We argue that an astrophysical solution to the ultrahigh energy cosmic ray (UHECR) problem is viable. The detailed study of UHECR energy spectra is performed. The spectral features of extragalactic protons interacting with the cosmic microwave background (CMB) are calculated in a model-independent way. Using the power-law generation spectrum $\ensuremath{\propto}{E}^{\ensuremath{-}{\ensuremath{\gamma}}_{g}}$ 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 the CMB, to be the most robust feature, existing in energy range $1\ifmmode\times\else\texttimes\fi{}{10}^{18}\char21{}4\ifmmode\times\else\texttimes\fi{}{10}^{19}\text{ }\text{ }\mathrm{eV}$. Its shape is stable relative to various phenomena included in calculations: discreteness of the source distribution, different modes of UHE proton propagation (from rectilinear to diffusive), local overdensity or deficit of the sources, large-scale inhomogeneities in the universe, and interaction fluctuations. The dip is well confirmed by observations of the AGASA, HiRes, Fly's Eye, and Yakutsk detectors. With two free parameters (${\ensuremath{\gamma}}_{g}$ and flux normalization constant) the dip describes about 20 energy bins with ${\ensuremath{\chi}}^{2}/\mathrm{d}.\mathrm{o}.\mathrm{f}.\ensuremath{\approx}1$ for each experiment. The best fit is reached at ${\ensuremath{\gamma}}_{g}=2.7$, with the allowed range 2.55\char21{}2.75. The dip is used for energy calibration of the detectors. For each detector independently, the energy is shifted by factor $\ensuremath{\lambda}$ to reach the minimum ${\ensuremath{\chi}}^{2}$. We found ${\ensuremath{\lambda}}_{\mathrm{Ag}}=0.9$, ${\ensuremath{\lambda}}_{\mathrm{Hi}}=1.2$, and ${\ensuremath{\lambda}}_{\mathrm{Ya}}=0.75$ for the AGASA, HiRes, and Yakutsk detectors, respectively. Remarkably, after this energy shift the fluxes and spectra of all three detectors agree perfectly, with discrepancy between AGASA and HiRes at $Eg1\ifmmode\times\else\texttimes\fi{}{10}^{20}\text{ }\text{ }\mathrm{eV}$ being not statistically significant. The excellent agreement of the dip with observations should be considered as confirmation of UHE proton interaction with the CMB. The dip has two flattenings. The high energy flattening at $E\ensuremath{\approx}1\ifmmode\times\else\texttimes\fi{}{10}^{19}\text{ }\text{ }\mathrm{eV}$ automatically explains ankle, the feature observed in all experiments starting from the 1980s. The low-energy flattening at $E\ensuremath{\approx}1\ifmmode\times\else\texttimes\fi{}{10}^{18}\text{ }\text{ }\mathrm{eV}$ reproduces the transition to galactic cosmic rays. This transition is studied quantitatively in this work. Inclusion of primary nuclei with a fraction of more than 20% upsets the agreement of the dip with observations, which we interpret as an indication of the acceleration mechanism. We study in detail the formal problems of spectra calculations: energy losses (the new detailed calculations are presented), the analytic method of spectrum calculations, and the study of fluctuations with the help of a kinetic equation. 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 $1\ifmmode\times\else\texttimes\fi{}{10}^{18}\char21{}1\ifmmode\times\else\texttimes\fi{}{10}^{20}\text{ }\text{ }\mathrm{eV}$ to be measured in the nearest future by the Auger detector. We also predict the spectral signature of nearby sources, if they are observed by Auger. This paper is long and contains many technical details. For those who are interested only in physical content we recommend the Introduction and Conclusions, which are written as autonomous parts of the paper.

On astrophysical solution to ultrahigh energy cosmic rays

http://particle.astro.ru.nl/pub/JPPNP63-293.pdf

Cosmic rays from the knee to the highest energies

Design and Initial Performance of the Askaryan Radio Array Prototype EeV Neutrino Detector at the South Pole

Gamma-ray bursts (GRBs) are one of the candidates of ultrahigh-energy ($\ensuremath{\gtrsim}{10}^{18.5}\text{ }\text{ }\mathrm{eV}$) cosmic-ray (UHECR) sources. We investigate high-energy cosmic-ray acceleration including heavy nuclei in GRBs by using Geant 4, and discuss its various implications, taking both high-luminosity (HL) and low-luminosity (LL) GRBs into account. This is because LL GRBs may also make a significant contribution to the observed UHECR flux if they form a distinct population. We show that not only protons, but also heavier nuclei can be accelerated up to ultrahigh energies in the internal, (external) reverse, and forward shock models. We also show that the condition for ultrahigh-energy heavy nuclei such as iron to survive is almost the same as that for $\ensuremath{\sim}\mathrm{TeV}$ gamma rays to escape from the source and for high-energy neutrinos not to be much produced. The multimessenger astronomy by neutrino and GeV-TeV gamma-ray telescopes such as IceCube and KM3Net, GLAST and MAGIC will be important to see whether GRBs can be accelerators of ultrahigh-energy heavy nuclei. We also demonstrate expected spectra of high-energy neutrinos and gamma rays, and discuss their detectabilities. In addition, we discuss implications of the GRB-UHECR hypothesis. We point out, since the number densities of HL GRBs and LL GRBs are quite different, its determination by UHECR observations is also important.

D.V. Semikoz

Papers

Earth-skimming UHE tau neutrinos at the fluorescence detector of Pierre Auger Observatory

Ultra-high energy cosmic rays from a finite number of point sources