Turbulent dissipation, CH${}^{+}$ abundance, H${}_2$ line luminosities, and polarization in the cold neutral medium

In the cold neutral medium, high out-of-equilibrium temperatures are created by intermittent dissipation processes, including shocks, viscous heating, and ambipolar diffusion. The high-temperature excursions are thought to explain the enhanced abundance of CH${}^{+}$ observed along diffuse molecular sight-lines. Intermittent high temperatures should also have an impact on H${}_2$ line luminosities. We carry out simulations of MHD turbulence in molecular clouds including heating and cooling, and post-process them to study H${}_2$ line emission and hot-gas chemistry, particularly the formation of CH${}^{+}$. We explore multiple magnetic field strengths and equations of state. We use a new H${}_2$ cooling function for $n_{\mathrm{H}}\le {10}^5{\mathrm{c}\mathrm{m}}^{-3}$, $T\leq 5000,{\rm K}$,andvariableH$_2$ fraction. We make two important simplifying assumptions: (i) the ${\mathrm{H}}_2\mathrm{/}\mathrm{H}$ fraction is fixed everywhere, and (ii) we exclude from our analysis regions where the ion-neutral drift velocity is calculated to be greater than 5 km/s. Our models produce H${}_2$ emission lines in accord with many observations, although extra excitation mechanisms are required in some clouds. For realistic r.m.s. magnetic field strengths ($\approx 10$ $\mu$G) and velocity dispersions, we reproduce observed CH${}^{+}$ abundances. These findings contrast with those of Valdivia et al. (2017). Comparison of predicted dust polarization with observations by {\it Planck} suggests that the mean field $\gtrsim 5\mu$G, so that the turbulence is sub-Alfv'enic. We recommend future work treating ions and neutrals as separate fluids to more accurately capture the effects of ambipolar diffusion on CH${}^{+}$ abundance.