# Harvard Astronomy 201b

The left-hand panel shows the centroid velocity: in each little beam-size cell, one has a Gaussian-esque line profile, with some centroid whose velocity can be calculated using the line’s red or blue shift.  The right-hand panel shows, in each little beam size cell, what the width of this profile is.  Interestingly, one can compare the sigma of the centroid velocities in the boxed region of the left panel occupied by the filament with the sigma in each beam-sized cell and use this ratio to test the geometry of the structure in the region.  This is essentially because of Larson’s Laws: Philip Mocz’s post on Larson’s laws explains how this ratio depends on the geometry, and calculates it for several idealized cases.  The most relevant one for us is the long sheet, which in 2-d projection would look similar to a filament.  The ratio predicted for such a geometry is 2.67.  Estimating by eye the needed quantities from Figure 2 (try this yourself), we find $\sigma_v/\Delta \sigma_v\sim 3$—offering somewhat independent confirmation that we have a filament.  Note this calculation will be somewhat sensitive to how you choose the region over which to calculate the ratio—but we already know what we are looking for (the filament), so can choose the region accordingly. However, this is why I qualified this with “somewhat” above.