Analytical Models for Secular Descents in Hierarchical Triple Systems

Three-body systems are prevalent in nature, from planetary to stellar to supermassive black hole scales. In a hierarchical triple system, oscillations of the inner orbit’s eccentricity and inclination can be induced on secular timescales. Over many cycles, the octupole-level terms in the secular equ...

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Bibliographic Details
Published in:The Astrophysical journal Vol. 974; no. 2; pp. 302 - 313
Main Authors: Weldon, Grant C., Naoz, Smadar, Hansen, Bradley M. S.
Format: Journal Article
Language:English
Published: Philadelphia The American Astronomical Society 01.10.2024
IOP Publishing
Subjects:
Approximation
Astronomical models
Binary stars
Black holes
Equations of motion
Exoplanet dynamics
Extrasolar planets
Gas giant planets
Hot Jupiters
Mathematical analysis
Mathematical models
Numerical models
Numerical simulations
Planetary dynamics
Planetary orbits
Roche limit
Stellar dynamics
Supermassive black holes
Systems analysis
Three-body problem
Tidal disruption
ISSN:0004-637X, 1538-4357
Online Access:Get full text
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Summary:Three-body systems are prevalent in nature, from planetary to stellar to supermassive black hole scales. In a hierarchical triple system, oscillations of the inner orbit’s eccentricity and inclination can be induced on secular timescales. Over many cycles, the octupole-level terms in the secular equations of motion can drive the system to extremely high eccentricities via the eccentric Kozai–Lidov (EKL) mechanism. The overall decrease in the inner orbit’s pericenter distance has potentially dramatic effects for realistic systems, such as tidal disruption events. We present an analytical approximation in the test-particle limit to describe individual stepwise increases in eccentricity of the inner orbit. A second approximation, also in the test-particle limit, is obtained by integrating the equations of motion and calibrating to numerical simulations to estimate the overall octupole-level time evolution of the eccentricity. The latter approach is then extended beyond the test particle to the general case. The three novel analytical approximations are compared to numerical solutions to show that the models accurately describe the form and timescale of the secular descent from large distances to a close-encounter distance (e.g., the Roche limit). By circumventing the need for numerical simulations to obtain the long-term behavior, these approximations can be used to readily estimate properties of close encounters and descent timescales for populations of systems. We demonstrate this by calculating rates of EKL-driven migration for Hot Jupiters in stellar binaries.
Bibliography:AAS55574
The Solar System, Exoplanets, and Astrobiology
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ISSN:0004-637X
1538-4357
DOI:10.3847/1538-4357/ad77a9