Gamma-Ray Burst Energetics

We estimate the fraction of the total energy in a gamma-ray burst (GRB) that is radiated in photons during the main burst. Random internal collisions among different shells limit the efficiency for converting bulk kinetic energy to photons. About 1% of the energy of explosion is converted to radiation, in the 10-10 3 keV energy band in the observer frame, for long-duration bursts (lasting 10 s or more); the efficiency is significantly smaller for shorter duration bursts. Moreover, about 50% of the energy of the initial explosion could be lost to neutrinos during the early phase of the burst if the initial fireball temperature is ~10 MeV. If isotropic, the total energy budget of the brightest GRBs is ≳10 55 ergs, a factor of ≳20 larger than previously estimated. Anisotropy of explosion, as evidenced in two GRBs, could reduce the energy requirement by a factor of 10-100. Putting these two effects together, we find that the energy release in the most energetic bursts is about 10 54 ergs.