Table of Contents
- Intermediate Velocity Clouds
Intermediate Velocity Clouds
In the previous post the MLE calculation found from a chance intermediate-velocity cloud along the line of sight in Perseus reproduced the observed in the Lee+12 dataset. The image below shows the channel at -45 km/s. Overplotted is the mask.
Perseus emission at -45 km/s overlaid with mask contour. Several IVCs are present, however only the south-west IVC will affect the MLE calculation.
IVCs are present in the north-west and south-west corners of the region. This additional emission, at -45 km/s, would only be included in the Perseus map if the velocity width were about 100 km/s. This is exactly what the MLE code finds in the Lee+12 data (See Figure 1. of this post). There are two peaks in the likelihood space, one at 40 km/s and one at 100 km/s. This means that the dust column density along the line of sight includes some dust contributed by these IVCs.
Taurus is a similar case to Perseus: an IVC shows up along the line of sight in Taurus. In previous calculations where the width was allowed to be up to 100 km/s, the MLE calculation favored 100 km/s widths. Again, the IVC is contributing to and dust emission along the line of sight. See Figure 3. of this post.
Taurus emission at -33 km/s overlaid with mask contour.
These results suggest the code is doing its job: finding the which best traces the dust column density. It is up to us to exclude widths which are unrealistic for GMCs.
Selecting the Velocity Range
Imara et al. (2011a) searched for cloud emission across an width of km/s around the CO line center for clouds in the Milky Way. In their study of M33 clouds (Imara et al. 2011b), they consider a larger range, km/s, over which to search for a GMC’s extent.
We therefore allow the MLE calculation widths less than 50 km/s.
We first must confirm that the Lee+12 and the Planck yield the same results, given that the two maps correlate well with each other. I performed the MLE calculation using the Lee+12 data, the Planck data masked by the Lee+12 data, and the Planck data without masking. The likelihoods show very similar derived parameters. The Lee+12 data favors a higher DGR, more narrow width, and higher intercept than the Planck data. All three parameters derived from the different data are within errors of each other.
When the Planck data is not masked initially by the Lee+12 , the parameters all slightly different: the Planck data favor a smaller DGR, narrower width and lower intercept.
Overall the differences between the Lee+12-derived and the Planck-derived parameters are small.
Perseus likelihoods with Lee+12 data.
Perseus likelihoods with Planck data, initially masked by the Lee+12 IRIS map.
Perseus likelihoods with Planck data.
Next we can consider Taurus and California.
Taurus likelihoods with Planck data. After changing the maximum allowable width, we find a narrow width for Taurus explains the dust emission best.
California likelihoods with Planck data. A high DGR, wide width, and negative intercept are favored.
We can examine the and CO spectra of each cloud. Below show the total, unmasked median and CO spectra, and the masked median spectra. The masked and the unmasked spectra hardly differ.
and CO spectra of each cloud with the MLE for the width. The errors in the widths for California and Perseus hardly affect the derived considering the spectra are quite shallow at these widths. However, the error in the width for Taurus will strongly affect the in Taurus, since the spectrum is steep at these widths. In other words, the column density is uncertain below column densities corresponding to a width of km/s.
Below are distributions of vs. , with the MLE and polynomial fits overlaid. The top plots of each figure are the binned, masked data, to which the DGR and intercept were fit. The bottom plots are the unbinned unmasked data.
Perseus vs. using Planck data.
Taurus vs. .
California vs. .
We should also consider what the distribution is as a function of to make sure the fit between and worked correctly.
Perseus, Taurus, and California vs. distributions derived from Planck data. The distribution is much different in Taurus with the smaller favored width . The spans a much smaller range, and has less well-defined peaks than in the case where a large width of 100 km/s is favored by the MLE analysis (see Figure 9. of this post).