We study the effects of radiative transfer on the Probability Distribution Functions ( PDFs ) of simulations of magnetohydrodynamic turbulence in the widely studied ^ { 13 } CO 2-1 transition .
We find that the integrated intensity maps generally follow a log-normal distribution , with the cases that have \tau \approx 1 best matching the PDF of the column density .
We fit a 2D variance-sonic Mach number relationship to our logarithmic PDFs of the form \sigma _ { ln ( \Sigma / \Sigma _ { 0 } ) } ^ { 2 } = A \times ln ( 1 + b ^ { 2 } { \cal M } _ { s } ^ { 2 } ) and find that , for parameter b = 1 / 3 , parameter A depends on the radiative transfer environment .
We also explore the variance , skewness , and kurtosis of the linear PDFs finding that higher moments reflect both higher sonic Mach number and lower optical depth .
Finally , we apply the Tsallis incremental PDF function and find that the fit parameters depend on both Mach numbers , but also are sensitive to the radiative transfer parameter space , with the \tau \approx 1 case best fitting the incremental PDF of the true column density .
We conclude that , for PDFs of low optical depth cases , part of the gas is always sub-thermally excited so that the spread of the line intensities exceeds the spread of the underlying column densities and hence the PDFs do not reflect the true column density .
Similarly , PDFs of optically thick cases are dominated by the velocity dispersion and therefore do not represent the true column density PDF .
Thus , in the case of molecules like carbon monoxide , the dynamic range of intensities , structures observed and consequently , the observable PDFs , are less determined by turbulence and more-often determined by radiative transfer effects .