The Cosmic-Ray Ionization Rate in the Galactic Disk, as Determined from Observations of Molecular Ions

We have obtained estimates for the cosmic-ray ionization rate (CRIR) in the Galactic disk, using a detailed model for the physics and chemistry of diffuse interstellar gas clouds to interpret previously-published measurements of the abundance of four molecular ions: ArH$^+$, OH$^+$, H$_2$O$^+$ and H$_3^+$. For diffuse $atomic$ clouds at Galactocentric distances in the range $R_g \sim 4 - 9$ kpc, observations of ArH$^+$, OH$^+$, and H$_2$O$^+$ imply a mean primary CRIR of $(2.2 \pm 0.3) \exp [(R_0-R_g)/4.7\,\rm{kpc}] \times 10^{-16} \rm \, s^{-1}$ per hydrogen atom, where $R_0=8.5$ kpc. Within diffuse $molecular$ clouds observed toward stars in the solar neighborhood, measurements of H$_3^+$ and H$_2$ imply a primary CRIR of $(2.3 \pm 0.6) \times 10^{-16}\,\,\rm s^{-1}$ per H atom, corresponding to a total ionization rate per H$_2$ molecule of $(5.3 \pm 1.1) \times 10^{-16}\,\,\rm s^{-1},$ in good accord with previous estimates. These estimates are also in good agreement with a rederivation, presented here, of the CRIR implied by recent observations of carbon and hydrogen radio recombination lines along the sight-line to Cas A. Here, our best-fit estimate for the primary CRIR is $2.9 \times 10^{-16}\,\,\rm s^{-1}$ per H atom. Our results show marginal evidence that the CRIR in diffuse molecular clouds decreases with cloud extinction, $A_{\rm V}({\rm tot})$, with a best-fit dependence $\propto A_{\rm V}({\rm tot})^{-1}$ for $A_{\rm V}({\rm tot}) \ge 0.5$.