ExoMOD II. A Statistical Model of Transit Timing Variations in Kepler Multi-Planet Systems

Abstract: In Paper I (Nesvorný et al. 2026), we forward modeled transit observations of the Kepler telescope to characterize the orbital properties of close-in planetary systems. The new population model, ExoMOD, was calibrated on Kepler's DR25 data. Here we use ExoMOD to statistically predict Transit Timing Variations (TTVs) from gravitationally interacting planets in the close-in systems, and compare these predictions with TTVs actually detected in the Kepler data. We find that planet-planet interactions are not expected to produce significant {\it short-period} TTVs, $P_{\rm TTV}/P_{\rm orb}<10$, where $P_{\rm TTV}$ and $P_{\rm orb}$ are the TTV and orbital periods, often enough to explain the short-period TTV signals inferred from the Kepler data. Most measured short-period signals must therefore have a different origin. The statistics of {\it long-period} TTVs -- likely arising from the gravitational interaction between planets -- indicates that single transiting planets have TTV-inducing companions nearly as often as doubles, thus ruling out multiplicity distributions with a prevalence of intrinsic singles. The fraction of planets with measured long-period TTVs increases to $\simeq 15$-18\% for observed multiplicities $m \geq 3$, suggesting a change in the orbital architecture. High-multiplicity planetary systems have low gap complexities and probably retained a memory of their formation conditions. Ultimately, our work aims at developing a more informative feedback between observations and planet formation theories.