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 < q KBO < −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.

A molecular wind blows out of the Kuiper belt

“…To answer these questions, we first extrapolated the gas production rate in our KB from the most recent extrasolar models. To do so, we computed the dust mass-loss rate in the KB due to collisions using a state-of-the-art model of dust in our Solar System (Vitense et al 2012;Morbidelli et al 2021). According to extrasolar models that fit most observations to date (Kral et al 2017), the gas production rate is proportional to the mass-loss rate of the belt's collisional cascade, and we find (see Appendix B) that ∼10 −9 M ⊕ Myr −1 of CO gas should be released in the current KB.…”

“…We modelled the gas release rate due to thermal heating over time. First, we assumed that the CO mass contained in N b bodies of size s (taken from a state-of-the-art collisional model of the KB; Morbidelli et al 2021)…”

“…Therefore, the released CH 4 would also be more difficult to observe than CO. We also note that collisions would increase the predicted rate because they would expose some fresh CO ices that can be released faster than on a thermal timescale; however, the collisional timescale for bodies larger than 4 km are longer than the age of our Solar System, and this contribution will be negligible for the current KB. Collisions that happened in the early stages of the trans-Neptunian disk could have affected the size distribution of small bodies and released CO on the surface of these bodies, but we note that we used a state-of-the-art size distribution based on observations (Morbidelli et al 2021) that already accounts for previous evolution. Therefore, the early collisional evolution is implicitly taken into account in our calculations.…”

Collisions of Small Kuiper Belt Objects With (486958) Arrokoth: Implications for Its Spin Evolution and Bulk Density

“…of the KBO SFD byMorbidelli et al (2021) argues for a relatively steeper SFD differential slope over the size range in which we are interested: the respective log dN slopes are −4 for 𝐴𝐴 𝐴𝐴 𝐴 30 m and −2.2 for d from 30 m to 2 km. Steeper SFD slopes downplay the importance of larger impacts.…”

“…To compensate, we allow for a larger upper bound for the maximum impactor size d max . We thus conducted a series of simulations with the two different SFD models, from Singer, Spencer et al (2019) andMorbidelli et al (2021), and d max of 1 and 2 km. Larger impactors, if fast and non-oblique, have a greater potential to cause catastrophic disruption of TA, or indeed the individual lobes of Arrokoth, but we still find this to be an unlikely model outcome (though not entirely ruled out).The cumulative results of alternate SFD slopes with different values for d max are summarized in Table 2.…”