On the Vertical Structure of the Protolunar Disk

The vertical structure of a post-impact, pre-lunar disk is examined. We adopt the equations introduced by Thompson & Stevenson for a silicate disk in two-phase equilibrium (vapor plus liquid) and derive an analytical solution to the system. This largely reproduces their low-gas mass fraction, x ≪ 1, profiles of the disk but is also employed to examine higher x cases. The latter are generally gravitationally stable and are used to develop a stratified disk model consisting of a gravitationally unstable magma layer surrounded by a stable, primarily vapor atmosphere. Initially, the atmosphere contains the majority of the disk mass, while the surface density of the magma layer is determined by requiring its viscous energy dissipation supply the disk's radiation budget. The magma layer viscously spreads on a ∼50 yr timescale during which vapor continuously condenses into droplets that settle to the layer, maintaining its surface density and dissipation rate. Material flowing outward, past the Roche boundary, can become incorporated into accreting moonlets, and this supply persists until the vapor reservoir is depleted in ∼250 yr.