Lorentz Factor-Isotropic Luminosity/Energy Correlations of GRBS and Their Interpretation

TL;DR

This paper confirms and refines correlations between the Lorentz factor of GRB ejecta and their isotropic gamma-ray energy and luminosity, providing a physical interpretation involving neutrino-cooled hyperaccretion disks around black holes.

Contribution

It establishes tighter correlations between Lorentz factor and gamma-ray properties of GRBs and offers a theoretical model linking these to black hole accretion physics.

Findings

Confirmed Gamma_0–E_{gamma,iso} correlation with updated data.

Discovered a tighter Gamma_0–L_{gamma,iso} correlation.

Derived Gamma_0–L_{gamma,iso} relation from a physical model.

Abstract

The bulk Lorentz factor of the gamma-ray burst (GRB) ejecta (Gamma_0) is a key parameter to understand the GRB physics. Liang et al. have discovered a correlation between Gamma_0 and isotropic gamma-ray energy: Gamma_0\proptoE_{gamma,iso,52}^{0.25}. By including more GRBs with updated data and more methods to derive Gamma_0, we confirm this correlation and obtain Gamma_0~91E_{gamma,iso,52}^{0.29}. Evaluating the mean isotropic gamma-ray luminosities L_{gamma,iso} of the GRBs in the same sample, we discover an even tighter correlation Gamma_0~249 L_{gamma,iso,52}^{0.30}. 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 Gamma_0\proptoL_{gamma,iso}^{0.22}, which is well 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.