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Abstract

The W isotope composition of the bulk silicate Earth exhibits a small but resolvable excess in the abundance of ¹⁸²W relative to that found in chondrites, indicating that core formation in Earth took place within the life-time of now extinct ¹⁸²Hf. This ¹⁸²W excess provides a firm constraint for the lower limit of the time of core formation in Earth. Separation and segregation of metal into Earth's core cannot have ceased earlier than ∼30 Myr after the start of the solar system. Determining the exact timing of core formation, however, requires knowledge of the degree of equilibration of newly accreted material with Earth's mantle. Conversely, if independent age constraints for the formation of Earth's core are available, the ¹⁸²W excess of Earth's mantle relative to chondrites can be used to constrain the degree of metal-silicate equilibration during Earth's accretion. Provided that the Moon-forming event is the last large impact, the latest time core formation can have ceased in Earth is provided by the age of the oldest lunar samples and is ∼70-100 Myr after the start of the solar system. If, as seems likely, the impactor's core did not re-equilibrate extensively with the silicate proto-Earth, the Moon cannot have formed before ∼40 Myr resulting in an age of the Earth and the Moon of 40-70 Myr after the start of the solar system. The ¹⁸²W excess of the bulk silicate Earth relative to chondrites of ∼2ɛ units is substantially smaller than the 15-20ɛ_W range expected if Earth's core formed by merging of metal cores of early differentiated planetesimals, indicating significant re-homogenization of newly accreted planetesimals with Earth's mantle. In continuous core formation models that assume growth of Earth at an exponentially decreasing rate, more than ∼70% of the newly accreted material must have equilibrated with Earth's mantle. Including the Moon-forming impact into these models such that Earth was 89% accreted at the time of the impact and 10% was added by the impactor implies more than ∼50% metal-silicate equilibration in the silicate proto-Earth. Such high degrees of metal-silicate equilibration can only be achieved if core formation occurred by the physical separation of liquid metal from mostly molten silicate providing strong support for the hypothesis of a terrestrial magma ocean. Model calculations show that formation of a magma ocean by a late Moon-forming impact is not sufficient in removing radiogenic ¹⁸²W from Earth's mantle that would have accumulated as a result of early core formation. A high degree of metal-silicate equilibration of at least 50% must have been established prior to Moon formation, implying that metal segregation in the proto-Earth already occurred in a magma ocean. Therefore, the Moon-forming impact is not the only impact that led to the formation of a magma ocean, indicating multiple formations of magma oceans or a protracted life-time of the magma ocean.