Spins of large asteroids: A hint of a primordial distribution in their Spin rates

The Asteroid Belt and the Kuiper Belt are relics from the formation of our solar system. Understanding the size and spin distribution of the two belts is crucial for a deeper understanding of the formation of our solar system and the dynamical processes that govern it. In this paper, we investigate the effect of collisions on the evolution of the spin distribution of asteroids and KBOs. We find that the power law nature of the impactors' size distribution leads to a Levy distribution of the spin rates. This results in a power law tail in the spin distribution, in stark contrast to the usually quoted Maxwellian distribution. We show that for bodies larger than 10 km, collisions alone lead to spin rates peaking at 0.15-0.5 revolutions per day. Comparing that to the observed spin rates of large asteroids (R > 50 km), we find that the spins of large asteroids, peaking at ∼1-2 revolutions per day, are dominated by a primordial component that reflects the formation mechanism of the asteroids. Similarly, the Kuiper Belt has undergone virtually no collisional spin evolution, assuming current densities. Collisions contribute a spin rate of ∼0.01 revolutions per day, thus the observed fast spin rates of KBOs are also primordial in nature.