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

It has recently been proposed that ultrahigh energy ($\gtrsim 10^{19}$ eV)cosmic rays (UHECRs) are accelerated by the blast waves associated with GRBs.We calculate the observed synchrotron radiation spectrum from protons andenergetic leptons formed in the cascades initiated by photopion production,taking into account $\gamma\gamma$ attenuation at the source. Normalizing tothe emission characteristics of GRB~970508, we predict $\sim 10$ MeV - 100 GeVfluxes at a level which may have been observed with EGRET from bright GRBs, andcould be detected with the proposed GLAST experiment or with ground-based air\v Cerenkov telescopes having thresholds $\lesssim $ several hundred GeV. Thetemporal decay of the UHECR-induced high-energy $\gamma$-ray afterglows issignificantly slower than that of the lower-energy burst and associatedsynchrotron self-Compton (SSC) radiation, which provides a direct way to testthe hadronic origin of a high-energy GRB afterglow. Besides testing the UHECRorigin hypothesis, the short wavelength emission and afterglows can be used toprobe the level of the diffuse intergalactic infrared radiation field orconstrain redshifts of GRB sources.Comment: Accepted for publication in ApJ Letter