Anti-GZK effect in UHECR spectrum

In this paper we discuss the anti-GZK effect that arises in the framework of the diffusive propagation of Ultra High Energy (UHE) protons. This effect consists in a jump-like increase of the maximum distance from which UHE protons can reach the observer. The position of the jump is independent of the Intergalactic Magnetic Field (IMF) strength and depends only on the energy losses of protons, namely on the transition energy from adiabatic and pair-production energy losses. The Ultra High Energy Cosmic Rays (UHECR) spectrum presents a low-energy steepening approximately at this energy, which is very close to the position of the observed second knee. The dip, seen in the universal spectrum as a signature of the proton interaction with the Cosmic Microwave Background (CMB) radiation, is also present in the case of diffusive propagation in magnetic fields.Comment: 4 pages, 4 eps figures, talk given at IFAE 2005: Incotri Fisica Alte Energie, Catania, Italy, 30 March - 2 April 200

Diffusive propagation of UHECR and the propagation theorem

We present a detailed analytical study of the propagation of ultra high energy (UHE) particles in extragalactic magnetic fields. The crucial parameter which affects the diffuse spectrum is the separation between sources. In the case of a uniform distribution of sources with a separation between them much smaller than all characteristic propagation lengths, the diffuse spectrum of UHE particles has a {\em universal} form, independent of the mode of propagation. This statement has a status of theorem. The proof is obtained using the particle number conservation during propagation, and also using the kinetic equation for the propagation of UHE particles. This theorem can be also proved with the help of the diffusion equation. In particular, it is shown numerically, how the diffuse fluxes converge to this universal spectrum, when the separation between sources diminishes. We study also the analytic solution of the diffusion equation in weak and strong magnetic fields with energy losses taken into account. In the case of strong magnetic fields and for a separation between sources large enough, the GZK cutoff can practically disappear, as it has been found early in numerical simulations. In practice, however, the source luminosities required are too large for this possibility.Comment: 16 pages, 13 eps figures, discussion of the absence of the GZK cut-off in strong magnetic field added, a misprint in figure 6 corrected, version accepted for publication in Ap

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 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. The dip is only 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 \lsim 1\times 10^{18} eV. We show that at energies lower than a characteristic value $E_{\rm cr}\approx 1\times 10^{18}$ eV, 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 $E_{\rm cr}$, 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.Comment: Version Accepted for Publication in Astroparticle Physics (minor changes

Ultra High Energy Cosmic Rays Spectra in Top-Down models

In this work we present a detailed computation of the spectra of UHECR in the top-down scenario. We compare the spectra of hadrons obtained by two different methods in QCD and supersymmetric (SUSY) QCD with large primary energies $\sqrt{s}$ up to $10^{16}$ GeV. The two methods discussed are a Monte Carlo (MC) simulation and the evolution of the hadron fragmentation functions as described by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations. The hadron spectra obtained by the two methods agree fairly well in the interesting energy range $10^{-5}M_{X}<E<0.3M_{X}$ ($M_X$ is the energy scale of the process $M_{X}\ge 10^{12}$ GeV). We have also computed the spectra of photons, neutrinos and nucleons obtaining a good agreement with other published results. The consistency of the spectra computed by different methods allows us to consider the spectral shape as a signature of the production model for UHECR, such as the decay of super heavy relic particles or topological defects.Comment: 8 pages, 4 figures, talk presented at the CRIS 2004 conferenc

Anti-GZK effect in Ultra High Energy Cosmic Rays diffusive propagation

We discuss the antiGZK effect in the diffusive propagation of ultra high energy protons in intergalactic magnetic fields, which consists in a jump-like increase of the maximum distance from which ultra high energy protons can reach an observer. The position of this jump, $E_j \approx 2\times 10^{18}$ eV, is determined exclusively by energy losses (transition from adiabatic to pair-production energy losses) and it is independent of the diffusion parameters. The diffuse spectrum presents a low-energy steepening approximately at this energy, which is very close to the position of the second knee observed in the cosmic ray spectrum. The dip, seen in the universal spectrum as a signature of the interaction with the cosmic microwave background radiation, is also present in the case of diffusive propagation in magnetic fields.Comment: 19 pages, 8 figures, a typo correcte

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.Comment: The paper is the first part of a two papers series, it is composed by 41 pages, 4 appendixes and 27 eps figures, version accepted for publication in Astroparticle Physic