Abstract

Context. From stars to active galactic nuclei, many astrophysical systems are surrounded by an equatorial distribution of dusty material that is, in a number of cases, spatially unresolved even with cutting edge facilities. Aims. In this paper, we investigate if and how one can determine the unresolved and heterogeneous morphology of dust distribution around a central bright source using time-resolved polarimetric observations. Methods. We used polarized radiative transfer simulations to study a sample of circumnuclear dusty morphologies. We explored a grid of geometrically variable models that are uniform, fragmented, and density stratified in the near-infrared, optical, and ultraviolet bands, and we present their distinctive time-dependent polarimetric signatures. Results. As expected, varying the structure of the obscuring equatorial disk has a deep impact on the inclination-dependent flux, polarization degree and angle, and time lags we observe. We find that stratified media are distinguishable by time-resolved polarimetric observations, and that the expected polarization is much higher in the infrared band than in the ultraviolet. However, because of the physical scales imposed by dust sublimation, the average time lags of months to years between the total and polarized fluxes are important; these time lags lengthens the observational campaigns necessary to break more sophisticated, and therefore also more degenerated, models. In the ultraviolet band, time lags are slightly shorter than in the infrared or optical bands, and, coupled to lower diluting starlight fluxes, time-resolved polarimetry in the UV appears more promising for future campaigns. Conclusions. Equatorial dusty disks differ in terms of inclination-dependent photometric, polarimetric, and timing observables, but only the coupling of these different markers can lead to inclination-independent constraints on the unresolved structures. Even though it is complex and time consuming, polarized reverberation mapping in the ultraviolet-blue band is probably the best technique to rely on in this field.