Timing of Martian Core Formation from Models of Hf-W Evolution Coupled with N-body Simulations.

Determining how and when Mars formed has been a long-standing challenge for planetary scientists. The size and orbit of Mars are difficult to reproduce in classical simulations of planetary accretion, and this has inspired models of inner solar system evolution that are tuned to produce Mars-like planets. However, such models are not always coupled to geochemical constraints. Analyses of Martian meteorites using the extinct hafnium-tungsten (Hf-W) radioisotopic system, which is sensitive to the timing of core formation, have indicated that the Martian core formed within a few million years of the start of the solar system itself. This has been interpreted to suggest that, unlike Earth's protracted accretion, Mars grew to its modern size very rapidly. These arguments, however, generally rely on simplified growth histories for Mars. Here, we combine likely accretionary histories from a large number of N-body simulations with calculations of metal-silicate partitioning and Hf-W isotopic evolution during core formation to constrain the range of conditions that could have produced Mars. We find that there is no strong correlation between the final masses or orbits of simulated Martian analogs and their 182W anomalies, and that it is readily possible to produce Mars-like Hf-W isotopic compositions for a variety of accretionary conditions. The Hf-W signature of Mars is very sensitive to the oxygen fugacity (fO2) of accreted material because the metal-silicate partitioning behavior of W is strongly dependent on redox conditions. The average fO2 of Martian building blocks must fall in the range of 1.3-1.6 log units below the iron-wüstite buffer to produce a Martian mantle with the observed Hf/W ratio. Other geochemical properties (such as sulfur content) also influence Martian 182W signatures, but the timing of accretion is a more important control. We find that while Mars must have accreted most of its mass within ~5 million years of solar system formation to reproduce the Hf-W isotopic constraints, it may have continued growing afterwards for over 50 million years. There is a high probability of simultaneously matching the orbit, mass, and Hf-W signature of Mars even in cases of prolonged accretion if giant impactor cores were poorly equilibrated and merged directly with the proto-Martian core.

The origin of the Moon's Earth-like tungsten isotopic composition from dynamical and geochemical modeling.

The Earth and Moon have identical or very similar isotopic compositions for many elements, including tungsten. However, canonical models of the Moon-forming impact predict that the Moon should be made mostly of material from the impactor, Theia. Here we evaluate the probability of the Moon inheriting its Earth-like tungsten isotopes from Theia in the canonical giant impact scenario, using 242 N-body models of planetary accretion and tracking tungsten isotopic evolution, and find that this probability is <1.6-4.7%. Mixing in up to 30% terrestrial materials increases this probability, but it remains <10%. Achieving similarity in stable isotopes is also a low-probability outcome, and is controlled by different mechanisms than tungsten. The Moon's stable isotopes and tungsten isotopic composition are anticorrelated due to redox effects, lowering the joint probability to significantly less than 0.08-0.4%. We therefore conclude that alternate explanations for the Moon's isotopic composition are likely more plausible.

Ancient helium and tungsten isotopic signatures preserved in mantle domains least modified by crustal recycling.

Rare high-3He/4He signatures in ocean island basalts (OIB) erupted at volcanic hotspots derive from deep-seated domains preserved in Earth's interior. Only high-3He/4He OIB exhibit anomalous 182W-an isotopic signature inherited during the earliest history of Earth-supporting an ancient origin of high 3He/4He. However, it is not understood why some OIB host anomalous 182W while others do not. We provide geochemical data for the highest-3He/4He lavas from Iceland (up to 42.9 times atmospheric) with anomalous 182W and examine how Sr-Nd-Hf-Pb isotopic variations-useful for tracing subducted, recycled crust-relate to high 3He/4He and anomalous 182W. These data, together with data on global OIB, show that the highest-3He/4He and the largest-magnitude 182W anomalies are found only in geochemically depleted mantle domains-with high 143Nd/144Nd and low 206Pb/204Pb-lacking strong signatures of recycled materials. In contrast, OIB with the strongest signatures associated with recycled materials have low 3He/4He and lack anomalous 182W. These observations provide important clues regarding the survival of the ancient He and W signatures in Earth's mantle. We show that high-3He/4He mantle domains with anomalous 182W have low W and 4He concentrations compared to recycled materials and are therefore highly susceptible to being overprinted with low 3He/4He and normal (not anomalous) 182W characteristic of subducted crust. Thus, high 3He/4He and anomalous 182W are preserved exclusively in mantle domains least modified by recycled crust. This model places the long-term preservation of ancient high 3He/4He and anomalous 182W in the geodynamic context of crustal subduction and recycling and informs on survival of other early-formed heterogeneities in Earth's interior.

Core Formation and Geophysical Properties of Mars.

The chemical and physical properties of the interiors of terrestrial planets are largely determined during their formation and differentiation. Modeling a planet's formation provides important insights into the properties of its core and mantle, and conversely, knowledge of those properties may constrain formational narratives. Here, we present a multi-stage model of Martian core formation in which we calculate core-mantle equilibration using parameterizations from high pressure-temperature metal-silicate partitioning experiments. We account for changing core-mantle boundary (CMB) conditions, composition-dependent partitioning, and partial equilibration of metal and silicate, and we evolve oxygen fugacity (fO2) self-consistently. The model successfully reproduces published meteorite-based estimates of most elemental abundances in the bulk silicate Mars, which can be used to estimate core formation conditions and core composition. This composition implies that the primordial material that formed Mars was significantly more oxidized (0.9-1.4 log units below the iron-wüstite buffer) than that of the Earth, and that core-mantle equilibration in Mars occurred at 42-60% of the evolving CMB pressure. On average, at least 84% of accreted metal and at least 40% of the mantle were equilibrated in each impact, a significantly higher degree of metal equilibration than previously reported for the Earth. In agreement with previous studies, the modeled Martian core is rich in sulfur (18-19 wt%), with less than one weight percent O and negligible Si. We have used these core and mantle compositions to produce physical models of the present-day Martian interior and evaluate the sensitivity of core radius to crustal thickness, mantle temperature, core composition, core temperature, and density of the core alloy. Trade-offs in how these properties affect observable physical parameters like planetary mass, radius, moment of inertia, and tidal Love number k2 define a range of likely core radii: 1620-1870 km. Seismic velocity profiles for several combinations of model parameters have been used to predict seismic body-wave travel times and planetary normal mode frequencies. These results may be compared to forthcoming Martian seismic data to further constrain core formation conditions and geophysical properties.

The carbon content of Earth and its core.

Earth's core is likely the largest reservoir of carbon (C) in the planet, but its C abundance has been poorly constrained because measurements of carbon's preference for core versus mantle materials at the pressures and temperatures of core formation are lacking. Using metal-silicate partitioning experiments in a laser-heated diamond anvil cell, we show that carbon becomes significantly less siderophile as pressures and temperatures increase to those expected in a deep magma ocean during formation of Earth's core. Based on a multistage model of core formation, the core likely contains a maximum of 0.09(4) to 0.20(10) wt% C, making carbon a negligible contributor to the core's composition and density. However, this accounts for ∼80 to 90% of Earth's overall carbon inventory, which totals 370(150) to 740(370) ppm. The bulk Earth's carbon/sulfur ratio is best explained by the delivery of most of Earth's volatiles from carbonaceous chondrite-like precursors.

Constraints on terrestrial planet formation timescales and equilibration processes in the Grand Tack scenario from Hf-W isotopic evolution.

We examine 141 N-body simulations of terrestrial planet late-stage accretion that use the Grand Tack scenario, coupling the collisional results with a hafnium-tungsten (Hf-W) isotopic evolution model. Accretion in the Grand Tack scenario results in faster planet formation than classical accretion models because of higher planetesimal surface density induced by a migrating Jupiter. Planetary embryos which grow rapidly experience radiogenic ingrowth of mantle tungsten which is inconsistent with the measured terrestrial value, unless much of the tungsten is removed by an impactor core that mixes thoroughly with the target mantle. For physically Earth-like surviving planets, we find that the fraction of equilibrating impactor core kcore ≥ 0.6 is required to produce results agreeing with observed terrestrial tungsten anomalies (assuming equilibration with relatively large volumes of target mantle material; smaller equilibrating mantle volumes would require even larger kcore ). This requirement of substantial core re-equilibration may be difficult to reconcile with fluid dynamical predictions and hydrocode simulations of mixing during large impacts, and hence this result disfavors the rapid planet building of Grand Tack accretion.

Radial mixing and Ru-Mo isotope systematics under different accretion scenarios.

The Ru-Mo isotopic compositions of inner Solar System bodies may reflect the provenance of accreted material and how it evolved with time, both of which are controlled by the accretion scenario these bodies experienced. Here we use a total of 116 N-body simulations of terrestrial planet accretion, run in the Eccentric Jupiter and Saturn (EJS), Circular Jupiter and Saturn (CJS), and Grand Tack scenarios, to model the Ru-Mo anomalies of Earth, Mars, and Theia analogues. This model starts by applying an initial step function in Ru-Mo isotopic composition, with compositions reflecting those in meteorites, and traces compositional evolution as planets accrete. The mass-weighted provenance of the resulting planets reveals more radial mixing in Grand Tack simulations than in EJS/CJS simulations, and more efficient mixing among late-accreted material than during the main phase of accretion in EJS/CJS simulations. We find that an extensive homogenous inner disk region is required to reproduce Earth's observed Ru-Mo composition. EJS/CJS simulations require a homogeneous reservoir in the inner disk extending to ≥3-4 AU (≥74-98% of initial mass) to reproduce Earth's composition, while Grand Tack simulations require a homogeneous reservoir extending to ≥3-10 AU (≥97-99% of initial mass), and likely to ≥6-10 AU. In the Grand Tack model, Jupiter's initial location (the most likely location for a discontinuity in isotopic composition) is ~3.5 AU; however, this step location has only a 33% likelihood of producing an Earth with the correct Ru-Mo isotopic signature for the most plausible model conditions. Our results give the testable predictions that Mars has zero Ru anomaly and small or zero Mo anomaly, and the Moon has zero Mo anomaly. These predictions are insensitive to wide variations in parameter choices.

Effects of core formation on the Hf-W isotopic composition of the Earth and dating of the Moon-forming impact.

Earth's core formation set the initial compositions of the core and mantle. Various aspects of core formation, such as the degree of metal-silicate equilibration, oxygen fugacity, and depth of equilibration, have significant consequences for the resulting compositions, yet are poorly constrained. The Hf-W isotopic system can provide unique constraints on these aspects relative to other geochemical or geophysical methods. Here we model the Hf-W isotopic evolution of the Earth, improving over previous studies by combining a large number of N-body simulations of planetary accretion with a core formation model that includes self-consistent evolution of oxygen fugacity and a partition coefficient of tungsten that evolves with changing pressure, temperature, composition, and oxygen fugacity. The effective average fraction of equilibrating metal is constrained to be k > 0.2 for a range of equilibrating silicate masses (for canonical accretion scenarios), and is likely <0.55 if the Moon formed later than 65 Ma. These values of k typically correspond to an effective equilibration depth of ~0.5-0.7× the evolving core-mantle boundary pressure as the planet grows. The average mass of equilibrating silicate was likely at least 3× the impactor's silicate mass. Equilibration temperature, initial fO2 initial differentiation time, semimajor axis, and planetary mass (above ~0.9 M⊕) have no systematic effect on the 182W anomaly, or on f Hf/W (except for fO2), when applying the constraint that the model must reproduce Earth's mantle W abundance. There are strong tradeoffs between the effects of k, equilibrating silicate mass, depth of equilibration, and timing of core formation, so the terrestrial Hf-W isotopic system should be interpreted with caution when used as a chronometer of Earth's core formation. Because of these strong tradeoffs, the Earth's tungsten anomaly can be reproduced for Moon-forming impact timescales spanning at least 10-175 Ma. Early Moon formation ages require a higher degree of metal-silicate equilibration to produce Earth's 182W anomaly.