Title: A general polarimetric model for transiting and non-transiting ringed exoplanets

Abstract: We explore the potential of polarimetry as a tool for detecting and characterizing exorings. For that purpose, we have improved the publicly available photometric code Pryngles by adding the results of radiative transfer calculations that fully include polarization and scattering by irregularly shaped particles. With this improved code, we compute the total and polarized fluxes and the degree of polarization of a ringed gas giant along its orbit. We vary key model parameters such as the orbit inclination, ring size and orientation, particle albedo and optical thickness, and demonstrate the versatility of our code by predicting the total and polarized fluxes of the "puffed-up" planet HIP41378f assuming this planet has an opaque dusty ring. We find that spatially unresolved dusty rings can significantly modify the flux and polarization signals of the light that is reflected. Rings are expected to have a low polarization signal and will generally decrease the degree of polarization as the ring casts a shadow on the planet and/or blocks part of the light the planet reflects. During ring-plane crossings, when the thin ring is illuminated edge-on, a ringed exoplanet's flux and degree of polarization are close to those of a ring-less planet and generally appear as sharp changes in the flux and polarization curves. Ringed planets in edge-on orbits tend to be difficult to distinguish from ring-less planets in reflected flux and degree of polarization. We show that if HIP41378f is surrounded by a ring, its reflected flux (compared to the star) will be of the order of $10^{-9}$, and the ring would decrease the degree of polarization in a detectable way. The improved version of the photometric code Pryngles that we present here shows that dusty rings may produce distinct polarimetric features in light curves across a wide range of orbital configurations, orientations and ring optical properties.