Exploring Lee+12 HI Width
By Elijah Bernstein-Cooper, August 10, 2015, 0 comments.

## Lee+12 method of deriving HI width

Lee+12 derived the HI width a priori to deriving the DGR for Perseus. They used 2MASS $A_V$ data to correlate with N(HI) derived using different HI widths. They used a velocity center of 5 km/s, then used velocity integration ranges for widths around the center increasing from 2 to 80 km/s. Their methods are outlined here. An important step they made was to mask all pixels with signal to noise ratio less than 5. With an uncertainty of about 0.2 mag in this data, all pixels below $A_V$ = 1.2 mag are masked. See below for the corresponding region in the 2MASS data.

#### Figure 1

Lee+12 2MASS $A_V$ data smoothed to 5 arcmin resolution. The contour represents the SNR = 5 threshold. Only pixels above this threshold are used to correlate N(HI) with $A_V$. The diffuse lines of sight, where we expect $A_V$ to correlate best with HI are excluded from this analysis, instead only lines of sight which we expect $H_2$ to be present are used to calculate the HI width.

We can see that using this threshold means that only the dense lines of sight were used to calculate the HI width which best correlated N(HI) with $A_V$. This is the opposite of how we have assumed to derive the HI width.

I decided to run this same experiment of calculating the HI width, except by keeping the diffuse lines of sight and excluding the denser lines of sight. Below is a comparable figure to Figure 3 of Lee et al. (2012). I plotted three different correlations using different $A_V$ maps with different masks:

• Lee+12 2MASS $A_V$ data, masked in the same way as in Lee et al. (2012), ‘Lee+12 Mask’

• Lee+12 2MASS $A_V$ data, all lines-of-sight with $A_V$ > 1.2 mag are masked, ‘Diffuse Mask’. Only diffuse lines-of-sight are used to calculate correlation coefficient.

• Planck $A_V$ data, all lines-of-sight with $A_V$ > 1.2 mag are masked, ‘Diffuse Mask’. Only diffuse lines-of-sight are used to calculate correlation coefficient.

#### Figure 2

Pearson correlation coefficient between $A_V$ and N(HI) data as a function of HI width centered at 5 km/s. The Lee+12 mask correlations are from the $A_V$ data masked in the same way as Lee et al. (2012). We can see that the diffuse lines-of-sight favor a larger HI width, as shown by the correlations which mask the dense lines-of-sight, ‘Diffuse mask’.

We see that larger HI widths than found in Lee et al. (2012) are favored when using only the diffuse lines-of-sight. This makes the previous results which favored HI widths of around 30 km/s believable.

## Deriving HI width with Gaussian fitting

I followed the methods of Imara et al. (2011) whereby they fit Gaussian functions to the average HI spectrum for a molecular cloud, and determine the HI velocity range by the width of the Gaussians. In this experiment I fit multiple Gaussians to each spectrum, then set the HI width to +/- 2 times the standard deviation of the tallest Gaussian.

Perseus

Taurus

California

#### Figure 3

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).