Probability Density Functions
By Elijah Bernstein-Cooper, September 11, 2015, 0 comments.

# Probability Density Functions

Burkhart et al. (2015) just published a paper using the Lee et al. (2015) optical-depth-corrected HI and H2 in Perseus to examine the PDF of the gas and dust of the molecular cloud. The HI-to-H2 transition was found to be around the peak in the $A_V$ PDF of Perseus. We show a similar plot to their Figure 2 below.

##### Figure 1

PDFs of N(HI), N(H$_2$) and $A_V$ for each cloud. The gray shaded range corresponds to the range of $A_V$ at the HI-to-H2 transition from 10 core regions in each molecular core. PDFs for $A_V < 1$ mag are likely very uncertain due to background subtraction and region selection.

## PDF Precision

Lombardi et al. (2015) compared several molecular cloud PDFs using Planck/Herschel data. In Figures 1 and 2 two they show that the PDF of Orion varies largely for $A_K < 0.2$ mag, about $A_V = 1.8$ mag, given different boundaries and background subtractions. To be safe, we compare these PDFs for $A_V > 1$ mag.

## Cloud PDF Discussion

### California

The peak of California’s PDF is about $A_V = 2$ mag. Lombardi et al. (2015) shows a peak of around $A_K = 0.2$ mag. This is about 1.8 mag. This difference is within the error in the background for California derived from Planck and 2MASS $A_V$.

### Perseus

The PDF of Perseus seems to show similarity to that of Burkhart et al. (2015) (B+15). Our $A_V$ PDF peak is slightly shifted to $A_V$ of 1 mag, compared to the $A_V$ peak of 0.8 mag in B+15. This can be explained by the positive offset (background) we calculated for Perseus $A_V$. The HI peak is slightly higher than in B+15 by about 0.1 mag. This could be due to our higher DGR, different region selection, and slightly different HI range.

A better comparison with B+15 would be to measure the widths of Gaussians fitted to the rising side of the HI and $A_V$ PDFs.

### Taurus

The dust and HI in Taurus is less centrally concentrated than in Perseus and California. This wider distribution in HI is due to the gradient in N(HI) seen from the East to West in Taurus. Lombardi et al. (2015) shows a peak of about $A_V$ = 1 mag, similar to what we have found.