deletions | additions       diff --git a/subsection_Fourier_Statistics_VCA_VCS__.tex b/subsection_Fourier_Statistics_VCA_VCS__.tex  index 2637f1b..a8c35a8 100644  --- a/subsection_Fourier_Statistics_VCA_VCS__.tex  +++ b/subsection_Fourier_Statistics_VCA_VCS__.tex 
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Velocity Channel Analysis (VCA) and Velocity Coordinate Spectrum (VCS) are techniques that isolate how fluctuations in velocity contribute to differences between spectral cubes. VCA produces a 1D power spectrum as a function of spatial frequency, while VCS yields a 1D power spectrum as a function of velocity-channel frequency (frequency equivalent of velocity). For outputs W1T2t0.2 and T2t0, we first compute the three-dimensional power spectrum. To obtain the VCA, we calculate a one-dimensional power spectrum by integrating the 3D power spectrum over the velocity channels and then radially averaging over the two-dimensional spatial frequencies. A portion (look back when you get a chance to see what this portion physically is) of the resultant 1D power spectrum is then fit to a power law. For VCS, we reduce each 3D power spectrum to one dimension by averaging over the spatial frequencies. This yields two distinct power laws, which we fit individually using the segmented linear model described in K15. The fit at larger scales describes bulk gas velocity-dominated motion; the fit at smaller scales describes gas density-dominated motions (Chepurnov and Lazarian 2009).   %To quantity the VCS, we fit the 1D power spectrum to the segmented linear model used Koch et al. (2015).   Figures 5 and 6 show the VCA and VCS power law fits, respectively, for outputs W1T2t0.2 and T2t0. VCA produces similarly sloped power laws for both runs, but there is a constant horizontal offset. This implies that at all spatial scales output W1T2t0.2, our run with feedback, has more energy than that of output T2t0. However, since the curves are otherwise indistinguishable, we conclude VCA is not useful for characterizing feedback properties or comparing the turbulent properties of different clouds.   In Figure 6, VCS also shows a horizontal offset between the two curves.