The Energy Budget of GRBs Based on a Large Sample of Prompt and Afterglow Observations

We compare the isotropic equivalent 15-2000 keV γ-ray energy, E _γ, emitted by a sample of 91 swift Gamma-Ray Bursts 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 _γ, which spans the range of ∼10⁵¹ to ∼10^53.5 erg, is ≈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 _γ and E _fb to be tightly correlated. The average(std) of are -0.34(0.60), and the upper limit on the intrinsic spread of η _γ is approximately 0.5 ( is the fraction of energy carried by electrons and is inferred from the X-ray flux at x hours). and are similar, with an average(std) of of 0.04(0.28). The small variance of η _γ implies that burst-to-burst variations in and in the efficiency of fireball energy conversion to γ-rays are small, and suggests that both are of order unity. The small variance of η _γ and the similarity of and further imply that deviations from a simple fireball model description, if present, are small. This puts stringent constraints on models incorporating such modifications (due e.g., to radiative losses, energy injection, off-axis viewing).