deletions | additions       diff --git a/subsection_Fourier_Statistics_VCA_VCS__.tex b/subsection_Fourier_Statistics_VCA_VCS__.tex  index a8c35a8..d71f5d6 100644  --- a/subsection_Fourier_Statistics_VCA_VCS__.tex  +++ b/subsection_Fourier_Statistics_VCA_VCS__.tex 
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\subsubsection{Velocity Channel Analysis and Velocity Coordinate Spectrum} \label{VCA}  %SSRO Note power spectra - lower case; to cite text add label as \label{VCA} and then add (e.g., \ref{VCA}) in the text  Velocity Channel Analysis (VCA) and Velocity Coordinate Spectrum (VCS) are techniques that isolate how fluctuations in velocity contribute to differences between spectral cubes. cubes \citep[e.g.,]{Lararian \& Pogosyan 2000, Heyer \& Brunt 2002, Lazarian \& Pogosyan 2004}.  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). \citep{kowal07} find that the density-dominated regime is sensitive to the magnetic field strength, where stronger fields correspond to steeper slopes.  %To quantity the VCS, we fit the 1D power spectrum to the segmented linear model used Koch et al. (2015).  
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The output without feedback   %Can use both w/wo feedback and pure turbulence.  %(our purely turbulent run? Go back and denotes everything like this?)   appears to have a larger range over which it is dominated by velocity fluctuations ($k\simeq 1-0.05$). The velocity-dominated regime is smaller for the run with feedback ($k\simeq 1-0.1$), such that changes in gas density affect a greater portion of the structure in the cloud emission. It makes sense that feedback extends the density-dominated regime since the winds create density enhancements on larger scales by sweeping up material.  Thus, variation in the breakpoint location, could provide useful insight into the underlying turbulent driving and the importance of feedback. % (here than in the other run...trying to be grammatically correct with comparisons while including sentence variation--not sure if this sentance is grammatically correct). %SSRO Good job. made some small edits to address content.