Traditional formation scenarios fail to explain 4:3 mean motion resonances

TL;DR

This study systematically evaluates traditional dynamical formation scenarios for 4:3 mean motion resonances in multi-planet systems, finding none successfully reproduce observed systems, thus challenging existing migration-based theories.

Contribution

The paper provides a comprehensive analysis showing that standard formation scenarios fail to produce observed 4:3 resonant systems, highlighting the need for alternative explanations.

Findings

Traditional scenarios do not form enough 4:3 resonant systems

Migration and scattering models are insufficient for 4:3 resonance formation

Results contrast with successful formation of 2:1 and 3:2 resonances

Abstract

At least two multi-planetary systems in a 4:3 mean motion resonance have been found by radial velocity surveys. These planets are gas giants and the systems are only stable when protected by a resonance. Additionally the Kepler mission has detected at least 4 strong candidate planetary systems with a period ratio close to 4:3. This paper investigates traditional dynamical scenarios for the formation of these systems. We systematically study migration scenarios with both N-body and hydro-dynamic simulations. We investigate scenarios involving the in-situ formation of two planets in resonance. We look at the results from finely tuned planet-planet scattering simulations with gas disk damping. Finally, we investigate a formation scenario involving isolation-mass embryos. Although the combined planet-planet scattering and damping scenario seems promising, none of the above scenarios is successful in forming enough systems in 4:3 resonance with planetary masses similar to the observed ones. This is a negative result but it has important implications for planet formation. Previous studies were successful in forming 2:1 and 3:2 resonances. This is generally believed to be evidence of planet migration. We highlight the main differences between those studies and our failure in forming a 4:3 resonance. We also speculate on more exotic and complicated ideas. These results will guide future investigators toward exploring the above scenarios and alternative mechanisms in a more general framework.