Hydrodynamical simulations of proto-Moon degassing

Modeling the isotopic and elemental abundance of the bulk silicate Moon represent major challenges. Similarities in the non-mass dependent isotopic composition of refractory elements with the bulk silicate Earth suggest that both the Earth and the Moon formed from the same material reservoir. On the other hand, the Moon's volatile depletion and isotopic composition of moderately volatile elements points to a global devolatilization processes, most likely during a magma ocean phase of the Moon. Here, we investigate the devolatilization of the molten Moon due to a tidally-assisted hydrodynamic escape, first proposed by Charnoz et al. (2021) , with a focus on the dynamics of the evaporated gas. Unlike the 1D steady-state approach of Charnoz et al. (2021) , we use 2D time-dependent hydrodynamic simulations carried out with the FARGOCA code modified to take into account the magma ocean as a gas source. Near the Earth's Roche limit, where the proto-Moon likely formed, evaporated gases from the lunar magma ocean form a circum-Earth disk of volatiles, with less than 30% of material being re-accreted by the Moon. We find that the measured depletion of K and Na on the Moon can be achieved if the lunar magma-ocean had a surface temperature of about 1800-2000 K. After about 1000 years, a thermal boundary layer or a flotation crust forms a lid that inhibits volatile escape. Mapping the volatile velocity field reveals varying trends in the longitudes of volatile reaccretion on the Moon's surface: material is predominantly re-accreted on the trailing side when the Moon-Earth distance exceeds 3.5 Earth radii. For k 2 / Q values of 0.0003 and 0.03, 60% and more than 99% of the volatile material, respectively, is re-accreted on the trailing side, suggesting a dichotomy in volatile abundances between the leading and trailing sides of the Moon. This dichotomy may provide insights on the tidal conditions of the early molten Earth. In conclusion, tidally-driven atmospheric escape effectively devolatilizes the Moon, matching the measured abundances of Na and K on timescales compatible with the formation of a thermal boundary layer or an anorthite flotation crust. • The reduction of the Moon's Roche lobe due to Earth's tides assists the thermal escape of volatiles from the proto-Moon. • The hydrodynamic escape on the Moon gives rise to a circum-Earth volatile disk. • The Moon's magma ocean must have had temperatures of 1800-2000 K to match the observed Na and K abundances on the satellite. • Volatile loss ceases after the formation of a stagnant lid, on a timescale of 10 3 years. • Volatile material is predominantly re-accreted on the Moon's trailing side.