On the Energy of Gamma-Ray Bursts

Abstract

We show that gamma-ray burst (GRB) afterglow observations strongly suggest, within the fireball model framework, that radiating electrons are shock accelerated to a power-law energy distribution, with universal index p \\approx 2.2, and that the fraction of shock energy carried by electrons, \\xi_e, is universal and close to equipartition, \\xi_e ~ 1/3. For universal p and \\xi_e, a single measurement of the X-ray afterglow flux on the time scale of a day provides a robust estimate of the fireball energy per unit solid angle, Applying our analysis to BeppoSAX afterglow data we find that: (i) Fireball energies are in the range of 4\\pi\\epsilon=10^{51.5} to 10^{53.5} erg; (ii) The ratio of observed $\\gamma$-ray to total fireball energy per unit solid angle, abs[log10(\\epsilon_\\gamma/\\epsilon)]<0.5; (iii) If fireballs are jet like, their opening angle should satisfy \\theta>=0.1. Our results imply that if typical opening angles are \\theta ~ 0.1, a value consistent with our analysis, the total energy associated with a GRB event is in the range of 10^{50} erg to 10^{51.5} erg.