Anisotropy of Magnetohydrodynamic Turbulence and Polarization of the Spectral Lines of Molecules

The anisotropy of velocities in MHD turbulence is demonstrated explicitly by calculating the velocity gradients as a function of direction in representative simulations of decaying turbulence. It follows that the optical depths of spectral lines are anisotropic when there is MHD turbulence, and that this anisotropy influences the polarization characteristics of the emergent radiation. We calculate the linear polarization that results for the microwave lines of the CO molecule in star-forming gas and show that it is comparable to the polarization that is observed. This and our earlier result—that the anisotropy of MHD turbulence may be the cause for the absence of the Zeeman π-components in the spectra of OH mainline masers—are the first demonstrations of the occurrence of anisotropy in the optical depths caused by MHD turbulence. A non-local approximation is developed for the radiative transfer and the results are compared with those from a local (LVG) approximation. Subject headings: ISM: magnetic fields — ISM: molecules — radio lines: ISM — polarization — turbulence