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

AbstractPlanetary 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.Plain Language Summary: Planetary formation involved a large number of very energetic collisions. Such impacts generated shock waves which led to widespread melting and the formation of magma oceans. Understanding the dynamics of impacts into magma oceans is of great importance as these collisions set the initial temperature and composition of terrestrial planets and satellites. Laboratory experiments and numerical simulations have been used to investigate large impacts. However, each approach has pros and cons. Liquid impact experiments can produce the small scales responsible for the mixing between the impactor and the target, but they fail to reproduce shock waves and supersonic speeds. In contrast, current numerical simulations reach supersonic conditions but produce a limited amount of turbulence and mixing. In this study, we bridge the gap between these two methods and improve our understanding of the effect of the impact velocity on the cratering process. Using the code iSALE, we numerically reproduce water impact experiments at low subsonic velocities. We then explore supersonic conditions in impact simulations. We obtain a new scaling law predicting the crater depth in more realistic impact conditions and show that it is limited only by the sound speed for large impact velocities.Key Points: The shock physics code iSALE is successfully benchmarked against subsonic water impact experiments A scaling law is proposed for the crater depth as a function of the Mach and Froude numbers which are varied as independent parameters In the limit of high Mach numbers, our scaling suggests that the maximum crater depth is controlled by the sound velocity and gravity, but not by the impact speed DFGEPSRCNational Aeronautics and Space AdministrationNSF Physics Frontier CenterProgramme National de PlanétologieCNESAlfred P. Sloan Foundationhttps://isale-code.github.io

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

International audiencePlanetary 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