Planetary rings seem to be a common feature 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 reflected light, but those studies have not included the polarization of light. Using the developed model, the effect that rings have on reflected flux, polarized flux, and degree of polarization was characterized by varying orbit orientation, ring orientation, ring size, optical thickness, and ring particle properties.

Our study showed that rings introduce unique features in both flux and degree of polarization curves. In particular, ring-plane crossings, when the ring is illuminated from the side, produce distinct features in the light curves. Adding polarimetric capabilities to the next generation of telescopes could help determine the presence of rings due to the different scattering behavior of the ring and planet.

The model also allows fast generation of light curves, enabling two additional studies. The first involved fitting the transit of a planet with a potential ring. The result suggests that there is likely no ring; however, because the model was not designed to handle 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 object J1407b, which is suspected to host a large circumplanetary disk, were computed to assess detectability. These results were compared to unpublished SPHERE/ZIMPOL observations that detected no signal. The computed flux and degree of polarization lie well below the detection limit and are consistent with these observations.