By Elijah Bernstein-Cooper, October 22, 2015, 0 comments.

## Deriving Cloud ISRF

The previous post discussed how we use dust temperature to determine the ISRF parameter, $I_{UV}$ for the Sternberg model. We however would like to use the global cloud dust temperature to derive the ISRF since the model accounts for the ISRF incident on the molecular cloud, and not within core regions.

Figure 1 below shows the dust temperature CDFs for each cloud.

##### Figure 1

Dust temperature CDFs for each cloud. I plan to use the median dust temperature as the global dust temperature to calculate the cloud ISRF, i.e., the dust temperature where CDF = 0.5.

## Scatter in $\Sigma_{HI}$

In order to check whether the derived HI transition surface density is reasonable at all, we can plot the $\Sigma_{HI}$ CDF for each core, and the predicted HI transition, see Figure 2.

##### Figure 2

$\Sigma_{HI}$ CDF for California, Perseus and Taurus. The black dash line is the Sternberg-predicted HI threshold, and the uncertainty of the threshold is represented by the shaded region. G174.70-15.47 exhibits a larger scatter than other cores, consistent with the HI vs H relationship. However there is less than a factor of two variation in $\Sigma_{HI}$ for all cores.

## Interpreting Model Parameters

We will be most confident interpreting the fitted model parameters, $\phi_{CNM}$ and $\alpha G$, first. Then we can attempt to compare predicted ISM properties with observations, i.e., neutral gas temperature. I will begin the interpretation of the fitted model parameters now that we have likely converged on the correct model fits.

See Figure 3 for the model parameter maps, Figure 4 for the predicted ISM properties, and Figure 5 for the PDFs of the $A_V$, H$_2$ and HI for each cloud. Finally Table 1 shows the fitted parameters after running 10,000 monte carlo simulations.

##### Figure 3

Map of fitted model parameters. The HI transition is predicted from the Sternberg model. We see that the variation in each parameter is much larger in Taurus than in Perseus / California. All $\alpha G$ values predict a sharp HI-to-H$_2$ transition.

##### Figure 4

Map of predicted ISM parameters from the Sternberg model.

##### Figure 5

Normalized Probability Density Functions (PDFs) of the atomic gas, molecular gas, and optical dust extinction ($A_V$) of California, Perseus, and Taurus. We used Planck IR observations to measure $A_V$, and GALFA-HI observations to measure HI SD. The H2 SD and HI SD were scaled by the dust-to-gas ratio of each cloud to be compared with $A_V$. The PDFs are likely uncertain for $A_V < 1$\,mag due to background subtraction and region selection uncertainties. The gray shaded region shows the range of the HI-to-H2 transitions of the cores in each cloud. The HI-to-H2 transition in Perseus corresponds to the $A_V$ PDF peak, as found in Burkhart+15. However the transitions for Taurus and California do not align with the $A_V$ PDFs.