On the Collisional Environment, Accretion Time Scales, and Architecture of the Massive, Primordial Kuiper Belt.

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Abstract
Our previous collisional modeling has suggested that the mass of the primordial Kuiper Disk between 30 and 50 AU was probably of order 10 to 50Msun. We explore the consequences of a massive, primordial Kuiper Disk using a collision rate model that assumes the dominant growth mechanism in the 35-50 AU region was pairwise accretion. We find that the growth of QB1-class objects from seeds only kilometers in diameter required a very low eccentricity environment, with mean random eccentricities of order 1% or less. Duncan et al. [Al, 110, 333, (1995)] have shown that the presence of Neptune induces characteristic eccentricities throughout the 30-50 AU region of a few percent or greater. We therefore conclude that growth of objects in the 30 to 50 AU zone to at least this size must have occurred before Neptune reached a fraction of its final mass. Once Neptune grew sufficiently to induce eccentricities exceeding ≍1%, we find that the disk environment became highly erosive for objects with radii smaller than ̃20-30 kilometers, which likely created a flattening in the disk's population power law slope between radius scales of ≍30 to ≍100 km, depending on the density and strength of such objects. This erosive environment could have resulted in sufficient mass depletion to evolve the disk to its present, low-mass state, independent of dynamical losses (which surely also played an important role). During the period of rapid erosive mass loss, the disk probably exhibited optical depths of 10-4 to 10-5 - (reminiscent of β Pictoris), for a time scale of ̃108 to ̃109 years. As a result of the evolution of the disk inside 50 AU, we suggest that (i) the present-day Solar System' s surface mass density edge near 30 AU is actually only the inner edge of a surface mass density trough, and (ii) that the surface mass density of solids may rise back beyond ̃50 AU, where the giant planets have never induced erosive high eccentricities. Indeed, the growth of objects in the region beyond 50 AU may be continuing to the present; the exploration of this region is encouraged.

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