Principal Component Analysis studies of turbulence in optically thick
  gas
  In this work we investigate the Principal Component Analysis (PCA)
sensitivity to the velocity power spectrum in high opacity regimes of the
interstellar medium (ISM). For our analysis we use synthetic
Position-Position-Velocity (PPV) cubes of fractional Brownian motion (fBm) and
magnetohydrodynamics (MHD) simulations, post processed to include radiative
transfer effects from CO. We find that PCA analysis is very different from the
tools based on the traditional power spectrum of PPV data cubes. Our major
finding is that PCA is also sensitive to the phase information of PPV cubes and
this allows PCA to detect the changes of the underlying velocity and density
spectra at high opacities, where the spectral analysis of the maps provides the
universal -3 spectrum in accordance with the predictions of Lazarian \&
Pogosyan (2004) theory. This makes PCA potentially a valuable tool for studies
of turbulence at high opacities provided that the proper gauging of the PCA
index is made. The later, however, we found to be not easy, as the PCA results
change in an irregular way for data with high sonic Mach numbers. This is in
contrast to synthetic Brownian noise data used for velocity and density fields
that show monotonic PCA behavior. We attribute this difference to the PCA's
sensitivity to Fourier phase information.
