Application of chaos indicators in the study of dynamics of S-type extrasolar planets in stellar binaries

Abstract

The orbits of two individual planets in two known binary star systems, γCephei and HD 196885 are numerically integrated using various numerical techniques to assess the chaotic or quasi-periodic nature of the dynamical system considered. The Hill stability (HS) function which measures the orbital perturbation of a planet around the primary star due to the secondary star is calculated for each system. The maximum Lyapunov exponent (MLE) time series are generated to measure the divergence/convergence rate of stable manifolds, which are used to differentiate between chaotic and non-chaotic orbits. Then, we calculate dynamical Mean Exponential Growth factor of Nearby Orbits (MEGNO) maps from solving the variational equations along with the equations of motion. These maps allow us to accurately differentiate between stable and unstable dynamical systems. The results obtained from the analysis of HS, MLE, and MEGNO maps are analysed for their dynamical variations and resemblance. The HS test for the planets shows stability and quasi-periodicity for at least ten million years. The MLE and the MEGNO maps have also indicated the local quasi-periodicity and global stability in a relatively short integration period. The orbital stability of the systems is tested using each indicator for various values of planet inclinations (i_{pl} \le 25^\circ) and binary eccentricities. The reliability of HS criterion is also discussed based on its stability results compared with the MLE and MEGNO maps.

12 pages, 12 figures, 2 tables; accepted for publication in MNRAS

References in corpus (4)

• Properties of planets in binary systems. The role of binary separation
• Two Suns in The Sky: Stellar Multiplicity in Exoplanet Systems
• A comparison of different indicators of chaos based on the deviation vectors. Application to symplectic mappings
• The long-term stability of extrasolar system HD 37124. Numerical study of resonance effects

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• Extremely Inclined Orbit of S-type Planet $\gamma$ Cep Ab Induced by Eccentric Kozai-Lidov Mechanism
• Exomoons in Systems with a Strong Perturber: Applications to $\alpha$ Cen AB
• The PAIRS project: a global formation model for planets in binaries. II. Gravitational perturbation effects from secondary stars
• Breaking the Mass Inclination Degeneracy of Radial Velocity Measurements via Monitoring von Zeipel-Lidov-Kozai Cycles: Implications in the HD 41004 System
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