CNM Temperature Prescription
By Elijah Bernstein-Cooper, February 15, 2016, 0 comments.

# Krumholz Model CNM Temperature

K+09 assumes that all shielding comes from dust associated with the CNM and this results in the overestimation of the CNM density (the major difference with S+14 predictions).  But the problem is, this overestimation of the CNM density is hardly reflected in the CNM temperature.  You can easily see this from Equation (19) of K+09, where the exponents for the CNM temperature terms are small (-0.2 and 0.5), which means that the CNM temperature is not very sensitive to the change in the CNM density. For example, the change in $\phi_{CNM}$ (thus the CNM density) from ~3 to ~12 results in less than a factor of 2 difference in the CNM temperature (from ~100 to ~60).  So even though K+09 overestimates the CNM density (by a factor of a few), we really cannot see the impact of this overestimation on the CNM temperature.

Instead of using the analytical prescriptions of the CNM temperature given heating and cooling rates (Wolfire et al. 2003), we can estimate the CNM temperature $(T_{CNM})$ by adopting

$$$T_{CNM} = n_{CNM} * k / P.$$$

where $n_{CNM}$ is the volume number density of the CNM and $P / k \sim\,3580$ is the pressure of the hydrogen gas in units of K / cm$^{-3}$. The figure below shows the CDFs of the observed spin temperature and the predicted CNM temperature. The predicted $T_{CNM}$ temperature distribution calculated from pressure equilibrium is wider than when using the analytical Wolfire prescription. See also Table 1 for a list of the predicted $T_{CNM}$ values.