The Kuiper Belt is a population of icy bodies beyond the orbit of Neptune. The complex orbital structure of the Kuiper Belt, including several categories of objects inside and outside of resonances with Neptune, emerged as a result of Neptune's migration into an outer planetesimal disk. An outstanding problem with the existing migration models is that they invariably predict excessively large resonant populations, while observations show that the non-resonant orbits are in fact common (e.g., the main belt population is 2–4 times larger than Plutinos in the 3:2 resonance). Here we show that this problem can be resolved if it is assumed that Neptune's migration was grainy, as expected from scattering encounters of Neptune with massive planetesimals. The grainy migration acts to destabilize resonant bodies with large libration amplitudes, a fraction of which ends up on stable non-resonant orbits. Thus, the non-resonant-to-resonant ratio obtained with the grainy migration is higher, up to ~10 times higher for the range of parameters investigated here, than in a model with smooth migration. In addition, the grainy migration leads to a narrower distribution of the libration amplitudes in the 3:2 resonance. The best fit to observations is obtained when it is assumed that the outer planetesimal disk below 30 au contained 1000–4000 Plutos. We estimate that the combined mass of Pluto-class objects in the original disk represented 10%–40% of the estimated disk mass ( ). This constraint can be used to better understand the accretion processes in the outer solar system.
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