2016ApJ...824..127W

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 η_γ^{11 hr}≡log_{10}({E}γ/(3ε_{e}{E}{fb}^{11 hr})) are -0.34(0.60), and the upper limit on the intrinsic spread of η_ γ_ is approximately 0.5 ( ε_{e} is the fraction of energy carried by electrons and {E}_{fb}^{x hr} is inferred from the X-ray flux at x hours). {E}_{fb}^{3 hr} and {E}_{fb}^{11 hr} are similar, with an average(std) of log_{10}({E}{fb}^{{3 hr}/{E}}{fb}^{11 hr}) of 0.04(0.28). The small variance of η_ γ_ implies that burst-to-burst variations in ε_{e} 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 {E}_{fb}^{3 hr} and {E}_{fb}^{11 hr} 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).