A Multivariate Fit Luminosity Function and World Model for Long GammaRay Bursts
Abstract
It is proposed that the luminosity function, the restframe spectral correlations, and distributions of cosmological longduration (TypeII) gammaray bursts (LGRBs) may be very well described as a multivariate lognormal 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 restframe distribution of the isotropic peak luminosity (L _{iso}), total isotropic emission (E _{iso}), the timeintegrated 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 ~10^{49} erg and observed spectral peak energies (E_{p} ) as low as ~5 keV. LGRBs with restframe duration T _{90, z } <~ 1 s or observerframe duration T _{90} <~ 2 s appear to be rare events (lsim 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 _{iso} and E _{iso} with T _{90, z } and moderate correlation between L _{iso} and 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 _{☉} ~ 0.20.5, assuming no luminosityredshift evolution.
 Publication:

The Astrophysical Journal
 Pub Date:
 April 2013
 DOI:
 10.1088/0004637X/766/2/111
 arXiv:
 arXiv:1209.4647
 Bibcode:
 2013ApJ...766..111S
 Keywords:

 dark energy;
 gammaray burst: general;
 methods: statistical;
 Astrophysics  High Energy Astrophysical Phenomena;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 Accepted to ApJ (March 10, 2013, V7652). Partial correlation analysis and a brief comparison with the model of Bromberg, Nakar, Piran &