### 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

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

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