A re-assessment of the Kuiper belt size distribution for sub-kilometer objects

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≤ 10km. 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 of bodies with diameter d>2km on Arrokoth, integrated over the age of the Solar System, that we compare with the corresponding impact probability on Charon. Our result, together with the observed density of sub-km craters on Arrokoth's imaged surface, constrains the power law slope of the crater production function. Other constraints come from the absence of craters with 1<D<7km on Arrokoth, the existence of a single crater with D>7km and the relationship between the spatial density of sub-km craters on Arrokoth and of D ~ 20km craters on Charon. Together, these data 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<q_KBO<-1.0. These values are close to the cumulative slope of main belt asteroids in the 0.2-2km range, a population in collisional equilibrium (Bottke et al. 2020). For KBOs, however, this slope appears to extend 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 become steep again below approximately 30m. All these considerations strongly indicate that the size distribution of the KBO population is in collisional equilibrium.