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The role of neutral hydrogen in setting the abundances of molecular species in the Milky Way's diffuse interstellar medium. II. Comparison between observations and theoretical models

We compare observations of HI from the Very Large Array (VLA) and the Arecibo Observatory and observations of HCO$^+$ from the Atacama Large Millimeter/submillimeter Array (ALMA) and the Northern Extended Millimeter Array (NOEMA) in the diffuse ($A_V\lesssim1$) interstellar medium (ISM) to predictions from a photodissociation region (PDR) chemical model and multi-phase ISM simulations. Using a coarse grid of PDR models, we estimate the density, FUV radiation field, and cosmic ray ionization rate (CRIR) for each structure identified in HCO$^+$ and HI absorption. These structures fall into two categories. Structures with $T_s<40~\mathrm{K}$, mostly with $N(\mathrm{HCO^+})\lesssim10^{12}~\mathrm{cm^{-2}}$, are consistent with modest density, FUV radiation field, and CRIR models, typical of the diffuse molecular ISM. Structures with spin temperature $T_s>40~\mathrm{K}$, mostly with $N(\mathrm{HCO^+})\gtrsim10^{12}~\mathrm{cm^{-2}}$, are consistent with high density, FUV radiation field, and CRIR models, characteristic of environments close to massive star formation. The latter are also found in directions with a significant fraction of thermally unstable HI. In at least one case, we rule out the PDR model parameters, suggesting that alternative mechanisms (e.g., non-equilibrium processes like turbulent dissipation and/or shocks) are required to explain the observed HCO$^+$ in this direction. Similarly, while our observations and simulations of the turbulent, multi-phase ISM agree that HCO$^+$ formation occurs along sightlines with $N(\mathrm{HI})\gtrsim10^{21}~\mathrm{cm^{-2}}$, the simulated data fail to explain HCO$^+$ column densities $\gtrsim\rm{few}\times10^{12}~\mathrm{cm^{-2}}$. Since a majority of our sightlines with HCO$^+$ had such high column densities, this likely indicates that non-equilibrium chemistry is important for these lines of sight.