Effect of equilibration of the impactor’s core with the terrestrial MO on the bulk composition and size of the impactor
This protocol is extracted from research article:
Delivery of carbon, nitrogen, and sulfur to the silicate Earth by a giant impact
Sci Adv, Jan 23, 2019; DOI: 10.1126/sciadv.aau3669

The results presented in Fig. 4 (B to D) do not take into account the effect of equilibration of the impactor’s core with the post-merger mantle (proto-Earth’s mantle + impactor’s mantle). Accretion models based on Hf/W and U/Pb chronometry predict that only 36% of Earth’s core must have formed in equilibrium with Earth’s mantle (60). Model calculations using high P-T alloy-silicate partition coefficients of Ni, Co, and W to match their BSE abundances predict that the initial 60 to 70% of the accretion of Earth’s mass was from smaller planetesimals and planetary embryos, the cores of which would efficiently equilibrate with the growing Earth’s mantle, while the last 30 to 40% of Earth’s accreted mass was provided by larger impactors, the cores of which did not equilibrate with proto-Earth’s MO (21). Therefore, the late-stage merger of a large impactor would imply that its core would undergo a small degree of equilibration, if any, with the mantle of the growing Earth before it coalesced with the proto-Earth’s core (Fig. 4A). As a result, we varied the degree of equilibration with the impactor’s core over a range of 0 to 20%.

The effect of equilibration of the impactor’s core with the proto-Earth’s silicate fraction was calculated by assuming an MO depth at P = 50 GPa and T = 4000 K (31). As metal segregation happens at much faster rates than accretion (60), before the merger of the impactor, proto-Earth’s mantle would be metal free. This would mean that the only metal that would be equilibrating with the post-merger MO would be from the impactor’s core, i.e., the S-rich metal from the impactor’s core. Experimental constraints on the Embedded Image and Embedded Image under the relevant conditions for S-rich alloys are lacking, although there was a recent study that constrained the Embedded Image (30) under these conditions. We varied the Embedded Image between 100 and 500, Embedded Image from 10 to 25, and Embedded Image from 10 to 150 for a postimpact MO equilibration with the impactor’s core in accordance with our calculations at lower P-T conditions, taking into account the possible roles of P-T and S in the alloy on the parameterized Embedded Image (Eq. 4). Our calculations show that variation of the Embedded Image, Embedded Image, and Embedded Image do not show any significant effect on the calculations as the degree of equilibration of the impactor’s core is the controlling variable under these conditions (Fig. 6, A and B).

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