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

Abstract

We consider a sample of ten GRBs with long lasting ( 10 2 sec) emission detected by Fermi/LAT and for which X-ray data around 1 day 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 day, 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: 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 10 53 erg < E 0,kin < 10 55 erg corresponding to large lower limits on the collimated energies, in the range 10 52 erg < E θ,kin < 5 × 10 52 erg for an ISM environment with n ∼ 1cm −3 and 10 52 erg < E θ,kin < 10 53 erg for a wind environment with A * ∼ 1. These energies are larger than those estimated from the Xray 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.

Temporal Evolution of the Gamma-ray Burst Afterglow Spectrum for an Observer: GeV–TeV Synchrotron Self-Compton Light Curve

“…Sironi & Spitkovsky 2009;Lemoine & Pelletier 2010;Sironi et al 2013) from the theoretical point of view, the low magnetization implied from recent broadband observations of the afterglows (e.g. Kumar & Barniol Duran 2009;Lemoine et al 2013;Santana et al 2014;Beniamini et al 2015;Zhang et al 2015) seems to be consistent with the theoretical argument.…”

“…Santana et al 2014;Zhang et al 2015) suggest much lower magnetization. Beniamini et al (2015Beniamini et al ( , 2016 pointed out that the high-efficiency problem in the prompt emission will be resolved by a very small ǫ B . In this case, the X-ray-emitting electrons are in the slow cooling regime, and the synchrotron flux in the X-ray band can be suppressed by the IC cooling.…”

Magnetars in Ultra-Long Gamma-Ray Bursts and GRB 111209A

“…Energy lost here ends up in the GRB afterglow. The latter process can be up to 50 per cent efficient (Beniamini et al 2015), meaning that the total isotropic equivalent energy release summed across all wavelengths is at least double the observed value of E γ,iso .…”

Multi-messenger Light Curves from Gamma-Ray Bursts in the Internal Shock Model

“…However, if the internal energy is carried by thermal protons or confined cosmic rays, it is natural to expect the reconversion of the internal energy into the kinetic energy; see Appendix C. It has been shown that this effect increases the gamma-ray emission efficiency, represented by the ratio of prompt gamma-ray energy to afterglow kinetic energy, calculated in an approach where shells reflects off each other after colliding, i.e., collisions are not perfectly inelastic (Kobayashi & Sari 2001). Recent results on afterglow modeling also suggest a small value of the gamma-ray emission efficiency (Beniamini et al 2015).…”