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J. Hahn (Lunar and Planetary Institute), R. Malhotra (University of Arizona)
N-body simulations have shown that the orbits of the giant planets would migrate away from each other as they cleared the natal planetesimal disk. The evidence for orbital migration is in the Kuiper Belt; had Neptune's orbit expanded outwards by 8 AU, its sweeping 3:2 resonance would have captured numerous Kuiper Belt Objects (KBOs) and pumped eccentricities up to up to the observed value of e~0.3.
Early simulations of this phenomenon effected planet-migration by applying a smooth torque to the planets' orbits (Malhotra 1995). Resonance capture is extremely efficient at depositing nearly all KBOs into eccentric, low-inclination, resonant orbits. However these models are not in full agreement with observations showing that about a third of all known KBOs reside in the Classical Disk which lies between Neptune's 2:1 and 3:2.
However it should be recognized that planet-migration is driven by the stochastic scatterings of planetesimals at the planets. To mimic this, we add some random `jitter' to the planet-migration torque. This causes Neptune's orbit to dance to-and-fro as it expands. When sufficient jitter is applied, the resonance capture efficiency is reduced to ~50 which allows some KBOs to slip through the advancing 2:1. These bodies enter the Classical disk with eccentricities of e~0.1, which is comparable to the observed e. Jitter also increases the KBO inclinations.
We also suspect that the observed underabundance of KBOs at the 2:1 resonance (and beyond) is due to a radial gradient in the KBO size-distribution, namely, that smaller KBOs formed at greater distances from the Sun.
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