On transiton from galactic to extragalactic cosmic rays

The dip is a feature in the diffuse spectrum of UHE protons in energy range 1× 1018− 4× 10 eV, which is caused by electron-positron pair production on CMB photons. Calculated for power-law generation spectrum with index γg = 2.7, the shape of the dip is confirmed with high accuracy by data of Akeno AGASA, HiRes, Yakutsk and Fly’s Eye detectors. The predicted shape of the dip is robust: it is valid for the rectilinear and diffusive propagation, for different discretenesses in the source distribution, for local source overdensity and deficit, for source inhomogeneities on scale ∼̀ 100 Mpc etc. Below the characteristic energy Ec ≈ 1×1018 eV the spectrum of the dip flattens for both diffusive and rectilinear propagation, and more steep galactic spectrum becomes dominant at E < Ec. The energy of transition Etr < Ec approximately coincides with the position of the second knee E2kn observed in the cosmic ray spectrum. The critical energy Ec is determined by the energy Eeq = 2.3 × 10 eV, where adiabatic and pair-production energy losses are equal. Thus, position of the second knee is explained by proton energy losses on CMB photons. The transition from galactic to extragalactic cosmic rays is quantitatively described by the AGN model for UHECR. PACS numbers: 12.60.Jv, 95.35.+d, 98.35.Gi On transiton from galactic to extragalactic cosmic rays 2