Evolution of Planetary Chaotic Zones in Planetesimal Disks

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 $T_{\mathrm{c}\mathrm{l}}$ 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 $\propto {\mu }^{-6\mathrm{/}7}$ and $\propto {\mu }^{-2}$ have been revealed in the dependence $T_{\mathrm{c}\mathrm{l}}(\mu )$. 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.