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 withmeasured jet breaks. We show that there is a significant dispersion in theX-ray fluxes, and hence isotropic X-ray luminosities (L_{X,iso}), normalized to10 hr. However, there is a strong correlation between L_{X,iso} and the beamingfractions, f_b=[1-cos(\theta_j)]. As a result, the true X-ray luminosity of GRBafterglows, L_X=f_b L_{X,iso}, is approximately constant, with a dispersion ofonly a factor of two. Since \epsilon_e E_b \propto L_X, the strong clusteringof L_X directly implies that the adiabatic blastwave kinetic energy in theafterglow phase, E_b, is tightly clustered. The narrow distribution of L_X alsosuggests that p\approx 2, that inverse Compton emission does not in generaldominate the observed X-ray luminosity, and that radiative losses at t<10 hrare relatively small. Thus, despite the large diversity in the observedproperties of GRBs and their afterglows the energy imparted by the GRB centralengine to the relativistic ejecta is approximately constant.Comment: Submitted to ApJL; 17 pages; 2 tables; 2 figure