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 (P s ) with respect to their equilibrium values (P sat ). The observed enrichment in heavy stable isotopes of Zn and K (Paniello et al. 2012; Wang and Jacobsen 2016) constrain P s /P sat >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.

The Extent, Nature, and Origin of K and Rb Depletions and Isotopic Fractionations in Earth, the Moon, and Other Planetary Bodies

“…In that scenario, MVEs are lost incrementally at a temperature of ∼1600-1800 K. Tang & Young (2020) made the case that the vapor generated would have the opportunity to equilibrate with the surface of the magma ocean, thereby limiting escape efficiency and isotopic fractionation. Charnoz et al (2021) showed, however, that tidal pull from Earth would have been able to sustain a vigorous hydrodynamic escape flow that could Canup et al (2015). In that model, a proto-Moon representing ∼40% of the final lunar mass is rapidly formed beyond the Roche limit.…”

“…(3) Sossi et al (2019) and Charnoz et al (2021) considered a model involving loss of MVE from the LMO by hydrodynamic escape facilitated by the tidal pull of Earth (Figure 11(c)). In that scenario, MVEs are lost incrementally at a temperature of ∼1600-1800 K. Tang & Young (2020) made the case that the vapor generated would have the opportunity to equilibrate with the surface of the magma ocean, thereby limiting escape efficiency and isotopic fractionation.…”

“…MVEs lost onto Earth are constantly replenished by evaporation from the liquid layer. (d) Tidally driven hydrodynamic escape of MVEs from the LMO (Sossi et al 2019;Charnoz et al 2021). Escape of MVEs from the LMO is a two-step process involving evaporation from silicate melt, followed by hydrodynamic escape to space facilitated by tidal pull from Earth.…”

“…have driven significant undersaturation in the vapor in contact with the LMO, allowing the production of significant kinetic isotope effects needed to explain available isotopic data (Nie & Dauphas 2019). According to Charnoz et al (2021), this hydrodynamic wind would have been sufficient to drive the loss of Na, K, and Zn in less than ∼ 1000 yr before the LMO was capped by a solid flotation crust. This model cannot explain simultaneously the depletions of Na, K, and Zn.…”

“…This model cannot explain simultaneously the depletions of Na, K, and Zn. The reason for the discrepancy between Tang & Young (2020) and Charnoz et al (2021) is that Tang & Young (2020) prescribed a diffusive boundary layer at the vapor/magma interface that limits escape efficiency, while Charnoz et al (2021) describe the atmosphere as a single layer with advective transport throughout.…”