Varying Dust Opacity and Gas Temperatures
By Elijah Bernstein-Cooper, November 4, 2015, 0 comments.

# Varying the dust opacity, $\sigma_g$

The dust opacity, $\sigma_g$, in the Sternberg model determines the behavior of HI-to-H$_2$ transition as well as the predicted average gas temperature. In the model

where $\phi_g$ is the dimensionless dust grain absorption factor and $Z_g$ is the gas-phase metallicity, where $\phi_g$ = 1 and $Z_g = 1 Z_\odot$ for the galactic dust opacity.

Since each monte carlo simulation leads to a different empirical DGR (essentially the dust grain opacity), itâ€™s natural to assume that the For each simulation, $\phi_g$ should vary. I scale $\phi_g$ by the scalar between the galactic DGR and the simulation DGR / (DGR$_{\rm galactic}$).

For each cloud $\phi_g$ is, Taurus: $\phi_g = 1.82^{+0.48}_{-0.46}$, California: $\phi_g = 1.32^{+0.43}_{-0.43}$, Perseus: $\phi_g = 2.40^{+0.55}_{-0.49}$

## Comparing Both Models to Observations

In the last post I showed results comparing the average line-of-sight spin temperature to the Sternberg gas temperature predictions. Unfortunately I made a mistake in calculating the average line of sight temperatures. The average LOS temperature should be

which should lead to temperatures in the 1000s for the LOSs in Stanimirovic+14. The previous post showed temperatures in the 100s.

However, after further scrutiny, perhaps it is best to use the optical-depth-weighted average temperature along each line of sight to compare to the average temperature predicted from S+14. Since the optical depth of a gas component is proportional to the column density, the optical depth should also be proportional to the gas density along the LOS. Thus the optical-depth-weighted average temperature may be the closest measure of the average density-weighted temperature of the gas along the line of sight.

See Figure 1 below for an updated version with the optical-depth-weighted temperatures from Stanimirovic+14 and the updated S+14 predicted temperatures with $phi_g$ values calculated from the simulation.

##### Figure 1

Cumulative distributions of temperatures predicted and observed within the Taurus-California-Perseus region. 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 optical-depth-weighted 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.