Gamma-ray bursts in the comoving frame

We estimate the bulk Lorentz factor Gamma(0) of 31 gamma-ray bursts (GRBs) using the measured peak time of their afterglow light curves. We consider two possible scenarios for the estimate of Gamma(0): the case of a homogeneous circumburst medium or a wind density profile. The values of Gamma(0) are broadly distributed between few tens and several hundreds with average values similar to 138 and similar to 66 for the homogeneous and wind density profile, respectively. We find that the isotropic energy and luminosity correlate in a similar way with Gamma(0), i.e. E-iso. proportional to Gamma(2)(0) and L-iso proportional to Gamma(2)(0), while the peak energy E-peak proportional to Gamma(0). These correlations are less scattered in the wind density profile than in the homogeneous case. We then study the energetics, luminosities and spectral properties of our bursts in their comoving frame. The distribution of L-iso' is very narrow with a dispersion of less than a decade in the wind case, clustering around L-iso' similar to 5 x 10(48) erg s(-1). Peak photon energies cluster around E-peak' similar to 6 keV. The newly found correlations involving Gamma(0) offer a general interpretation scheme for the spectral energy correlation of GRBs. The E-peak-E-iso and E-peak-L-iso correlations are due to the different Gamma(0) factors and the collimation-corrected correlation, E-peak-E-gamma (obtained by correcting the isotropic quantities for the jet opening angle theta(j)), can be explained if theta(2)(j) Gamma(0) = constant. Assuming the E-peak-E-gamma correlation as valid, we find a typical value of theta(2)(j) Gamma(0) similar to 6-20, in agreement with the predictions of magnetically accelerated jet models.