Lorentz factor - Beaming Corrected Energy/Luminosity Correlations and GRB Central Engine Models

TL;DR

This study analyzes correlations between Lorentz factors and energy/luminosity in GRBs, testing theoretical models of black hole central engines and finding stronger support for magnetized jet mechanisms.

Contribution

It confirms existing correlations and introduces new ones involving beaming corrected energies and luminosities, comparing observational data with theoretical jet launching models.

Findings

Data favor the Blandford-Znajek mechanism over neutrino annihilation.

Correlations between Lorentz factor and beaming corrected energies are confirmed.

Total energy and luminosity show rough correlations with larger scatter.

Abstract

We work on a GRB sample whose initial Lorentz factors ($\Gamma_0$) are constrained with the afterglow onset method and the jet opening angles ($\theta_{\rm j}$) are determined by the jet break time. We confirm the $\Gamma_0$ - $E_{\gamma,\rm iso}$ correlation by Liang et al. (2010), and the $\Gamma_0$ - $L_{\gamma,\rm iso}$ correlation by L{\"u} et al. (2012). Furthermore, we find correlations between $\Gamma_0$ and the beaming corrected $\gamma$-ray energy ($E_{\gamma}$) and mean $\gamma$-ray luminosity ($L_{\gamma}$). By also including the kinetic energy of the afterglow, we find rough correlations (with larger scatter) between $\Gamma_0$ and the total ($\gamma$-ray plus kinetic) energy and the total mean luminosity, both for isotropic values and beaming corrected values: these correlations allow us to test the data with GRB central engine models. Limiting our sample to the GRBs that likely have a black hole central engine, we compare the data with theoretical predictions of two types of jet launching mechanisms from BHs, i.e. the non-magnetized $\nu \bar\nu$ - annihilation mechanism, and the strongly magnetized Blandford-Znajek (BZ) mechanism. We find that the data are more consistent with the latter mechanism, and discuss the implications of our findings for GRB jet composition.