Terrestrial planet formation under migration: systems near the 4:2:1 mean motion resonance

In this work, we investigate extensively the formation of near 4:2:1 mean motion resonance (MMR) configurations by performing two sets of N-body simulations. We model the eccentricity damping, gas drag, type I and type II planetary migration of planetesimals, planetary embryos and giant planets in the first set. For simulations of giant planets with type II migration, massive terrestrial planets with a mass up to several Earth masses are likely produced in these systems. We further show that by shepherding and/or scattering mechanisms through a Jovian planet's type II migration, the terrestrial and giant planets in the systems can be evolved into near 4:2:1 MMRs. Moreover, the models are applicable to the formation of the Kepler-238 and 302 systems. In the second set of simulations, we study 4:2:1 MMR formation in terrestrial planetary systems, where the planets undergo type I migration and eccentricity damping. By considering type I migration, ∼17.1 per cent of the simulations indicate that terrestrial planets are evolved into 4:2:1 MMRs. However, this probability should depend on the initial conditions of the planets. Hence, we conclude that both type I and type II migration can play a crucial role in close-in terrestrial planet formation.