Near Mean Motion Resonance of Terrestrial Planet Pair Induced by Giant Planet: Application to Kepler-68 System

TL;DR

This study uses numerical simulations to explore how a distant gas giant influences the formation and orbital resonances of inner terrestrial planets, with implications for the Kepler-68 system.

Contribution

It demonstrates how giant planet perturbations can lead to specific mean motion resonances and orbital configurations of terrestrial planets, providing a formation scenario for such systems.

Findings

Inner planets can be trapped in 5:3 or 7:4 MMRs due to giant planet eccentricity.

Giant planet mass influences the eccentricity of inner planets.

The formation scenario explains observed configurations like Kepler-68.

Abstract

In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) 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 $M_J$,otherwise the terrestrial planets are inclined to remain near-circular orbits. Our study may provide a likely formation scenario for the planetary systems that harbor several terrestrial planets near MMRs inside and one gas-giant exterior to them.