Accretion in the Edgeworth-kuiper Belt: Forming 100{1000 Km Radius Bodies at 30 Au and beyond Running Title: Accretion in the Kuiper Belt

We employ a time-dependent collisional evolution code to study the conditions under which the 50{200 km radius Edgeworth-Kuiper Objects (EKOs) in the region between 30 and 50 AU (now called the Edgeworth-Kuiper Belt, or EKB; Edgeworth 1943, 1949; Kuiper 1951) were formed. Assuming that these bodies were created by pairwise accretion from 1 to 10 km building blocks, we nd that three conditions were required, namely: (i) at least 10 M and more likely 35 M of solids in the primordial 30 to 50 AU zone, (ii) mean random orbital eccentricities of order 0.002 or smaller, and (iii) mechanically strong building blocks. Furthermore, we nd that the accretion of 100{200 km radius bodies in the 30 to 50 AU region from collisions among a starting population of 1 to 10 km building blocks required 108{109 years, with the lower range only being reached for 30 to 50 AU zone masses approaching 100 M of solids or mean random orbital eccentricities <0.005 (which we do not believe is realistic after gas dissipation). Therefore, unless accretion had already produced many building blocks signi cantly larger than 10 km in diameter at the time the nebular gas was removed, our results also indicate that Neptune did not form on a timescale much shorter than 70 Myr, and could well have required many hundreds of Myr to approach its nal mass. We also explore the growth of Pluto-scale (i.e., radius 1000{ 1200 km) objects in the 30 to 50 AU region under a variety of assumptions. We further nd that once 300 hundred kilometer radius objects were formed, the growth of 1000 km radius and larger objects occurs relatively easily and comparatively quickly. The lack of many Plutos in the 30 to 50 AU zone therefore argues strongly that growth was terminated in that region rather abruptly at the time the presently observed population of 100{200 km radius EKOs were being completed. In the region beyond 50 AU where Neptune's dynamical in uence was much reduced, model runs yield 100 km to 1000 km radius, and perhaps even larger bodies which should be detectable with on-going or soon-to-be started surveys. We suggest that if dynamical conditions did not remain calm enough to allow Pluto itself to be grown in the 30 to 50 AU zone before perturbations from Neptune created a dynamically erosive, low-mass environment there, then it may be that Pluto was grown beyond the in uence of Neptune's perturbations and later transported inward, perhaps in part via the Charon-forming collision. 1