We use a kinetic-equation approach to describe the propagation of ultra high energy cosmic ray protons and nuclei and calculate the expected spectra and mass composition at the Earth for different assumptions on the source injection spectra and chemi
cal abundances. When compared with the spectrum, the elongation rate $X_{max}(E)$ and dispersion $sigma(X_{max})$ as observed with the Pierre Auger Observatory, several important consequences can be drawn: a) the injection spectra of nuclei must be very hard, $sim E^{-gamma}$ with $gammasim 1-1.6$; b) the maximum energy of nuclei of charge $Z$ in the sources must be $sim 5Ztimes 10^{18}$ eV, thereby not requiring acceleration to extremely high energies; c) the fit to the Auger spectrum can be obtained only at the price of adding an {it ad hoc} light extragalactic component with a steep injection spectrum ($sim E^{-2.7}$). In this sense, at the ankle ($E_{A}approx 5times 10^{18}$ eV) all the components are of extragalactic origin, thereby suggesting that the transition from Galactic to extragalactic cosmic rays occurs below the ankle. Interestingly, the additional light extragalactic component postulated above compares well, in terms of spectrum and normalization, with the one recently measured by KASCADE-Grande.
The signatures of Ultra High Energy (E >1 EeV) proton propagation through CMB radiation are pair-production dip and GZK cutoff. The visible characteristics of these two spectral features are ankle, which is intrinsic part of the dip, beginning of GZK
cutoff in the differential spectrum and E_{1/2} in integral spectrum. Measured by HiRes and Telescope Array (TA) these characteristics agree with theoretical predictions. However, directly measured mass composition remains a puzzle. While HiRes and TA detectors observe the proton dominated mass composition, the data of Auger detector strongly evidence for nuclei mass composition becoming progressively heavier at energy higher than 4 EeV and reaching Iron at energy about 35 EeV. The models based on the Auger and HiRes/TA data are considered independently and classified using the transition from galactic to extragalactic cosmic rays. The ankle cannot provide this transition. since data of all three detector at energy (1 - 3) EeV agree with pure proton composition (or at least not heavier than Helium). If produced in Galaxy these particles result in too high anisotropy. This argument excludes or strongly disfavours all ankle models with ankle energy E_a > 3 EeV. The calculation of elongation curves, X_{max}(E), for different ankle models strengthens further this conclusion. Status of other models, the dip, mixed composition and Auger based models are discussed.
The signatures of UHE proton propagation through CMB are pair-production dip and GZK cutoff. The visible manifestations of these spectral features are ankle, beginning of GZK cutoff in the differential spectrum and E_{1/2} in integral spectrum. Obser
ved in all experiments, the ankle is usually interpreted as transition from galactic to extragalactic cosmic rays. Using the mass composition measured by HiRes, Telescope Array (TA) and Auger detectors at energy (1-3) EeV, calculated anisotropy of galactic cosmic rays at these energies, and the elongation curves we strongly argue against the interpretation of the ankle given above. The transition must occur at lower energy, most probably at the second knee as the dip model predicts. The other prediction of this model, the shape of the dip, is well confirmed by HiRes, TA, AGASA and Yakutsk detectors, and, after recalibration of energies, by Auger detector. Predicted beginning of GZK cutoff and E_{1/2} agree well with HiRes and TA data. However, directly measured mass composition remains a puzzle. While HiRes and TA detectors observe the proton-dominated mass composition, as required by the dip model, the data of Auger detector strongly evidence for nuclei mass composition becoming steadily heavier at energy higher than 4 EeV and reaching Iron at energy about 35 EeV. The Auger-based scenario is consistent with another interpretation of the ankle at energy E_a=4 EeV as transition from extragalactic protons to extragalactic nuclei. The heavy- nuclei dominance at higher energies may be provided by low-energy of acceleration for protons E_{max} sim 4 EeV and rigidity-dependent E_{max}^A =Z E_{max}$ for nuclei. The highest energy suppression may be explained as nuclei-destroying cutoff.
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.
We present a systematic study of different methods for the analytic calculation of ultra-high energy nuclei diffuse spectra. Nuclei propagating in the intergalactic space are photo-disintegrated and decrease their Lorentz factor due to the interactio
n with cosmic microwave background and extragalactic background light. We calculate the evolution trajectories in the backward time, that describe how atomic mass number $A$ and Lorentz factor $Gamma$ change with redshift $z$. Three methods of spectra calculations are investigated and compared: {it (i)} trajectory method, {it(ii)} kinetic equation combined with trajectory calculations and {it (iii)} coupled kinetic equations. We believe that these three methods exhaust at least the principal possibilities for any analytic solution of the problem. In the most straightforward method {it(i)} only trajectory calculations are used to connect the observed nuclei flux with the production rate of primary (accelerated) nuclei $A_0$. In the second method {it (ii)} the flux (space density) of primary nuclei, and secondary nuclei and protons are calculated with the help of kinetic equation and trajectories are used only to determine the generation rates of these nuclei. The third method {it (iii)} consists in solving the complete set of coupled kinetic equations, written starting with primary nuclei $A_0$, then for $A_0-1$ etc down to the $A$ of interest. The solution of the preceding equation gives the generation rate for the one which follows. An important element of the calculations for all methods is the systematic use of Lorentz factor instead of energy. We consider here the interaction of nuclei only with the cosmic microwave background, this case is particularly suitable for understanding the physical results.
We reconsider the model of neutrino production during the bright phase, first suggested in 1977, in the light of modern understanding of the role of Pop III stars and acceleration of particles in supernova shocks. We concentrate on the production of
cosmogenic UHE neutrinos in supernova explosions that accompany the death of Pop III stars. Accelerated protons produce neutrinos in collisions with CMB photons. We deliberately use simplified assumptions which make our results transparent. Pop III stars are assumed to be responsible for the reionization of the universe as observed by WMAP. Since the evolution of Pop III stars is much faster than the Hubble rate, we consider the burst of UHE proton production to occur at fixed redshift (z_b=10-20). We discuss the formation of collisionless shocks and particle acceleration in the early universe. The composition of accelerated particles is expected to be proton dominated. A simple calculation is presented to illustrate the fact that the diffuse neutrinos flux from the bright phase burst is concentrated in a relatively narrow range around $7.5 times 10^{15}(20/z_b)^2$ eV. The $ u_mu$ flux may be detectable by IceCube without violating the cascade upper limit and the expected energetics of SNe associated with Pop III stars. A possible signature of the neutrino production from Pop III stars may be the detection of resonant neutrino events. For the burst at $z_b=20$ and $bar{ u}_e$-flux at the cascade upper limit, the number of resonant events in IceCube may be as high as 10 events in 5 years of observations. These events have equal energies, $E=6.3times 10^{15}$ eV, in the form of e-m cascades. Given the large uncertainties in the existing predictions of UHE cosmogenic neutrino fluxes, we argue that neutrinos from the first stars might become one of the most reliable hopes for UHE neutrino astronomy.
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.
The short review of theoretical aspects of ultra high energy (UHE) neutrinos. The accelerator sources, such as Supernovae remnants, Gamma Ray Bursts, AGN etc are discussed. The top-down sources include Topological Defects (TDs), Superheavy Dark Matte
r (SHDM) and Mirror Matter. The diffuse fluxes are considered accordingly as that of cosmogenic and top-down neutrinos. Much attention is given to the cascade upper limit to the diffuse neutrino fluxes in the light of Fermi-LAT data on diffuse high energy gamma radiation. This is most general and rigorous upper limit, valid for both cosmogenic and top-down models. At present upper limits from many detectors are close to the cascade upper limit, and 5 yr IceCube upper limit will be well below it.
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 discuss the problem of ultra high energy nuclei propagation in extragalactic background radiations. The present paper is the continuation of the accompanying paper I where we have presented three new analytic methods to calculate the fluxes and sp
ectra of ultra high energy cosmic ray nuclei, both primary and secondary, and secondary protons. The computation scheme in this paper is based on the analytic solution of coupled kinetic equations, which takes into account the continuous energy losses due to the expansion of the universe and pair-production, together with photo-disintegration of nuclei. This method includes in the most natural way the production of secondary nuclei in the process of photo-disintegration of the primary nuclei during their propagation through extragalactic background radiations. In paper I, in order to present the suggested analytical schemes of calculations, we have considered only the case of the cosmic microwave background radiation, in the present paper we generalize this computation to all relevant background radiations, including infra-red and visible/ultra-violet radiations, collectively referred to as extragalactic background light. The analytic solutions allow transparent physical interpretation of the obtained spectra. Extragalactic background light plays an important role at intermediate energies of ultra high energy cosmic ray nuclei. The most noticeable effect of the extragalactic background light is the low-energy tail in the spectrum of secondary nuclei.
