The Kuiper Belt as a Resonant Cavity

The orbital inclinations of a bounded, self-gravitating particle population subject to secular perturbations from an inclined planet are studied. The particle disk is shown to have discrete modes and pattern speeds in which the wave behavior is very pronounced compared with the nonwave behavior. The response is in the form of a standing wave pattern produced by wave reflection at the finite outer edge of the disk. In the absence of dissipation, the perpendicular torque between disk and perturber vanishes, with equal incoming and outgoing angular momentum fluxes carried by the wave trains. This resonant cavity theory is applied to Neptune perturbations of the primordial Kuiper belt. If the nodal precession rate of Neptune was near one of the diskʹs mode frequencies, very high inclinations could be produced for this population. There are a number of mechanisms in the early solar system that could have tuned the system to pass through one or more resonant states.