An island of linearly stable non-hierarchical unequal mass periodic three-body orbits — A harbinger of circumbinary exoplanets?

Abstract

We analyze all publicly available planar periodic three-body orbits in Newtonian gravity with zero angular momentum, which pass through a symmetrical collinear configuration. We find correlations between scale-invariant parameters, such as the ratio m3/m of the central and equal mass, the topological quantifier Lf of an orbit, the scale-invariant period T|E|3/2 , and the distribution of marginally linearly stable orbits. The elliptical (S) and marginal (M) linearly stable orbits are contained in a compact, non-zero measure domain with an apparently continuous boundary in the space spanned by the topological index Lf and the mass ratio m3/m. The distribution of S and M orbits predicts a sharp increase of both numbers of S and M orbits in this region as m3 is lowered below m/2. This indicates an island of stability of non-hierarchical three-body systems consisting of a light object (planet) orbiting two heavier ones (binary stars). We also find one-dimensional (sub)manifolds in the phase space of initial conditions that contain many of these linearly stable orbits. Orbits with increasingly longer periods populate/converge to these manifolds which suggests these manifolds are attractors.