Revisiting the Formation Rate and the Redshift Distribution of LGRBs

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 $\gamma$-rays and the distribution of the aperture angle of the emission cone. The best fit between simulated and observed fluence distributions permits to estimate the parameters of the model. An evolution of the median energy of the bursts is required in order to reproduce adequately the observed redshift distribution of the events if the formation rate of $\gamma$-ray bursts follows the cosmic star formation rate. For our preferred model, the median jet energy evolves as $E_J \propto e^{0.5(1+z)}$ and the mean expected jet energy is $3.0\times 10^{49}$ erg, which agrees with the mean value derived from afterglow data. The estimated local formation rate is $R_{grb}=290 Gpc^{-3}yr^{-1}$, representing less than 9% of the local formation rate of type Ibc supernovae. The present result suggests also that the progenitors of long gamma ray bursts have masses $\geq 90 M_\odot$ if a Miller-Scalo initial mass function is assumed.