Propagation and origin of ultra high-energy cosmic rays

Propagation of UHE protons through CMB radiation leaves the imprint on energy spectrum in the form of Greisen-Zatsepin-Kuzmin (GZK) cutoff, bump (pile-up protons) and dip. The dip is a feature in energy range 1 x 10(18)-4 x 10(19) eV, caused by electron-positron pair production on CMB photons. Calculated for power-law generation spectrum with index gamma(g) = 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 discreteness in the source distribution, for local source overdensity, deficit, etc. This property of the dip allows us to use it for energy calibration of the detectors. The energy shift lambda for each detector is determined by minimum chi(2) in comparison of observed and calculated dip. After this energy calibration the absolute fluxes, measured by AGASA, HiRes and Yakutsk detectors remarkably coincide in energy region 1 x 10(18)-1 x 10(20) eV. Below the characteristic energy E-c approximate to 1 x 10(18) eV the spectrum of the dip flattens for both diffusive and rectilinear propagation, and more steep galactic spectrum becomes dominant at E < E-c. The energy of transition E-tr < E-c approximately coincides with the position of the second knee E-2kn, observed in the cosmic ray spectrum. The dip-induced transition from galactic to extragalactic cosmic rays at the second knee is compared with traditional model of transition at ankle, the feature observed at energy similar to 1 x 10(19) eV. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.