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 r(i) greater than or similar to 1000 km on a timescale tau(r) proportional to M(0)(-1)e(0)(x), where M(0) is the initial mass in the annulus, e(0) is the initial eccentricity of the planetesimals, and x approximate to 1-2. Runaway growth occurs in 100 Myr for M(0) approximate to 10M(E) and e(0) approximate to 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, M(0) similar to 10M(E), and small eccentricities, e approximate to 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, tau(r), proportional to M(0)(-1), 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.