Accretion in the Early Kuiper Belt. I. Coagulation and Velocity Evolution

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Abstract
We describe planetesimal accretion calculations in the Kuiper Belt. Our evolution code simulates planetesimal growth in a single annulus and includes velocity evolution but not fragmentation. Test results match analytic solutions and duplicate previous simulations at 1 AU. In the Kuiper Belt, simulations without velocity evolution produce a single runaway body with a radius ri 1000 km on a timscale τr ∝ Me, where M0 is the initial mass in the annulus, e0 is the initial eccentricity of the planetesimals, and x ≈ 1–2. Runaway growth occurs in 100 Myr for M0 ≈ 10ME and e0 ≈ 10-3 in a 6 AU annulus centered at 35 AU. This mass is close to the amount of dusty material expected in a minimum-mass solar nebula extrapolated into the Kuiper Belt. Simulations with velocity evolution produce runaway growth on a wide range of timescales. Dynamical friction and viscous stirring increase particle velocities in models with large (8 km radius) initial bodies. This velocity increase delays runaway growth by a factor of 2 compared with models without velocity evolution. In contrast, collisional damping dominates over dynamical friction and viscous stirring in models with small (80–800 m) initial bodies. Collisional damping decreases the timescale to runaway growth by factors of 4–10 relative to constant-velocity calculations. Simulations with minimum-mass solar nebulae, M0 ~ 10ME, and small eccentricities, e ≈ 10-3, reach runaway growth on timescales of 20–40 Myr with 80 m initial bodies, 50–100 Myr with 800 m bodies, and 75–250 Myr for 8 km initial bodies. These growth times vary linearly with the mass of the annulus, τr ∝ M, but are less sensitive to the initial eccentricity than constant-velocity models. In both sets of models, the timescales to produce 1000+ km objects are comparable to estimated formation timescales for Neptune. Thus, Pluto-sized objects can form in the outer solar system in parallel with the condensation of the outermost large planets.
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