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 similar to 10 MeV. If isotropic, the total energy budget of the brightest GRBs is greater than or similar to 10(55) ergs, a factor of greater than or similar to 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.