On the relation between dynamics and geometry in GRBs

We estimate the initial bulk Lorentz factors Gamma_0 for GRBs that show the onset of the afterglow in their optical light curves. We find that Gamma_0 is strongly correlated with both the isotropic equivalent luminosity L_iso and energy E_iso and, with a larger scatter, also with the rest frame peak energy E_peak. These new correlations allow us to interpret the spectral energy correlations E_peak-L_iso (-E_iso) as a sequence of Gamma_0 factors. By accounting for the beaming effects, we find that the comoving frame properties of GRBs result clustered around typical values (e.g. L'_iso~5x10^48 erg/s). Moreover, it is theoretically predicted that there should be a link between the jet dynamics (Gamma_0) and its geometry (theta_jet). Through a population synthesis code we reconstruct the Gamma_0 and theta_jet distributions and search for a possible link between them. We find that Gamma_0 and theta_jet in GRBs should have log-normal distributions and they should be anti correlated (i.e. theta_jet^2*Gamma_0=const).