Lorentz-factor-isotropic-luminosity/energy correlations of gamma-ray bursts and their interpretation

Abstract

The bulk Lorentz factor of the gamma-ray burst (GRB) ejecta (Γ<inf>0</inf>) is a key parameter to understanding GRB physics. Liang et al. have discovered a correlation between Γ<inf>0</inf> and isotropic γ-ray energy: Γ<inf>0</inf>E ^0.25 <inf>γ, iso, 52</inf>. By including more GRBs with updated data and more methods to derive Γ<inf>0</inf>, we confirm this correlation and obtain Γ<inf>0</inf> ≃ 91E ^0.29 <inf>γ, iso, 52</inf>. Evaluating the mean isotropic γ-ray luminosities L <inf>γ, iso</inf> of the GRBs in the same sample, we discover an even tighter correlation Γ<inf>0</inf> ≃ 249L ^0.30 <inf>γ, iso, 52</inf>. We propose an interpretation to this later correlation. Invoking a neutrino-cooled hyperaccretion disk around a stellar mass black hole as the central engine of GRBs, we derive jet luminosity powered by neutrino annihilation and baryon loading from a neutrino-driven wind. Applying beaming correction, we finally derive Γ<inf>0</inf>L ^0.22 <inf>γ, iso</inf>, which is consistent with the data. This suggests that the central engine of long GRBs is likely a stellar mass black hole surrounded by a hyper-accreting disk. © 2012. The American Astronomical Society. All rights reserved.