The blast energy efficiency of gamma-ray bursts

Using data mostly assembled by previous authors, we note a linear correlation for 17 of 22 gamma-ray bursts (GRBs) between the apparent radiative efficiency ε_γ (defined as the ratio of isotropic equivalent radiative output to inferred isotropic equivalent kinetic energy of the blast) and E_peak^α, where, for linearity, the exponent α is empirically determined to be in the range 1.4 < α < 2. This is consistent with the hypothesis that ε_γ and E_peak are influenced by viewing angle. We suggest a more general theoretically derived expression for this correlation that could be tested with a richer data set. If the reduction in both ε_γ and E _peak is due to viewing angle effects, then the actual radiative efficiency is ∼7. We also find preliminary evidence (with the remaining small sample of five GRBs) for a separate class of weak GRB afterglows.