2007MNRAS.382..342C

We study the spectral and energetics properties of 47 long-duration gamma-ray bursts (GRBs) with known redshift, all of them detected by the Swift satellite. Due to the narrow energy range (15-150 keV) of the Swift-BAT detector, the spectral fitting is reliable only for fitting models with two or three parameters. As high uncertainty and correlation among the errors is expected, a careful analysis of the errors is necessary. We fit both the power law (PL, two parameters) and cut-off power law (CPL, three parameters) models to the time-integrated spectra of the 47 bursts, and we present the corresponding parameters, their uncertainties and the correlations among the uncertainties. The CPL model is reliable only for 29 bursts for which we estimate the νf_ν peak energy E_pk. For these GRBs, we calculate the energy fluence and the rest-frame isotropic-equivalent radiated energy, E_γ,iso, as well as the propagated uncertainties and correlations among them. We explore the distribution of our homogeneous sample of GRBs on the rest-frame diagram E'_pk versus E_γ,iso. We confirm a significant correlation between these two quantities (the `Amati' relation) and we verify that, within the uncertainty limits, no outliers are present. We also fit the spectra to a Band model with the high-energy PL index frozen to -2.3, obtaining a rather good agreement with the `Amati' relation of non-Swift GRBs.