Polarization of Rayleigh scattered Ly{\alpha} in active galactic nuclei

The unification scheme of active galactic nuclei (AGNs) invokes an optically thick molecular torus component hiding the broad emission line region. Assuming the presence of a thick neutral component in the molecular torus characterized by a \ion{H}{I} column density > $10^{22}{\rm\ cm^{-2}}$, we propose that far UV radiation around Ly$\alpha$ can be significantly polarized through Rayleigh scattering. Adopting a Monte Carlo technique we compute polarization of Rayleigh scattered radiation near Ly$\alpha$ in a thick neutral region in the shape of a slab and a cylindrical shell. It is found that radiation near Ly$\alpha$ Rayleigh reflected from a very thick slab can be significantly polarized in a fairly large range of wavelength $\Delta\lambda\sim 50$ \AA\ exhibiting a flux profile similar to the incident one. Rayleigh transmitted radiation in a slab is characterized by the central dip with a complicated polarization behavior. The optically thick part near Ly$\alpha$ center is polarized in the direction perpendicular to the slab normal, which is in contrast to weakly polarized wing parts in the direction parallel to the slab normal. A similar polarization flip phenomenon is also found in the case of a tall cylindrical shell, in which the spatial diffusion along the vertical direction near the inner cylinder wall for core photons leads to a tendency of the electric field aligned to the direction perpendicular to the vertical axis. Observational implications are briefly discussed including spectropolarimetry of the quasar PG~1630+377 by Koratkar et al. in 1990 where Ly$\alpha$ is strongly polarized with no other emission lines polarized.