Disk-planets interactions and the diversity of period ratios in Kepler's multi-planetary systems

TL;DR

This paper explores how wake-planet interactions in protoplanetary disks can cause divergent migration, explaining the observed diversity in period ratios of Kepler's multi-planet systems, especially for planets beyond ten days.

Contribution

It introduces a new mechanism involving wake-planet interactions that can reverse convergent migration, accounting for the diversity of period ratios in Kepler's multi-planet systems.

Findings

Wake-planet interactions can significantly increase period ratios.

Divergent evolution is efficient when at least one planet opens a partial gap.

The mechanism explains the period ratio of Kepler-46b and c.

Abstract

The Kepler mission is dramatically increasing the number of planets known in multi-planetary systems. Many adjacent planets have orbital period ratios near resonant values, with a tendency to be larger than required for exact first-order mean-motion resonances. This intriguing feature has been shown to be a natural outcome of orbital circularization of resonant planetary pairs due to star-planet tidal interactions. However, this feature holds in multi-planetary systems with periods longer than ten days, for which tidal circularization is unlikely to provide efficient divergent evolution of the planets orbits. Gravitational interactions between planets and their parent protoplanetary disk may instead provide efficient divergent evolution. For a planet pair embedded in a disk, we show that interactions between a planet and the wake of its companion can reverse convergent migration, and significantly increase the period ratio from a near-resonant value. Divergent evolution due to wake-planet interactions is particularly efficient when at least one of the planets opens a partial gap around its orbit. This mechanism could help account for the diversity of period ratios in Kepler's multiple systems comprising super-Earth to sub-jovian planets with periods greater than about ten days. Diversity is also expected for planet pairs massive enough to merge their gap. The efficiency of wake-planet interactions is then much reduced, but convergent migration may stall with a variety of period ratios depending on the density structure in the common gap. This is illustrated for the Kepler-46 system, for which we reproduce the period ratio of Kepler-46b and c.