• radiation mechanisms: non-thermal;
  • gamma-ray burst: general


We estimate the bulk Lorentz factor Γ0 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 Γ0: the case of a homogeneous circumburst medium or a wind density profile. The values of Γ0 are broadly distributed between few tens and several hundreds with average values ∼138 and ∼66 for the homogeneous and wind density profile, respectively. We find that the isotropic energy and luminosity correlate in a similar way with Γ0, i.e. inline image and inline image, while the peak energy Epeak∝Γ0. 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 inline image is very narrow with a dispersion of less than a decade in the wind case, clustering around inline image erg s−1. Peak photon energies cluster around inline image∼ 6 keV. The newly found correlations involving Γ0 offer a general interpretation scheme for the spectral energy correlation of GRBs. The EpeakEiso and EpeakLiso correlations are due to the different Γ0 factors and the collimation-corrected correlation, EpeakEγ (obtained by correcting the isotropic quantities for the jet opening angle θj), can be explained if inline image= constant. Assuming the EpeakEγ correlation as valid, we find a typical value of θjΓ0∼ 6–20, in agreement with the predictions of magnetically accelerated jet models.