Compositional outcomes of Earth formation from a narrow ring

The origin of Earth's formation material remains controversial. Here we address the problem from the elemental point of view. We use an approach similar to that of Rubie et al. (2015), with the technical improvements presented in Dale et al. (2023) to simulate the chemical evolution of the Earth's mantle during a series of metal-silicate partial equilibration events associated with accretional collisions. However, we introduce two radical differences. First, we consider the dynamical model in which Earth forms from a dense ring of planetesimals and planetary embryos near 1 AU, with a low-density extension of the planetesimal population into the asteroid belt. Second, we divide the ring and asteroid belt population into four zones. The zone closest to the Sun is assumed to be populated by planetesimals and embryos enriched in elements more refractory than Si relative to CI concentrations and fully depleted in volatile elements including S and C. This material is not sampled in the meteorite record, except potentially in angrites. Moving further away from the Sun, the remaining three zones are populated by material with the compositions of enstatite chondrites, ordinary chondrites and CI chondrites respectively. Using this model, we fit the chemical composition of the bulk silicate Earth in terms of relative abundances of the oxides of Al, Mg, Fe, Si, Ni, Co, Nb, V, Cr, W, Mo and C by adjusting the boundaries of the above compositional zones and the refractory enrichment in the innermost zone thus giving us four compositional free parameters. A fifth and final fitting parameter concerns the depth of planetesimal equilibration in a magma ocean produced following a giant impact. We considered twenty-two simulations of the ring model, all of which produced at least one planet of similar mass and semi-major axis as the Earth. Each simulation of the chemical evolution of the Earth assumed either an initially hot or cold target for collisions producing a total of forty-eight Earth analogues. Seventeen of the analogues represent a planet with bulk mantle chemistry quite similar to that of the observed bulk silicate Earth (BSE) despite their differing hierarchical growth sequences. However, these differences in the sequence, size and initial position of the impactors result in different values of the five fitting parameters. This equates to differences in the proportion of each meteorite type required to obtain a chemical composition similar to the BSE, though some similarities remain such as the requirement for the Earth to accrete the majority (60-80%) of its material from the innermost refractory enriched region. This implies that, paired with the right hierarchical growth sequence and with some constraints, more than one ring model compositional structure can produce an Earth analogue consistent with the BSE, with very similar final mantle compositions for all considered elements.