Stochastic accretion of the Earth

The Earth is depleted in volatile elements relative to chondritic meteorites, its possible building blocks. Abundances of volatile elements descend roughly log-linearly with their calculated volatilities during solar nebula condensation [1, 2]. This depletion, however, is not accompanied by any stable isotope fractionation, which would otherwise be expected during vaporisation/condensation and atmospheric loss attending accretion [3, 4]. Thus, the physical processes that led to the formation of the Earth are yet to be reconciled with its chemical composition. Here, we integrate N-body simulations of planetary formation [5] within a framework that combines estimates for the compositions of planetary building blocks with volatile element losses during collisions, to link Earth’s elemental- and isotopic make-up with accretion mechanisms. The smooth pattern of volatile depletion in the Earth reflects the stochastic accretion of numerous, smaller, partially-vaporised precursor bodies whose elemental abundances are set by the heliocentric distances at which they formed. Impact events engender vaporisation, but atmospheric loss is only efficient during the early stages of accretion when volatile species can readily escape the gravitational pull of the proto-Earth. The chemical and isotopic compositions of the most volatile elements are controlled by that of late-accreting material, during which time the proto-Earth is sufficiently large so as to limit atmospheric loss. Stable isotopes of moderately- and highly volatile elements thus retain near-chondritic compositions.

[1] O’Neill and Palme (2008), Phil. Trans. R. Soc. 4205-38 [2] Braukmüller et al. (2019), Nat. Geosci., 564-9 [3] Wang and Jacobsen (2016), Nature, 521-4 [4] Sossi et al. 2018, Chem. Geol. 73-84 [5] Jacobson and Morbidelli (2014), Phil. Trans. R. Soc. 20130174