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

We work on a GRB sample whose initial Lorentz factors ($Γ_0$) are constrained with the afterglow onset method and the jet opening angles ($θ_{\rm j}$) are determined by the jet break time. We confirm the $Γ_0$ - $E_{γ,\rm iso}$ correlation by Liang et al. (2010), and the $Γ_0$ - $L_{γ,\rm iso}$ correlation by L{ü} et al. (2012). Furthermore, we find correlations between $Γ_0$ and the beaming corrected $γ$-ray energy ($E_γ$) and mean $γ$-ray luminosity ($L_γ$). By also including the kinetic energy of the afterglow, we find rough correlations (with larger scatter) between $Γ_0$ and the total ($γ$-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 $ν\barν$ - 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.

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