High inclination orbits in the secular quadrupolar three-body problem

TL;DR

This paper explores high inclination orbits in the secular quadrupolar three-body problem, revealing new stable equilibria and providing an analytical framework for understanding their behavior in both restricted and non-restricted scenarios.

Contribution

It introduces a novel perspective by analyzing the outer body in the restricted problem and develops a simple vectorial formalism to describe high inclination equilibria.

Findings

High inclination equilibria exist in the restricted problem.

Stable high inclination orbits are linked to observed circumbinary systems.

The analytical framework aids in understanding the evolution of these orbits.

Abstract

The Lidov-Kozai mechanism allows a body to periodically exchange its eccentricity with inclination. It was first discussed in the framework of the quadrupolar secular restricted three-body problem, where the massless particle is the inner body, and later extended to the quadrupolar secular nonrestricted three body problem. In this paper, we propose a different point of view on the problem by looking first at the restricted problem where the massless particle is the outer body. In this situation, equilibria at high mutual inclination appear, which correspond to the population of stable particles that Verrier & Evans (2008,2009) find in stable, high inclination circumbinary orbits around one of the components of the quadruple star HD 98800. We provide a simple analytical framework using a vectorial formalism for these situations. We also look at the evolution of these high inclination equilibria in the non restricted case.