2013MNRAS.432.1196M

A fraction of multiple planet candidate systems discovered from transits by the Kepler mission contain pairs of planet candidates that are in orbital resonance or are spaced slightly too far apart to be in resonance. We focus here on the four-planet system, KOI-730, that has planet periods satisfying the ratios 8:6:4:3. By numerically integrating four planets assumed to initially be in a resonant configuration in proximity to an initially exterior cold planetesimal disc, we find that of the order of a Mars mass of planet-orbit-crossing planetesimals is sufficient to pull this system out of resonance. Approximately one Earth mass of planet-orbit-crossing planetesimals increases the interplanetary spacings sufficiently to resemble the multiple planet candidate Kepler systems that lie just outside of resonance. This suggests that the closely spaced multiple planet Kepler systems, host only low-mass debris discs or their debris discs have been extremely stable. We find that the planetary inclinations increase as a function of the mass in planetesimals that have crossed the orbits of the planets. If systems are left at zero inclination and in resonant chains after depletion of the gas disc, then we would expect a correlation between distance to resonance and mutual planetary inclinations. This may make it possible to differentiate between dynamical mechanisms that account for the fraction of multiple planet systems just outside of resonance.