Modeling optical and UV polarization of AGNs III. From uniform-density to clumpy regions

A growing body of evidence suggests that part of, if not all, scattering regions of active galactic nuclei (AGNs) are clumpy. Hence. in this paper, we run radiative transfer models in the optical/UV for a variety of AGN reprocessing regions with different distributions of clumpy scattering media. We use the latest version of the Monte Carlo code STOKES presented in the first two papers of this series to model AGN reprocessing regions of increasing morphological complexity. We replace previously uniform-density media with up to thousands of constant-density clumps. We couple a continuum source to fragmented equatorial scattering regions, polar outflows, and toroidal, obscuring dust regions and investigate a wide range of geometries. We also consider different levels of fragmentation in each scattering region to evaluate importance of fragmentation for the net polarization of the AGN. We find that, in comparison with uniform-density models, equatorial distributions of gas and dust clouds result in grayer spectra, and show a decrease of the net polarization percentage at all lines of sight. The resulting polarization position angle depends on the morphology of the clumpy structure, with extended tori favoring parallel polarization while compact tori produce orthogonal polarization position angles. In the case of polar scattering regions, fragmentation increases the net polarization unless the cloud filling factor is small. A complete set of AGN models constructed from the individual, fragmented regions is investigated. Our modeling shows that the introduction of fragmented dusty tori significantly alters the resulting net polarization of an AGN. Comparison of our models to polarization observations of large AGN samples greatly favors geometrically compact clumpy tori over extended ones.