Asteroid collisional evolution: I. Angular momentum splash: Despinning asteroids through catastrophic collisions

Abstract

When an asteroid suffers a catastrophic impact, with only a fraction of the initial mass reaccumulating into a “rubble pile,” a significant amount of angular momentum is carried away by the escaping material. The reaccumulated core will have a lower rotation rate than it would without this effect, and may even have a net spin-down, relative to its preimpact spin rate, due largely to the preferential escape of high-angular-momentum fragments. We call this effect angular momentum splash in analogy with the angular momentum drain mechanism studied by A.R. Dobrovolskis and J.A. Burns (1984, Icarus 57, 464–476) for smaller cratering impacts. It is quantitatively assessed using the model for catastrophic fragmentation events developed by P. Paolicchi, A. Cellino, P. Farinella, and V. Zappalà (1989, Icarus 77, 187–212). The splash mechanism is most effective at intermediate asteroids sizes (∼100 km), where the ejection velocities of fragments are of the same order as the escape velocities of the targets; the corresponding relative spin-down is found to be of the order of the core/target mass ratio. The splash-related spin-down is in competition with the spin-up due to angular momentum transfer from the projectile in noncentral impacts. Although the outcome depends on several collisional parameters, net spin-down prevails in a range of target sizes around 100 km, while larger objects are more often spun up by shattering impacts. This result holds for a wide range of collisional parameters and is in good agreement with the observed distribution of asteroid rotation rates with size.