Region Dependence
By Elijah Bernstein-Cooper, July 30, 2015, 0 comments.

In the last couple of days I have found that by varying the masking parameters, such as what qualifies a convergent DGR, or then number of pixels included in each fractional mask, the mask can vary wildly. These different masks lead to wildly varying maximum likelihood estimates of the DGR, $HI$ width and the intercept. This is not acceptable.

Instead, the only safe avenue I see fit to be confident in is to include as many pixels as possible. We can do this by setting a very stringent DGR convergence criterion: two DGRs between iterations in masking must be similar to within 0.1%. This essentially means every pixel not masked by the residual masking will be included in the analysis.

Below show the masked maps of each cloud.

#### Figure 1

Perseus, Taurus, and California $A_V$ maps. For each plot, top: Original resolution $A_V$ map overlaid with mask contour, bottom: binned image, with pixels used to calculate the $HI$ width, DGR and intercept in color, and masked pixels in gray.

## Dependence on Region Selection

We expect that the derived parameters do not depend heavily on the region selected. The masking should include / exclude the relevant pixels given a unique region selection. Below are results for dividing Taurus and Perseus into two regions.

Unfortunately it looks like there is region dependence on the parameters. Perseus and Taurus both show drastic changes in their parameters between the two regions.

### Perseus

The masks for dividing Perseus into two regions both include similar number of pixels.

#### Figure 2

Clockwise from top-left: Perseus, Perseus-South, and Perseus-North maps. For each plot, top: Original resolution $A_V$ map overlaid with mask contour, bottom: binned image, with pixels used to calculate the $HI$ width, DGR and intercept in color, and masked pixels in gray.

#### Figure 3

Likelihoods for Perseus.

#### Figure 4

Likelihoods for Perseus North region.

#### Figure 5

Likelihoods for Perseus South region.

### Taurus

#### Figure 6

Clockwise from top-left: Taurus, Taurus-South, and Taurus-North maps. For each plot, top: Original resolution $A_V$ map overlaid with mask contour, bottom: binned image, with pixels used to calculate the $HI$ width, DGR and intercept in color, and masked pixels in gray.

#### Figure 7

Likelihoods for Taurus.

#### Figure 8

Likelihoods for Taurus North region.

#### Figure 9

Likelihoods for Taurus South region.

## $N(HI)$ in California

We continue to find a negative intercept for California, interpreted as an $HI$ background:

#### Figure 10

Likelihoods for California.

If we examine the relationship between $N(H2)$ and $N(HI)$ in California, shown in the last post, we see that there seem to be two distributions of $N(HI)$. One distribution is less than $\sim 17 \times 10^{20}$ cm$^{-2}$, and one above, each with associated $N(H2)$ present. This is because I had a bug in the code which did not exclude pixels outside of the region, and instead included all pixels in the image.

Below is the $N(H2)$ and $N(HI)$ distribution in California, excluding pixels outside of the region.

#### Figure 11

$N(H2)$ and $N(HI)$ distribution in California. There seem to be a number of negative $N(H2)$ pixels. This is likely due to the large $A_V$ gradient present in the mask, shown in Figure 1.

We would like confirm that the $HI$ background found in California, shown by the negative intercept, is truly present. Below is the $N(HI)$ map from different $HI$ widths centered on the peak $HI$ velocity in California. I am unable to pick out any structure resembling California. The high $N(HI)$ near California, RA = 4h 20m, Dec=36 deg, resembles a background in $HI$.

#### Figure 12

California $N(HI)$ maps from integrating $HI$ with different widths.

## Dependence on Initial $HI$ Width

I have found there to be a dependence of final parameters on the initial $HI$ width chosen to create the $N(HI)$ map used for mapping. This is likely because there are pixels where the $A_V$ does not correlate perfecting with the gas, and if we are not including all of the $HI$ along the line of sight. Perhaps it would be best to use an initial $HI$ width which is our best guess for the cloud $HI$ width. This would hopefully exclude pixels with excess $A_V$ not associated with the cloud.