Polarization of the Lyα line from an anisotropically expanding H I shell in primeval galaxies

We compute the polarization of the Ly alpha photons emerging from an anisotropically expanding and optically thick medium, which is expected to operate in many Ly alpha-emitting primeval objects, including damped Ly alpha absorbers and Lyman break galaxies. In the case of a highly optically thick medium, the escape of resonance-line photons is achieved by a large number of local resonant scatterings followed by a small number of damping-wing scatterings. We show that some polarization can develop because wing scatterings are coupled with strong spatial diffusion that depends on the scattering geometry and kinematics. The case of a slab with a finite scattering optical depth and an expansion velocity of similar to 100 km s(-1) is investigated. When the typical scattering optical depth tau greater than or similar to 10(4), it is found that the emergent Ly alpha photons are linearly polarized with a degree of polarization up to 0.1 in the direction perpendicular to the slab plane. We subsequently investigate the polarization of the Ly alpha photons emerging from a hemispherical shell obscured partially by an opaque component, and we obtain similar to 5% of the polarization. We propose that the polarimetry of Ly alpha emission may provide important clues to the geometrical and kinematical structures of the H I shells in primeval galaxies and nearby starburst galaxies.