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S. J. Weidenschilling (Planetary Science Institute)
The Kuiper Belt appears to have an outer edge near 50 AU; the lack of detections beyond this distance implies that the surface density, mean size and/or albedo decreases abruptly. Conditions for accretion and collisional evolution vary only gradually with heliocentric distance, there is no obvious reason the solar nebula’s outer boundary should have been sharp. However, a steep gradient in surface density is a natural outcome of particle migration during planetesimal formation.
Nebular gas drag causes solid particles to spiral inward, with the peak radial velocity ~ 50 m/s, or ~ 1 AU century. Accreting bodies migrate inward while growing through the critical size range. The peak velocity is insensitive to heliocentric distance (or nebular surface density), but the growth time increases with distance. Particles starting farther from the Sun experience more orbital decay during their growth, steepening the surface density gradient of solids. Bodies having the highest radial velocity are too large to be stirred by turbulence, but too small to be affected by gravitational perturbations. They settle into a thin layer in the nebular midplane, and are swept up when they first encounter bodies large enough (~ 100 m) to resist orbital decay. Thus, solid material tends to pile up at the distance at which such bodies form.
I have modified my numerical coagulation/settling model to 2D, with radial transport as well as vertical settling. A low-mass nebula with gas surface density varying as R-1 to 90 AU produces a steep edge in the range 40-50 AU, with solids depleted beyond that distance. The location of the edge is more sensitive to the gradient of gas surface density than to nebular mass; an index steeper than R-3/2 puts the edge well inside Neptune's distance. The solar nebula probably was much larger in extent than the current size of the Kuiper Belt, but there is little prospect for an undiscovered belt at greater distance.
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Bulletin of the American Astronomical Society, 34, #3< br> © 2002. The American Astronomical Soceity.