Eccentricity generation in hierarchical triple systems with non-coplanar and initially circular orbits

TL;DR

This paper extends a method for estimating eccentricity in hierarchical triple systems to non-coplanar orbits, accounting for the Kozai effect, and validates it with numerical simulations.

Contribution

It generalizes an existing eccentricity estimation technique to non-coplanar orbits with specific inclination constraints, considering the Kozai effect.

Findings

Method successfully estimates eccentricity for certain non-coplanar configurations.

Theoretical predictions agree with numerical integration results.

Applicable to systems with initial inclinations below 39.23° or above 140.77°.

Abstract

In a previous paper, we developed a technique for estimating the inner eccentricity in coplanar hierarchical triple systems on initially circular orbits, with comparable masses and with well separated components, based on an expansion of the rate of change of the Runge-Lenz vector. Now, the same technique is extended to non-coplanar orbits. However, it can only be applied to systems with ${I_{0}<39.23^{\circ}}$ or ${I_{0}>140.77^{\circ}}$, where ${I}$ is the inclination of the two orbits, because of complications arising from the so-called 'Kozai effect'. The theoretical model is tested against results from numerical integrations of the full equations of motion.