Testing K+09 Av
By Elijah Bernstein-Cooper, August 3, 2015, 0 comments.

Table of Contents

## Kainulainen $A_V$

In this post we are using only the Jouni Kainulainen’s $A_V$ image derived from 2MASS observations. These data are derived from background stellar extinction. The absolute amount of extinction is determined from the background extinction in diffuse regions. A more detailed outline of the data is provided here.

Two notable differences between the 2MASS data to the Planck data:

• The 2MASS data are background subtracted. Jouni used several reference fields to create an interpolated zero-point map.

• The 2MASS data should not have correlated pixels, as the Planck map does because of the cosmic infrared background. This means that we can use the full resolution 2MASS data for our analysis.

### Masking

#### 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.

#### Figure 2

Clockwise from top-left: Perseus, Taurus and California residual distribution evolution. 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.

## 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.

The dependence of the parameters on the region is not as severe as when using the Planck data. However, a dependence is still present: Perseus North favors an $HI$ width two times smaller than Perseus South, and Taurus North and Taurus South $HI$ widths differ by a factor of about 2 as well.

### Perseus

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

#### 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.

#### Figure 4

Likelihoods for Perseus. These are somewhat similar parameter values for when using Planck data, however the 2MASS data favor a lower DGR and a much higher intercept, about 0.8 mag in difference. This means that the Planck $A_V$ data correlate better with the $HI$ within the unmasked pixels than the 2MASS data.

#### Figure 5

Likelihoods for Perseus North region.

#### Figure 6

Likelihoods for Perseus South region.

### Taurus

#### Figure 7

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 8

Likelihoods for Taurus. These are somewhat similar parameter values for when using Planck data, however the 2MASS data favor a lower DGR and a higher intercept. This means that the Planck $A_V$ data correlate better with the $HI$ within the unmasked pixels than the 2MASS data. This is a similar result to the comparison between 2MASS and Planck for Perseus.

#### Figure 9

Likelihoods for Taurus North region.

#### Figure 10

Likelihoods for Taurus South region.

### California

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

#### Figure 11

Likelihoods for California.

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

#### Figure 12

$N(H2)$ and $N(HI)$ distribution in California. There are not as many negative $N(H_2)$ pixels as found using Planck. This is likely due to the background subtraction used to create the 2MASS image.

## Fixing the $HI$ Width

Instead of attempting to solve for the $HI$ width, we could instead fix the $HI$ width at a value reasonable for a Milky Way molecular cloud, e.g. 20 km/s. There would be no degeneracy between the DGR and the intercept. Most importantly however, we would use this width to create the $N(HI)$ map needed for masking. Fixing the $HI$ width avoids needing to understand the complex dependence of the resultant mask on the initial $HI$ width.

### Using 2MASS Data

#### Figure 13

Clockwise from top-left: Perseus, Taurus and California likelihoods using 2MASS $A_V$ data. The likelihood space is more constrained because we have reduced the number of free parameters.

### Using Planck Data

#### Figure 14

Clockwise from top-left: Perseus, Taurus and California likelihoods using Planck $A_V$ data.

Comparison between parameter results from Figure 13 and Figure 14 show clearly that the derived parameters are severely dependent on the type of $A_V$ data used, and that our estimated uncertainties are greatly underestimating the systematic uncertainties present in either $A_V$ dataset. If our uncertainties were much greater, then the difference in the derived width, DGR and intercept when changing masking parameters or binning would not be significant.

For instance we expect the DGR to vary by at least a factor of two. The width should also be much more uncertain.

Perhaps we estimate some error on the $A_V$ based on the difference between the two datasets? The Planck team quantified this difference.