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

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 time scale τr ∝ M −1 0 e x 0 , 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 ≈ 10 M⊕ 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 time scales. 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 two compared to models without velocity evolution. In contrast, collisional damping dominates over dynamical friction and viscous stirring in models with small (80–800 m radius) initial bodies. Collisional damping decreases the time scale to runaway growth by factors of 4–10 relative to constant velocity calculations. Simulations with minimum mass solar nebulae, M0 ∼ 10 M⊕, and small eccentricities, e ≈ 10−3, reach runaway growth on time scales 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 0 , but are less sensitive to the initial eccentricity than constant velocity models. In both sets of models, the time scales to produce 1000+ km objects are comparable to estimated formation time scales for Neptune. Thus, Pluto-sized objects can form in the outer solar system in parallel with the condensation of the outermost large planets.