The study of the transition between galactic and extragalactic cosmic rays can shed more light on the end of the Galactic cosmic rays spectrum and the beginning of the extragalactic one. Three models of transition are discussed: ankle, dip and mixed
composition models. All these models describe the transition as an intersection of a steep galactic component with a flat extragalactic one. Severe bounds on these models are provided by the Standard Model of Galactic Cosmic Rays according to which the maximum acceleration energy for Iron nuclei is of the order of $E_{rm Fe}^{rm max} approx 1times 10^{17}$ eV. In the ankle model the transition is assumed at the ankle, a flat feature in the all particle spectrum which observationally starts at energy $E_a sim (3 - 4)times 10^{18}$ eV. This model needs a new high energy galactic component with maximum energy about two orders of magnitude above that of the Standard Model. The origin of such component is discussed. As observations are concerned there are two signatures of the transition: change of energy spectra and mass composition. In all models a heavy galactic component is changed at the transition to a lighter or proton component.
Data of Pierre Auger Observatory show a proton-dominated chemical composition of ultrahigh-energy cosmic rays spectrum at (1 - 3) EeV and a steadily heavier composition with energy increasing. In order to explain this feature we assume that (1 - 3) E
eV protons are extragalactic and derive their maximum acceleration energy, E_p^{max} simeq 4 EeV, compatible with both the spectrum and the composition. We also assume the rigidity-dependent acceleration mechanism of heavier nuclei, E_A^{max} = Z x E_p^{max}. The proposed model has rather disappointing consequences: i) no pion photo-production on CMB photons in extragalactic space and hence ii) no high-energy cosmogenic neutrino fluxes; iii) no GZK-cutoff in the spectrum; iv) no correlation with nearby sources due to nuclei deflection in the galactic magnetic fields up to highest energies.
We discuss the superluminal problem in the diffusion of ultra high energy protons with energy losses taken into account. The phenomenological solution of this problem is found with help of the generalized Juttner propagator, originally proposed for r
elativization of the Maxwellian gas distribution. It is demonstrated that the generalized Juttner propagator gives the correct expressions in the limits of diffusive and rectilinear propagation of the charged particles in the magnetic fields, together with the intermediate regime, in all cases without superluminal velocities. This solution, very general for the diffusion, is considered for two particular cases: diffusion inside the stationary objects, like e.g. galaxies, clusters of galaxies etc, and for expanding universe. The comparison with the previously obtained solutions for propagation of UHE protons in magnetic fields is performed.
We develop a model for explaining the data of Pierre Auger Observatory (Auger) for Ultra High Energy Cosmic Rays (UHECR), in particular, the mass composition being steadily heavier with increasing energy from 3 EeV to 35 EeV. The model is based on th
e proton-dominated composition in the energy range (1 - 3) EeV observed in both Auger and HiRes experiments. Assuming extragalactic origin of this component, we argue that it must disappear at higher energies due to a low maximum energy of acceleration, E_p^{max} sim (4 - 10) EeV. Under an assumption of rigidity acceleration mechanism, the maximum acceleration energy for a nucleus with the charge number Z is ZE_p^{max}, and the highest energy in the spectrum, reached by Iron, does not exceed (100 - 200) EeV. The growth of atomic weight with energy, observed in Auger, is provided by the rigidity mechanism of acceleration, since at each energy E=ZE_p^{max} the contribution of nuclei with Z < Z vanishes. The described model has disappointing consequences for future observations in UHECR: Since average energies per nucleon for all nuclei are less than (2 - 4) EeV, (i) pion photo-production on CMB photons in extragalactic space is absent; (ii) GZK cutoff in the spectrum does not exist; (iii) cosmogenic neutrinos produced on CMBR are absent; (iv) fluxes of cosmogenic neutrinos produced on infrared - optical background radiation are too low for registration by existing detectors and projects. Due to nuclei deflection in galactic magnetic fields, the correlation with nearby sources is absent even at highest energies.
We discuss the production of ultra high energy secondary protons by cosmic ray primary nuclei propagating in the intergalactic space through Cosmic Microwave Background (CMB) and Infrared (IR) radiations. Under the assumption that only primary nuclei
with a fixed atomic mass number $A_0$ are accelerated, the spectrum of secondary protons is calculated. It is found that for all $A_0$ the diffuse flux of secondary protons starts to dominate over that of primary nuclei at energy $E sim (1 - 2)times 10^{19}$ eV, and thus the standard Greisen-Zatsepin -Kuzmin (GZK) cutoff is produced.
We study the solution of the diffusion equation for Ultra-High Energy Cosmic Rays in the general case of an expanding universe, comparing it with the well known Syrovatsky solution obtained in the more restrictive case of a static universe. The forma
l comparison of the two solutions with all parameters being fixed identically reveals an appreciable discrepancy. This discrepancy is less important if in both models a different set of best-fit parameters is used.
