2017AJ....154..236W

The Kepler mission has released over 4496 planetary candidates, among which 3483 planets have been confirmed as of 2017 April. 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 plenty of planet pairs could have first been captured into mean-motion resonances (MMRs) in planetary formation. Subsequently, these planets depart from exact resonant locations to be near-MMR configurations. Through type I migration, two low-mass planets have a tendency to be trapped in first-order MMRs (2:1 or 3:2 MMRs); however, two scenarios of mass accretion of planets and potential outward migration play important roles 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 a 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.