Stochastic accretion of the Earth

TL;DR

This paper uses N-body simulations to explain Earth's volatile element depletion and isotope ratios, suggesting stochastic accretion from bodies formed at different temperatures and rapid early planetesimal formation.

Contribution

It introduces a stochastic accretion model that accounts for Earth's volatile depletion and isotope ratios, integrating impact loss and formation timing effects.

Findings

Earth's volatile depletion follows a normal distribution pattern.

Impact loss was efficient only during the proto-Earth's small size phase.

Rapid planetesimal formation occurred within approximately 1 million years.

Abstract

Earth is depleted in volatile elements relative to chondritic meteorites, its possible building blocks. The extent of this depletion increases with decreasing condensation temperature, and is approximated by a cumulative normal distribution, unlike that in any chondrite. However, moderately volatile elements, occupying the mid-range of the distribution, have chondritic isotope ratios, contrary to that expected from loss by partial vaporisation/condensation. Here we reconcile these observations by showing, using N-body simulations, that Earth accreted stochastically from many precursor bodies whose variable compositions reflect the temperatures at which they formed. Impact-induced atmospheric loss was efficient only when the proto-Earth was small, and elements that accreted thereafter retain near-chondritic isotope ratios. Earth's composition is reproduced when initial temperatures of planetesimal- to embryo-sized bodies are set by disk accretion rates of (1.08 $\pm$ 0.17) $\times$ 10$^{-7}$ solar masses/yr, although they may be perturbed by $^{26}$Al heating on bodies formed at different times. The model implies a heliocentric gradient in composition and rapid planetesimal formation within $\sim$ 1 Myr, in accord with radiometric volatile depletion ages of Earth.