Kelvin Revisited: Cooling and Core Formation after the Giant Impact

The 182Hf-182W chronometer is now accepted as indicating relatively rapid accretion and core formation on Earth. Assuming that all accreting material mixed isotopically with the silicate earth the 182W/184W ratio of the mantle yields a mean-life of accretion of 15 Myr after the origin of the solar system. In contrast, if we assume that Pb is siderophile, the U-Pb system indicates much slower rates of core segregation, with substantial accretion of the Earth after the moon-forming impact at 45 /- 5 Myr. This means either that the late loss of Pb from the silicate Earth is due to some mechanism other than core formation or the U-Pb age reflects a later stage of core formation than does Hf-W. Recent metal-silicate partitioning data, when applied to the current composition of the mantle, support the `deep magma ocean' model of core formation, combined with a substantial increase of oxygen fugacity during accretion. Here we argue that the increase of oxygen fugacity during accretion was a consequence of the crystallization of silicate perovskite in the lower mantle. Due to the affinity of this phase for ferric iron, a planet larger than Mars should undergo progressive self-oxidation during accretion and core segregation. The oxidation process leads to destabilization of metal so that sulphide is the only `metallic' phase which can coexist with the silicate. Our explanation of the two timescales of core-formation is, therefore, as follows. The Hf-W timescale refers to the principal phase of core-formation before the giant impact. Crystallisation of silicate perovskite in the lower mantle during this phase produced Fe3 which was released during the giant impact. This oxidation resulted in later segregation of sulphur-rich metal into which Pb dissolved readily, re-setting the U-Pb age of the Earth. Separation of the latter metal occurred 30 /-10 Myrs after the Moon-forming impact. Over this timespan the Earth cooled by about 4000K in returning from a fully-molten to a partially crystalline state. The result is in surprisingly good agreement with Lord Kelvin's estimate of the cooling age of the Earth.