Star forming galaxies found in the early universe exhibit asymmetric Lyα emission line that results from multiple scattering in a neutral thick medium surrounding the Lyα emission source. It is expected that emergent Lyα will be significantly polarized through a large number of resonance scattering events followed by a number of successive wing scatterings. In this study we adopt a Monte Carlo method to calculate the polarization of Lyα transferred in a very thick static slab of Hi. Resonantly scattered radiation associated with transitions between 1S1 2 − 2P1 2 , 3 2 is only weakly polarized and therefore linear polarization of the emergent Lyα is mainly dependent on the number of off-resonant wing scattering events. The number of wing scattering events just before escape from the slab is determined by the product of the Doppler parameter a and the line center optical depth τ0, which, in turn, determines the behavior of the linear polarization of Lyα. This result is analogous to the study of polarized radiative transfer of Thomson scattered photons in an electron slab, where the emergent photons are polarized in the direction perpendicular to the slab when the scattering optical depth is small and polarized in the parallel direction when the slab is optically thick. Our simulated spectropolarimetry of Lyα shows that the line center is negligibly polarized, the near wing parts polarized in the direction parallel to the slab and the far wing parts are polarized in the direction perpendicular to the slab. We emphasize that the flip of polarization direction in the wing parts of Lyα naturally reflects the diffusive nature of the Lyα transfer process in thick neutral media.

Abstract
1. INTRODUCTION
2. MODEL
    2.1. Radiative Transfer in a Very Thick Medium
    2.2. Density Matrix Formalism for Scattering of Lyα
3. RESULTS
    3.1. Degree of Linear Polarization
    3.2. Spectropolarimetry of Lyα
    3.3. Angular distribution of the polarized Lyα flux
4. CONCLUSIONS
REFERENCES

• Sang-Hyeon Ahn(Korea Astronomy and Space Science Institute) Corresponding author
• Hee-Won Lee(Department of Astronomy and Space Science, Sejong University)