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&#39;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.