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Keywords:

  • methods: analytical;
  • methods: numerical;
  • planets and satellites: formation

ABSTRACT

At least two multi-planetary systems in a 4:3 mean motion resonance have been found by radial velocity surveys.1 These planets are gas giants and the systems are only stable when protected by a resonance. Additionally the Kepler mission has detected at least four 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 hydrodynamic 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 disc 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 towards exploring the above scenarios and alternative mechanisms in a more general framework.