The Turbulence Power Spectrum in Optically Thick Interstellar Clouds

TL;DR

This study numerically confirms that the spectral slope of line intensity maps in optically thick interstellar clouds saturates at -3, aligning with theoretical predictions, and explores how optical depth and turbulence regimes affect the power spectrum.

Contribution

First numerical validation of Lazarian & Pogosyan's prediction that the spectral slope saturates at -3 in optically thick media, including effects of radiative transfer in MHD simulations.

Findings

Spectral slope saturates at -3 in optically thick conditions.

Optically thin supersonic gas shows shallower spectral slopes.

Mixed optical depth regimes exhibit varied spectral slope behaviors.

Abstract

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.