Abstract:

Earth’s core formation set the initial compositions of the core and mantle. Various aspects of core formation, such as the degree of metal–silicate equilibration, oxygen fugacity, and depth of equilibration, have significant consequences for the resulting compositions, yet are poorly constrained. The Hf–W isotopic system can provide unique constraints on these aspects relative to other geochemical or geophysical methods. Here we model the Hf–W isotopic evolution of the Earth, improving over previous studies by combining a large number of N-body simulations of planetary accretion with a core formation model that includes self-consistent evolution of oxygen fugacity and a partition coefficient of tungsten that evolves with changing pressure, temperature, composition, and oxygen fugacity. The effective average fraction of equilibrating metal is constrained to be k > 0.2 for a range of equilibrating silicate masses (for canonical accretion scenarios), and is likely <0.55 if the Moon formed later than 65 Ma. These values of k typically correspond to an effective equilibration depth of ~0.5–0.7x the evolving core–mantle boundary pressure as the planet grows. The average mass of equilibrating silicate was likely at least 3x the impactor’s silicate mass. Equilibration temperature, initial fO₂, initial differentiation time, semimajor axis, and planetary mass (above ~0.9 Earth masses) have no systematic effect on the ¹⁸²W anomaly, or on f^Hf/W (except for fO₂), when applying the constraint that the model must reproduce Earth’s mantle W abundance. There are strong tradeoffs between the effects of k, equilibrating silicate mass, depth of equilibration, and timing of core formation, so the terrestrial Hf–W isotopic system should be interpreted with caution when used as a chronometer of Earth’s core formation. Because of these strong tradeoffs, the Earth’s tungsten anomaly can be reproduced for Moon-forming impact timescales spanning at least 10–175 Ma. Early Moon formation ages require a higher degree of metal–silicate equilibration to produce Earth’s ¹⁸²W anomaly.