We present a comprehensive sample of X-ray observations of 41 γ-ray burst (GRB) afterglows, as well as jet opening angles, θj, 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 (LX,iso), normalized to t = 10 hr. However, there is a strong correlation between LX,iso and the beaming fractions, fb ≡ [1 - cos(θj)]. As a result, the true X-ray luminosity of GRB afterglows, LX = fbLX,iso, is approximately constant, with a dispersion of only a factor of 2. Since eEb ∝ LX, the strong clustering of LX directly implies that the adiabatic blast wave kinetic energy in the afterglow phase, Eb, is tightly clustered. The narrow distribution of LX also 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.
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