Gamma-ray bursts in the comoving frame

Abstract

We estimate the bulk Lorentz factor Gamma_0 of 31 GRBs using the measured\npeak time of their afterglow light curves. We consider two possible scenarios\nfor the estimate of Gamma_0: the case of a homogeneous circumburst medium or a\nwind density profile. The values of Gamma_0 are broadly distributed between few\ntens and several hundreds with average values ~138 and ~66 for the homogeneous\nand wind density profile, respectively. We find that the isotropic energy and\nluminosity correlate in a similar way with Gamma_0, i.e. Eiso Gamma_0^2 and\nLiso Gamma_0^2, while the peak energy Epeak Gamma_0. These correlations are\nless scattered in the wind density profile than in the homogeneous case. We\nthen study the energetics, luminosities and spectral properties of our bursts\nin their comoving frame. The distribution of Liso' is very narrow with a\ndispersion of less than a decade in the wind case, clustering around\nLiso'=5x10^48 erg/s. Peak photon energies cluster around Epeak'=6 keV. The\nnewly found correlations involving Gamma_0 offer a general interpretation\nscheme for the spectral-energy correlations of GRBs. The Epeak-Eiso and\nEpeak-Liso correlations are due to the different Gamma_0 factors and the\ncollimation-corrected correlation, Epeak-Egamma (obtained by correcting the\nisotropic quantities for the jet opening angle theta_j), can be explained if\ntheta_j^2*Gamma_0=constant. Assuming the Epeak-Egamma correlation as valid, we\nfind a typical value of theta_j*Gamma_0 ~ 6-20, in agreement with the\npredictions of magnetically accelerated jet models.\n