LORENTZ-FACTOR-ISOTROPIC-LUMINOSITY/ENERGY CORRELATIONS OF GAMMA-RAY BURSTS AND THEIR INTERPRETATION

The bulk Lorentz factor of the gamma-ray burst (GRB) ejecta ([Gamma] sub(0)) is a key parameter to understanding GRB physics. Liang et al. have discovered a correlation between [Gamma] sub(0) and isotropic gamma -ray energy: [Gamma] sub(0) [is proportional to] E super(0.25) gamma ,iso,52. By including more GRBs with updated data and more methods to derive [Gamma] sub(0), we confirm this correlation and obtain [Gamma] sub(0) [Asymptotically = to] 91E super(0.29) gamma ,iso,52. Evaluating the mean isotropic gamma -ray luminosities L gamma ,iso of the GRBs in the same sample, we discover an even tighter correlation [Gamma] sub(0) [Asymptotically = to] 249L super(0.30) gamma ,iso,52. 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] sub(0) [is proportional to] L super(0.22) gamma ,iso, 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.