The Maximum Isotropic Equivalent Energy of Gamma-Ray Bursts

In the cannonball model of gamma-ray bursts (GRBs), a highly relativistic jet of plasmoids of ordinary stellar matter that is ejected during stellar collapse or shortly after by fallback matter, produces simultaneously a GRB and a cosmic-ray burst by scattering light and charged particles in its path. This association and the observed knee at ∼1 TeV in the energy spectrum of Galactic cosmic-ray electrons imply a maximum peak energy ∼2.25 MeV in the energy spectrum of GRBs in the 1 keV–10 MeV band. Such a peak energy and the Amati correlation in GRBs imply a maximum isotropic equivalent energy release of ∼3.8 × 1054 erg in GRBs, in the 1 keV–10 MeV band. Both predictions are in good agreement with up-to-date observations.