Exploring the Orbital Landscape of Perturbing Planets in Single Planet Systems via TTVs

The orbital periods of unseen perturbing planets inferred via transit timing variations (TTVs) detected in single planet systems are notoriously multi-modal. We present an approach to break this orbital period degeneracy for a perturbing planet using TTV data alone. Using TTVFast for planet-planet N-body simulations, we show how one can decompose a planet-planet TTV signal into several periodic components, and then can use this to down-select the allowed modes to a subset, even a unique solution. There are hundreds of single-planet systems in Kepler data that show unexplained yet significant periodic TTVs. Using this periodic decomposition method, one can then aim to investigate these hundreds of single planet Kepler TTVs in order to statistically predict whether the TTVs are induced by an unseen perturbing planet or by another astrophysical source (ie. a moon or stellar activity). Additionally, we present our finding that a perturbing planet will never induce a TTV with an observed dominant period less than half its own orbital period. This “exoplanet edge” is the manifestation of an observational alias of the true TTV period. The presence of an anomalous dominant TTV period, in a two-planet system, that doesn’t fall on the exoplanet edge would demonstrate that there exists additional mass in the system, besides the two known exoplanets. We investigate several two-planet systems, in Kepler data, that don’t lie on the exoplanet edge, and discuss several possible explanations for additional mass in the system.