2003ApJ...590..379B

We present a comprehensive sample of X-ray observations of 41 γ-ray burst (GRB) afterglows, as well as jet opening angles, θ_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 t=10 hr. However, there is a strong correlation between L_X,isoand the beaming fractions, f_b≡[1-cos(θ_j)]. As a result, the true X-ray luminosity of GRB afterglows, L_X=f_bL_X,iso, is approximately constant, with a dispersion of only a factor of 2. Since ε_eE_b∝L_X, the strong clustering of L_Xdirectly implies that the adiabatic blast wave kinetic energy in the afterglow phase, E_b, is tightly clustered. The narrow distribution of L_Xalso suggests that p~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.