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

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 (${\theta }_{\mathrm{j}}$) are determined by the jet break time. We confirm the ${\Gamma }_0$ - $E_{\gamma ,\mathrm{iso}}$ correlation by Liang et al. (2010), and the ${\Gamma }_0$ - $L_{\gamma ,\mathrm{iso}}$ correlation by L{ü} 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.

12 pages; 3 figures; 2 tables; accepted by Journal of High Energy Astrophysics