Eccentricity evolution in hierarchical triple systems with eccentric outer binaries

TL;DR

This paper presents a new analytical method to estimate the evolution of inner orbit eccentricity in hierarchical triple systems with eccentric outer binaries, validated by numerical simulations.

Contribution

It introduces a combined approach using short period and secular perturbation theories to accurately predict eccentricity evolution in specific triple systems.

Findings

The method accurately matches numerical simulations.

It effectively estimates eccentricity changes over time.

Applicable to coplanar, well-separated systems with comparable masses.

Abstract

We develop a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular, while the outer one is eccentric. We consider coplanar systems with well separated components and comparable masses. The derivation of short period terms is based on an expansion of the rate of change of the Runge-Lenz vector. Then, the short period terms are combined with secular terms, obtained by means of canonical perturbation theory. The validity of the theoretical equations is tested by numerical integrations of the full equations of motion.