# Terrestrial Planets Formation under Migration: the Systems near 4:2:1 Mean Motion Resonance

## TL;DR

This study uses N-body simulations to explore how planetary migration and damping processes can lead to the formation of terrestrial planets in near 4:2:1 mean motion resonances, relevant to observed exoplanet systems.

## Contribution

It demonstrates that both type I and type II planetary migration mechanisms can produce near 4:2:1 MMR configurations, with implications for Kepler systems and terrestrial planet formation.

## Key findings

- Massive terrestrial planets can form via type II migration.
- Near 4:2:1 MMRs can result from shepherding and scattering.
- Approximately 17.1% of simulations with type I migration produce 4:2:1 MMRs.

## Abstract

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