Stochastic accretion of the Earth

Abstract

Chondritic meteorites are thought to be representative of the material that formed the Earth. However, the Earth is depleted in volatile elements in a manner unlike that observed in any chondrite, and yet these elements retain chondritic isotope ratios. Here we use N-body simulations to show that the Earth did not form only from chondrites, but by stochastic accretion of many precursor bodies whose variable compositions reflect the temperatures at which they formed. Earth’s composition is reproduced when the initial temperatures of planetesimal- to embryo-sized bodies are set by disk accretion rates of (1.08 ± 0.17) × 10−7 solar masses per year, although they may be perturbed by 26Al heating on bodies formed at different times. Our model implies that a heliocentric gradient in composition was present in the protoplanetary disk and that planetesimals formed rapidly within ~1 Myr, consistent with radiometric volatile depletion ages of the Earth. N-body simulations show that the Earth might have accreted stochastically from various precursor bodies with different compositions depending on their formation temperature. This scenario fits the elemental isotope composition of the bulk Earth and suggests the presence of a radial gradient in the composition of the protoplanetary disk.