Ultrahigh-energy cosmic-ray spectrum

Abstract

We analyze the evolution of the ultrahigh-energy cosmic-ray spectrum upon traversing the 2.7 \ifmmode^\circ\else\textdegree\fi{}K microwave background with respect to pion photoproduction, pair-production reactions, and cosmological effects. Our approach employs exact transport equations which manifestly conserve nucleon number and embody the laboratory details of these reactions. A spectrum enhancement appears around 6\ifmmode\times\else\texttimes\fi{}${10}^{19}$ eV due to the ``pile-up'' of energy-degraded nucleons, and a ``dip'' occurs around ${10}^{19}$ eV due to combined effects. Both of these features appear in the observational spectrum. We analyze the resulting neutrino spectrum and the effects of cosmological source distributions. We present a complete model of the ultrahigh-energy spectrum and anisotropy in reasonable agreement with observation and which predicts an observable electron-neutrino spectrum.