Metallicity Variations in Core Regions
By Elijah Bernstein-Cooper, April 11, 2016, 0 comments.

S+14 relates $\alpha G$ to the K+09 radiation field $\chi_{K+09}$ by the $H_2$-dust absorption bandwidth for beamed radiation fields given by

$$$\alpha G = \chi_{S+14} = w \chi_{K+09}$$$

where $w$ is the dissociation bandwidth by $H_2$-dust equal to $1/[1+(2.64 \phi_g Z_g)^{1/2}]$. $\phi_g$ is a dimensionless measure of dust grain absorption efficiency, and $Z_g$ is the gas phase metallicity. For our case with higher $Z$ or $\phi_g$, $w < 1$ and we should see $\alpha G < \chi$.

S+14 describes the comparison between $\chi_{K+09}$ and $\alpha G$ in Section 4.1. To follow their comparison I am now using beamed radiation instead of isotropic radiation in the S+14 model in which case

$$$\Sigma_{HI} = \frac{11.9}{1.4 \phi_g Z_g}\,{\rm ln}[\alpha G / 2 + 1]$$$.

After making this correction I find that $\chi$ is about equal to $\alpha G$ for every core region. See Table 1 for $\chi$. However $w < 1$ for every core region because $\phi_g$ is greater than 1, thus $\chi_{S+14}$ becomes several factors larger than $\chi_{K+09}$. The predicted radiation fields between the two models are dissimilar.

##### Table 1

Table summarizing model parameters for fitting only $\phi_{\rm CNM}$ and $\alpha G$. $\chi_{S+14}$ is reasonably close to $\chi_{K+09}$ but still systematically higher.

# Varying Metallicity

We can also try to vary the metallicity in order to explain the observed $\Sigma_{HI}$ instead of the gas densities through $\phi_{\rm CNM}$ or $\alpha G$. Tables 2 and 3 show results from fitting both $\phi_{\rm CNM}$ and the gas-phase metallicity, $Z_{K+09}$, in the K+09 model and $\alpha G$ and the gas-phase metallicity, $Z_{S+14}$, in the S+14 model. Table 2 presents the same results as Table 1. Table 3 shows the fitted gas-phase metallicities for both models.

Table 1 shows that the radiation fields, $\chi_{K+09}$ and $\chi_{S+14}$, are in much larger disagreement when the metallicity is allowed as a free parameter in the fitting compared to the metallicity held at $Z = Z_\odot$.

##### Table 2

Model parameters from fitting both $\phi_{\rm CNM}$ and the gas-phase metallicity, $Z_{K+09}$, in the K+09 model and $\alpha G$ and the gas-phase metallicity, $Z_{S+14}$, in the S+14 model. The radiation fields, $\chi_{K+09}$ and $\chi_{S+14}$, are in much larger disagreement when the metallicity is allowed as a free parameter in the fitting.

##### Table 3

Summary of model parameters from fitting both $\phi_{\rm CNM}$ and the gas-phase metallicity, $Z_{K+09}$, in the K+09 model and $\alpha G$ and the gas-phase metallicity, $Z_{S+14}$, in the S+14 model. The K+09 model is able to predict $\Sigma_{HI}$ by variations in metallicity. The S+14 model does not provide as much confidence due to the larger and more varying metallicities fit for each core region, especially in Taurus.