Planetary chaotic zone clearing: Destinations and timescales
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.
celestial mechanics, chaos, planetdisk interactions, planets and satellites: dynamical evolution and stability
Morrison, Sarah, and Renu Malhotra. "Planetary chaotic zone clearing: Destinations and timescales." The Astrophysical Journal 799, no. 1 (2015): 41.