A new planet in the Kepler-159 system from transit timing variations

The Kepler Space Telescope has discovered thousands of planets via the transit method. The transit timing variations of these planets allows us not only to infer the existence of other planets, transiting or not, but to characterize a number of parameters of the system. Using the transit timing variations of the planets Kepler-159b and 159c, the transit simulator TTVFast, and the Bayesian Inference tool MultiNest, we predict a new non-transiting planet, Kepler-159d, in a resonant 2:1 orbit with Kepler-159c. This configuration is dynamically stable on at least 10 Myr time scales, though we note that other less stable, higher order resonances could also produce similar TTVs during the three-year window Kepler was in operation.