the star formation rate of their host galaxies, which reads . Using the measured jet break time (t jet) of 11 SGRBs, we tentatively investigate the E iso–E p,z–t jet,z and L iso–E p,z–t jet,z correlations of SGRBs and find that three-parameter correlations of SGRBs also exist and are different from those of LGRBs. Based on the E iso–E p,z–t jet,z correlation, we estimate the t jet,z values of other SGRBs and calculate the opening angles of SGRBs. We find that the median value of the SGRB opening angle is 7.°5, which is larger than that of LGRBs.