The shape and ionization of equatorial matter near compact objects from X-ray polarization reflection signatures

Motivated by the success of the Imaging X-ray Polarimetry Explorer (IXPE) providing observational evidence that our Universe is substantially polarized in X-rays, we elucidate what can be inferred about 3D matter structures forming about the equatorial plane of accreting compact objects from 0.1--100 keV linear polarization induced by non-relativistic large-scale reflection. We constructed a model of an optically thick elevated axially symmetric reflecting medium with an arbitrary ionization profile representing the known diverse scattering environments, from thick winds and super-Eddington funnel structures formed around black holes and neutron stars to Compton-thick dusty tori of active galactic nuclei and their broad-line regions. We assumed a central X-ray power-law source with an isotropic, cosine, and slab-coronal angular distribution, including possible intrinsic polarization. The reprocessing is based on X-ray constant-density local reflection tables produced with a Monte Carlo method combined with detailed statistical equilibrium radiative transfer, although we also show the corresponding examples of fully neutral and fully ionized reflection, including classical (semi-)analytical prescriptions. We conclude that varying ionization has a similarly strong impact on observed polarization as the observer's inclination and the skew and opening angle of the reflector's inner walls, altogether producing up to tens of percent of reflected polarization both parallel and perpendicular to the projected system axis, depending on the combination of parameter values. After testing three different ad hoc shapes of the reflector (i.e., a cone, an elliptical torus, and a bowl), we concluded that while in some configurations their altered curvature produces a more than 30% absolute difference in observed total polarization, in others, the adopted shape has a marginal impact. Lastly, we discuss the change of the observed polarization due to relaxing the optically thick assumption on equatorial winds and accreted matter, providing a continuous range of energy-dependent examples between the optically thick and thin scenarios.