Model Interpretation
By Elijah Bernstein-Cooper, October 14, 2015, 0 comments.

## Core Selection

We wish to test the presence of, and the properties of the H i-to-H 2 transition, thus we should select mature core regions with high N (H 2 ) contents. For each cloud, we adopt the ten clumps in the Planck cold clump catalogue (C3PO) with the highest N (H 2 ), totalling to 30 core regions in our entire sample.

Next we pick the extent of the core regions by hand. We adopt a wedge shape for each core region in order to include many diffuse, atomic-dominated LOS, and the dense, molecular-dominated LOS. We rotate the wedges so that all core regions include independent LOS, and do not include multiple dense clumps. See Figure 4 for our chosen core regions. The cores we identified from the C3PO are similar to dense core regions outlined by Lombardi et al. (2010). See Figure 1 for a map of core regions chosen.

##### Figure 1

$A_V$ map overplotted with 10 highest N(H$_2$) core regions in each cloud.

## Analysis

To analyze the Sternberg et al. (2014) (S+14) model we fit each core region $\Sigma_{HI}$ with

where $Z^\prime$ is the metallicity relative to solar, $\phi_g$ is a scalar of order unity of the dust-absorption cross-section dependent on the dust population. $\alpha$ is the ratio of free space dissociation rate to the \htwo\ formation rate. $G$ is the cloud-averaged self-shielding factor, a measure of the dust-absorption efficiency of the $H_2$-dissociating photons. $G$ depends on the competition of $H_2$ line absorption and $H_2$ dust absorption.

To perform the S+14 fits I assumed that $\phi_g$ = 1, and $Z^\prime$ = 1 for each cloud. Table 1 at the bottom of the post shows the fitted $\alpha G$ values (as well as the Krumholz et al. 2009 $\phi_{CNM}$ values) and the $\Sigma_{HI}$ threshold derived from the K+09 fit. Figure 2 shows the fitted models and their uncertainties for each core.

Our fitted $\alpha G$ values are systematically lower than found by Bialy et al. (2015) (B+15), who fit the Sternberg model to Perseus cores in Lee et al. (2012). They found $\alpha G$ parameters were greater than 6 for all cores. B+15 argued that Perseus dust may have a larger dust-absorption cross-section $\phi_g$, or a higher gas-phase metallicity, as evidenced by the higher DGR than galactic value found by L+12.

Our fitted $\alpha G$ parameters are much more consistent with B+15 if I set $\phi_g$ = 2.

## Planned interpretation

1. Derive the predicted neutral gas temperature and number densities predicted from both models. Highlight how the S+14 model interprets sharper transitions for high-metallicity/-dust-absorbing systems as multiple phases of neutral gas, and the K+09 model assumes all neutral gas to be in CNM.

2. Compare predicted neutral gas temperatures to Stanimirovic et al. (2014) and Heiles & Troland (2003).

3. Compare predicted star-formation thresholds to star-formation rates in each cloud.

4. Compare $A_V$, N(HI) and N(H$_2$) PDFs to HI threshold.

5. If time permits, quantify $I_{UV}$ for each core region using the Planck radiance map to get a better estimate of the neutral gas densities.

6. Interpret the spatial distribution of model parameters in the three clouds, see Figure 3.

## Questions

1. Should I fit for the $\phi_g$ parameter, or assume a value? How should I determine what value to use for $\phi_g$?

2. How does the $\phi_g$ parameter effect the interpretation of the $\alpha G$ parameter as a probe for the phases of the neutral gas?

3. Is there any other discussion / interpretation which I should include?

4. What is the best way to calculate the radiation field? I currently imagine assuming some grain sizes and efficiencies, and using the dust temperatures to calculate the ambient ISRF.

##### Figure 2

HI vs. H for different cores with fitted models as solid lines, and the shaded regions as the 68% confidence regions for the model fits.

##### Figure 3

$A_V$ contour map of clouds with model parameters overplotted. Perseus and California show little variation in $\alpha G$, $\phi_{CNM}$ and $\Sigma_{HI}$ threshold while Taurus shows a large variation (about a factor of 3 in $\Sigma_{HI}$ threshold.)

##### Table 1

$% $