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 6% of the energy of explosion is converted to radiation for long duration bursts (lasting 10s 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 ∼ 10erg, 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 erg. Subject headings: gamma-rays: bursts – gamma-rays: theory