Lyman-$\alpha$ (Ly$\alpha$) is a powerful astrophysical probe. Not only is it ubiquitous at high redshifts, it is also a resonant line, which makes Ly$\alpha$ photons scatter. This scattering process depends on the physical conditions of gas through which Ly$\alpha$ propagates, and these are imprinted on observables such as the Ly$\alpha$ spectrum and its surface brightness profile. In this work, we focus on a less used observable that can probe any scattering process: polarization. We implement the density matrix formalism of polarization into the Monte-Carlo radiative transfer code tlac. This allows us to treat it as a quantum mechanical process where single photons develop and lose polarization from scatterings in arbitrary gas geometries. We explore static and expanding ellipsoids, biconical outflows and clumpy, multiphase media. We find that photons become increasingly polarized as they scatter and diffuse into the wings of the line profiles, making scattered Ly$\alpha$ polarized in general. The degree and orientation Ly$\alpha$ polarization depends on the kinematics and distribution of the scattering HI gas. The degree of polarization generally increases with the degree of asymmetry of the gas (in terms of its physical distribution, or distribution in velocity space), and the orientation generally aligns tangentially to the source of emission. We show that the spectra, the surface brightness profile and the polarization of Ly$\alpha$ photons leave signatures that are degenerate between different models when studied separately. However, we show that such degeneracies can be broken when observables are combined. We conclude by revealing how a joint analysis of these can help us extract unique physical information on galaxies and their environments from their strongest, most prominent emission line.
M. Eide, M. Gronke, M. Dijkstra, et. al.
Wed, 14 Feb 18
Comments: 26 pages, 12 figures, submitted to ApJ