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Role of line-of-sight cosmic ray interactions in forming the spectra of distant blazars in TeV gamma rays and high-energy neutrinos

Active galactic nuclei (AGN) can produce both gamma rays and cosmic rays. The observed high-energy gamma-ray signals from distant blazars may be dominated by secondary gamma rays produced along the line of sight by the interactions of cosmic-ray protons with background photons. This explains the surprisingly low attenuation observed for distant blazars, because the production of secondary gamma rays occurs, on average, much closer to Earth than the distance to the source. Thus the observed spectrum in the TeV range does not depend on the intrinsic gamma-ray spectrum, while it depends on the output of the source in cosmic rays. We apply this hypothesis to a number of sources and, in every case, we obtain an excellent fit, strengthening the interpretation of the observed spectra as being due to secondary gamma rays. We explore the ramifications of this interpretation for limits on the extragalactic background light and for the production of cosmic rays in AGN. We also make predictions for the neutrino signals, which can help probe acceleration of cosmic rays in AGN.