Accretion and differentiation of the terrestrial planets with implications for the compositions of early-formed Solar System bodies and accretion of water

In order to test accretion simulations as well as planetary differentiation scenarios, we have integrated a multistage core-mantle differentiation model with N-body accretion simulations. Impacts between embryos and planetesimals are considered to result in magma ocean formation and episodes of core formation. The core formation model combines rigorous chemical mass balance with metal-silicate element partitioning data and requires that the bulk compositions of all starting embryos and planetesimals are defined as a function of their heliocentric distances of origin. To do this, we assume that non-volatile elements are present in Solar System (CI) relative abundances in all bodies and that oxygen and H₂O contents are the main compositional variables. The primary constraint on the combined model is the composition of the Earth's primitive mantle. In addition, we aim to reproduce the composition of the martian mantle and the mass fractions of the metallic cores of Earth and Mars. The model is refined by least squares minimization with up to five fitting parameters that consist of the metal-silicate equilibration pressure and 1-4 parameters that define the starting compositions of primitive bodies. This integrated model has been applied to six Grand Tack N-body accretion simulations. Investigations of a broad parameter space indicate that: (1) accretion of Earth was heterogeneous, (2) metal-silicate equilibration pressures increase as accretion progresses and are, on average, 60-70% of core-mantle boundary pressures at the time of each impact, and (3) a large fraction (70-100%) of the metal of impactor cores equilibrates with a small fraction of the silicate mantles of proto-planets during each core formation event. Results are highly sensitive to the compositional model for the primitive starting bodies and several accretion/core-formation models can thus be excluded. Acceptable fits to the Earth's mantle composition are obtained only when bodies that originated close to the Sun, at <0.9-1.2AU, are highly reduced and those from beyond this distance are increasingly oxidized. Reasonable concentrations of H₂O in Earth's mantle are obtained when bodies originating from beyond 6-7AU contain 20wt% water ice (icy bodies that originated between the snow line and this distance did not contribute to Earth's accretion because they were swept up by Jupiter and Saturn). In the six models examined, water is added to the Earth mainly after 60-80% of its final mass has accreted. The compositional evolution of the mantles of Venus and Mars are also constrained by the model. The FeO content of the martian mantle depends critically on the heliocentric distance at which the Mars-forming embryo originated. Finally, the Earth's core is predicted to contain 8-9wt% silicon, 2-4wt% oxygen and 10-60ppm hydrogen, whereas the martian core is predicted to contain low concentrations (<1wt%) of Si and O.