Planetary Chaotic Zone Clearing

Planetary chaotic zone clearing: destinations and timescales
Authors:

Morrison et al

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 Rp≥0.001RH 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, Tcl, has a broken power-law dependence on μ. A shallower power-law, Tcl∼μ−1/3, prevails at small μ where particles are cleared primarily by collisions with the planet; a steeper power law, Tcl∼μ−3/2, prevails at larger μ where scattering dominates the particle loss. In the limit of vanishing planet radius, we find Tcl≈0.024μ−32. 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, Δacl,int≃1.2μ0.28ap; the outer boundary is better described by Δacl,ext≃1.7μ0.31ap, where ap is the planet-star separation.