Metrics for Optimizing Searches for Tidally Decaying Exoplanets

Tidal interactions between short-period exoplanets and their host stars drive orbital decay and have likely led to engulfment of planets by their stars. Precise transit timing surveys, with baselines now spanning decades for some planets, are directly detecting orbital decay for a handful of planets, with corroboration for planetary engulfment coming from independent lines of evidence. More than that, recent observations have perhaps even caught the moment of engulfment for one unfortunate planet. These portentous signs bolster prospects for ongoing surveys, but optimizing such a survey requires considering the astrophysical parameters that give rise to robust timing constraints and large tidal decay rates, as well as how best to schedule observations conducted over many years. The large number of possible targets means it is not feasible to continually observe all planets that might exhibit detectable tidal decay. In this study, we explore astrophysical and observational properties for a short-period exoplanet system that can maximize the likelihood for observing tidally driven transit timing variations. We consider several fiducial observational strategies and real exoplanet systems reported to exhibit decay. We show that moderately frequent (a few transits per year) observations may suffice to detect tidal decay within just a few years. Tidally driven timing variations take time to grow to detectable levels, so we estimate how long that growth takes as a function of timing uncertainties and tidal decay rate and provide thresholds for deciding that tidal decay has been detected.