An Orbit-flip Mechanism by Eccentric Lidov–Kozai Effect with Stellar Oblateness

Abstract

Orbit flips have been previously found under the eccentric Lidov–Kozai effect (ELK) in hierarchical three-body systems. Recently, we have found that, in certain conditions, the orbit can flip its orientation in a much different manner, where the stellar oblateness plays an important role. In this paper, orbit-flip behaviors with the ELK effect are investigated as the stellar oblateness varies within a wide range. This is of significance because recent works have shown that the oblateness of young stars has a widespread distribution and may have critical effects on sculpting the final orbital states of close-in planets. Our dynamical model includes the secular potential of the perturber to octupole order and the secular effects of the stellar oblateness. An alignment between the orbit plane of the outer perturber and the stellar bulge is assumed. Our findings mainly consist of two aspects. (i) A new type of orbit-flipping mechanism induced by a combination of the ELK and stellar oblateness effects, referred to as the ELK–J 2 effect, is discovered and confirmed. (ii) We demonstrate that, in the considered aligned configuration, the stellar oblateness suppresses orbit flips due to the ELK effect and produces new flips through the ELK–J 2 effect. Moreover, if the stellar oblateness perturbations are of the same order as the octupole perturbations of the outer perturber, the ELK-induced orbit flips are almost entirely suppressed, while the ELK–J 2 effect reaches its peak for the considered strength of the octupole perturbations. However, from a global view, stellar oblateness always reduces flipping orbits.