2010MNRAS.401.1465C

We investigate the properties of both the prompt and X-ray afterglows of gamma-ray bursts (GRBs) in the burst frame with a sample of 33 Swift GRBs. Assuming that the steep decay segment in the canonical X-ray afterglow light curves is due to the curvature effect, we fit the light curves with a broken power law to derive the zero time of the last emission epoch of the prompt emission (t₁) and the beginning as well as the end time of the shallow decay segment (t₂ and t₃). We show that both the isotropic peak gamma-ray luminosity (L_peak,γ) and gamma-ray energy (E_iso,γ) are correlated with the isotropic X-ray energy (E_iso,X) of the shallow decay phase and the isotropic X-ray luminosity at). We infer the properties of the progenitor stars based on a model proposed by Kumar et al. who suggested that both the prompt gamma-rays and the X-ray afterglows are due to the accretions of different layers of materials of the GRB progenitor star by a central black hole (BH). We find that most of the derived masses of the core layers are M_c= 0.1 ∼ 5M_☉, and their average accretion rates in the prompt gamma-ray phase are, with a radius of r_c= 10⁸ ∼ 10¹⁰ cm. The rotation parameter is correlated with the burst duration, being consistent with the expectation of collapsar models. The estimated radii and the masses of the fall-back materials for the envelope layers are r_e= 10¹⁰ ∼ 10¹² cm and M_e = 10^–3 ∼ 1M_☉, respectively. The average accretion rates in the shallow decay phase are correlated with those in the prompt gamma-ray phase, but they are much lower, i.e.. The r_e values are smaller than the photospheric radii of Wolf-Rayet stars. In our calculation, we assume a uniform mass of the central BH (M_BH= 10M_☉). Therefore, we may compare our results with simulation results. It is interesting that the assembled mass density profile for the bursts in our sample is well consistent with the simulation for a pre-supernova star with mass M = 25M_☉.