We describe analytical and numerical collisional evolution calculations for the size distribution of icy bodies in the Kuiper Belt. For a wide range of bulk properties, initial masses, and orbital parameters, our results yield power-law cumulative size distributions, NC ∝ r −q, with qL ≈ 3.5 for large bodies with radii, r � 10–100 km, and qs ≈ 2.5–3 for small bodies with radii, r � 0.1–1 km. The transition between the two power laws occurs at a break radius, rb ≈ 1–30 km. The break radius is more sensitive to the initial mass in the Kuiper Belt and the amount of stirring by Neptune than the bulk properties of individual Kuiper Belt objects (KBOs). Comparisons with observations indicate that most models can explain the observed sky surface density σ(m) of KBOs for red magnitudes R ≈ 22–27. For R � 22 and R � 28, the model σ(m) is sensitive to the amount of stirring by Neptune, suggesting that the size distribution of icy planets in the outer solar system provides independent constraints on the formation of Neptune. Subject headings: planetary systems – solar system: formation – stars: formation – circumstellar matter 1
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