Linear polarization of radio frequency lines in molecular clouds and circumstellar envelopes

We predict that interstellar lines possess a few percent linear polarization provided that the optical depth in the source region is both anisotropic and of order unity and the radiative rates are at least comparable to the collision rates. These conditions are expected to be met in many sources which emit radio and far-infrared line radiation. Under circumstances in which the Zeeman splitting exceeds both the radiative and collisional rates the linear polarization is aligned either parallel or perpendicular to the projection of the magnetic field on the plane of the sky. This "strong magnetic field" limit is expected to apply to all radio frequency lines and to many of those far infrared lines which form between levels whose magnetic moments are comparable to the Bohr magneton. The "weak magnetic field" limit is relevant to most far-infrared lines formed between levels with magnetic moments of order the nuclear magneton. In this limit the polarization direction is determined by the orientation of the propagation direction with respect to the anisotropic optical depth