On weak redshift dependence of gamma-ray spectra of distant blazars

Line-of-sight interactions of cosmic rays provide a natural explanation of the hard gamma-ray spectra of distant blazars, which are believed to be capable of producing both gamma rays and cosmic rays. For sources with redshifts z> 0.1, secondary gamma rays produced in cosmic-ray interactions with background photons close to an observer can dominate over primary gamma rays originating at the source. The transition from one component to another is accompanied by a change in the spectral index depending on the source redshift. We present theoretical predictions and show that they agree with the data from Fermi Large Area Telescope. This agreement, combined with the spectral data from Atmospheric Cherenkov Telescopes, provides evidence of cosmic ray acceleration by active galactic nuclei and opens new opportunities for studying photon backgrounds and intergalactic magnetic fields.