The Moon-forming giant impact extensively melts and partially vaporizes the silicate Earth and delivers a substantial mass of metal to Earth's core. The subsequent evolution of the magma ocean and overlying atmosphere has been described by theoretical models but observable constraints on this epoch have proved elusive. Here, we report thermodynamic and climate calculations of the primordial atmosphere during the magma ocean and water ocean epochs respectively and forge new links with observations to gain insight into the behavior of volatiles on the Hadean Earth. As accretion wanes, Earth's magma ocean crystallizes, outgassing the bulk of its volatiles into the primordial atmosphere. The redox state of the magma ocean controls both the chemical composition of the outgassed volatiles and the hydrogen isotopic composition of water oceans that remain after hydrogen escape from the primordial atmosphere. The climate modeling indicates that multi-bar H-2-rich atmospheres generate sufficient greenhouse warming and rapid kinetics resulting in ocean-atmosphere H2O-H-2 isotopic equilibration. Whereas water condenses and is mostly retained, molecular hydrogen does not condense and can escape, allowing large quantities (similar to 10(2) bars) of hydrogen - if present - to be lost from the Earth in this epoch. Because the escaping inventory of H can be comparable to the hydrogen inventory in primordial water oceans, equilibrium deuterium enrichment can be large with a magnitude that depends on the initial atmospheric H-2 inventory. With rapid kinetics, the water molecule concentrates deuterium and, to the extent that hydrogen in other forms (e.g., H-2) are significant species in the outgassed atmosphere, pronounced D/H enrichments (similar to 1.5-2x) in the oceans are expected from equilibrium partitioning in this epoch. By contrast, the common view that terrestrial water has a carbonaceous chondritic source requires the oceans to preserve the isotopic composition of that source, undergoing minimal D-enrichment via equilibration with H-2 followed by hydrodynamic escape. Such minimal enrichment places upper limits on the amount of primordial atmospheric H-2 in contact with Hadean water oceans and implies oxidizing conditions (logfO(2) > 1W+1, H-2/H2O < 0.3) for outgassing from the magma ocean. Preservation of an approximate carbonaceous chondrite DIM signature in the oceans thus provides evidence that the observed oxidation of silicate Earth occurred before crystallization of the final magma ocean, yielding a new constraint on the timing of this critical event in Earth history. The seawater-carbonaceous chondrite "match" in D/H (to similar to 10-20%) further constrains the prior existence of an atmospheric H-2 inventory - of any origin - on post-giant-impact Earth to <20 bars, and suggests that the terrestrial mantle supplied the oxidant for the chemical resorption of metals during terrestrial late accretion. (C) 2019 Elsevier B.V. All rights reserved.
