On the evolution of the protolunar disc

The structure and viscous evolution of a post-impact, protolunar disc is examined. The equations for a silicate disc in two-phase (vapour-liquid) equilibrium are employed to derive an analytical solution to vertical structure. Both a vertically mixed phase disc and a stratified disc, where a magma layer exists in the mid-plane surrounded by a vapour reservoir, are considered. The former largely reproduces the low gas mass fraction, x≪1, profiles of the disc described in earlier literature that proposed that the disc would hover on the brink of gravitational instability. In the latter, the vapour layer has x∼1 and is generally gravitationally stable, while the magma layer is vigorously unstable. The viscous evolution of the stratified model is then explored. Initially, the disc quickly settles to a quasi-steady state with a vapour reservoir containing the majority of the disc mass. The magma layer viscously spreads on a time scale of approximately 3-4 years, during which vapour continuously condenses into droplets that settle to the mid-plane, maintaining the magma surface density in spite of disc spreading. Material flowing inwards is accreted by the Earth; material flowing outwards past the Roche boundary can become incorporated into accreting moonlets. This evolution persists until the vapour reservoir is depleted in approximately 50-100 years, depending on its initial mass.