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 ${\eta }_{\gamma }^{11hr}\equiv {log}_{10}\left(E_{\gamma }/\right(3{\epsilon }_e{E}_{fb}^{11hr}\left)\right)$ are −0.34(0.60), and the upper limit on the intrinsic spread of η _γ is approximately 0.5 (${\epsilon }_e$ is the fraction of energy carried by electrons and $E_{fb}^{xhr}$ is inferred from the X-ray flux at x hours). $E_{fb}^{3hr}$ and $E_{fb}^{11hr}$ are similar, with an average(std) of ${log}_{10}\left(E_{fb}^{3hr}/E_{fb}^{11hr}\right)$ of 0.04(0.28). The small variance of η _γ implies that burst-to-burst variations in ${\epsilon }_e$ 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 $E_{fb}^{3hr}$ and $E_{fb}^{11hr}$ 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).