The Energy of Long-Duration Gamma-Ray Bursts

The energy release in gamma-ray bursts (GRBs) is one of the most useful clues to the nature of their "inner engines." We show that within the framework of the relativistic external shock afterglow model, the narrowness of the observed X-ray flux of GRB afterglows implies that the energy of the GRB jets, after the early-afterglow phase, spans less than 1 order of magnitude. This result is not affected by uncertainties in the electron energy, magnetic field strength, or external medium density. We argue that the afterglow kinetic energy is within a factor of 2 of the initial energy in the relativistic ejecta; therefore, the energy output of the central engine of a long-duration GRB has a universal value.