High-energy Gamma Rays from Ultra–high-energy Cosmic-Ray Protons in Gamma-Ray Bursts

Abstract
It has recently been proposed that ultra-high-energy (1019 eV) cosmic rays (UHECRs) are accelerated by the blast waves associated with GRBs. We calculate the observed synchrotron spectrum from protons and energetic leptons formed in the cascades initiated by photopion production, taking into account γγ attenuation at the source. Normalizing to the emission characteristics of GRB 970508, we predict ~10 MeV-100 GeV fluxes at a level that may have been observed with EGRET from bright GRBs and could be detected with the proposed GLAST experiment or with ground-based air Čerenkov telescopes having thresholds several hundred GeV. The temporal decay of the UHECR-induced high-energy γ-ray afterglows is significantly slower than that of the lower energy burst and associated synchrotron self-Compton (SSC) radiation, which provides a direct way to test the hadronic origin of a high-energy GRB afterglow. Besides testing the UHECR origin hypothesis, the short-wavelength emission and afterglows can be used to probe the level of the diffuse intergalactic infrared radiation field or constrain redshifts of GRB sources.