# 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 non-test 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 quasi-periodic orbital evolution by studying the surfaces of sections. Furthermore, including general relativity, we showcase the long-term 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 Plata-CONICET-UNLP 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; THREE-BODY PROBLEM

### Citation Formats

```
Naoz, Smadar, Li, Gongjie, Zanardi, Macarena, De Elía, Gonzalo Carlos, and Di Sisto, Romina P., E-mail: snaoz@astro.ucla.edu.
```*The Eccentric Kozai–Lidov Mechanism for Outer Test Particle*. United States: N. p., 2017.
Web. doi:10.3847/1538-3881/AA6FB0.

```
Naoz, Smadar, Li, Gongjie, Zanardi, Macarena, De Elía, Gonzalo Carlos, & Di Sisto, Romina P., E-mail: snaoz@astro.ucla.edu.
```*The Eccentric Kozai–Lidov Mechanism for Outer Test Particle*. United States. doi:10.3847/1538-3881/AA6FB0.

```
Naoz, Smadar, Li, Gongjie, Zanardi, Macarena, De Elía, Gonzalo Carlos, and Di Sisto, Romina P., E-mail: snaoz@astro.ucla.edu. Sat .
"The Eccentric Kozai–Lidov Mechanism for Outer Test Particle". United States.
doi:10.3847/1538-3881/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., E-mail: 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 non-test 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 quasi-periodic orbital evolution by studying the surfaces of sections. Furthermore, including general relativity, we showcase the long-term evolution of individual debris disk particles under the influence of a far-away 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 = {10.3847/1538-3881/AA6FB0},

journal = {Astronomical Journal (Online)},

number = 1,

volume = 154,

place = {United States},

year = {Sat Jul 01 00:00:00 EDT 2017},

month = {Sat Jul 01 00:00:00 EDT 2017}

}