Lunar accretion from a Roche-interior fluid disk

We use a hybrid numerical approach to simulate the formation of the Moon from an impact-generated disk, consisting of a fluid model for the disk inside the Roche limit and an N-body code to describe accretion outside the Roche limit. As the inner disk spreads due to a thermally regulated viscosity, material is delivered across the Roche limit and accretes into moonlets that are added to the N-body simulation. Contrary to an accretion timescale of a few months obtained with prior pure N-body codes, here the final stage of the Moon's growth is controlled by the slow spreading of the inner disk, resulting in a total lunar accretion timescale of ~10^2 years. It has been proposed that the inner disk may compositionally equilibrate with the Earth through diffusive mixing, which offers a potential explanation for the identical oxygen isotope compositions of the Earth and Moon. However, the mass fraction of the final Moon that is derived from the inner disk is limited by resonant torques between the disk and exterior growing moons. For initial disks containing < 2.5 lunar masses (ML), we find that a final Moon with mass > 0.8ML contains < 60% material derived from the inner disk, with this material preferentially delivered to the Moon at the end of its accretion.