Repelling Planet Pairs by Ping-pong Scattering

The Kepler mission reveals a peculiar trough-peak feature in the orbital spacing of close-in planets near mean-motion resonances: a deficit and an excess that are, respectively, a couple of percent interior to and wide of the resonances. This feature has received two main classes of explanations: one involving eccentricity damping and the other scattering with small bodies. Here, we point out a few issues with the damping scenario and study the scattering scenario in more detail. We elucidate why scattering small bodies tends to repel two planets. As the small bodies random-walk in energy and angular momentum space, they tend to absorb fractionally more energy than angular momentum. This, which we call “ping-pong repulsion,” transports angular momentum from the inner to the outer planet and pushes the two planets apart. Such a process, even if ubiquitous, leaves identifiable marks only near first-order resonances: diverging pairs jump across the resonance quickly and produce the mean-motion resonance asymmetry. To explain the observed positions of the trough-peaks, a total scattering mass of order a few percent of the planet masses is required. Moreover, if this mass is dominated by a handful of Mercury-sized bodies, one can also explain the planet eccentricities as inferred from transit-time variations. Last, we suggest how these conditions may have naturally arisen during the late stages of planet formation.