# Circumbinary planets: migration, trapping in mean-motion resonances, and ejection

**Authors:** Emmanuel Gianuzzi, Cristian A. Giuppone, Nicolás Cuello  
**arXiv:** [2211.08520](https://arxiv.org/abs/2211.08520)  
**Date:** 2022-11-15  
**Summary page:** https://www.summarizepaper.com/en/paper/2211.08520v1/

## Key points

- Most planetary systems around binary stars are located at approximately three semi-major axes from the barycentre of their system, which is close to low-order mean-motion resonances (MMRs).
- The formation mechanism of these circumbinary planets is not yet fully understood.
- In situ formation is challenging due to the strong interaction with the binary.
- Interactions between these planets and the surrounding protoplanetary disc cause them to migrate at velocities dependent on the nature of the disc and mass of exoplanet.
- Researchers used direct n-body simulations approach to model a large variety of parameters at much lower cost than hydrodynamical simulations.
- Using an ensemble learning method for classification, they identified capture probability for different N/1 MMRs, where 4/1 was found to be most prone to capturing exoplanets with a 37% probability followed by MMR 5/1 with $\sim$23% probability.
- The eccentricity of the binary was found to be the most important parameter in determining MMR capture followed by mass ratio and initial eccentricity of planet.
- Higher binary eccentricity led to higher value predominant capture MMRs.
- Rint = 4 was mainly obtained for simulations with eB = {0.01, 0.03, 0.05}, while each remaining Rint had only one principal binary eccentricity associated with it.
- The study provides insights into how planets migrate within circumbinary discs and can help us understand where and for how long circumbinary planets can survive around stellar binaries.
- Researchers suggest assuming recipes for planetary accretion and disc dissipation timescale in future models as this could be important in determining outcomes in runaway regimes for large planets (>20M⊕).

## Summary

The discovery of planetary systems around binary stars has revealed that most of these systems are located at approximately three semi-major axes from the barycentre of their system, which is curiously close to low-order mean-motion resonances (MMRs). However, the formation mechanism of these circumbinary planets is not yet fully understood. In situ formation is extremely challenging due to the strong interaction with the binary. One possible explanation is that after their formation, interactions between these planets and the surrounding protoplanetary disc cause them to migrate at velocities dependent on the nature of the disc and the mass of the exoplanet. To better understand this migration process, researchers have used direct n-body simulations approach to model a large variety of parameters at much lower cost than hydrodynamical simulations. The goal was to identify the main parameters responsible for ejection of planets at different resonances with the inner binary. The team performed 4200 n-body simulations with Stokes-like forces and analyzed their evolution and outcome as a function of each system's properties. Using an ensemble learning method for classification, they identified capture probability for different N/1 MMRs, where 4/1 was found to be most prone to capturing exoplanets with a 37% probability followed by MMR 5/1 with $\sim$23% probability. The eccentricity of the binary was found to be the most important parameter in determining MMR capture followed by mass ratio and initial eccentricity of planet. Further analysis showed that higher binary eccentricity led to higher value predominant capture MMRs. Additionally, Rint = 4 was mainly obtained for simulations with eB = {0.01, 0.03, 0.05}, while each remaining Rint had only one principal binary eccentricity associated with it. The study provides insights into how planets migrate within circumbinary discs and can help us understand where and for how long circumbinary planets can survive around stellar binaries. To further improve understanding in this area, researchers suggest assuming recipes for planetary accretion and disc dissipation timescale in future models as this could be important in determining outcomes in runaway regimes for large planets (> 20 M⊕).