Abstract

The Kuiper Belt is a remnant from the early solar system and its size distribution contains many important constraints that can be used to test models of planet formation and collisional evolution. We show, by comparing observations with theoretical models, that the observed Kuiper Belt size distribution is well matched by coagulation models, which start with an initial planetesimal population with radii of about 1 km, and subsequent collisional evolution. We find that the observed size distribution above R similar to 30 km is primordial, i.e., it has not been modified by collisional evolution over the age of the solar system, and that the size distribution below R similar to 30 km has been modified by collisions and that its slope is well matched by collisional evolution models that use published strength laws. We investigate in detail the resulting size distribution of bodies ranging from 0.01 km to 30 km and find that its slope changes several times as a function of radius before approaching the expected value for an equilibrium collisional cascade of material strength dominated bodies for R less than or similar to 0.1 km. Compared to a single power-law size distribution that would span the whole range from 0.01 km to 30 km, we find in general a strong deficit of bodies around R similar to 10 km and a strong excess of bodies around 2 km in radius. This deficit and excess of bodies are caused by the planetesimal size distribution left over from the runaway growth phase, which left most of the initial mass in small planetesimals while only a small fraction of the total mass is converted into large protoplanets. This excess mass in small planetesimals leaves a permanent signature in the size distribution of small bodies that is not erased after 4.5 Gyr of collisional evolution. Observations of the small Kuiper Belt Object (KBO) size distribution can therefore test if large KBOs grew as a result of runaway growth and constrained the initial planetesimal sizes. We find that results from recent KBO occultation surveys and the observed KBO size distribution can be best matched by an initial planetesimal population that contained about equal mass per logarithmic mass bin in bodies ranging from 0.4 km to 4 km in radius. We further find that we cannot match the observed KBO size distribution if most of the planetesimal mass was contained in bodies that were 10 km in radius or larger simply because their resulting size distribution cannot be sufficiently depleted over 4.5 Gyr to match observations.