Eccentricity generation in hierarchical triple systems: the planetary regime

TL;DR

This paper tests previously developed formulas for estimating eccentricity in hierarchical triple systems with planetary mass ratios through numerical integration, and discusses the planetary system HD217107.

Contribution

It validates earlier eccentricity estimation formulas specifically for systems with planetary mass ratios using numerical simulations.

Findings

Formulas are accurate for planetary mass ratios.

Numerical results support previous theoretical estimates.

Discussion of HD217107's planetary companions.

Abstract

In previous papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. We considered systems with well separated components and different initial setups (e.g. coplanar and non-coplanar orbits). However, the systems we examined had comparable masses. In the present paper, the validity of some of the formulae derived previously is tested by numerically integrating the full equations of motion for systems with smaller mass ratios (from ${10^{-3} \hspace{0.2cm} \mbox{to} \hspace{0.2cm} 10^{3}}$, i.e. systems with Jupiter-sized bodies). There is also discussion about HD217107 and its planetary companions.