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 literature , but none of these correlations is valid for both long GRBs and short GRBs .
In this paper we report the discovery of a universal correlation which 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-integtated prompt emission spectrum E _ { peak } , and the ” high signal ” timescale T _ { 0.45 } , L _ { iso } \propto E _ { peak } ^ { 1.94 } T _ { 0.45 } ^ { 0.37 } .
This universal correlation just involves properties of GRB prompt emission and does not require any information of afterglow phase , which can be used as a relatively unbiased redshift estimator .
Here we use this correlation to estimate the pseudo–redshifts for short Gamma Ray Bursts and then use Lynden-Bell method to obtain a non-parametric estimate of their luminosity function and formation rate .
The luminosity function is \psi ( L _ { 0 } ) \propto { L _ { 0 } ^ { -0.63 \pm { 0.07 } } } for dim SGRBs and \psi ( L _ { 0 } ) \propto { L _ { 0 } ^ { -1.96 \pm { 0.28 } } } for bright SGRBs , with the break point 6.95 _ { -0.76 } ^ { +0.84 } \times 10 ^ { 50 } erg / s .
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 .