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

Abstract

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 $n_{\rm H} \leq 10^5\,{\rm cm}^{-3}$, $T\leq 5000\,{\rm K}$, and variable H$_2$ fraction. We make two important simplifying assumptions: (i) the ${\rm H}_2/{\rm H}$ 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 ($\approx 10$ $μ$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 $\gtrsim 5 μ$G, so that the turbulence is sub-Alfvénic. We recommend future work treating ions and neutrals as separate fluids to more accurately capture the effects of ambipolar diffusion on CH$^+$ abundance.