Planetary rings seem to be a common appearance around large planets because every large planet in the solar system has them. They have, however, not yet definitively been detected around exoplanets. Because the formation of rings might be closely related to planetary formation, as well as the formation of moons, much could be learned from discovering rings around exoplanets. To aid in this search, we developed a radiative transfer model that includes all orders of scattering and polarization and can calculate the reflected and transmitted light for any planetary orbit and ring geometry. Previous studies have analyzed the effect that rings have on a transit as well as on the reflected light but those studies have not included the polarization of light. Using the developed model, the effect that rings have on the reflected flux, polarized flux, and the degree of polarization was characterized by varying the orbit orientation, ring orientation, ring size, the optical thickness of a ring, and the ring particle properties. Our study showed that rings introduce unique features in both the flux and degree of polarization curves. Especially the existence of ring-plane crossings, when the ring is illuminated from the side, causes distinct features in the light curves. Adding polarimetric capabilities to the next generation of telescopes could help with determining the presence of rings due to the different scattering behavior of the ring and planet.
The developed model allows for a fast and easy generation of accurate light curves which allowed for two additional studies to be done. These were a bit smaller in scope and the first involved fitting the transit of a planet with a potential ring. The result of the fit and subsequent analysis is that there is likely no ring. However, because the model was not initially designed to deal with the close proximity of the planet to its star no definitive conclusion can be drawn. In the second study, the reflected flux and polarization of the transiting planet J1407b, which is suspected to have a large circumplanetary disk, were computed to assess the detectability. These generated light curves and values were then compared to unpublished observations made with the SPHERE/ZIMPOL instrument that detected no signal. The computed flux and degree of polarization lie well below the detection limit and are thus in agreement with the SPHERE/ZIMPOL observations.