Transits of Planets with Small Intervals in Circumbinary Systems
  Transit times around single stars can be described well by a linear ephemeris. However, transit times in circumbinary systems are influenced both by the gravitational perturbations and the orbital phase variations of the central binary star. Adopting a coplanar analog of Kepler-16 as an example, we find that circumbinary planets can transit the same star more than once during a single planetary orbit, a phenomenon we call "tight transits". In certain geometric, the projected orbital velocity of the planet and the secondary star can approach zero and change sign, resulting in very long transits and/or 2-3 transits during a single binary orbit. Whether tight transits are possible for a particular system depends primarily on the binary mass ratio and the orbital architecture of both the binary and the planet. We derive a time-dependent criterion to judge when tight transits are possible for any circumbinary system. These results are verified with full dynamical integrations that also reveal other tight transit characteristics, i.e., the transit durations and the intervals between tight transits. For the seven currently known circumbinary systems, we estimate these critical parameters both analytically and numerically. Due to the mutual inclination between the planet and the binary, tight transits can only occur across the less massive star B in Kepler-16, -34, -35, and -47 (for both planets). The long-term average frequency of tight transits (compared to typical transits) for Kepler-16, -34, and -35 are estimated to be several percent. Using full numerical integrations, the next tight transit for each system is predicted and the soonest example appears to be Kepler-47b and -47c, which are likely to have tight transits before 2025. These unique and valuable events often deserve special observational scrutiny. 
Hui-Gen Liu, Ying Wang, Hui Zhang and Ji-Lin Zhou
astro-ph.EP