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Polarization of Rayleigh scattered Lyα 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$α$ can be significantly polarized through Rayleigh scattering. Adopting a Monte Carlo technique we compute polarization of Rayleigh scattered radiation near Ly$α$ in a thick neutral region in the shape of a slab and a cylindrical shell. It is found that radiation near Ly$α$ Rayleigh reflected from a very thick slab can be significantly polarized in a fairly large range of wavelength $Δλ\sim 50$ Å 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$α$ 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$α$ is strongly polarized with no other emission lines polarized.