Energies of GRB blast waves and prompt efficiencies as implied by modelling of X-ray and GeV afterglows

Abstract

We consider a sample of 10 gamma-ray bursts with long-lasting ( ≳ 10<SUP>2</SUP> s) emission detected by Fermi/Large Area Telescope and for which X-ray data around 1 d are also available. We assume that both the X-rays and the GeV emission are produced by electrons accelerated at the external forward shock, and show that the X-ray and the GeV fluxes lead to very different estimates of the initial kinetic energy of the blast wave. The energy estimated from GeV is on average ̃50 times larger than the one estimated from X-rays. We model the data (accounting also for optical detections around 1 d, if available) to unveil the reason for this discrepancy and find that good modelling within the forward shock model is always possible and leads to two possibilities: (i) either the X-ray emitting electrons (unlike the GeV emitting electrons) are in the slow-cooling regime or (ii) the X-ray synchrotron flux is strongly suppressed by Compton cooling, whereas, due to the Klein-Nishina suppression, this effect is much smaller at GeV energies. In both cases the X-ray flux is no longer a robust proxy for the blast wave kinetic energy. On average, both cases require weak magnetic fields and relatively large isotropic kinetic blast wave energies corresponding to large lower limits on the collimated energies, in the range for an ISM (interstellar medium) environment with n ̃ 1 cm<SUP>-3</SUP> and 10^{52} erg<{E}_{θ ,kin}<10^{53} erg for a wind environment with A<SUB>*</SUB> ̃ 1. These energies are larger than those estimated from the X-ray flux alone, and imply smaller inferred values of the prompt efficiency mechanism, reducing the efficiency requirements on the still uncertain mechanism responsible for prompt emission.