Fixing the HI Width
By Elijah Bernstein-Cooper, August 11, 2015, 0 comments.

## Using the HI width with Gaussian fitting

In yesterday’s post I used the method of Imara et al. (2011) of fitting Gaussians to the median HI spectrum to determine the HI width. We then fix this HI width throughout the rest of the analysis, i.e. in the masking and the MLE calculation. We only fit for the intercept and DGR.

### HI Widths

Below are the median spectra of each cloud fitted with as few Gaussians as seem reasonable.

Perseus

Taurus

California

#### Figure 1

Median HI spectra with model fit in purple, and the HI velocity range used as the gray shaded region. The velocity widths are consistent with what was done in Imara et al. (2012).

### Lee+12 IRIS $A_V$, threshold masking

We compare Lee+12 DGR by masking at an $A_V$ threhsold of 1.2 mag and perform the MLE calculation.

Perseus

#### Figure 3

Top: Original resolution masked $A_V$ map overlaid with mask contour, bottom: binned image, with pixels used to calculate the DGR and intercept in color, and masked pixels in gray.

The likelihoods are quite different from Lee et al. (2012) given an HI width of 20 km/s.

#### Figure 2

Likelihoods using the Lee+12 IRIS $A_V$ data, and masking at $A_V$ of 1.2 mag.

We should make sure the pixels used in the MLE calculation have reasonable errors and follow a linear trend. In previous posts I was incorrectly displaying the errors in this plot. This is because when binning, I was not accounting for the standard deviation about the mean of the bin. I was only considering the binned errors as the unbinned errors added in quadrature. Now the binned errors are calculated as follows

where Var() is the variance.

The threshold-masking approach leaves quite a large scatter in the pixels used to fit $A_V$ vs. N(HI).

#### Figure 6

Left: masked $A_V$ vs. N(HI), right: N(H$_2$) vs. N(HI) for Perseus region.

### Lee+12 IRIS $A_V$, residual masking

We compare Lee+12 DGR by masking with the residual masking technique and perform the MLE calculation. We find that the residual masking is necessary, as opposed to the threshold masking to reproduce the work done by Lee et al. (2012).

Perseus

#### Figure 3

Top: Original resolution masked $A_V$ map overlaid with mask contour, bottom: binned image, with pixels used to calculate the DGR and intercept in color, and masked pixels in gray.

The likelihoods show a DGR very similar to that of Lee et al. (2012).

#### Figure 2

Likelihoods using the Lee+12 IRIS $A_V$ data, and masking with residuals.

We should make sure the pixels used in the MLE calculation have reasonable errors and follow a linear trend.

The residual-masking approach reduces the scatter in the pixels used to fit $A_V$ vs. N(HI).

#### Figure 6

Left: masked $A_V$ vs. N(HI), right: N(H$_2$) vs. N(HI) for Perseus region.

With an HI width similar to that of Lee et al. (2012), around 20 km/s for each cloud, we now get much more reasonable likelihood values.