I have added additional cores to the analysis, because why not? Below are the regions selected for each core region. Regions were chosen to include a diffuse part and separate from other structures. The identified regions are from Lombardi et al. (2010), described in this post. I included additional regions besides the ones listed by Lombardi 2010, by labeling the new region as a second part of the nearest region.
Below are the results for each cloud. The contours represent binned counts in logarithmic points. Cores contain a few hundred points each.
Distance from galactic plane
Next result is furthering the result from the latter half of this post, which discusses the predicted from the K+09 model vs. galactic latitude. Here we take it a step further and consider the core region distance from the galactic plane. To calculate the distance from the galactic plane take the following geometry
where is the scale height of the sun wrt the galactic plane, is the scale height of the cloud wrt the galactic plane, is the cloud distance from the galactic plane along the LOS from the sun, is the distance between the sun and the galactic plane along the LOS, and is the distance to the cloud. Given
we can solve for as
This gives us the following trend between and distance from the galactic plane (not much of a trend)