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 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.