The Collimation‐corrected Gamma‐Ray Burst Energies Correlate with the Peak Energy of Their ν F ν Spectrum

We consider all bursts with known redshift and $\\nu F_\\nu$ peak energy, $E^{obs}_{peak}$. For a good fraction of them an estimate of the jet opening angle is available from the achromatic break of their afterglow light curve. This allows the derivation of the collimation--corrected energy of the bursts, $E_\\gamma$. The distribution of the values of $E_\\gamma$ is more spread with respect to previous findings, covering about two orders of magnitude. We find a surprisingly tight correlation between $E_\\gamma$ and the source frame $E_{peak}$: $E^{obs}_{peak}(1+z) \\propto E_\\gamma^{0.7}$. This correlation can shed light on the still uncertain radiation processes for the prompt GRB emission. More importantly,…