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تسجيل مستخدم جديدEccentricity evolution in hierarchical triple systems with eccentric outer binaries
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Nikolaos Georgakarakos
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We develop a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular, while the outer one is eccentric. We consider coplanar systems with well separated components and comparable masses. The derivation of short period terms is based on an expansion of the rate of change of the Runge-Lenz vector. Then, the short period terms are combined with secular terms, obtained by means of canonical perturbation theory. The validity of the theoretical equations is tested by numerical integrations of the full equations of motion.
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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.
In a previous paper, we developed a technique for estimating the inner eccentricity in coplanar hierarchical triple systems on initially circular orbits, with comparable masses and with well separated components, based on an expansion of the rate of
change of the Runge-Lenz vector. Now, the same technique is extended to non-coplanar orbits. However, it can only be applied to systems with ${I_{0}<39.23^{circ}}$ or ${I_{0}>140.77^{circ}}$, where ${I}$ is the inclination of the two orbits, because of complications arising from the so-called Kozai effect. The theoretical model is tested against results from numerical integrations of the full equations of motion.
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It is usually thought that viscous torque works to align a circumbinary disk with the binarys orbital plane. However, recent numerical simulations suggest that the disk may evolve to a configuration perpendicular to the binary orbit (polar alignment)
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