Spectrum and ionization rate of low-energy Galactic cosmic rays

Abstract

We consider the rate of ionization of diffuse and molecular clouds in the interstellar medium by Galactic cosmic rays (GCRs) in order to constrain its low-energy spectrum. We extrapolate the GCR spectrum obtained from PAMELA at high energies (≥200 GeV nucleon-1) and a recently derived GCR proton flux at 1-200 GeV from observations of gamma-rays from molecular clouds, and find that the observed average Galactic ionization rate can be reconciled with this GCR spectrum if there is a low-energy cut-off for protons at 10-100 MeV. We also identify the flattening below a few GeV as being due to (a) decrease of the diffusion coefficient and dominance of convective loss at low energy and (b) the expected break in energy spectrum for a constant spectral index in momentum. We show that the inferred CR proton spectrum of ? for Ekin≤ few GeV is consistent with a power-law spectrum in momentum p-2.45± 0.4, which we identify as the spectrum at source. Diffusion loss at higher energies then introduces a steepening by E-α with α˜ 1/3, making it consistent with high-energy measurements.