Planetary Impacts: Scaling of Crater Depth From Subsonic to Supersonic Conditions

Abstract

Planetary impacts have shaped the surfaces and interiors of planets. They were particularly critical in the last stage of planetary accretion, as they have eventually formed terrestrial planets. During these large supersonic collisions, shock waves melted the impactor and the target, and formed silicate magma oceans. Because the propagation of shock waves and the melting is faster than the excavation of an impact crater, the cratering stage can be considered as a purely hydrodynamic process. Here, we use both laboratory impact experiments in water and numerical simulations to investigate the crater dimensions resulting from the impact of a liquid impactor onto a liquid target. We show that our numerical models reproduce the laboratory experiments at subsonic impact velocities. We then explore the effect of both the Froude number, which is the ratio of the impactor kinetic energy to gravity, and the Mach number, which is the ratio of the impact speed to the sound speed. We vary these two parameters independently in impact simulations, going from subsonic to supersonic conditions. We obtain a new scaling law for the crater dimensions that describes the transition from subsonic to supersonic impacts. Our results indicate that the transition between these two regimes results from a change in the partitioning of the impactor kinetic energy into potential energy in the crater and internal energy. Finally, our scaling suggests that, in the limit of large Mach numbers, the crater depth depends only on the sound velocity and gravity, and is independent of the impact speed.