Region Dependence of Intercepts
By Elijah Bernstein-Cooper, June 25, 2015, 0 comments.

I have investigated the dependence of derived parameters, $HI$ width, DGR, and intercept based on the selection of region in the California cloud.

## Confined region without low-$A_V$ pixels

Below is an image of the selected region to be included when calculating the three parameters. The green lines represent the boundaries of California. While the map in this image shows missing pixels on the left side, this is not the case in the calculation. All pixels on the left bounded by the region are considered.

In this case I am excluding the diffuse region to the south-west while calculating the three parameters. This leads to large uncertainties in the derived parameters, but a positive estimate of an intercept. We expect there to be a positive intercept given the diffuse background seen far away from California on order of $A_V \sim 0.6$ mag. Lombardi et al. (2015) found a background of $A_K = 0.1$ mag for California, corresponding to $A_V \sim 0.9$ mag.

The progression of residual pixel masking (See Planck XXIV) is shown by the following animation. The image with the most pixels is the first iteration without masking, leading to more and more pixels masked with further iterations.

## Extended regions with low-$A_V$ pixels

In this case I am including the diffuse region to the south-west while calculating the three parameters. See below to compare with confined region. The diffuse pixels in the south-east corner now being included are on order of $A_V \sim 1.7$ mag.

Next I consider two cases, one with subtracting $0.9$ mag manually and deriving the three parameters, one without the subtraction.

### Without background subtraction

The derived parameters certainly favor a very negative intercept, beyond the range considered in this likelihood estimation, i.e., $% $ mag.

And the progression of residual masked-maps:

### With background subtraction

By first manually subtracting $0.9$ mag manually first, the derived parameters are not favoring a smaller magnitude intercept, but rather are increasing the DGR to account for the lower $A_V$.

And the progression of residual masked-maps:

## Summary

The derived parameters, DGR, $HI$ width, and intercept are obviously sensitive on the selection of bounding region in California. I do not have an explanation for this dependence.