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

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 ×10 ^50 erg, and 3.22 × 10 ^51 erg s ^−1 , respectively. We update the spectrum–energy correlations, and report ${E}_{{\rm{p}},{\rm{z}}}\propto {E}_{\mathrm{iso}}^{0.36\pm 0.05}$ and ${E}_{{\rm{p}},{\rm{z}}}\propto {L}_{\mathrm{iso}}^{0.33\pm 0.04}$ , 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 $\mathrm{sSFR}\propto {E}_{\mathrm{iso}}^{0.38\pm 0.11}$ . 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.