Near mean motion resonance of terrestrial planet pair induced by giant planet: application to Kepler-68 system

In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMR) induced by the perturbation of a distant gas giant for the Kepler-68 system, by conducting thousands of numerical simulations. The results show that the formation of terrestrial planets is relevant to the speed of type I migration, the mass of planets, and the existence of giant planet. The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the system. The inner planet pair can be trapped in 5:3 or 7:4 MMRs if the giant planet revolves the central star with an eccentric orbit, which is similar to the observed configuration of Kepler-68. Moreover, we find that the eccentricity of the middle planet can be excited to roughly 0.2 if the giant planet is more massive than 5 MJ; otherwise, the terrestrial planets are inclined to remain in near-circular orbits. Our study may provide a likely formation scenario for the planetary systems that harbour several terrestrial planets near MMRs inside and one gas giant exterior to them.