Re-evaluation of the cosmic-ray ionization rate in diffuse clouds

All current estimates of the cosmic-ray (CR) ionization rate rely on assessments of the gas density along the probed sight lines. Until now, these have been based on observations of different tracers, with C$_2$ being the most widely used in diffuse molecular clouds for this purpose. However, three-dimensional dust extinction maps have recently reached sufficient accuracy as to give an independent measurement of the gas density on parsec scales. In addition, they allow us to identify the gas clumps along each sight line, thus localizing the regions where CR ionization is probed. We re-evaluate H$_3^+$ observations, which are often considered as the most reliable method to measure the H$_2$ ionization rate $\zeta_{\rm H_2}$ in diffuse clouds. The peak density values derived from the extinction maps for 12 analyzed sight lines turn out to be, on average, an order of magnitude lower than the previous estimates, and agree with the values obtained from revised analysis of C$_2$ data. We use the extinction maps in combination with the 3D-PDR code to self-consistently compute the H$_3^+$ and H$_2$ abundances in the identified clumps for different values of $\zeta_{\rm H_2}$. For each sight line, we obtain the optimum value by comparing the simulation results with observations. We show that $\zeta_{\rm H_2}$ is systematically reduced with respect to the earlier estimates by a factor of $\approx 9$ on average, to $\approx6\times10^{-17}$ s$^{-1}$, primarily as a result of the density reduction. We emphasize that these results have profound consequences for all available measurements of the ionization rate.