Evolution of the protolunar disk: Dynamics, cooling timescale and implantation of volatiles onto the Earth

It is thought that the Moon accreted from the protolunar disk that was assembled after the last giant impact on Earth. Due to its high temperature, the protolunar disk may act as a thermochemical reactor in which the material is processed before being incorporated into the Moon. Outstanding issues like devolatilisation and istotopic evolution are tied to the disk evolution, however its lifetime, dynamics and thermodynamics are unknown. Here, we numerically explore the long term viscous evolution of the protolunar disk using a one dimensional model where the different phases (vapor and condensed) are vertically stratified. Viscous heating, radiative cooling, phase transitions and gravitational instability are accounted for whereas Moon's accretion is not considered for the moment. The viscosity of the gas, liquid and solid phases dictates the disk evolution. We find that (1) the vapor condenses into liquid in ∼10 years, (2) a large fraction of the disk mass flows inward forming a hot and compact liquid disk between 1 and 1.7 Earth's radii, a region where the liquid is gravitationally stable and can accumulate, (3) the disk finally solidifies in 103 to 105 years. Viscous heating is never balanced by radiative cooling. If the vapor phase is abnormally viscous, due to magneto-rotational instability for instance, most of the disk volatile components are transported to Earth leaving a disk enriched in refractory elements. This opens a way to form a volatile-depleted Moon and would suggest that the missing Moon's volatiles are buried today into the Earth. The disk cooling timescale may be long enough to allow for planet/disk isotopic equilibration. However large uncertainties on the disk physics remain because of the complexity of its multi-phased structure.