Spectrum and ionization rate of low energy Galactic cosmic rays

TL;DR

This paper constrains the low energy Galactic cosmic ray spectrum using ionization rates in interstellar clouds, proposing a low energy cutoff and analyzing spectral features to reconcile observations across energy ranges.

Contribution

It introduces a model linking cosmic ray ionization rates to a low energy cutoff and spectral features, integrating high and low energy observations.

Findings

Low energy cutoff for protons at 10-100 MeV is necessary.

The inferred proton spectrum at source is approximately E^{-2.45} in momentum.

Spectral steepening at higher energies aligns with diffusion loss models.

Abstract

We consider the rate of ionization of diffuse and molecular clouds in the interstellar medium by Galactic cosmic rays (GCR) in order to constrain its low energy spectrum. We extrapolate the GCR spectrum obtained from PAMELA at high energies ($\ge 200$ GeV/ nucleon) and a recently derived GCR proton flux at $1\hbox{--}200$ 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 cutoff for protons at $10\hbox{--}100$ 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 $\Phi \propto E_{kin}^{-1.7\pm0.2}$ for $E_{kin} \le$ few GeV, is consistent with a power-law spectrum in momentum $p^{-2.45\pm0.4}$, which we identify as the spectrum at source. Diffusion loss at higher energies then introduces a steepening by $E^{-\alpha}$ with $\alpha \sim 1/3$, making it consistent with high energy measurements.