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PeV neutrinos from intergalactic interactions of cosmic rays emitted by active galactic nuclei

The observed very high energy spectra of distant blazars are well described by secondary gamma rays produced in line-of-sight interactions of cosmic rays with background photons. In the absence of the cosmic-ray contribution, one would not expect to observe very hard spectra from distant sources, but the cosmic ray interactions generate very high energy gamma rays relatively close to the observer, and they are not attenuated significantly. The same interactions of cosmic rays are expected to produce a flux of neutrinos with energies peaked around 1 PeV. We show that the diffuse isotropic neutrino background from many distant sources can be consistent with the neutrino events recently detected by the IceCube experiment. We also find that the flux from any individual nearby source is insufficient to account for these events. The narrow spectrum around 1 PeV implies that some active galactic nuclei can accelerate protons to EeV energies.