Circumbinary planets II - when transits come and go

Circumbinary planets are generally more likely to transit than equivalent single-star planets, but practically the geometry and orbital dynamics of circumbinary planets make the chance of observing a transit inherently time-dependent. In this follow-up paper to Martin & Triaud (2015), the time-dependence is probed deeper by analytically calculating when and for how long the binary and planet orbits overlap, allowing for transits to occur. The derived equations are applied to the known transiting circumbinary planets found by Kepler to predict when future transits will occur, and whether they will be observable by upcoming space telescopes TESS, CHEOPS and PLATO. The majority of these planets spend less than 50% of their time in a transiting configuration, some less than 20%. From this it is calculated that the known Kepler eclipsing binaries likely host an additional ~ 17 - 30 circumbinary planets that are similar to the ten published discoveries, and they will ultimately transit some day, potentially during the TESS and PLATO surveys.