2013ApJ...771..123B

The Fourier power spectrum is one of the most widely used statistical tools to analyze the nature of magnetohydrodynamic (MHD) turbulence in the interstellar medium. Lazarian & Pogosyan 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 for testing these results. We analyze the spatial power spectrum of MHD simulations with a wide range of sonic and Alfvénic Mach numbers, which include radiative transfer effects of the ¹³CO transition. We numerically confirm the predictions of Lazarian & Pogosyan 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 the order of unity, shows mixed behavior: for super-Alfvénic 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-Alfvénic turbulence the spectral slopes are steeper with values near -3 which are similar to the very optically thick regime.