Extremely Inclined Orbit of the S-type Planet γ Cep Ab Induced by the Eccentric Kozai–Lidov Mechanism

Abstract

Abstract γ Cep Ab is a typical S-type planet, which occupies a nearly perpendicular planetary orbit relative to the binary. Here, we use a Markov Chain Monte Carlo sampler to conduct a full N-body fitting and derive self-consistent orbital solutions for this hierarchical system. We then employ the eccentric Kozai–Lidov (EKL) mechanism to explain the extremely inclined orbit of the S-type planet γ Cep Ab. The EKL mechanism plays an essential part in our exploration of the significant oscillations of the mutual inclination i mut between the planet and the secondary star. We perform a qualitative analysis and use extensive numerical integrations to investigate the flip conditions and timescales of γ Cep Ab’s orbit. When the planetary mass is 15 M Jup, the planet can reach i mut ∼ 113° given the critical initial conditions of i mut < 60° and e 1 < 0.7. The timescale for the first orbital flip decreases with the increase of the perturbation Hamiltonian. The flipping orbits of γ Cep Ab are confirmed to have a large possibility of remaining 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 ≤ 0.1, where the most intense excitation of i mut occurs when a 1/a 2 = 0.1 and e 2 ∼ 0.8, and the variation in planetary mass mainly affects the flip possibility where e 1 ≤ 0.3.