Tidal pull of the Earth strips the proto-Moon of its volatiles

Abstract

Prevailing models for the formation of the Moon invoke a giant impact between a planetary embryo and the proto-Earth (Canup, 2004; Ćuk et al., 2016). Despite similarities in the isotopic and chemical abundances of refractory elements compared to Earth's mantle, the Moon is depleted in volatiles (Wolf and Anders, 1980). Current models favour devolatilisation via incomplete condensation of the proto-Moon in an Earth-Moon debris-disk (Charnoz and Michaut, 2015; Canup et al., 2015; Lock et al., 2018). However the physics of this protolunar disk is poorly understood and thermal escape of gas is inhibited by the Earth's strong gravitational field (Nakajima and Stevenson, 2014). Here we investigate a simple process, wherein the Earth's tidal pull promotes intense hydrodynamic escape from the liquid surface of a molten proto-Moon assembling at 3–6 Earth radii. Such tidally-driven atmospheric escape persisting for less than 1 Kyr at temperatures ~1600 − 1700 K reproduces the measured lunar depletion in K and Na, assuming the escape starts just above the liquid surface. These results are also in accord with timescales for the rapid solidification of a plagioclase lid at the surface of a lunar magma ocean (Elkins-Tanton et al., 2011). We find that hydrodynamic escape, both in an adiabatic or isothermal regime, with or without condensation, induces advective transport of gas away from the lunar surface, causing a decrease in the partial pressures of gas species (Ps) with respect to their equilibrium values (Psat). The observed enrichment in heavy stable isotopes of Zn and K (Paniello et al., 2012; Wang and Jacobsen, 2016) constrain Ps/Psat > 0.99, favouring a scenario in which volatile loss occurred at low hydrodynamic wind velocities (<1% of the sound velocity) and thus low temperatures. We conclude that tidally-driven atmospheric escape is an unavoidable consequence of the Moon's assembly under the gravitational influence of the Earth, and provides new pathways toward understanding lunar formation.