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.

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.

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.

Ultra High Energy Cosmic Rays Diffusion in an Expanding Universe

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 formal 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.