Polarization Profiles of Scattered Emission Lines. I. General Formalism for Optically Thin Rayleigh Scattering

A general theoretical framework is developed for interpreting spectropolarimetric observations of optically thin emission line scattering from small dust particles. Spatially integrated and spatially resolved line profiles of both scattered intensity and polarization are calculated analytically from a variety of simple kinematic models. These calculations will provide a foundation for further studies of emission line scattering from dust and electrons in such diverse astrophysical environments as Herbig-Haro objects, symbiotic stars, starburst galaxies and active galactic nuclei.