Accretion of the Moon from an Impact-Generated Disk

Abstract

We present the first published numerical calculations of accretion of an impact-generated protolunar disk into a single large Moon. Our calculations are based on the model developed by R. M. Canup and L. W. Esposito (Icarus113, 331–352, 1995) to describe accretion in the Roche zones around the giant planets. Previous numerical simulations of a large impact event predict the formation of a disk of material centered near or within the Roche limit (∼2.9R⊕). A natural expectation based on our previous results and comparison with the satellite systems of the outer planets would be for multiple small moons to arise from such a protolunar disk. Multiple moonlets could accrete to form a single Moon if they evolved into crossing orbits due to tidal interaction with the Earth. This would occur if the innermost moonlet in the disk were also the most massive, so that it evolved outward at the relatively fastest rate and swept up all exterior material. Our calculations, which include both moonlet accretion and orbital evolution, demonstrate that forming massive moonlets in the inner disk near the Roche limit is extremely difficult. We conclude that an Earth system with multiple moons is the final result unless some particularly severe constraints on initial conditions in the disk are met. A disk with a lunar mass of material exterior toa∼ 3.5–4R⊕or an extremely steep radial surface density profile at the onset of collisional growth is required for a single, lunar-sized body to result from accretion of silicate density material in a protolunar disk. The former corresponds most closely to disks produced by impactors with nearly twice the mass of Mars and about twice the angular momentum of the current Earth/Moon system. Other processes, such as gravitational instability or primary accretion of an iron core in the inner disk, might be able to “seed” accretional growth and allow for the formation of a single Moon if disk temperature and compositional requirements are met. Our analysis demonstrates the need for more detailed, higher resolution impact simulations.