Planetary chaotic zone clearing: destinations and timescales

Sarah Morrison; Renu Malhotra

doi:10.1088/0004-637X/799/1/41

paper

Planetary chaotic zone clearing: destinations and timescales

arXiv:1411.1378 · doi:10.1088/0004-637X/799/1/41

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 $1 0^{- 9}$ to $1 0^{- 1.5}$ , 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 $R_{p} \geq 0.001 R_{H}$ where $R_{H}$ is the planet's Hill radius, we find that most chaotic zone particles collide with the planet for $μ ≲ 1 0^{- 5}$ ; particle scattering to large distances is significant only for higher mass planets. For fixed ratio $R_{p} / R_{H}$ , the particle clearing timescale, $T_{c l}$ , has a broken power-law dependence on $μ$ . A shallower power-law, $T_{c l} \sim μ^{- 1/3}$ , prevails at small $μ$ where particles are cleared primarily by collisions with the planet; a steeper power law, $T_{c l} \sim μ^{- 3/2}$ , prevails at larger $μ$ where scattering dominates the particle loss. In the limit of vanishing planet radius, we find $T_{c l} \approx 0.024 μ^{- \frac{3}{2}}$ . 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, $Δ a_{c l, in t} ≃ 1.2 μ^{0.28} a_{p}$ ; the outer boundary is better described by $Δ a_{c l, e x t} ≃ 1.7 μ^{0.31} a_{p}$ , where $a_{p}$ is the planet-star separation.

20 pages, 7 figures; accepted for publication in ApJ

Planetary chaotic zone clearing: destinations and timescales

Abstract

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