Radiation transfer models of the polarization structure of galaxies are presented. These models include dust scattering and dichroic extinction (the mechanism believed to be responsible for producing the observed interstellar polarization within our own Galaxy). As with previous efforts to model galactic polarization maps, the scattering-only models produce a centrosymmetric pattern of the polarization vectors when one is viewing a galaxy pole-on and vectors perpendicular to the galactic plane for highly inclined galaxies. In general, polarization observations of galaxies show vectors that are parallel to the galactic plane or that follow the spiral arm structure, which indicates that the dominant polarization mechanism is from the transmission of light through aligned grains (dichroic extinction). When we include a toroidal magnetic field to align the dust grains and the resulting dichroic polarization in our radiation transfer simulations, we do indeed find that the polarization is parallel to the galactic disk. Depending on the optical depth of the galaxy and the dust properties (albedo, phase function, peak scattering polarization), the polarization patterns at different regions within the galaxy show the signatures of dichroism, scattering, and null points owing to cancellation between the two polarizing mechanisms. We find that in order to reproduce the polarization structure of external galaxies, it is essential to include dichroic extinction in the radiation transfer.
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