ExoMOD I. A Forward Model for the Orbital Architecture of Kepler Multi-Planet Systems

Abstract: Transit observations only detect planets with favorable, near edge-on orientation of orbits as seen by a distant observer, which leaves much freedom for various interpretations in terms of the underlying planetary system architecture. Here we forward model transit observations of the Kepler telescope to characterize the orbital properties of close-in planetary systems. We make sensible choices about the underlying distributions of planet radii, masses and orbital periods, parameterize the orbital excitation with the Angular Momentum Deficit (AMD), and adopt an accurate method to account for transit detection. The fits to Kepler's DR25 data are executed with {\tt MultiNest}. We find that the orbital period distributions of Kepler singles and multis are statistically different from each other -- possibly a consequence of Kepler's observational baseline. The observed gap complexity distribution is reproduced when planets in high multiplicity systems ($m \geq 5$) are assigned ideally correlated period ratios. The high-multiplicity systems probably retained a memory of their formation conditions. The gap complexity metric also helps to constrain the AMD distribution. We find that systems with positive radius monotonicities typically harbor smaller planets, as expected if the radius monotonicity is influenced by non-detections. A FGK dwarf in the Kepler field should host $\simeq 2.4 \pm 0.2$ planets on average with radii $0.5 < R_{\rm pl}/R_\oplus < 7$ and orbital periods $3<P_{\rm orb}<300$ d. For a detected planetary system, there is roughly a 50\% chance that Kepler transit observations missed at least one inner or intermediate-period planet.