A standard kinetic energy reservoir in gamma-ray burst afterglows

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,L-iso), normalized to t = 10 hr. However, there is a strong correlation between L-X,L-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 2. Since epsilon(e)E(b) proportional to L-X, the strong clustering of L-X directly implies that the adiabatic blast wave kinetic energy in the afterglow phase, E-b, is tightly clustered. The narrow distribution of L-X also suggests that p approximate to 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.