2020ApJ...896...83G

Gamma-ray bursts (GRBs) are known to be the most violent explosions in the universe, and a variety of correlations between observable GRB properties have been proposed in the literature, but none of these correlations are valid for both long and short GRBs. In this paper we report the discovery of a universal correlation that is suitable for both long and short GRBs using three prompt emission properties of GRBs, i.e., the isotropic peak luminosity L_iso, the peak energy of the time-integrated prompt emission spectrum E_peak, and the "high signal" timescale T_0.45, L_iso∝E_peak^1.94T_0.45^0.37. This universal correlation involves properties of GRB prompt emission and does not require knowledge of the afterglow phase, which can be used as a relatively unbiased redshift estimator. Here we use this correlation to estimate the pseudoredshifts for short GRBs and then use the Lynden-Bell method to obtain a nonparametric estimate of their luminosity function and formation rate. The luminosity function is ψ(L₀)∝L₀^-0.63±0.07^ for dim SGRBs and ψ(L₀)∝L₀^-1.96±0.28^ for bright SGRBs, with the break point 6.95_–0.76^+0.84×10⁵⁰ergs^–1. The local formation rate of SGRBs is about 15 events Gpc^–3 yr^–1 . This universal correlation may have important implications for GRB physics, implying that the long and short GRBs should share similar radiation processes.