The Eccentric Kozai–Lidov Mechanism for Outer Test Particle
Abstract
The secular approximation of the hierarchical three body systems has been proven to be very useful in addressing many astrophysical systems, from planets to stars to black holes. In such a system, two objects are on a tight orbit and the tertiary is on a much wider orbit. Here, we study the dynamics of a system by taking the tertiary mass to zero and solve the hierarchical three body system up to the octupole level of approximation. We find a rich dynamics that the outer orbit undergoes due to gravitational perturbations from the inner binary. The nominal result of the precession of the nodes is mostly limited for the lowest order of approximation; however, when the octupole level of approximation is introduced, the system becomes chaotic, as expected, and the tertiary oscillates below and above 90°, similarly to the nontest particle flip behavior. We provide the Hamiltonian of the system and investigate the dynamics of the system from the quadrupole to the octupole level of approximations. We also analyze the chaotic and quasiperiodic orbital evolution by studying the surfaces of sections. Furthermore, including general relativity, we showcase the longterm evolution of individual debris disk particles under the influence of amore »
 Authors:
 Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 (United States)
 Harvard Smithsonian Center for Astrophysics, Institute for Theory and Computation, 60 Garden Street, Cambridge, MA 02138 (United States)
 Instituto de Astrofísica de La Plata, CCT La PlataCONICETUNLP Paseo del Bosque S/N (1900), La Plata (Argentina)
 Publication Date:
 OSTI Identifier:
 22663486
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Astronomical Journal (Online); Journal Volume: 154; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; ASTEROIDS; ASTROPHYSICS; BLACK HOLES; CHAOS THEORY; DISTURBANCES; EVOLUTION; GENERAL RELATIVITY THEORY; HAMILTONIANS; MASS; OCTUPOLES; ORBITS; PERIODICITY; PLANETS; PRECESSION; QUADRUPOLES; STARS; TEST PARTICLES; THREEBODY PROBLEM
Citation Formats
Naoz, Smadar, Li, Gongjie, Zanardi, Macarena, De Elía, Gonzalo Carlos, and Di Sisto, Romina P., Email: snaoz@astro.ucla.edu. The Eccentric Kozai–Lidov Mechanism for Outer Test Particle. United States: N. p., 2017.
Web. doi:10.3847/15383881/AA6FB0.
Naoz, Smadar, Li, Gongjie, Zanardi, Macarena, De Elía, Gonzalo Carlos, & Di Sisto, Romina P., Email: snaoz@astro.ucla.edu. The Eccentric Kozai–Lidov Mechanism for Outer Test Particle. United States. doi:10.3847/15383881/AA6FB0.
Naoz, Smadar, Li, Gongjie, Zanardi, Macarena, De Elía, Gonzalo Carlos, and Di Sisto, Romina P., Email: snaoz@astro.ucla.edu. 2017.
"The Eccentric Kozai–Lidov Mechanism for Outer Test Particle". United States.
doi:10.3847/15383881/AA6FB0.
@article{osti_22663486,
title = {The Eccentric Kozai–Lidov Mechanism for Outer Test Particle},
author = {Naoz, Smadar and Li, Gongjie and Zanardi, Macarena and De Elía, Gonzalo Carlos and Di Sisto, Romina P., Email: snaoz@astro.ucla.edu},
abstractNote = {The secular approximation of the hierarchical three body systems has been proven to be very useful in addressing many astrophysical systems, from planets to stars to black holes. In such a system, two objects are on a tight orbit and the tertiary is on a much wider orbit. Here, we study the dynamics of a system by taking the tertiary mass to zero and solve the hierarchical three body system up to the octupole level of approximation. We find a rich dynamics that the outer orbit undergoes due to gravitational perturbations from the inner binary. The nominal result of the precession of the nodes is mostly limited for the lowest order of approximation; however, when the octupole level of approximation is introduced, the system becomes chaotic, as expected, and the tertiary oscillates below and above 90°, similarly to the nontest particle flip behavior. We provide the Hamiltonian of the system and investigate the dynamics of the system from the quadrupole to the octupole level of approximations. We also analyze the chaotic and quasiperiodic orbital evolution by studying the surfaces of sections. Furthermore, including general relativity, we showcase the longterm evolution of individual debris disk particles under the influence of a faraway interior eccentric planet. We show that this dynamics can naturally result in retrograde objects and a puffy disk after a long timescale evolution (a few Gyr) for initially aligned configuration.},
doi = {10.3847/15383881/AA6FB0},
journal = {Astronomical Journal (Online)},
number = 1,
volume = 154,
place = {United States},
year = 2017,
month = 7
}

The KozaiLidov mechanism can be applied to a vast variety of astrophysical systems involving hierarchical threebody systems. Here, we study the KozaiLidov mechanism systematically in the test particle limit at the octupole level of approximation. We investigate the chaotic and quasiperiodic orbital evolution by studying the surfaces of section and the Lyapunov exponents. We find that the resonances introduced by the octupole level of approximation cause orbits to flip from prograde to retrograde and back as well as cause significant eccentricity excitation, and chaotic behavior occurs when the mutual inclination between the inner and the outer binary is high. Wemore »

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STEADYSTATE PLANET MIGRATION BY THE KOZAILIDOV MECHANISM IN STELLAR BINARIES
We study the steadystate orbital distributions of giant planets migrating through the combination of the KozaiLidov (KL) mechanism due to a stellar companion and friction due to tides raised on the planet by the host star. We run a large set of Monte Carlo simulations that describe the secular evolution of a starplanetstar triple system including the effects from general relativistic precession, stellar and planetary spin evolution, and tides. Our simulations show that KL migration produces Hot Jupiters (HJs) with semimajor axes that are generally smaller than in the observations and they can only explain the observations if the followingmore »