2012MNRAS.420..483G

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 Γ₀are 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. E_ISO \proto Γ₀² and L_ISO\proto Γ_n², while the peak energy E_peak∝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 L'_isc is very narrow with a dispersion of less than a decade in the wind case, clustering around L'_ISO ∼ 5x10⁴⁸ erg/s. Peak photon energies cluster around E'_peak ∼ 6 keV. The newly found correlations involving Γ₀ offer a general interpretation scheme for the spectral energy correlation of GRBs. The E_peak-E_iso and E_peak-L_isocorrelations are due to the different Γ₀ factors and the collimation-corrected correlation, E_peak-E_γ(obtained by correcting the isotropic quantities for the jet opening angle θ_j), can be explained if Θ_i²Γ₀= constant. Assuming the E_peak-E_γ correlation as valid, we find a typical value of θ_jΓ₀ ∼ 6-20, in agreement with the predictions of magnetically accelerated jet models.