On the relation between GRB bulk Lorentz factors and jet opening angles

Author: Giancarlo Ghirlanda

Abstract: Gamma Ray Burst energies and luminosities, in the comoving frame, appear remarkably similar and correlations between the bulk Lorentz factor and the global energetics seem to exist. The large diversity of bursts energies (and the nature and dispersion of the spectral-energy correlations) could be due to the different bulk Lorentz factor Γ and jet aperture angle θjet. Through a population synthesis code and a complete sample of Swift GRBs we constrain the typical distributions of Γ and θjet (∼270 and ∼8.5deg) and find that they should be related as θjet2.5 Γ =const: the narrower the jet angle, the larger the bulk Lorentz factor. We predict that ∼ 6% of the bursts that point to us should not show any jet break in their afterglow light curve since their beaming is larger than their collimation [1/Γ > sin(θjet)]. Finally, we estimate that the local rate of GRBs is ∼0.3% of all local SNIb/c and ∼4.3% of local hypernovae, i.e. SNIb/c with broad absorption lines.