Gamma-Ray Burst Energetics

We estimate the fraction of the total energy in a Gamma-Ray Burst (GRB) thatis radiated in photons during the main burst. Random internal collisions amongdifferent shells limit the efficiency for converting bulk kinetic energy tophotons. About 1% of the energy of explosion is converted to radiation, in10-1000 kev energy band in the observer frame, for long duration bursts(lasting 10s or more); the efficiency is significantly smaller for shorterduration bursts. Moreover, about 50% of the energy of the initial explosioncould be lost to neutrinos during the early phase of the burst if the initialfireball temperature is about 10 Mev or greater. If isotropic, the total energybudget of the brightest GRBs is about $10^{55}$erg, a factor of more than 20larger than previously estimated. Anisotropy of explosion, as evidenced in twoGRBs, could reduce the energy requirement by a factor of 10-100. Putting thesetwo effects together we find that the energy release in the most energeticbursts is about 10$^{54}$ erg.Comment: 10 pages & 1 figure, final version as will appear in ApJ lette