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

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.Comment: 12 pages, 6 figures, accepted for publication in A

The scattering outcomes of Kepler circumbinary planets: planet mass ratio

Recent studies reveal that the free eccentricities of Kepler-34b and Kepler-413b are much larger than their forced eccentricities, implying that the scattering events may take place in their formation. The observed orbital configuration of Kepler-34b cannot be well reproduced in disk-driven migration models, whereas a two-planet scattering scenario can play a significant role of shaping the planetary configuration. These studies indicate that circumbinary planets discovered by Kepler may have experienced scattering process. In this work, we extensively investigate the scattering outcomes of circumbinary planets focusing on the effects of planet mass ratio. We find that the planetary mass ratio and the the initial relative locations of planets act as two important parameters which affect the eccentricity distribution of the surviving planets. As an application of our model, we discuss the observed orbital configurations of Kepler-34b and Kepler-413b. We first adopt the results from the disk-driven models as the initial conditions, then simulate the scattering process occurred in the late evolution stage of circumbinary planets. We show that the present orbital configurations of Kepler-34b and Kepler-413b can be well reproduced when considering two unequal-mass planet ejection model. Our work further suggests that some of the currently discovered circumbinary single-planet systems may be the survivals of original multiple-planet systems. The disk-driven migration and the scattering events occurring in the late stage both play an irreplaceable role in sculpting the final systems.Comment: 18 pages, 9 figures, accepted for publication in A