The Turbulence Power Spectrum in Optically Thick Interstellar Clouds
  The Fourier power spectrum is one of the most widely used statistical tools
to analyze the nature of magnetohydrodynamic turbulence in the interstellar
medium. Lazarian & Pogosyan (2004) predicted that the spectral slope should
saturate to -3 for an optically thick medium and many observations exist in
support of their prediction. However, there have not been any numerical studies
to-date testing these results. We analyze the spatial power spectrum of MHD
simulations with a wide range of sonic and Alfv\'enic Mach numbers, which
include radiative transfer effects of the $^{13}$CO transition. We confirm
numerically the predictions of Lazarian & Pogosyan (2004) that the spectral
slope of line intensity maps of an optically thick medium saturates to -3.
Furthermore, for very optically thin supersonic CO gas, where the density or CO
abundance values are too low to excite emission in all but the densest shock
compressed gas, we find that the spectral slope is shallower than expected from
the column density. Finally, we find that mixed optically thin/thick CO gas,
which has average optical depths on order of unity, shows mixed behavior: for
super-Alfv\'enic turbulence, the integrated intensity power spectral slopes
generally follow the same trend with sonic Mach number as the true column
density power spectrum slopes. However, for sub-Alfv\'enic turbulence the
spectral slopes are steeper with values near -3 which are similar to the very
optically thick regime.
