On the Kinetic Energy and Radiative Efficiency of Gamma-Ray Bursts

Using measured X-ray luminosities of 17 gamma-ray bursts (GRBs) during the afterglow phase and accounting for radiative losses, we calculate the kinetic energy of these bursts and investigate its relation to other GRB properties. We then use the observed radiated energy during the prompt phase to determine the radiative efficiency of these bursts and explore how the efficiency relates to other GRB observables. We find that the kinetic energy in the afterglow phase is directly correlated with the radiated energy, total energy, and possibly the jet opening angle and spectral peak energy. More importantly, we find the intriguing fact that the efficiency is correlated with the radiated energy and mildly with the total energy, jet opening angle, and spectral peak energy. XRF 020903 also seems to follow the trends we find for our GRB sample. We discuss the implications of these results for the GRB radiation and jet models.