Dynamics of the Trans-Neptune Region: Apsidal Waves in the Kuiper Belt

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Abstract
The role of apsidal density waves propagating in a primordial trans-Neptune disk (i.e., Kuiper belt) is investigated. It is shown that Neptune launches apsidal waves at its secular resonance near 40 AU that propagate radially outward, deeper into the particle disk. The wavelength of apsidal waves is considerably longer than waves that might be launched at Lindblad resonances, because the pattern speed, gs, resulting from the apsis precesssion of Neptune is much slower than its mean motion, Ωs. If the early Kuiper belt had a sufficient surface density, σ, the disk's wave response to Neptune's secular perturbation would have spread the disturbing torque radially over a collective scale λ* ≈ r(2μd Ω/|r dg/dr|)1/2, where μd ≡ πσr2/(1 M⊙) and Ω(r) and g(r) are respectively the mean motion and precession frequency of the disk particles. This results in considerably smaller eccentricities at resonance than had the disk particles been treated as noninteracting test particles. Consequently, particles are less apt to be excited into planet-crossing orbits, implying that the erosion timescales reported by earlier test-particle simulations of the Kuiper belt may be underestimated. It is also shown that the torque the disk exerts upon the planet (due to its gravitational attraction for the disk's spiral wave pattern) damps the planet's eccentricity and further inhibits the planet's ability to erode the disk.