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

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 r i ∼ > 1000 km on a time scale τ r ∝ M −1 0 e x 0 , where M 0 is the initial mass in the annulus, e 0 is the initial eccentricity of the planetesimals, and x ≈ 1-2. Runaway growth occurs in 100 Myr for M 0 ≈ 10 M ⊕ and e 0 ≈ 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, M 0 ∼ 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, τ r ∝ M −1 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.

Large Bodies in the Kuiper Belt

“…If the size distributions of the classical and scattered KBOs are identical, then a similar number of bodies should be present in the scattered Kuiper Belt, which has approximately the same number of bodies . These results are consistent with the Kuiper Belt growth models of Kenyon & Luu (1998, 1999, using velocity evolution and collisional fragmentation. In these models, several Pluto-sized bodies grow concurrently in a low-mass (D10 disk.…”

Evolution of Jovian planets in a self-gravitating planetesimal disk

“…Most of them have diameters (D) larger than 100 km, while there are roughly a dozen giant objects with diameters of about 1000 km or more, such as Pluto 1 MPCs: http://www.cfa.harvard.edu/iau/lists/TNOs.html (D ≈ 2320 km) and 2003 UB313 (D ≈ 2400 km). Previous studies show that the current belt mass between 30 and 50 AU of less than 0.1 M ⊕ could not produce the KBOs in situ (Stern 1996;Stern & Colwell 1997;Kenyon & Luu 1998;Kenyon & Luu 1999). Thus, the KBOs should form in a denser region much closer to the Sun and were subsequently transported outwards to their present locations (Levison & Morbidelli 2003;Gomes 2003).…”

Planet Formation by Coagulation: A Focus on Uranus and Neptune

“…Although particle-in-a-box simulations represent a great simplification relative to N-body simulations, they are still computationally expensive (Kenyon & Luu 1998, for example, ran their simulations on a CRAY supercomputer). Moreover, the results of the simulations are very difficult to interpret.…”