Lya Polarisation in Thick H I Media

We have investigated the linear polarisation of Lya transferred in a static, dustless, and thick plane-parallel slab that is uniformly filled with neutral hydrogen. Because the scattering phase function is characterised by the dipole type for wing scatterings of Lya, which is in high contrast with more isotropic scattering phase function associated with resonant scatterings, the polarisation of the emergent Lya is dominantly controlled by the number of wing scatterings before escape from the slab. When the scattering medium is extremely thick, photons emergent in the grazing direction are polarised in the direction perpendicular to the slab normal up to 12%, which coincides with the limit attained by the Thomson scattered radiation in a semi-infinite thick medium investigated by Chandrasekhar in 1960. The number of wing scatterings before escape is sensitively dependent on the product of the Voigt parameter $a$ and the line-centre optical depth $\tau_0$, with which the variation of the degree of polarisation can also be explained in comparison with the Thomson scattering case. The polarisation direction is parallel to the slab normal when $a\tau_0<10^3$, while it is perpendicular when $a\tau_0>10^3$. Our simulated spectropolarimetry of Lya from a highly thick medium is characterised by negligible polarisation around the line centre, parallel polarisation in the near wing parts and perpendicular polarisation in the far wing parts, where the polarisation direction is measured with respect to the slab normal. The polarisation flip naturally reflects the diffusive nature of the Lya transfer process in both real space and frequency space. We also discuss the beaming effect that is associated with the parallel polarisation in the near wing parts of the emission.