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

We consider a sample of 10 gamma-ray bursts with long-lasting (≳10² 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 (10^-6 ≲_∈B ≲10^-3) and relatively large isotropic kinetic blast wave energies 10⁵³ erg < E_0,kin < 10⁵⁵ erg corresponding to large lower limits on the collimated energies, in the range 10⁵² erg < E_θ,kin < 5 × 10⁵² erg for an ISM (interstellar medium) environment with n ~ 1 cm^-3 and 10⁵² erg < E_θ,kin < 10⁵³ erg for a wind environment with A_* ~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.