Statistical Constraints from Siderophile Elements on Earth's Accretion, Differentiation, and Initial Core Stratification

Abstract:

Abundances of siderophile elements in the primitive mantle constrain the conditions of Earth's core/mantle differentiation. Core growth occurred as Earth accreted from collisions between planetesimals and larger embryos of unknown original provenance, so geochemistry is directly related to the overall dynamics of Solar System formation. Recent studies claim that only certain conditions of equilibration (pressure, temperature, and oxygen fugacity) during core formation can reproduce the available data. Typical analyses, however, only consider the effects of varying a few out of tens of free parameters in continuous core formation models. Here we describe the Markov chain Monte Carlo method, which simultaneously incorporates the large uncertainties on Earth's composition and the parameterizations that describe elemental partitioning between metal and silicate. This Bayesian technique is vastly more computationally efficient than a simple grid search and is well suited to models of planetary accretion that involve a plethora of variables.

In contrast to previous work, we find that analyses of siderophile elements alone cannot yield a unique scenario for Earth's accretion. Our models predict a wide range of possible light element contents for the core, encompassing all combinations permitted by seismology and mineral physics. Specifically, we are agnostic between silicon and oxygen as the dominant light element, and the addition of carbon or sulfur is also permissible but not well constrained. Redox conditions may have remained roughly constant during Earth's accretion or relatively oxygen-rich material could have been incorporated before reduced embryos. Pressures and temperatures of equilibration, likewise, may only increase slowly throughout accretion. Therefore, we do not necessarily expect a thick (>500 km), compositionally stratified layer that is stable against convection to develop at the top of the core of Earth (or, by analogy, Venus). A thinner stable layer might inhibit the initialization of the dynamo.