### Abstract

We investigate the orbital evolution of particles in a planet's chaotic zone to determine their final destinations and their timescales of clearing. There are four possible final states of chaotic particles: collision with the planet, collision with the star, escape, or bounded but non-collision orbits. In our investigations, within the framework of the planar circular restricted three body problem for planet-star mass ratio μ in the range 10^{-9} to 10^{-1.5}, we find no particles hitting the star. The relative frequencies of escape and collision with the planet are not scale-free, as they depend upon the size of the planet. For planet radius R_{p} ≥ 0.001 R_{H} where R_{H} is the planet's Hill radius, we find that most chaotic zone particles collide with the planet for μ ≲ 10^{-5}; particle scattering to large distances is significant only for higher mass planets. For fixed ratio R_{p} /R_{H} , the particle clearing timescale, T _{cl}, has a broken power-law dependence on μ. A shallower power law, T _{cl} μ^{-1/3}, prevails at small μ where particles are cleared primarily by collisions with the planet; a steeper power law, T _{cl} μ^{-3/2}, prevails at larger μ where scattering dominates the particle loss. In the limit of vanishing planet radius, we find T _{cl} 0.024 μ^{-3/2}. The interior and exterior boundaries of the annular zone in which chaotic particles are cleared are increasingly asymmetric about the planet's orbit for larger planet masses; the inner boundary coincides well with the classical first order resonance overlap zone, Δa _{cl}, int ≃ 1.2 μ^{0.28} a_{p} ; the outer boundary is better described by Δa _{cl}, ext ≃ 1.7 μ^{0.31} a_{p} , where a_{p} is the planet-star separation.

Original language | English (US) |
---|---|

Article number | 41 |

Journal | Astrophysical Journal |

Volume | 799 |

Issue number | 1 |

DOIs | |

State | Published - Jan 20 2015 |

### Fingerprint

### Keywords

- celestial mechanics
- chaos
- planetdisk interactions
- planets and satellites: dynamical evolution and stability

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Astrophysical Journal*,

*799*(1), [41]. https://doi.org/10.1088/0004-637X/799/1/41

**Planetary chaotic zone clearing : Destinations and timescales.** / Morrison, Sarah; Malhotra, Renu.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 799, no. 1, 41. https://doi.org/10.1088/0004-637X/799/1/41

}

TY - JOUR

T1 - Planetary chaotic zone clearing

T2 - Destinations and timescales

AU - Morrison, Sarah

AU - Malhotra, Renu

PY - 2015/1/20

Y1 - 2015/1/20

N2 - We investigate the orbital evolution of particles in a planet's chaotic zone to determine their final destinations and their timescales of clearing. There are four possible final states of chaotic particles: collision with the planet, collision with the star, escape, or bounded but non-collision orbits. In our investigations, within the framework of the planar circular restricted three body problem for planet-star mass ratio μ in the range 10-9 to 10-1.5, we find no particles hitting the star. The relative frequencies of escape and collision with the planet are not scale-free, as they depend upon the size of the planet. For planet radius Rp ≥ 0.001 RH where RH is the planet's Hill radius, we find that most chaotic zone particles collide with the planet for μ ≲ 10-5; particle scattering to large distances is significant only for higher mass planets. For fixed ratio Rp /RH , the particle clearing timescale, T cl, has a broken power-law dependence on μ. A shallower power law, T cl μ-1/3, prevails at small μ where particles are cleared primarily by collisions with the planet; a steeper power law, T cl μ-3/2, prevails at larger μ where scattering dominates the particle loss. In the limit of vanishing planet radius, we find T cl 0.024 μ-3/2. The interior and exterior boundaries of the annular zone in which chaotic particles are cleared are increasingly asymmetric about the planet's orbit for larger planet masses; the inner boundary coincides well with the classical first order resonance overlap zone, Δa cl, int ≃ 1.2 μ0.28 ap ; the outer boundary is better described by Δa cl, ext ≃ 1.7 μ0.31 ap , where ap is the planet-star separation.

AB - We investigate the orbital evolution of particles in a planet's chaotic zone to determine their final destinations and their timescales of clearing. There are four possible final states of chaotic particles: collision with the planet, collision with the star, escape, or bounded but non-collision orbits. In our investigations, within the framework of the planar circular restricted three body problem for planet-star mass ratio μ in the range 10-9 to 10-1.5, we find no particles hitting the star. The relative frequencies of escape and collision with the planet are not scale-free, as they depend upon the size of the planet. For planet radius Rp ≥ 0.001 RH where RH is the planet's Hill radius, we find that most chaotic zone particles collide with the planet for μ ≲ 10-5; particle scattering to large distances is significant only for higher mass planets. For fixed ratio Rp /RH , the particle clearing timescale, T cl, has a broken power-law dependence on μ. A shallower power law, T cl μ-1/3, prevails at small μ where particles are cleared primarily by collisions with the planet; a steeper power law, T cl μ-3/2, prevails at larger μ where scattering dominates the particle loss. In the limit of vanishing planet radius, we find T cl 0.024 μ-3/2. The interior and exterior boundaries of the annular zone in which chaotic particles are cleared are increasingly asymmetric about the planet's orbit for larger planet masses; the inner boundary coincides well with the classical first order resonance overlap zone, Δa cl, int ≃ 1.2 μ0.28 ap ; the outer boundary is better described by Δa cl, ext ≃ 1.7 μ0.31 ap , where ap is the planet-star separation.

KW - celestial mechanics

KW - chaos

KW - planetdisk interactions

KW - planets and satellites: dynamical evolution and stability

UR - http://www.scopus.com/inward/record.url?scp=84921491633&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921491633&partnerID=8YFLogxK

U2 - 10.1088/0004-637X/799/1/41

DO - 10.1088/0004-637X/799/1/41

M3 - Article

AN - SCOPUS:84921491633

VL - 799

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1

M1 - 41

ER -