期刊
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
卷 452, 期 4, 页码 3610-3619出版社
OXFORD UNIV PRESS
DOI: 10.1093/mnras/stv1552
关键词
celestial mechanics; planets and satellites: dynamical evolution and stability; binaries: close
资金
- National Science Foundation under NSF AST Award [1313252]
- Division Of Astronomical Sciences
- Direct For Mathematical & Physical Scien [1313252] Funding Source: National Science Foundation
Kozai-Lidov (KL) oscillations in hierarchical triple systems have found application to many astrophysical contexts, including planet formation, Type Ia supernovae, and supermassive black hole dynamics. The period of these oscillations is known at the order-of-magnitude level, but dependences on the initial mutual inclination or inner eccentricity are not typically included. In this work I calculate the period of KL oscillations (t(KL)) exactly in the test particle limit at quadrupole order (TPQ). I explore the parameter space of all hierarchical triples at TPQ and show that except for triples on the boundary between libration and rotation, the period of KL oscillations does not vary by more than a factor of a few. The exact period may be approximated to better than 2 per cent for triples with mutual inclinations between 60 degrees and 120 degrees and initial eccentricities less than similar to 0.3. In addition, I derive an analytic expression for the period of octupole-order oscillations due to the 'eccentric KL mechanism' (EKM). I show that the time-scale for EKM oscillations is proportional to epsilon(-1/2)(oct) , where epsilon(oct) measures the strength of octupole perturbations relative to quadrupole perturbations.
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