Ultra high energy cosmic rays: implications of Auger data for source spectra and chemical composition

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 chemical 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.

Transition from galactic to extragalactic cosmic rays

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.

Analytic calculations of the spectra of ultra-high energy cosmic ray nuclei. I. The case of CMB radiation

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 interaction 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.

Disappointing model for ultrahigh-energy cosmic rays

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) EeV 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.

Superluminal problem in diffusion of relativistic particles and its phenomenological solution

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 relativization 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.

Analytic calculations of the spectra of ultra high energy cosmic ray nuclei. II. The general case of background radiation

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 spectra 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.

Ultra High Energy Cosmic Rays: The disappointing model

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 the 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.

Secondary protons from ultra high energy cosmic ray nuclei: is the Greisen-Zatsepin-Kuzmin cutoff unavoidable?

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.

Detection of GRB signals with Fluorescence Detectors

Gamma Ray Bursts are being searched in many ground based experiments detecting the high energy component (GeV $div$ TeV energy range) of the photon bursts. In this paper, Fluorescence Detectors are considered as possible candidate devices for these searches. It is shown that the GRB photons induce fluorescence emission of UV photons on a wide range of their spectrum. The induced fluorescence flux is dominated by GRB photons from 0.1 to about 100 MeV and, once the extinction through the atmosphere is taken into account, it is distributed over a wide angular region. This flux can be detected through a monitor of the diffuse photon flux, provided that its maximum value exceeds a threshold value, that is primarily determined by the sky brightness above the detector. The feasibility of this search and the expected rates are discussed on the basis of the current GRB observations and the existing fluorescence detectors.

Signatures of the transition from galactic to extragalactic cosmic rays

We discuss the signatures of the transition from galactic to extragalactic cosmic rays in different scenarios, giving most attention to the dip scenario. The dip is a feature in the diffuse spectrum of ultra-high energy (UHE) protons in the energy range $1times 10^{18} - 4times 10^{19}$ eV, which is caused by electron-positron pair production on the cosmic microwave background (CMB) radiation. The dip scenario provides a simple physical description of the transition from galactic to extragalactic cosmic rays. Here we summarize the signatures of the pair production dip model for the transition, most notably the spectrum, the anisotropy and the chemical composition. The main focus of our work is however on the description of the features that arise in the elongation rate and in the distribution of the depths of shower maximum $X_{rm max}$ in the dip scenario. We find that the curve for $X_{max}(E)$ shows a sharp increase with energy, which reflects a sharp transition from an iron dominated flux at low energies to a proton dominated flux at $Esim 10^{18}$ eV. We also discuss in detail the shape of the $X_{max}$ distributions for cosmic rays of given energy and demonstrate that this represents a powerful tool to discriminate between the dip scenario and other possible models of the transition.