Improved equations for eccentricity generation in hierarchical triple systems

Author: Georgakarakos, Nikolaos

Source: Monthly Notices of the Royal Astronomical Society, Volume 392, Number 3, January 2009 , pp. 1253-1263(11)

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Abstract:

In a series of papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. However, for certain combinations of the masses and the orbital elements, the secular part of the solution failed. In this paper, we derive a new solution for the secular part of the inner eccentricity, which corrects the previous weakness. The derivation applies to hierarchical triple systems with coplanar and initially circular orbits. The new formula is tested numerically by integrating the full equations of motion for systems with mass ratios from 10⁻³ to 10³. We also present more numerical results for short-term eccentricity evolution, in order to get a better picture of the behaviour of the inner eccentricity.

Keywords: celestial mechanics; binaries: close; binaries: general

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1365-2966.2008.14143.x

Publication date: 2009-01-01