Near Mean-motion Resonances in the Systems Observed by Kepler: Affected by Mass Accretion and Type I Migration

TL;DR

This paper investigates how mass accretion and Type I migration influence the formation of near mean-motion resonances in planetary systems observed by Kepler, explaining the observed period ratio distributions and resonance chains.

Contribution

It introduces a formation scenario incorporating mass accretion and outward migration to explain the observed near MMRs and resonance chains in Kepler planetary systems.

Findings

Mass accretion enables planets to cross 2:1 MMRs and enter 3:2 MMRs.

Outward migration increases the likelihood of planets being trapped in 3:2 MMRs.

Simulation results reproduce the observed period ratio peaks near 1.5 and 2.0.

Abstract

The Kepler mission has released over 4496 planetary candidates, among which 3483 planets have been confirmed as of April 2017. The statistical results of the planets show that there are two peaks around 1.5 and 2.0 in the distribution of orbital period ratios. The observations indicate that a plenty of planet pairs could have firstly been captured into mean motion resonances (MMRs) in planetary formation. Subsequently, these planets depart from exact resonant locations to be near MMRs configurations. Through type I migration, two low-mass planets have a tendency to be trapped into first-order MMRs (2:1 or 3:2 MMRs), however two scenarios of mass accretion of planets and potential outward migration play an important role in reshaping their final orbital configurations. Under the scenario of mass accretion, the planet pairs can cross 2:1 MMRs and then enter into 3:2 MMRs, especially for the inner pairs. With such formation scenario, the possibility that two planets are locked into 3:2 MMRs can increase if they are formed in a flat disk. Moreover, the outward migration can make planets have a high likelihood to be trapped into 3:2 MMRs. We perform additional runs to investigate the mass relationship for those planets in three-planet systems, and we show that two peaks near 1.5 and 2.0 for the period ratios of two planets can be easily reproduced through our formation scenario. We further show that the systems in chain resonances (e.g., 4:2:1, 3:2:1, 6:3:2 and 9:6:4 MMRs), have been observed in our simulations. This mechanism can be applicable to understand the formation of systems of Kepler-48, Kepler-53, Kepler-100, Kepler-192, Kepler-297, Kepler-399, and Kepler-450.