Lyman-$α$ (Ly$α$) is a powerful astrophysical probe. Not only is it ubiquitous at high redshifts, it is also a resonant line, making Ly$α$ photons scatter. This scattering process depends on the physical conditions of the gas through which Ly$α$ propagates, and these conditions are imprinted on observables such as the Ly$α$ spectrum and its surface brightness profile. In this work, we focus on a less-used observable capable of probing 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$α$ polarized in general. The degree and orientation of Ly$α$ polarization depends on the kinematics and distribution of the scattering HI gas. We find that it generally probes spatial or velocity space asymmetries and aligns itself tangentially to the emission source. We show that the mentioned observables, when studied separately, can leave similar signatures for different source models. We conclude by revealing how a joint analysis of the Ly$α$ spectra, surface brightness profiles, and polarization can break these degeneracies and help us extract unique physical information on galaxies and their environments from their strongest, most prominent emission line.
Unlocking the Full Potential of SKAO Extra-galactic Science with High-multiplex Optical Spectroscopy
University of Edinburgh（爱丁堡大学）；University of Bristol（布里斯托大学）；University of Hertfordshire（赫特福德大学）；University of Oxford（牛津大学）；North-West University（西北大学）；ASTRON, the Netherlands Institute for Radio Astronomy（荷兰射电天文研究所(ASTRON)）；University of Groningen（格罗宁根大学）；University Catholic of Lyon（里昂天主教大学）
