More Model Interpretation
By Elijah Bernstein-Cooper, October 18, 2015, 0 comments.

Table of Contents

Confirming Model Accuracy

Figure 1 shows the $R_{H2}$ plots for each cloud. We can see the agreement between the model and data and that shown in Lee+12 or Bialy+15.

Figure 1

$R_{H2}$ vs. H for different cores with fitted models.

Model Application

Determining $I_{UV}$

Given a dust temperature the ISRF heating dust grains (from all directions) can be actually easily calculated by

This relation is based on many observations showing that large interstellar silicates have an equilibrium temperature of 17.5 K in the solar neighborhood. Here U(M83) is the ISRF by Mathis+83 integrated from 0.09 micron to 8 micron.

But what we need to know is I_UV, the scaling factor for the Draine field. For the FUV range of 6 ~ 13.6 eV, the Draine field is a factor of ~1.5 stronger than the Mathis field. Hence

however I have not confirmed this last step myself. I will do so tomorrow.

Fitting: Holding $\phi_g$ constant

The simplest approach for fitting the Sternberg+14 model would be to hold all variables constant and fit for $\alpha G$. Following the steps from Bialy+15, who considered varying dust properties in Perseus, I set $\phi_g$ to 2. Typically the galactic value of $\phi_g$ is of order unity, but Lee+12 found a DGR about two times higher than galactic, thus the dust properties may differ from galactic. The dust opacity (proportional to the DGR), which determines $\alpha G$, is proportional to the product of the grain abundance, $Z_g$, (metallicity) and $\phi_g$.

$\phi_g$ and $Z_g$ are completely degenerate with each other in determining $\alpha G$, only their product changes $\alpha G$. However they affect the interpretation of the models differently. The gas volume density assuming pressure equilibrium is determined by

hence determining $\phi_g$. Then assuming a standard galactic pressure of P/k = 3,000 K / cm$^{-3}$ we can determine the gas temperature.

In the end determining the $\phi_g$ and $Z_g$ parameters affects our interpretation of what phases the neutral gas is in. See Table 1 for a rough idea of the derived values for the model parameters, measured and predicted ISM properties. Unfortunately the errors on the number densities are huge, though perhaps not unrealistic.

Table 1

Sanity check for model fitting

Just to confirm that we are sampling a reasonable range of $\alpha G$, Figure 2 shows the CDF of the fitted values for $\alpha G$. Indeed we see a most probable value within the center of the allowed range.

Figure 2

$\alpha G$ CDF for G171.49-14.91. There is an obvious most probable value, around 15. This would correspond to a large peak in the PDF.

Fitting: Varying $\phi_g$

Next we could attempt to fit for $\phi_g$ and $\alpha G$ simultaneously.

I fit for both $\alpha G$ and $\phi_g$ in the S+14 model. I allowed $\alpha G$ to go between 10$^{-2}$ to 5000 and $\phi_g$ from 0.01 to 10. The limits of $\phi_g$ seem beyond physical, given the solar dust composition has $\phi_g$ between 0.5 and 2.

Unfortunately the errors on each parameter are gigantic, with $\alpha G$ values in the thousands and $\phi_g$ values between 5 and 10, which seems much too large, unless the dust abundance, $Z_g$, were much lower than solar.

Below are the CDFs for the two parameters. We see that despite the large range available to $\alpha G$ the most probable value is on the edge of the range.

Figure 3

$\alpha G$ and $\phi_g$ CDFs for G171.49-14.91. There is an obvious most probable value for $\phi_g$, around 8. However the $\alpha G$ CDF shows the most probable value is at the edge of the fitting boundary, suggesting we should use a larger boundary. A value of $\phi_g$ = 8 seems unphysical given that the solar neighborhood is within a factor of 2 from 1.