High Energy Gamma Rays from Ultrahigh Energy Cosmic Rays in Gamma Ray Bursts

Abstract

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 and energetic leptons formed in the cascades initiated by photopion production, taking into account $\gamma\gamma$ attenuation at the source. Normalizing to the emission characteristics of GRB~970508, we predict $\sim 10$ MeV - 100 GeV fluxes at a level which may have been observed with EGRET from bright GRBs, and could be detected with the proposed GLAST experiment or with ground-based air \v Cerenkov telescopes having thresholds $\lesssim $ several hundred GeV. The temporal decay of the UHECR-induced high-energy $\gamma$-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.