Nbody simulations are used to examine the consequences of Neptune ’ s outward migration into the Kuiper Belt , with the simulated endstates being compared rigorously and quantitatively to the observations .
These simulations confirm the findings of ( 11 ) , 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 the 11:6 , 13:7 , 13:6 , 9:4 , 7:3 , 12:5 , 8:3 , 3:1 , 7:2 , and the 4:1 .
The more distant of these resonances , such as the 9:4 , 7:3 , 5:2 , and the 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 so–called 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 ^ { \circ } .

In order to rigorously compare the model endstate 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 : ( i . ) the observed 3:2 and 2:1 resonant populations are both depleted by a factor of \sim 20 relative to model expectations ; this depletion is likely due to unmodeled effects , possibly perturbations by other large planetesimals , ( ii . ) the size distribution of those KBOs inhabiting the 3:2 resonance is significantly shallower than the Main Belt ’ s size distribution , ( iii . ) the total number of KBOs having radii R > 50 km and orbiting interior to Neptune ’ s 2:1 resonance is N \sim 1.7 \times 10 ^ { 5 } ; these bodies have a total mass of M \sim 0.08 ( \rho / \mbox { 1 gm / cm$ { } ^ { 3 } $ } ) ( p / 0.04 ) ^ { -3 / 2 } M _ { \oplus } assuming they have a material density \rho 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 also 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 .