Revisiting the formation rate and redshift distribution of long gamma-ray bursts

Using a novel approach, the distribution of fluences of long gamma-ray bursts derived from the Swift-BAT catalog was reproduced by a jet-model characterized by the distribution of the total radiated energy in γ-rays and the distribution of the aperture angle of the emission cone. The best fit between simulated and observed fluence distributions permits one to estimate the parameters of the model. An evolution of the median energy of the bursts is required to adequately reproduce the observed redshift distribution of the events when the formation rate of γ-ray bursts follows the cosmic star formation rate. For our preferred model, the median jet energy evolves as EJ ∝ e0.5(1 + z) and the mean expected jet energy is 3.0 × 1049 erg, which agrees with the mean value derived from afterglow data. The estimated local formation rate is Rgrb = 290 Gpc-3 yr-1, representing less than 9% of the local formation rate of type Ibc supernovae. This result also suggests that the progenitors of long gamma-ray bursts have masses ≥ 90 M⊙ when a Miller-Scalo initial mass function is assumed.