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Register a new userAnalytic calculations of the spectra of ultra-high energy cosmic ray nuclei. I. The case of CMB radiation
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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.
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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.
We present new measurements of the energy spectra of cosmic-ray (CR) nuclei from the second flight of the balloon-borne experiment Cosmic Ray Energetics And Mass (CREAM). The instrument included different particle detectors to provide redundant charge identification and measure the energy of CRs up to several hundred TeV. The measured individual energy spectra of C, O, Ne, Mg, Si, and Fe are presented up to $sim 10^{14}$ eV. The spectral shape looks nearly the same for these primary elements and it can be fitted to an $E^{-2.66 pm 0.04}$ power law in energy. Moreover, a new measurement of the absolute intensity of nitrogen in the 100-800 GeV/$n$ energy range with smaller errors than previous observations, clearly indicates a hardening of the spectrum at high energy. The relative abundance of N/O at the top of the atmosphere is measured to be $0.080 pm 0.025 $(stat.)$ pm 0.025 $(sys.) at $sim $800 GeV/$n$, in good agreement with a recent result from the first CREAM flight.
(Abridged) Recent results from the Pierre Auger Observatory (PAO) indicate that the composition of ultra-high-energy cosmic rays (UHECRs) with energies above $10^{19}$ eV may be dominated by heavy nuclei. An important question is whether the distribution of arrival directions for such UHECR nuclei can exhibit observable anisotropy or positional correlations with their astrophysical source objects despite the expected strong deflections by intervening magnetic fields. For this purpose, we have simulated the propagation of UHECR nuclei including models for both the extragalactic magnetic field and the Galactic magnetic field. Assuming that only iron nuclei are injected steadily from sources with equal luminosity and spatially distributed according to the observed large scale structure in the local Universe, at the number of events published by the PAO so far, the arrival distribution of UHECRs would be consistent with no auto-correlation at 95% confidence if the mean number density of UHECR sources $n_s >~ 10^{-6}$ Mpc$^{-3}$, and consistent with no cross-correlation with sources within 95% errors for $n_s >~ 10^{-5}$ Mpc$^{-3}$. On the other hand, with 1000 events above $5.5 times 10^{19}$ eV in the whole sky, next generation experiments can reveal auto-correlation with more than 99% probability even for $n_s <~ 10^{-3}$ Mpc$^{-3}$, and cross-correlation with sources with more than 99% probability for $n_s <~ 10^{-4}$ Mpc$^{-3}$. In addition, we find that the contribution of Centaurus A is required to reproduce the currently observed UHECR excess in the Centaurus region. Secondary protons generated by photodisintegration of primary heavy nuclei during propagation play a crucial role in all cases, and the resulting anisotropy at small angular scales should provide a strong hint of the source location if the maximum energies of the heavy nuclei are sufficiently high.
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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.
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