Scattering polarization due to light source anisotropy

We consider the polarization arising from scattering in an envelope illuminated by a central anisotropic source. Spherical harmonics are used to describe both the light source anisotropy and the envelope density distribution functions of the scattering particles. This framework demonstrates how the net resultant polarization arises from a superposition of three basic "shape" functions: the distribution of source illumination, the distribution of envelope scatterers, and the phase function for dipole scattering. Specific expressions for the Stokes parameters and scattered flux are derived for the case of an ellipsoidal light source inside an ellipsoidal envelope, with principal axes that are generally not aligned. Two illustrative examples are considered: (a) axisymmetric mass loss from a rapidly rotating star, such as may apply to some Luminous Blue Variables, and (b) a Roche-lobe filling star in a binary system with a circumstellar envelope. As a general conclusion, the combination of source anisotropy with distorted scattering envelopes leads to more complex polarimetric behavior such that the source characteristics should be carefully considered when interpreting polarimetric data.