A dip in the UHECR spectrum and the transition from galactic to extragalactic cosmic rays

The dip is a feature in the diffuse spectrum of ultra-high energy (UHE) protons in the energy range 1 × 1018–4 × 1019 eV, which is caused by electron–positron pair production on the cosmic microwave background (CMB) radiation. For a power-law generation spectrum E−2.7, the calculated position and shape of the dip is confirmed with high accuracy by the spectra observed by the Akeno-AGASA, HiRes, Yakutsk and Fly’s Eye detectors. When the particle energies, measured in these detectors, are calibrated by the dip, their fluxes agree with a remarkable accuracy. The predicted shape of the dip is quite robust: it is modified very weakly when the discreteness and inhomogeneities in the source distribution are taken into account, and for different regimes of propagation (from rectilinear to diffusive). The cosmological evolution of the sources, with parameters inspired by observations of Active Galactic Nuclei (AGN), also results in the same shape of the dip. The dip is modified strongly when the fraction of nuclei heavier than protons is high at injection, which imposes some restrictions on the mechanisms of acceleration operating in UHECR sources. The existence of the dip, confirmed by observations, implies that the transition from galactic to extragalactic cosmic rays occurs at E ≲ 1 × 1018 eV. We show that at energies lower than a characteristic value Ecr ≈ 1 × 1018 eV, determined by the equality between the rate of energy losses due to pair production and adiabatic losses, the spectrum of extragalactic cosmic rays flattens in all cases of interest, and it provides a natural transition to a steeper galactic cosmic ray spectrum. This transition occurs at some energy below Ecr, corresponding to the position of the so-called second knee. We discuss extensively the constraints on this model imposed by current knowledge of acceleration processes and sources of UHECR and compare it with the traditional model of transition at the ankle.