2013ApJ...766..111S

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, 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 the BATSE detector with E_iso extending down to ∼10⁴⁹ erg and observed spectral peak energies (E_p) as low as ∼5 keV. LGRBs with rest-frame duration T_90, z_ ≲ 1 s or observer-frame duration T₉₀ ≲ 2 s appear to be rare events ( ≲ 0.1% chance of occurrence). The model predicts a fairly strong but highly significant correlation (ρ = 0.58±0.04) between E_iso and E_p, z_ of LGRBs. Also predicted are strong correlations of L_isoand E_iso with T_90, z_ and moderate correlation between L_isoand 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_☉∼ 0.2-0.5, assuming no luminosity-redshift evolution.