High energy gamma ray counterparts of astrophysical sources of ultra-high energy cosmic rays

If ultra-high energy cosmic rays (URECRs) are accelerated at astrophysical point sources, the identification of such sources can be achieved if there is some kind of radiation at observable wavelengths that may be associated with the acceleration and/or propagation processes. No radiation of this type has so far been detected or at least no such connection has been claimed. The process of photopion production during the propagation of UHECRs from the sources to the Earth results in the generation of charged and neutral pions. The neutral (charged) pions in turn decay to gamma quanta and electrons that initiate an electromagnetic cascade in the universal photon background. The ultra high energy protons interaction produces also electron positron pairs with typical energy of 700 TeV which initiate a faster electromagnetic cascade. We calculate the flux of the overall gamma radiation in the GeV-TeV energy range and find that for source luminosities compatible with those expected from small scale anisotropies in the directions of arrival of UHECRs, the fluxes can be detectable by future Cerenkov gamma ray telescopes, such as VERITAS and HESS for source distances comparable with the loss length for photopion production. The effects of a widespread extra-galactic magnetic field on the cascade flux are discussed for various intensities and simple configurations.