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, NC ∝ r for radii ∼< 0.3–3 km and NC ∝ r 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 their intrinsic tensile strength, S0; Pluto formation requires S0 ∼> 300 erg g. The timescale to produce Pluto-sized objects, τP , is roughly proportional to M 0 and e0, and is less sensitive to other input parameters. Our models yield τP ≈ 30–40 Myr for planetesimals with e0 = 10 in a Minimum Mass Solar Nebula. The production of several ‘Plutos’ and ∼ 10 50 km radius Kuiper Belt objects 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.