A dynamical stability study of Kepler Circumbinary Planetary systems with one planet

TL;DR

This study uses numerical simulations to analyze the long-term stability of six Kepler circumbinary planetary systems with one planet, providing insights into their formation and evolution.

Contribution

It offers a comprehensive stability analysis of Kepler's single-planet circumbinary systems using numerical experiments, including long-term integrations and stability mapping.

Findings

Long-term stability confirmed for nominal solutions

Identified critical semimajor axes for planetary orbits

Mapped stability regions in eccentricity-pericentre space

Abstract

To date, 17 circumbinary planets have been discovered. In this paper, we focus our attention on the stability of the Kepler circumbinary planetary systems with only one planet, i.e. Kepler-16, Kepler-34, Kepler-35, Kepler-38, Kepler-64 and Kepler-413. In addition to their intrinsic interest, the study of such systems is an opportunity to test our understanding of planetary system formation and evolution around binaries. The investigation is done by means of numerical simulations. We perform numerical integrations of the full equations of motion of each system with the aim of checking the stability of the planetary orbit. The investigation of the stability of the above systems consists of three numerical experiments. In the first one we perform a long term (1Gyr) numerical integration of the nominal solution of the six Kepler systems under investigation. In the second experiment, we look for the critical semimajor axis of the six planetary orbits, and finally, in the third experiment, we construct two dimensional stability maps on the eccentricity-pericentre distance plane. Additionally, using numerical integrations of the nominal solutions we checked if this solutions were close to the exact resonance.