Evolution of Planetary Chaotic Zones in Planetesimal Disks

TL;DR

This study conducts extensive numerical experiments to determine the timescales for planetary chaotic zone clearing in planetesimal disks, revealing key diffusional components and comparing results with existing theories.

Contribution

It provides high-accuracy numerical determination of chaotic zone clearing timescales as functions of planet-star mass ratio, including diffusional components, and compares findings with analytical models.

Findings

Identified diffusional components in clearing timescales: ∝ μ^{-6/7} and ∝ μ^{-2}

Determined separate timescales for outer and inner chaotic zones

Compared numerical results with analytical theories based on resonance overlap

Abstract

Extensive numerical experiments on the long-term dynamics of planetesimal disks with planets in systems of single stars have been carried out. The planetary chaotic zone clearing timescales $T_\mathrm{cl}$ as a function of mass parameter $\mu$ (planet-star mass ratio) have been determined numerically with a high accuracy separately for the outer and inner parts of the chaotic zone. Diffusional components $\propto \mu^{-6/7}$ and $\propto \mu^{-2}$ have been revealed in the dependence $T_\mathrm{cl}(\mu)$. The results obtained are discussed and interpreted in light of existing analytical theories based on the mean motion resonance overlap criterion and in comparison with previous numerical approaches to the problem.