Neptune's Migration into a Stirred-Up Kuiper Belt: A Detailed Comparison of Simulations to Observations

Abstract

We use N-body simulations to examine the consequences of Neptune's outward migration into the Kuiper Belt, with the simulated end states being compared rigorously and quantitatively to the observations. These simulations confirm the 2003 findings of Chiang and coworkers, who showed that Neptune's migration into a previously stirred-up Kuiper Belt can account for the Kuiper Belt objects (KBOs) known to librate at Neptune's 5 : 2 resonance. We also find that capture is possible at many other weak, high-order mean-motion resonances, such as 11 : 6, 13 : 7, 13 : 6, 9 : 4, 7 : 3, 12 : 5, 8 : 3, 3 : 1, 7 : 2, and 4 : 1. The more distant of these resonances, such as the 9 : 4, 7 : 3, 5 : 2, and 3 : 1, can also capture particles in stable, eccentric orbits beyond 50 AU, in the region of phase space conventionally known as the "Scattered Disk." Indeed, 90% of the simulated particles that persist over the age of the solar system in the Scattered-Disk zone never had a close encounter with Neptune but instead were promoted into these eccentric orbits by Neptune's resonances during the migration epoch. This indicates that the observed Scattered Disk might not be so scattered. This model also produced only a handful of Centaurs, all of which originated at Neptune's mean-motion resonances in the Kuiper Belt. However, a noteworthy deficiency of the migration model considered here is that it does not account for the observed abundance of Main Belt KBOs having inclinations higher than 15°. In order to rigorously compare the model end state with the observed Kuiper Belt in a manner that accounts for telescopic selection effects, Monte Carlo methods are used to assign sizes and magnitudes to the simulated particles that survive over the age of the solar system. If the model considered here is indeed representative of the outer solar system's early history, then the following conclusions are obtained: (1) The observed 3 : 2 and 2 : 1 resonant populations are both depleted by a factor of ∼20 relative to model expectations; this depletion is likely due to unmodeled effects, possibly perturbations by other large planetesimals. (2) The size distribution of those KBOs inhabiting the 3 : 2 resonance is significantly shallower than the Main Belt's size distribution. (3) The total number of KBOs having radii R > 50 km and orbiting interior to Neptune's 2 : 1 resonance is N ∼ 1.7 × 105; these bodies have a total mass of M ∼ 0.08(ρ/1 g cm-3)(p/0.04)-3/2 M⊕, assuming they have a material density ρ and an albedo p. We also report estimates of the abundances and masses of the Belt's various subpopulations (e.g., the resonant KBOs, the Main Belt, and the so-called Scattered Disk) and provide upper limits on the abundance of Centaurs and Neptune's Trojans, as well as upper limits on the sizes and abundances of hypothetical KBOs that might inhabit the a > 50 AU zone.