It is predicted that interstellar radio-frequency absorption lines in the direction of H II regions, supernova remnants, and hot cores of molecular clouds are linearly polarized. The amount of linear polarization may be as large as several percent if the optical depth is moderate and the number of extrema of the velocity component along the line of sight through the absorbing medium is small. The polarization is caused by the linear dichroism of the interstellar medium, which in turn arises from the non-LTE population of the magnetic sublevels. Analytic expressions are presented for the amount of polarization expected in radio-frequency lines from absorbing material undergoing one-dimensional, two-dimensional axisymmetric, and three-dimensional isotropic collapse. A relation is given between the polarization vector and the magnetic field direction. This relation applies when the Zeeman splitting exceeds both the collisional frequency and the radiative transition rate.
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N. D. Kylafis (1983) studied this question.