The Exoplanet Edge: Planets Do Not Induce Observable Transit Timing Variations with a Dominant Transit Timing Variation Period Faster than Half Their Orbital Period

Abstract Transit timing variations (TTVs) are observed for exoplanets at a range of amplitudes and periods, yielding an ostensibly degenerate forest of possible explanations. We offer some clarity in this forest, showing that systems with a distant perturbing planet preferentially show TTVs with a dominant period equal to either the perturbing planet’s period or half the perturbing planet’s period. We demonstrate that planet-induced TTVs are not expected with dominant TTV periods below this exoplanet edge (lower period limit) and that systems with TTVs that fall below this limit likely contain additional mass in the system. We present an explanation for both of these periods, showing that both aliasing of the conjunction-induced synodic period and the near 1:2 resonance superperiod and tidal effects induce TTVs at periods equal to either the perturber’s orbit or half-orbit. We provide three examples of known systems for which the recovered TTV period induced by a distant perturbing planet is equal to the perturber’s orbital period or half its orbital period. We then investigate Kepler two-planet systems with TTVs and identify 13 two-planet systems with TTVs below this TTV period lower limit, thus potentially uncovering the gravitational influence of new planets and/or moons. We conclude by discussing how the exoplanet edge effects can be used to predict the presence of distant companion planets in situations where TTVs are detected and where nearby companions can be ruled out by additional observations, such as radial velocity data.