Gas Temperatures
By Elijah Bernstein-Cooper, November 1, 2015, 0 comments.

# Comparing Predicted Core Temperatures

## Comparing Krumholz Temperatures

Since K+09 assumes that the dust associated with the CNM is the dominant shielding component for dust, the predicted gas density from the K+09 model is of the CNM. The most direct comparison of the predicted CNM temperature may be the spin temperatures, $T_s$, of individual components along LOS within the region.

## Comparing Sternberg Temperatures

As described in section 5 of Bialy+15, K+09 assumed the HI shielding envelops are dominated by the CNM, and estimated $\phi_{CNM}$ assuming $n = n_{CNM}$. The S+14 model includes an extra term in their $\alpha G$ parameter which accounts for the $H_2$-associated dust. This extra term will lead to a lower predicted gas number density.

The number density, $n$, predicted by the S+14 model includes both atomic and molecular gas, since dust is assumed to be associated with all phases of hydrogen gas in the model. Thus the average predicted temperature, $T_H$, should include contributions from all hydrogen phases.

The best we may be able to do is compare $T_H$ with the distribution of the average LOS of sight spin temperature of sightlines within the region. Using $T_s$ as a probe of the temperatures for each component along the line of sight will bias the temperature distribution towards CNM temperatures due to the sensitivity limits.

## Comparing Both Models to Observations

Figure 1 shows the cumulative distributions of the observed temperatures of all sightlines from Stanimirovic+14 within the Taurus-California-Perseus region.

We see that the spin temperatures of individual components agree well with the CNM temperature predicted by the K+09 model. However, the average spin temperature disagrees with the predicted gas temperature from the S+14 model by about a factor of 2 or 3, when we adopt our initial guess of $\phi_g = 2$.

An adjustment to the dust parameters could solve this discrepancy between observed and predicted S+14 average gas temperatures. In the S+14 model

where $T_H$ is the hydrogen temperature, $n$ is the hydrogen volume density, $phi_g$ is the dimensionless dust absorption factor, and $Z$ is the gas-phase metallicity.

$Z$ would have to be reduced from 1 $Z_\odot$ by a factor of 50 to reduce the $T_H$ by a factor of 2. However $\phi_g$ would only have to be reduced by a factor of 2 from 2 to show agreement between the average LOS spin temperature and the predicted average hydrogen temperature from the S+14 model.

Determining $\phi_g$ may be an integral step to comparing the predicted vs observed temperatures. Until now I have assumed $\phi_g$ = 2, the reasons outlined in this post.

##### Figure 1

Cumulative distributions of temperatures predicted and observed within the Taurus-California-Perseus region. Left: $\phi_g = 2$ in the S+14 model, right: $\phi_g$ = 1. The CDF of the spin temperature shows spin temperatures for individual components along the line of sight. These individual-component spin temperatures correspond to the temperatures of the CNM components, thus should be comparable with the predicted K+09 predicted $T_{CNM}$. Next is the observed average spin temperature along the line of sight. $% %]]>$ should be comparable with S+14 given that S+14 predicts the average temperature of the neutral gas along the line of sight ($T_H$). The various CDFs plotted for $T_{CNM}$ and $T_H$ correspond to different simulated CDFs in a Monte Carlo simulation considering varying pressures in the neutral gas.