Implications of electron acceleration for high-energy radiation from gamma-ray bursts

Abstract

In recent work we suggested that photons of energy >100 MeV detected from GRBs by the Fermi Satellite are produced via synchrotron emission in the external forward shock with a weak magnetic field - consistent with shock compressed upstream magnetic field of a few tens of micro-Gauss. Here we investigate whether electrons can be accelerated to energies such that they radiate synchrotron photons with energy up to about 10 GeV in this particular scenario. We do this using two methods: (i) we check if these electrons can be confined to the shock front; and (ii) we calculate radiative losses while they are being accelerated. We find that these electrons remain confined to the shock front, as long as the upstream magnetic field is >~ 10 micro-Gauss, and don't suffer substantial radiative losses, the only condition required is that the external reverse shock emission be not too bright: peak flux less than 1 Jy in order to produce photons of 100 MeV, and less than ~100 mJy for producing 1-GeV photons. We also find that the acceleration time for electrons radiating at 100 MeV is a few seconds (in observer frame), and the acceleration time is somewhat longer for electrons radiating at a few GeV. This could explain the lack of >100 MeV photons for the first few seconds after the trigger time for long GRBs reported by the Fermi Satellite, and also the slight lag between photons of GeV and 100 MeV energies. We model the onset of the external forward shock light curve in this scenario and find it consistent with the sharp rise observed in the 100-MeV light curve of GRB080916C and similar bursts.