Extremely Inclined Orbit of S-type Planet $\gamma$ Cep Ab Induced by Eccentric Kozai-Lidov Mechanism

TL;DR

This study investigates the highly inclined orbit of the S-type planet $ ext{γ}$ Cep Ab using orbital fitting and the Eccentric Kozai-Lidov mechanism, revealing conditions for orbit flipping and stability in hierarchical systems.

Contribution

It demonstrates how the EKL mechanism explains the extreme inclination of $ ext{γ}$ Cep Ab and extends its application to general S-type planetary systems with specific orbital configurations.

Findings

EKL mechanism causes significant inclination oscillations and orbit flips.

Stable highly inclined orbits are possible under certain initial conditions.

The flip timescale decreases with increased perturbation Hamiltonian.

Abstract

$\gamma$ Cep Ab is a typical S-type planet, which occupies a nearly perpendicular planetary orbit relative to the binary. Here we use the Markov Chain Monte Carlo (MCMC) sampler to conduct full N-body fitting and derive self-consistent orbital solutions for this hierarchical system. Then we employ the Eccentric Kozai-Lidov (EKL) mechanism to explain the extremely inclined orbit of S-type planet $\gamma$ Cep Ab. The EKL mechanism plays an essential role in exploring significant oscillations of the mutual inclination $i_{\mathrm{mut}}$ between the planet and the secondary star. We perform qualitative analysis and extensive numerical integrations to investigate the flip conditions and timescales of $\gamma$ Cep Ab's orbit. When the planetary mass is 15 $M_{\mathrm{Jup}}$, the planet can reach $i_{\mathrm{mut}} \sim$ 113$^{\circ}$ with the critical initial conditions of $i_{\mathrm{mut}} < 60^{\circ}$ and $e_1<0.7$. The timescale for the first orbital flip decreases with the increase of the perturbation Hamiltonian. Flipping orbits of $\gamma$ Cep Ab are confirmed to have a large possibility to retain stable based on surfaces of section and the secular stability criterion. Furthermore, we extend the application of EKL to general S-type planetary systems with $a_1/a_2\leq0.1$, where the most intense excitation of $i_{\mathrm{mut}}$ occurs when $a_1/a_2=0.1$ and $e_2 \sim 0.8$, and the variation of planetary mass mainly affect the flip possibility where $e_1\leq 0.3$.