Hadronic Models for LAT Prompt Emission Observed in Fermi Gamma-Ray Bursts

Abstract: This paper examines the possibility that hadronic processes produce the >100 MeV photons in the prompt phase of gamma-ray bursts (GRBs) observed by the Fermi-LAT. We calculate analytically the radiation from protons and from secondary electron-positron pairs produced by high energy protons interacting with gamma-rays inside of the GRB jet. We consider both photo-pion and Bethe-Heitler pair production processes to create secondary electrons and positrons that then radiate via inverse Compton and synchrotron processes. We also consider synchrotron radiation from the protons themselves. We calculate the necessary energy in protons to produce typical Fermi-LAT fluxes of a few microJy at 100 MeV. For both of the photo-pion and Bethe-Heitler processes, we find that the required energy in protons is larger than the observed gamma-ray energy by a factor of a thousand or more. For proton synchrotron, the protons have a minimum Lorentz factor ~2x10^6. This is much larger than expected if the protons are accelerated by relativistic collisionless shocks in GRBs. We also provide estimates of neutrino fluxes expected from photo-hadronic processes. Although the flux from a single burst is below IceCube detection limits, it may be possible to rule out photo-hadronic models by adding up the contribution of several bursts. Therefore, photo-hadronic processes seem an unlikely candidate for producing the Fermi-LAT radiation during the prompt phase of GRBs.