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Near 3:2 and 2:1 mean motion resonances formation in the systems observed by Kepler

The Kepler mission has released ~4229 transiting planet candidates. There are approximately 222 candidate systems with three planets. Among them, the period ratios of planet pairs near 1.5 and 2.0 reveal that two peaks exist for which the proportions of the candidate systems are ~7.0% and 18.0%, respectively. In this work, we study the formation of mean motion resonance (MMR) systems, particularly for the planetary configurations near 3:2 and 2:1 MMRs, and we concentrate on the interplay between the resonant configuration and the combination of stellar accretion rate, stellar magnetic field, speed of migration and additional planets. We perform more than 1000 runs by assuming a system with a solar-like star and three surrounding planets. From the statistical results, we find that under the formation scenario, the proportions near 1.5 and 2.0 can reach 14.5% and 26.0%, respectively. In addition, $\dot M=0.1\times 10^{-8} ~M_\odot ~{\rm yr^{-1}}$ is propitious toward the formation of 3:2 resonance, whereas $\dot M=2\times 10^{-8} ~M_\odot ~{\rm yr^{-1}}$ contributes to the formation of 2:1 resonance. The speed-reduction factor of type I migration $f_1\geq 0.3$ facilitates 3:2 MMRs, whereas $f_1\geq 0.1$ facilitates 2:1 MMRs. If additional planets are present in orbits within the innermost or beyond the outermost planet in a three-planet system, 3:2:1 MMRs can be formed, but the original systems trapped in 4:2:1 MMRs are not affected by the supposed planets. In summary, we conclude that this formation scenario will provide a likely explanation for Kepler candidates involved in 2:1 and 3:2 MMRs.