Repelling Planet pairs by Ping-pong Scattering

TL;DR

This paper proposes that small-body scattering causes a 'ping-pong' repulsion effect that explains the orbital spacing features near resonances in close-in planetary systems, supported by observed eccentricities.

Contribution

It introduces the 'ping-pong repulsion' mechanism driven by small-body scattering as an explanation for the orbital spacing features near mean-motion resonances.

Findings

Small-body scattering can push planets apart near resonances.

A few percent of planet mass in small bodies explains the observed features.

The mechanism accounts for observed eccentricities and resonance asymmetries.

Abstract

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 a couple percent to the narrow, respectively wide, of the resonances. This feature has received two main classes of explanations, one involving eccentricity damping, 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 MMR 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. Lastly, we suggest how these conditions may have naturally arisen during the late stages of planet formation.