Planetary chaotic zone clearing: destinations and timescales

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 $\mu$ 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 $R_p\ge 0.001R_H$ where $R_H$ is the planet's Hill radius, we find that most chaotic zone particles collide with the planet for $\mu \lesssim 10^{-5}$; 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 $\mu$. A shallower power-law, $T_{cl}\sim {\mu }^{-1/3}$, prevails at small $\mu$ where particles are cleared primarily by collisions with the planet; a steeper power law, $T_{cl}\sim {\mu }^{-3/2}$, prevails at larger $\mu$ where scattering dominates the particle loss. In the limit of vanishing planet radius, we find $T_{cl}\approx 0.024{\mu }^{-\frac{3}{2}}$. 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, $\Delta a_{cl,int}\simeq 1.2{\mu }^{0.28}{a}_p$; the outer boundary is better described by $\Delta a_{cl,ext}\simeq 1.7{\mu }^{0.31}{a}_p$, where $a_p$ is the planet-star separation.

20 pages, 7 figures; accepted for publication in ApJ

References in corpus (2)

• Direct Imaging of Multiple Planets Orbiting the Star HR 8799
• Probing for Exoplanets Hiding in Dusty Debris Disks: Disk Imaging, Characterization, and Exploration with HST/STIS Multi-Roll Coronagraphy

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