Spectra of Cosmic-Ray Protons and Helium Produced in Supernova Remnants

Data obtained in the Advanced Thin Ionization Calorimeter (ATIC-2), Cosmic Ray Energetics and Mass (CREAM), and Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) experiments suggest that the elemental interstellar spectra of cosmic rays below the knee at a few times 10⁶ GeV are not simple power laws, but that they experience hardening at a magnetic rigidity of about 240 GV. Another essential feature is the difference between proton and helium energy spectra, such that the He/p ratio increases by more than 50% in the energy range from 10² to 10⁴ GV. We consider the concavity of the particle spectrum resulting from the nonlinear nature of diffusive shock acceleration in supernova remnants (SNRs) as a possible reason for the observed spectrum hardening. The increase of the helium-to-proton ratio with energy can be interpreted as a consequence of cosmic-ray acceleration by forward and reverse shocks in SNRs. The contribution of particles accelerated by reverse shocks makes the concavity of the produced overall cosmic-ray spectrum more pronounced. The spectra of protons and helium nuclei accelerated in SNRs and released into the interstellar medium are calculated. The derived steady-state interstellar spectra are in reasonably good agreement with observations.