Examining Region Dependence
By Elijah Bernstein-Cooper, August 4, 2015, 0 comments.

## Region Dependence

We expand upon the results from yesterdayâ€™s post showing the dependence of derived paramenters on the region used within Perseus.

#### Figure 1

2MASS $A_V$ of Perseus, overlaid with mask contours. Green: entire Perseus region, red: Perseus-north region, blue: Perseus-south region. The individual regions reproduce nearly the same mask together as for the entire region. This means there is likely something fundamentally different between the regions, whether associated or unassociated with Perseus.

### Residual PDF Progression

#### Figure 2

Clockwise from top-left: Perseus, Perseus-South, and Perseus-North residual PDFs. These residual distributions have an odd skewness in the early iterations, corresponding to only the most diffuse pixels. However in later distributions, the skewed, positive pixels are excluded by the residual masking, as expected.

#### Figure 3

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.

### Likelihoods

#### Figure 4

Likelihoods for Perseus region.

#### Figure 5

Likelihoods for Perseus North region.

#### Figure 6

Likelihoods for Perseus South region.

### $A_V$ vs. N(HI)

The distributions of $A_V$ and N(HI) show quite a large spread. Perseus North seems to show two populations, compared to Perseus souths one population. However in the entire Perseus region, only one population seems to be present, suggesting that the $HI$ width changes the presence of different $HI$ populations.

#### Figure 7

Left: $A_V$ vs. N(HI), right: N(H$_2$) vs. N(HI) for Perseus region. The contours are 7 logarithmically-spaced levels from 99% to 70% of the data included. Total number of pixels: 20875.

#### Figure 8

Left: $A_V$ vs. N(HI), right: N(H$_2$) vs. N(HI) for Perseus North region. The contours are 7 logarithmically-spaced levels from 99% to 70% of the data included. Total number of pixels: 9605.

#### Figure 9

Left: $A_V$ vs. N(HI), right: N(H$_2$) vs. N(HI) for Perseus South region. The contours are 7 logarithmically-spaced levels from 99% to 70% of the data included. Total number of pixels: 11317.

## Sources of Uncertainty

Perhaps the likelihoods would best serve us if we overestimated the errors in our data. $A_V$ depends on a myriad of factors such as the dust opacity, the dust optical depth, the calibration of optical depth to color excess, and the total-to-selective extinction, $R_V$. Measurement errors exist for the latter three, while the dust opacity is assumed to be constant. We do not have a good handle on the uncertainties associated with $R_V$ or the dust opacity.

For example, we can use a crude error estimate on $R_V$. Using the cononical UV absorption study by Rachford et al. (2009) we can estimate the RMS of the $R_V$ values found for each sightline. These sightlines probe similar $A_V$ to the diffuse regions we are using for the MLE. The standard deviation of the $R_V$ for all the sightlines is about 0.7, which we adopt as the uncertainty in $R_V$.

Below are likelihoods for each cloud with the new errors on $A_V$. These likelihoods are from the using original uncertainties, not by calculating the variance between the model and the data.

Perseus

Taurus

California

#### Figure 10

The likelihood spaces for the DGR, velocity width, and intercept for each cloud. The contour represents the 95% confidence level. The plots on the side show the marginalized distribution for each parameter, where the dashed line is the best estimate, and the shaded region is the 68% confidence interval.