Transit Detectability of Ring Systems Around Extrasolar Giant Planets

We investigate whether rings around extrasolar planets could be detected from those planets' transit lightcurves. To this end we develop a basic theoretical framework for calculating and interpreting the lightcurves of ringed planet transits based on the existing framework used for stellar occultations, a technique which has been effective for discovering and probing ring systems in the solar system. We find that the detectability of large, Saturn-like ring systems is largest during ingress and egress, and that reasonable photometric precisions of $\sim 1-3 \times 10^{-4}$ with 15-minute time resolution should be sufficient to discover such ring systems. For some ring particle sizes, diffraction around individual particles leads to a detectable level of forward-scattering that can be used to measure modal ring particle diameters. An initial census of large ring systems can be carried out using high-precision follow-up observations of detected transits and by the upcoming NASA \emph{Kepler} mission. The distribution of ring systems as a function of stellar age and as a function of planetary semimajor axis will provide empirical evidence to help constrain how rings form and how long rings last.