Ly-alpha Radiative Transfer: A Stokes Vector Approach to Ly-alpha Polarization

The Monte Carlo Ly-alpha radiative transfer (RT) code LaRT is extended to deal with the polarization of Ly-alpha using the Stokes vector formalism. LaRT is superb, compared to the preexisting codes, in that it uses a smoothly and seamlessly varying phase function as frequency changes. We also provide the scattering matrix element for the circular polarization of Ly-alpha, which may be necessary to consider a system where dust coexists with hydrogen atoms. We apply LaRT to a few models to explore the fundamental polarization properties of Ly-alpha. Interestingly, individual Ly-alpha photon packets are found to be almost completely polarized by a sufficient number of scatterings (Nscatt = 10^4-10^5 in a static medium) or Doppler shifts induced by gas motion, even starting from unpolarized light. It is also found that the polarization pattern can exhibit a non-monotonically increasing pattern in some cases, besides the commonly-known trend that the polarization monotonically increases with radius. We argue that the polarization properties are primarily determined by the degree of polarization of individual photon packets and the anisotropy of the Ly-alpha radiation field, which are eventually controlled by the medium's optical depth and velocity field. If once Ly-alpha photon packets achieve ~100% polarization, the radial profile of polarization appears to correlate with the surface brightness profile. A steep surface brightness profile tends to yield a rapid increase of the linear polarization near the Ly-alpha source location. In contrast, a shallow surface brightness profile gives rise to a slowly increasing polarization pattern.