It is proposed that the luminosity function , the rest-frame spectral correlations and distributions of cosmological Long-duration ( Type-II ) Gamma-Ray Bursts ( LGRBs ) may be very well described as multivariate log-normal distribution .
This result is based on careful selection , analysis and modeling of LGRBs ’ temporal and spectral variables in the largest catalog of Gamma-Ray Bursts available to date : 2130 BATSE GRBs , while taking into account the detection threshold and possible selection effects .
Constraints on the joint rest-frame distribution of the isotropic peak luminosity ( L _ { iso } ) , total isotropic emission ( E _ { iso } ) , the time-integrated spectral peak energy ( E _ { p,z } ) and duration ( T _ { 90 ,z } ) of LGRBs are derived .
The presented analysis provides evidence for a relatively large fraction of LGRBs that have been missed by BATSE detector with E _ { iso } extending down to \sim 10 ^ { 49 } ~ { } [ erg ] and observed spectral peak energies ( E _ { p } ) as low as \sim 5 ~ { } [ keV ] .
LGRBs with rest-frame duration T _ { 90 ,z } \lesssim 1 [ s ] or observer-frame duration T _ { 90 } \lesssim 2 [ s ] appear to be rare events ( \lesssim 0.1 \% chance of occurrence ) .
The model predicts a fairly strong but highly significant correlation ( \rho = 0.58 \pm 0.04 ) between E _ { iso } & E _ { p,z } of LGRBs .
Also predicted are strong correlations of L _ { iso } & E _ { iso } with T _ { 90 ,z } and moderate correlation between L _ { iso } & E _ { p,z } .
The strength and significance of the correlations found , encourage the search for underlying mechanisms , though undermine their capabilities as probes of Dark Energy ’ s equation of state at high redshifts .
The presented analysis favors – but does not necessitate – a cosmic rate for BATSE LGRBs tracing metallicity evolution consistent with a cutoff { Z / Z _ { \sun } } \sim 0.2 - 0.5 , assuming no luminosity-redshift evolution .