The optical polarization of spiral galaxies

Scattering of starlight by dust, molecules and electrons in spiral galaxies will produce a modification of the direct intensity and a polarization in the observed light. We treat the case where the distribution of scatterers can be considered to be optically thin, and derive semi-analytic expressions for the resolved intensity and polarized intensity for Thomson, Rayleigh, and more general scattering mechanisms. These expressions are applied to a parametric model spiral galaxies. It is further shown that in the case of Thomson and Rayleigh scattering, and when scatterers and stars are distributed with rotational symmetry, the total polarized flux depends on the inclination, $i$, of the galactic axis to the line of sight according to a simple $\sin ^2 i$ law. This generalises the well known result for pointlike and spherical light sources. By using a method based on spherical harmonics, we generalise this law for more general mechanisms, and show that to good approximation, the $\sin ^2 i$ law still holds for the class of models considered.