2012MNRAS.425L..86N

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 Φ ∝for E_kin^–1.7±0.2 for E_kin ≤ 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.