On the dynamical evolution of hierarchical triple systems

• Main Author: Georgakarakos, Nikolaos
• Published: University of Edinburgh 2001
• Subjects: 519
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.651389

A hierarchical triple system consists of two bodies forming a binary system and a third body on a wider orbit. The evolution of the eccentricity of an initially circular inner binary of a hierarchical triple system with well separated components is examined. Systems with different mass ratios and orbital characteristics (e.g. inclination) are investigated and theoretical formulae are derived for each case. The derivation of these formulae is based on the expansion of the rate of change of the eccentric vector in terms of the orbital period ratio of the two binaries using first order perturbation theory. Some elements from secular theory are used wherever necessary. Special cases are also discussed (e.g. secular resonances). The validity of the results is tested by integrating the full equations of motion numerically and the agreement is satisfactory. The stability of hierarchical triple systems with initially circular and coplanar orbits and small initial period ratio is also examined. Mean motion resonances are found to play an important role in the dynamics of the system. Special reference to the 3 : 1 and 4 : 1 resonances is made and a theoretical criterion for the 3 : 1 resonance is developed. A more general stability criterion (applicable in principle to other resonances besides 3 : 1) is obtained through a canonical transformation of an averaged Hamiltonian, and comparison is made with other results on the subject.