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

On astrophysical solution to ultra high energy cosmic rays

We argue that an astrophysical solution to UHECR problem is viable. The pectral features of extragalactic protons interacting with CMB are calculated in model-independent way. Using the power-law generation spectrum $\propto E^{-\gamma_g}$ as the only assumption, we analyze four features of the proton spectrum: the GZK cutoff, dip, bump and the second dip. We found the dip, induced by electron-positron production on CMB, as the most robust feature, existing in energy range $1\times 10^{18} - 4\times 10^{19}$ eV. Its shape is stable relative to various phenomena included in calculations. The dip is well confirmed by observations of AGASA, HiRes, Fly's Eye and Yakutsk detectors. The best fit is reached at $\gamma_g =2.7$, with the allowed range 2.55 - 2.75. The dip is used for energy calibration of the detectors. After the energy calibration the fluxes and spectra of all three detectors agree perfectly, with discrepancy between AGASA and HiRes at $E> 1\times 10^{20}$ eV being not statistically significant. The agreement of the dip with observations should be considered as confirmation of UHE proton interaction with CMB. The dip has two flattenings. The high energy flattening at $E \approx 1\times 10^{19}$ eV automatically explains ankle. The low-energy flattening at $E \approx 1\times 10^{18}$ eV provides the transition to galactic cosmic rays. This transition is studied quantitatively. The UHECR sources, AGN and GRBs, are studied in a model-dependent way, and acceleration is discussed. Based on the agreement of the dip with existing data, we make the robust prediction for the spectrum at $1\times 10^{18} - 1\times 10^{20}$ eV to be measured in the nearest future by Auger detector.Comment: Revised version as published in Phys.Rev. D47 (2006) 043005 with a small additio

Small Scale Anisotropy Predictions for the Auger Observatory

We study the small scale anisotropy signal expected at the Pierre Auger Observatory in the next 1, 5, 10, and 15 years of operation, from sources of ultra-high energy (UHE) protons. We numerically propagate UHE protons over cosmological distances using an injection spectrum and normalization that fits current data up to \sim 10^{20}\eV. We characterize possible sources of ultra-high energy cosmic rays (UHECRs) by their mean density in the local Universe, $\bar{\rho} = 10^{-r}$ Mpc$^{-3}$, with $r$ between 3 and 6. These densities span a wide range of extragalactic sites for UHECR sources, from common to rare galaxies or even clusters of galaxies. We simulate 100 realizations for each model and calculate the two point correlation function for events with energies above 4 \times 10^{19}\eV and above 10^{20}\eV, as specialized to the case of the Auger telescope. We find that for r\ga 4, Auger should be able to detect small scale anisotropies in the near future. Distinguishing between different source densities based on cosmic ray data alone will be more challenging than detecting a departure from isotropy and is likely to require larger statistics of events. Combining the angular distribution studies with the spectral shape around the GZK feature will also help distinguish between different source scenarios.Comment: 15 pages, 6 figures, 6 tables, submitted to JCA

GZK Photons Above 10 EeV

We calculate the flux of "GZK-photons", namely the flux of photons produced by extragalactic nucleons through the resonant photoproduction of pions, the so called GZK effect. This flux depends on the UHECR spectrum on Earth, of the spectrum of nucleons emitted at the sources, which we characterize by its slope and maximum energy, on the distribution of sources and on the intervening cosmological backgrounds, in particular the magnetic field and radio backgrounds. For the first time we calculate the GZK photons produced by nuclei. We calculate the possible range of the GZK photon fraction of the total UHECR flux for the AGASA and the HiRes spectra. We find that for nucleons produced at the sources it could be as large as a few % and as low as 10^{-4} above 10 EeV. For nuclei produced at the sources the maximum photon fraction is a factor of 2 to 3 times smaller above 10 EeV but the minimum could be much smaller than for nucleons. We also comment on cosmogenic neutrino fluxes.Comment: 20 pages, 9 figures (21 panels), iopart.cls and iopart12.clo needed to typese

Composition of UHECR and the Pierre Auger Observatory Spectrum

We fit the recently published Pierre Auger ultra-high energy cosmic ray spectrum assuming that either nucleons or nuclei are emitted at the sources. We consider the simplified cases of pure proton, or pure oxygen, or pure iron injection. We perform an exhaustive scan in the source evolution factor, the spectral index, the maximum energy of the source spectrum Z E_{max}, and the minimum distance to the sources. We show that the Pierre Auger spectrum agrees with any of the source compositions we assumed. For iron, in particular, there are two distinct solutions with high and low E_{max} (e.g. 6.4 10^{20} eV and 2 10^{19} eV) respectively which could be distinguished by either a large fraction or the near absence of proton primaries at the highest energies. We raise the possibility that an iron dominated injected flux may be in line with the latest composition measurement from the Pierre Auger Observatory where a hint of heavy element dominance is seen.Comment: 19 pages, 6 figures (33 panels)- Uses iopart.cls and iopart12.clo- In version 2: addition of a few sentences and two reference

Implications of the cosmic ray spectrum for the mass composition at the highest energies

The significant attenuation of the cosmic-ray flux above $\sim 5 10^{19}$ eV suggests that the observed high-energy spectrum is shaped by the so-called GZK effect. This interaction of ultra-high-energy cosmic rays (UHECRs) with the ambient radiation fields also affects their composition. We review the effect of photo-dissociation interactions on different nuclear species and analyze the phenomenology of secondary proton production as a function of energy. We show that, by itself, the UHECR spectrum does not constrain the cosmic-ray composition at their extragalactic sources. While the propagated composition (i.e., as observed at Earth) cannot contain significant amounts of intermediate mass nuclei (say between He and Si), whatever the source composition, and while it is vastly proton-dominated when protons are able to reach energies above $10^{20}$ eV at the source, we show that the propagated composition can be dominated by Fe and sub-Fe nuclei at the highest energies, either if the sources are very strongly enriched in Fe nuclei (a rather improbable situation), or if the accelerated protons have a maximum energy of a few $10^{19}$ eV at the sources. We also show that in the latter cases, the expected flux above $3 10^{20}$ eV is very much reduced compared to the case when protons dominate in this energy range, both at the sources and at Earth.Comment: 16 pages, 7 figure