Stochastic effects in the planet migration and orbital distribution of the Kuiper Belt

Abstract

Assuming the Jovian planets experienced smooth orbital migrations, Malhotra successfully explained some important features of the Kuiper Belt by the mechanism of resonance capture. However, the migration should really be stochastic. In this paper we numerically simulate numerous orbital evolutions of test particles under such stochastic planet migrations. The main results are as follows. Given the proper parameters, the concentration of objects in the 3 : 2 resonance is distinct, while very few objects enter the 2 : 1 resonance, and consequently, the orbital distribution of Kuiper Belt objects matches the observational data very well. The stochastic effects excite the orbital eccentricities and inclinations of objects in the non-resonant regions. The introduction of stochastic effects also gives possible explanations of the mass depletion, and of the sources of the classical and scattered Kuiper Belt objects.