Journal
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Volume 449, Issue 4, Pages 4221-4245Publisher
OXFORD UNIV PRESS
DOI: 10.1093/mnras/stv452
Keywords
gravitation; celestialmechanics; planet-star interactions; stars: kinematics and dynamics
Categories
Funding
- Netherlands Research Council NWO [639.073.803, 614.061.608, 612.071.305]
- Netherlands Research School for Astronomy (NOVA)
- ISF [1829]
- European FP-7 CIG programme 'GRAND' [333644]
- BSF [2012384]
- Asher foundation
- Division Of Astronomical Sciences
- Direct For Mathematical & Physical Scien [847477] Funding Source: National Science Foundation
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We study the secular gravitational dynamics of quadruple systems consisting of a hierarchical triple system orbited by a fourth body. These systems can be decomposed into three binary systems with increasing semimajor axes, binaries A, B and C. The Hamiltonian of the system is expanded in ratios of the three binary separations, and orbit averaged. Subsequently, we numerically solve the equations of motion. We study highly hierarchical systems that are well described by the lowest order terms in the Hamiltonian. We find that the qualitative behaviour is determined by the ratio R-0 of the initial Kozai-Lidov (KL) time-scales of the binary pairs AB and BC. If R-0 << 1, binaries AB remain coplanar if this is initially the case, and KL eccentricity oscillations in binary B are efficiently quenched. If R-0 >> 1, binaries AB become inclined, even if initially coplanar. However, there are no induced KL eccentricity oscillations in binary A. Lastly, if R-0 similar to 1, complex KL eccentricity oscillations can occur in binary A that are coupled with the KL eccentricity oscillations in B. Even if binaries A and B are initially coplanar, the induced inclination can result in very high eccentricity oscillations in binary A. These extreme eccentricities could have significant implications for strong interactions such as tidal interactions, gravitational wave dissipation, and collisions and mergers of stars and compact objects. As an example, we apply our results to a planet+moon system orbiting a central star, which in turn is orbited by a distant and inclined stellar companion or planet, and to observed stellar quadruples.
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