One of the most perplexing results from New Horizons is the paucity of D < 10 km diameter craters found on Charon and Arrokoth. They suggest the KBO size frequency distribution (SFD) for projectiles between D ~30 m and ~1 km has a shallow cumulative power law slope (q ~ -1). A similarly-shaped projectile SFD can be derived from small primary craters found on Europa, Ganymede, and Enceladus, worlds predominantly hit by comets from the scattered disk. Using collisional models, we can now show this feature is likely a byproduct of collisional evolution in the primordial Kuiper belt, as argued by Morbidelli et al. (2021).
To explain how, it is useful to first describe collisional evolution in the main asteroid belt. Model results indicate the easiest bodies to disrupt from an energy per mass perspective are D ~200 m (e.g., Bottke et al. 2020). Objects smaller than 200 m grind themselves into a Dohnanyi-shaped SFD (i.e., q ~ -2.6) that in turn will disrupt bodies between 200 m and 2 km. The result is a q ~ -1 slope between these two inflection points and a wavy SFD.
We find collisional evolution in the Kuiper belt yields similar behavior, provided the easiest bodies to disrupt are not ~200 m but ~20 m. Using the Boulder collision code, we ran simulations using an initial SFD whose slope for D < 100 km bodies was q = -2.1. Early grinding generates a Dohnanyi-shaped SFD for D < 20 m that, in turn, decimates bodies between ~30 m and ~1 km. As with the main belt, this yields a q ~ -1 slope between the inflection points, reproducing observations.
Intriguingly, as grinding continues, the wavy SFD keeps growing to larger sizes; a steady state “bump" dominated by fragments develops near ~1 km that creates a deficit of ~10 km bodies. We find this shape is consistent with the crater SFDs made by km-sized projectiles on Pluto as well as those made by scattered disk objects striking worlds like Ganymede, Callisto, Tethys, Rhea, Iapetus, etc.
Our results also have interesting implications for the Lucy mission. The Kuiper belt (other than cold classicals), scattered disk, and Jupiter’s Trojans were all dynamically created from the primordial Kuiper belt during the giant planet instability. The Trojan SFD, however, is less wavy (i.e., less collisionally-evolved) than the other two. The implication is that considerable grinding occurred in the KBO/scattered disk regions in the aftermath of the giant planet instability. Accordingly, we predict that Trojans are more likely to be intact planetesimals than same-sized ecliptic comets or KBOs (excluding cold classicals).