A Standard Kinetic Energy Reservoir in Gamma-Ray Burst Afterglows

Abstract

We present a comprehensive sample of X-ray observations of 41 gamma-ray burst (GRB) afterglows, as well as jet opening angles, \theta_j for a subset with measured jet breaks. We show that there is a significant dispersion in the X-ray fluxes, and hence isotropic X-ray luminosities (L_{X,iso}), normalized to 10 hr. However, there is a strong correlation between L_{X,iso} and the beaming fractions, f_b=[1-cos(\theta_j)]. As a result, the true X-ray luminosity of GRB afterglows, L_X=f_b L_{X,iso}, is approximately constant, with a dispersion of only a factor of two. Since \epsilon_e E_b \propto L_X, the strong clustering of L_X directly implies that the adiabatic blastwave kinetic energy in the afterglow phase, E_b, is tightly clustered. The narrow distribution of L_X also suggests that p\approx 2, that inverse Compton emission does not in general dominate the observed X-ray luminosity, and that radiative losses at t<10 hr are relatively small. Thus, despite the large diversity in the observed properties of GRBs and their afterglows the energy imparted by the GRB central engine to the relativistic ejecta is approximately constant.