The energy budget of GRBs based on updated prompt \& afterglow observations

Abstract: We compare the isotropic equivalent 15-2000 keV gamma-ray energy, E_gamma, emitted by a sample of 91 swift Gamma-Ray Bursts (GRBs) with known redshifts, with the isotropic equivalent fireball energy, E_fb, as estimated within the fireball model framework from X-ray afterglow observations of these bursts. The uncertainty in E_gamma, which spans the range of ~10^51 erg to ~10^53.5 erg, is approximately 25% on average, due mainly to the extrapolation from the BAT detector band to the 15-2000 keV band. The uncertainty in E_fb is approximately a factor of 2, due mainly to the X-ray measurements' scatter. We find E_gamma and E_fb to be tightly correlated. The average(std) of {\eta}^11hr_gamma is approximately log_10(E_gamma/(3{\epsilon} _eE^11hr_fb)) are -0.34(0.60), and the upper limit on the intrinsic spread of {\eta}_gamma is approximately 0.5 ({\epsilon}_e is the fraction of shocked plasma energy carried by electrons and E^x hr_fb is inferred from the X-ray flux at x hours). We also find that E_fb inferred from X-ray observations at 3 and 11 hours are similar, with an average(std) of log_10(E^3hr_fb/E^11hr_fb) of 0.04(0.28). The small variance of {\eta}_gamma implies that burst-to-burst variations in {\epsilon}_e and in the efficiency of fireball energy conversion to gamma-rays are small, and suggests that both are of order unity. The small variance of {\eta}_gamma and the similarity of E^3hr_fb and E^11hr_fb further imply that {\epsilon}_e does not vary significantly with shock Lorentz factor, and that for most bursts the modification of fireball energy during the afterglow phase, by processes such as radiative losses or extended duration energy injection, are not significant. Finally, our results imply that if fireballs are indeed jets, then the jet opening angle satisfies {\theta}>0.1 for most cases. [abridged]