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

TL;DR

This paper presents a new analytical technique to estimate the inner eccentricity in hierarchical triple systems with initially circular, coplanar orbits, validated through numerical simulations and comparisons with existing results.

Contribution

It introduces a perturbation-based method combining short period and secular effects to derive a simple formula for inner binary eccentricity.

Findings

The formula accurately predicts eccentricity in tested systems.

Numerical integrations confirm the theoretical predictions.

Comparison shows improvements over previous models.

Abstract

We develop a technique for estimating the inner eccentricity in hierarchical triple systems with well separated components. We investigate systems with initially circular and coplanar orbits and comparable masses. The technique is based on an expansion of the rate of change of the Runge-Lenz vector for calculating short period terms by using first order perturbation theory. The combination of the short period terms with terms arising from octupole level secular theory, results in the derivation of a rather simple formula for the eccentricity of the inner binary. The theoretical results are tested against numerical integrations of the full equations of motion. Comparison is also made with other results on the subject.