A re-assessment of the Kuiper belt size distribution for sub-kilometer objects, revealing collisional equilibrium at small sizes

Abstract

In this work we combine several constraints provided by the crater records on Arrokoth and the worlds of the Pluto system to compute the size-frequency distribution (SFD) of the crater production function for craters with diameter D ≲ 10 km. For this purpose, we use a Kuiper belt objects (KBO) population model calibrated on telescopic surveys, that describes also the evolution of the KBO population during the early Solar System. We further calibrate this model using the crater record on Pluto, Charon and Nix. Using this model, we compute the impact probability on Arrokoth, integrated over the age of the Solar System. This probability is then used together with other observational constraints to determine the slope of the crater-production function on Arrokoth. These constraints are: (i) the spatial density of sub-km craters, (ii) the absence of craters with 1 < D < 7 km; (iii) the existence of a single crater with D > 7 km. In addition, we use our Kuiper belt model also to compare the impact rates and velocities of KBOs on Arrokoth with those on Charon, integrated over the crater retention ages of their respective surfaces. This allows us to establish a relationship between the spatial density of sub-km craters on Arrokoth and of D ~ 20 km craters on Charon. Together, all these considerations suggest the crater production function on these worlds has a cumulative power law slope of −1.5 < q < − 1.2. Converted into a projectile SFD slope, we find −1.2 < qKBO < − 1.0. These values are close to the cumulative slope of main belt asteroids in the 0.2–2 km range, a population in collisional equilibrium (Bottke et al., 2020). For KBOs, however, this slope appears to extend from ~2 km down to objects a few tens of meters in diameter, as inferred from sub-km craters on Arrokoth. From the measurement of the dust density in the Kuiper belt made by the New Horizons mission, we predict that the SFD of the KBOs becomes steep again below ~10–30 m. All these considerations strongly indicate that the size distribution of the KBO population is in collisional equilibrium.