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 ×10 50 erg, and 3.22 × 10 51 erg s −1 , respectively. We update the spectrum–energy correlations, and report E p , z ∝ E iso 0.36 ± 0.05 and E p , z ∝ L iso 0.33 ± 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 sSFR ∝ E iso 0.38 ± 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.

Yong-Rui Shi

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