CORE FORMATION CONDITION THAT SATISFIES THE Ni ABUNDANCE AND W ISOTOPIC RATIO

Introduction: Core-mantle differentiation is one of the most dramatic events in the Earth's history. As a result of core formation, the Earth's mantle is depleted in siderophile elements. Amounts of siderophile elements retained in the mantle give important clues for estimation of core formation condition. It is well known that the observed mantle abundance of Ni is larger than that predicted from low-pressure partitioning experiments [1]. Recent high-pressure experimental studies show that the high-pressure partitioning can resolve this problem. It is proposed that the observed Ni abundance is consistent with the equilibration of mantle with iron at 43-59 GPa (e.g., [2]). In other words, the lowermost part of the mantle is not equilibrated with iron. Hf-W chronometer is used to determine the age of core formation. Hafnium and tungsten are both highly refractory elements; hafnium is a lithophile element, whereas tungsten is a moderately siderophile element. Assuming the complete equilibration between the mantle and iron at the last giant impact, Yin et al. [3] estimated the age of core formation at 30 Myr after the formation of iron meteorites. However, as noted before, mantle abundance of Ni suggests relatively shallow magma ocean, which is apparently inconsistent with the assumption adopted in the Hf-W chronometry. Moreover, recent planetary formation suggests multiple occurrences of giant impacts [4, 5]. Here, we consider the effect of multiple giant impacts and investigate core formation condition and timing that satisfies both of the element abundance (Ni) and W isotope composition. Assumptions and model: We consider the two different stages: the protoplanet formation stage and the giant impact stage. In the protoplanet formation stage, we assume that the whole mantle of the protoplanet is molten (= magma ocean) and therefore accreting material completely equilibrates with the mantle. In the magma ocean, iron was divided into small droplets and their settling can achieve chemical equilibration between iron and molten silicate [6]. In the giant impact stage, we assume that a part of the target's mantle melts by each impact and equilibrates with iron in the impactor. In this stage we consider the possibility that only some fraction of impactor's core and target's mantle are involved in equilibration. Numerical simulations: Here, we represented the condition of giant impacts by four parameters: a, b, n, and dt. Fraction a of the impactor's iron is equilibrated