Evolution of a protolunar disk in vapor/melt equilibrium

A model of the viscous evolution of a two‐phase, vapor/melt protolunar disk is described. Droplets condense from the vapor and “rain out,” forming a stratified structure with a midplane magma layer surrounded by a vapor reservoir. The magma layer is gravitationally unstable, but material interior to the Roche distance cannot fragment, and instead develops an effective viscosity. However, magma flowing across the Roche limit can fragment and accrete into moonlets, while magma spreading inward is accreted by Earth. As mass leaves the melt layer, it is replenished by vapor condensation, leading to a quasi steady state (QSS). The layer's mass is maintained at ~13% of a lunar mass and replaced every ~ 3.2 years. The vapor atmosphere steadily decreases, and once exhausted, the disk would cool below condensation temperature and spread as a time‐dependent disk until it too is exhausted. The timescale of the QSS is regulated by the disk's ability to radiate all the released latent heat plus viscous dissipation energy to space at the photospheric temperature, i.e., ~2000 K for silicon phase equilibrium. For the protolunar disk, latent heat dominates viscous heating, and the QSS for a ~2 lunar mass disk lasts for ~ 50 years. For comparison, a hypothetical water/steam disk orbiting an ice giant planet in which viscous heating dominates is also modeled. The photospheric temperature is closer to ~373 K, and the replacement time of the water layer is ~136 years. Finally, disks confined by external torques at either the planet‐disk boundary or at its outer edge are also briefly examined.