A Multivariate Fit Luminosity Function and World Model for Long GRBs

TL;DR

This paper models the joint distribution of key properties of long gamma-ray bursts using a multivariate log-normal distribution, revealing correlations and potential biases in detection.

Contribution

It introduces a comprehensive multivariate model for LGRB properties based on the largest available catalog, accounting for selection effects and revealing new correlations.

Findings

LGRBs' properties are well described by a multivariate log-normal distribution.

Detected correlations include Eiso & Epkz with a rho of 0.58.

Many low-luminosity, low-energy LGRBs are likely missed by current detectors.

Abstract

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 (Liso), total isotropic emission (Eiso), the time-integrated spectral peak energy (Epkz) and duration (T90z) of LGRBs are derived. The presented analysis provides evidence for a relatively large fraction of LGRBs that have been missed by BATSE detector with Eiso extending down to ~ 10^49 [erg] and observed spectral peak energies (Epk) as low as ~ 5 [keV]. LGRBs with rest-frame duration T90z < 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 (rho=0.58 \pm 0.04) between Eiso & Epkz of LGRBs. Also predicted are strong correlations of Liso & Eiso with T90z and moderate correlation between Liso & Epkz. 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 ~ 0.2-0.5, assuming no luminosity-redshift evolution.