A Multivariate Fit Luminosity Function And World Model For Long Gamma-Ray Bursts
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 a 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 GRBs 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,E-z), and duration (T-90,T-z) of LGRBs are derived. The presented analysis provides evidence for a relatively large fraction of LGRBs that have been missed by the BATSE detector with E-iso extending down to similar to 10(49) erg and observed spectral peak energies (Ep) as low as similar to 5 keV. LGRBs with rest-frame duration T-90,T-z less than or similar to 1 s or observer-frame duration T-90 less than or similar to 2 s appear to be rare events (less than or similar to 0.1% chance of occurrence). The model predicts a fairly strong but highly significant correlation (rho = 0.58 +/- 0.04) between E-iso and E-p,E-z of LGRBs. Also predicted are strong correlations of L-iso and E-iso with T-90,T-z and moderate correlation between L-iso and E-p,E-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 Stateat 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(circle dot) similar to 0.2-0.5, assuming no luminosity-redshift evolution.