A revised analysis of gamma-ray bursts' prompt efficiencies

The prompt gamma-ray bursts' (GRBs) efficiency is an important clue on the emission mechanism producing the γ-rays. Previous estimates of the kinetic energy of the blast waves, based on the X-ray afterglow luminosity LX, suggested that this efficiency is large, with values above 90 per cent in some cases. This poses a problem to emission mechanisms and in particular to the internal shocks model. These estimates are based, however, on the assumption that the X-ray emitting electrons are fast cooling and that their Inverse Compton (IC) losses are negligible. The observed correlations between L_X (and hence the blast wave energy) and E_γ,iso, the isotropic equivalent energy in the prompt emission, has been considered as observational evidence supporting this analysis. It is reasonable that the prompt gamma-ray energy and the blast wave kinetic energy are correlated and the observed correlation corroborates, therefore, the notion L_X is indeed a valid proxy for the latter. Recent findings suggest that the magnetic field in the afterglow shocks is significantly weaker than was earlier thought and its equipartition fraction, ε_B, could be as low as 10^-4 or even lower. Motivated by these findings we reconsider the problem, taking now IC cooling into account. We find that the observed L_X - Eγ,iso correlation is recovered also when IC losses are significant. For small ε_B values the blast wave must be more energetic and we find that the corresponding prompt efficiency is significantly smaller than previously thought. For example, for ε_B ~ 10^-4 we infer a typical prompt efficiency of ~15 per cent.