The effect of eccentricity on three-body orbital stability criteria and its importance for triple star systems

Abstract

Previous investigations of prograde three-body hierarchical systems with eccentric orbits do not give consistent results. The problem is re-examined for mass configurations particularly important in triple star systems. It is found that, for systems with binaries moving on circular orbits, the regions of stability expand slightly in size for large mass ratios and contract slightly for small mass ratios as the eccentricity of the outer mass is increased. Comparison of the systems with their retrograde counterparts indicates that the retrograde are the more stable systems. Increasing the eccentricity of the binary can reduce stability significantly for small outer-body eccentricities and increase it for large values, but makes little difference for intermediate eccentricities. The analytical c2H criterion mirrors the same general behaviour in the prograde cases, but is not found to be a good quantitative indicator of orbital stability when eccentric orbits are present, unlike the situation found by Donnison & Mikulskis when all the orbits are circular. Actual triple star systems with visual binary components (visual triples) are compared with the critical condition for stability for both prograde and retrograde configurations, and are found to be within the stable region regardless of whether they are prograde or retrograde. It is also found that retrograde configurations tend to be the more stable when the binary eccentricity is small, while for systems with both large binary and outer-body eccentricities the prograde configurations are the more stable. Triple systems with spectroscopic binaries (spectroscopic-visual triples) are shown to lie well within the limits of stability for prograde and retrograde configurations.