The Intrinsic Statistical Properties and Correlations of Short Gamma-Ray Bursts
Si-Yuan Zhu, Zhiying Liu, Yong-Rui Shi, Xiao-Kang Ding, Wan-Peng Sun, Fu-Wen Zhang
Abstract
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">z</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>iso</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0.36</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.05</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">z</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>iso</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0.33</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.04</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>sSFR</mml:mi> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>iso</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0.38</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.11</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> . 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.