Accretion in the Early Kuiper Belt. II. Fragmentation

We describe new planetesimal accretion calculations in the Kuiper Belt that include fragmentation and velocity evolution. All models produce two power-law cumulative size distributions, N_C ∝ r^-2.5 for radii ≲0.3–3 km and N_C ∝ r^-3 for radii ≳1–3 km. The power-law indices are nearly independent of the initial mass in the annulus, M₀; the initial eccentricity of the planetesimal swarm, e₀; and the initial size distribution of the planetesimal swarm. The transition between the two power laws moves to larger radii as e₀ increases. The maximum size of objects depends on the intrinsic tensile strength, S₀; Pluto formation requires S₀ ≳ 300 ergs g^-1. The timescale to produce Pluto-sized objects, τ_P, is roughly proportional to M and e₀ and is less sensitive to other input parameters. Our models yield τ_P ≈ 30–40 Myr for planetesimals with e₀ = 10^-3 in a minimum mass solar nebula. The production of several "Plutos" and ∼10⁵ Kuiper Belt objects with 50 km radius leaves most of the initial mass in 0.1–10 km radius objects that can be collisionally depleted over the age of the solar system. These results resolve the puzzle of large Kuiper Belt objects in a small-mass Kuiper Belt.