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 hasx ∼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.