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

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.