arXiv subjects

David C. Rubie

Publications and source records attributed to David C. Rubie.

15 recordsLinked to original sources

arXiv2026

Oxidation Constraints on Terrestrial Planet Formation from a Ring

The present-day solar system comprises meteorites with varying oxidation levels, derived from different parent bodies. Previous studies (e.g. Rubie et al., 2011) of the partitioning of siderophile elements between mantle and core during planetary growth and differentiation showed that Earth must accrete reduced bodies first and oxidised bodies later. Here we show that, if the terrestrial planets formed from a narrow ring of planetesimals, this condition is not fulfilled, whatever heliocentric gradient of oxidation is assumed in the ring. The reason is that planetary embryos quickly accrete planetesimals from the whole width of the ring, incorporating both reduced and oxidised material. The partially oxidised state of all planetary embryos leads to mismatches with the composition of the bulk silicate Earth (BSE) because oxygen fugacity strongly affects the partitioning of siderophile elements. We demonstrate that reproducing the BSE composition requires reduced and oxidised reservoirs to remain segregated until embryo formation is almost complete. The delivery of oxidised material to the terrestrial planet-forming ring towards the end of the disc's lifetime is therefore a key requirement of any successful dynamical model of terrestrial planet formation.

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arXiv2025

Compositional Outcomes of Earth Formation from a Narrow Ring

We address Earth formation from an elemental perspective, using a method similar to Rubie et al. (2015) but with updates from Dale et al. (2023) to simulate the chemical evolution of Earth's mantle during metal-silicate equilibration events from accretional collisions. Our model introduces two key differences: (1) Earth forms from a dense ring of planetesimals and planetary embryos near 1 AU, extending into the asteroid belt, and (2) we divide this population into four zones. The innermost zone contains planetesimals enriched in refractory elements relative to Si and depleted in volatiles. The remaining zones represent enstatite, ordinary, and CI chondrites. We fit the Earth's bulk silicate composition by adjusting the boundaries of these zones and the refractory enrichment in the inner zone, giving us four compositional free parameters. A fifth parameter relates to the depth of planetesimal equilibration after a giant impact. We examined twenty-two ring model simulations, expanded to forty-eight based on hot or cold targets during collisions. Seventeen simulations resulted in a mantle chemistry resembling the bulk silicate Earth (BSE), despite differences in growth sequences. These variations lead to different fitting parameter values, altering the proportions of different meteorite types required to match the BSE. However, findings show Earth must accrete 60-80% of material from the innermost refractory-enriched zone. This indicates that, with the right growth sequence, multiple ring model structures can yield an Earth-anaologue composition consistent with the BSE.

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arXiv2023

Constraining the Origin of Mars via Simulations of Multi-Stage Core Formation

It remains an elusive goal to simultaneously model the astrophysics of Solar System accretion while reproducing the mantle chemistry of more than one inner terrestrial planet. Here, we used a multistage core-mantle differentiation model based on Rubie et al. (2011,2015) to track the formation and composition of Earth and Mars in various Grand Tack formation simulations. Prior studies showed that in order to recreate Earth's mantle composition, it must grow first from reduced (Fe-metal rich and O-poor) building blocks and then from increasingly oxidized (FeO rich) material. This accretion chemistry occurs when an oxidation gradient exists across the disk so that the innermost solids are reduced and increasingly oxidized material is found at greater heliocentric distances. For a suite of Grand Tack simulations, we investigated whether Earth and Mars can be simultaneously produced by the same oxidation gradient. Our model did not find an oxidation gradient that simultaneously reproduces the mantle composition of Earth and Mars. Due to its small mass and rapid formation, the formation history of Mars-like planets is very stochastic which decreases the likelihood of compatibility with an Earth-producing oxidation gradient in any given realization. To reconcile the accretion history and ideal chemistry of the Mars-like planet with the oxidation gradient of an Earth-producing disk, we determined where in the Earth-producing disk Mars must have formed. We find that the FeO-rich composition of the Martian mantle requires that Mars' building blocks must originate exterior to 1.0 astronomical units (AU).

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arXiv2021

Contemporary formation of early solar system planetesimals at two distinct radial locations

The formation of planetesimals is expected to occur via particle-gas instabilities that concentrate dust into self-gravitating clumps. Triggering these instabilities requires the prior pileup of dust in the protoplanetary disk. Until now, this has been successfully modeled exclusively at the disk's snowline, whereas rocky planetesimals in the inner disk were obtained only by assuming either unrealistically large particle sizes or an enhanced global disk metallicity. However, planetesimal formation solely at the snowline is difficult to reconcile with the early and contemporaneous formation of iron meteorite parent bodies with distinct oxidation states and isotopic compositions, indicating formation at different radial locations in the disk. Here, by modeling the evolution of a disk with ongoing accretion of material from the collapsing molecular cloud, we show that planetesimal formation may have been triggered within the first 0.5 million years by dust pileup at both the snowline (at approximately 5 au) and the silicate sublimation line (at approximately 1 au), provided turbulent diffusion was low. Particle concentration at approximately 1 au is due to the early outward radial motion of gas and is assisted by the sublimation and recondensation of silicates. Our results indicate that, although the planetesimals at the two locations formed about contemporaneously, those at the snowline accreted a large fraction of their mass (approximately 60 percent) from materials delivered to the disk in the first few 10,000 yr, whereas this fraction is only 30 percent for the planetesimals formed at the silicate line. Thus, provided that the isotopic composition of the delivered material changed with time, these two planetesimal populations should have distinct isotopic compositions, consistent with observations.

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arXiv2021

The Effect of Inefficient Accretion on Planetary Differentiation

Pairwise collisions between terrestrial embryos are the dominant means of accretion during the last stage of planet formation. Hence, their realistic treatment in N-body studies is critical to accurately model the formation of terrestrial planets and to develop interpretations of telescopic and spacecraft observations. In this work, we compare the effects of two collision prescriptions on the core-mantle differentiation of terrestrial planets: a model in which collisions are always completely accretionary (``perfect merging'') and a more realistic model based on neural networks that has been trained on hydrodynamical simulations of giant impacts. The latter model is able to predict the loss of mass due to imperfect accretion and the evolution of non-accreted projectiles in hit-and-run collisions. We find that the results of the neural-network model feature a wider range of final core mass fractions and metal-silicate equilibration pressures, temperatures, and oxygen fugacities than the assumption of perfect merging. When used to model collisions in N-body studies of terrestrial planet formation, the two models provide similar answers for planets more massive than 0.1 Earth's masses. For less massive final bodies, however, the inefficient-accretion model predicts a higher degree of compositional diversity. This phenomenon is not reflected in planet formation models of the solar system that use perfect merging to determine collisional outcomes. Our findings confirm the role of giant impacts as important drivers of planetary diversity and encourage a realistic implementation of inefficient accretion in future accretion studies.

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arXiv2021

Scaling laws for the geometry of an impact-induced magma ocean

Here, we develop scaling laws for (1) the distribution of impact-induced heat within the mantle and (2) shape of the impact-induced melt based on more than 100 smoothed particle hydrodynamic (SPH) simulations. We use Legendre polynomials to describe these scaling laws and determine their coefficients by linear regression, minimizing the error between our model and SPH simulations. The input parameters are the impact angle $θ$ ($0^{\circ}, 30^{\circ}, 60^{\circ}$, and $90^{\circ}$), total mass $M_T$ ($1M_{\rm Mars}-53M_{\rm Mars}$, where $M_{\rm Mars}$ is the mass of Mars), impact velocity $v_{\rm imp}$ ($v_{\rm esc} - 2v_{\rm esc}$, where $v_{\rm esc}$ is the mutual escape velocity), and impactor-to-total mass ratio $γ$ ($0.03-0.5$). We find that the equilibrium pressure at the base of a melt pool can be higher (up to $\approx 80 \%$) than those of radially-uniform global magma ocean models. This could have a significant impact on element partitioning. These melt scaling laws are publicly available on GitHub ($\href{https://github.com/mikinakajima/MeltScalingLaw}{https://github.com/mikinakajima/MeltScalingLaw}$).

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arXiv2018

The Delivery of Water During Terrestrial Planet Formation

The planetary building blocks that formed in the terrestrial planet region were likely very dry, yet water is comparatively abundant on Earth. We review the various mechanisms proposed for the origin of water on the terrestrial planets. Various in-situ mechanisms have been suggested, which allow for the incorporation of water into the local planetesimals in the terrestrial planet region or into the planets themselves from local sources, although all of those mechanisms have difficulties. Comets have also been proposed as a source, although there may be problems fitting isotopic constraints, and the delivery efficiency is very low, such that it may be difficult to deliver even a single Earth ocean of water this way. The most promising route for water delivery is the accretion of material from beyond the snow line, similar to carbonaceous chondrites, that is scattered into the terrestrial planet region as the planets are growing. Two main scenarios are discussed in detail. First is the classical scenario in which the giant planets begin roughly in their final locations and the disk of planetesimals and embryos in the terrestrial planet region extends all the way into the outer asteroid belt region. Second is the Grand Tack scenario, where early inward and outward migration of the giant planets implants material from beyond the snow line into the asteroid belt and terrestrial planet region, where it can be accreted by the growing planets. Sufficient water is delivered to the terrestrial planets in both scenarios. While the Grand Tack scenario provides a better fit to most constraints, namely the small mass of Mars, planets may form too fast in the nominal case discussed here. This discrepancy may be reduced as a wider range of initial conditions is explored. Finally, we discuss several more recent models that may have important implications for water delivery to the terrestrial planets.

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arXiv2017

Water and the interior structure of terrestrial planets and icy bodies

Water content and the internal evolution of terrestrial planets and icy bodies are closely linked. The distribution of water in planetary systems is controlled by the temperature structure in the protoplanetary disk and dynamics and migration of planetesimals and planetary embryos. This results in the formation of planetesimals and planetary embryos with a great variety of compositions, water contents and degrees of oxidation. The internal evolution and especially the formation time of planetesimals relative to the timescale of radiogenic heating by short-lived 26Al decay may govern the amount of hydrous silicates and leftover rock-ice mixtures available in the late stages of their evolution. In turn, water content may affect the early internal evolution of the planetesimals and in particular metal-silicate separation processes. Moreover, water content may contribute to an increase of oxygen fugacity and thus affect the concentrations of siderophile elements within the silicate reservoirs of Solar System objects. Finally, the water content strongly influences the differentiation rate of the icy moons, controls their internal evolution and governs the alteration processes occurring in their deep interiors.

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arXiv2017

Formation, stratification, and mixing of the cores of Earth and Venus

Earth possesses a persistent, internally-generated magnetic field, whereas no trace of a dynamo has been detected on Venus, at present or in the past, although a high surface temperature and recent resurfacing events may have removed paleomagnetic evidence. Whether or not a terrestrial body can sustain an internally generated magnetic field by convection inside its metallic fluid core is determined in part by its initial thermodynamic state and its compositional structure, both of which are in turn set by the processes of accretion and differentiation. Here we show that the cores of Earth- and Venus-like planets should grow with stable compositional stratification unless disturbed by late energetic impacts. They do so because higher abundances of light elements are incorporated into the liquid metal that sinks to form the core as the temperatures and pressures of metal-silicate equilibration increase during accretion. We model this process and determine that this establishes a stable stratification that resists convection and inhibits the onset of a geodynamo. However, if a late energetic impact occurs, it could mechanically stir the core creating a single homogenous region within which a long-lasting geodynamo would operate. While Earth's accretion has been punctuated by a late giant impact with likely enough energy to mix the core (e.g. the impact that formed the Moon), we hypothesize that the accretion of Venus is characterized by the absence of such energetic giant impacts and the preservation of its primordial stratifications.

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arXiv2016

Highly siderophile elements were stripped from Earth's mantle by iron sulfide segregation

Highly siderophile elements (HSEs) are strongly depleted in the bulk silicate Earth (BSE) but are present in near-chondritic relative abundances. The conventional explanation is that the HSEs were stripped from the mantle by the segregation of metal during core formation but were added back in near-chondritic proportions by late accretion, after core formation had ceased. Here we show that metal-silicate equilibration and segregation during Earth's core formation actually increased HSE mantle concentrations because HSE partition coefficients are relatively low at the high pressures of core formation within Earth. The pervasive exsolution and segregation of iron sulfide liquid from silicate liquid (the "Hadean matte") stripped magma oceans of HSEs during cooling and crystallization, before late accretion, and resulted in slightly suprachondritic palladium/iridium and ruthenium/iridium ratios.

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arXiv2016

Impact-induced melting during accretion of the Earth

Because of the high energies involved, giant impacts that occur during planetary accretion cause large degrees of melting. The depth of melting in the target body after each collision determines the pressure and temperature conditions of metal-silicate equilibration and thus geochemical fractionation that results from core-mantle differentiation. The accretional collisions involved in forming the terrestrial planets of the inner Solar System have been calculated by previous studies using N-body accretion simulations. Here we use the output from such simulations to determine the volumes of melt produced and thus the pressure and temperature conditions of metal-silicate equilibration, after each impact, as Earth-like planets accrete. For these calculations a parametrised melting model is used that takes impact velocity, impact angle and the respective masses of the impacting bodies into account. The evolution of metal-silicate equilibration pressures (as defined by evolving magma ocean depths) during Earth's accretion depends strongly on the lifetime of impact-generated magma oceans compared to the time interval between large impacts. In addition, such results depend on starting parameters in the N-body simulations, such as the number and initial mass of embryos. Thus, there is the potential for combining the results, such as those presented here, with multistage core formation models to better constrain the accretional history of the Earth.

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arXiv2016

Oxygen isotopic evidence for vigorous mixing during the Moon-forming Giant Impact

Earth and Moon are shown here to be composed of oxygen isotope reservoirs that are indistinguishable, with a difference in Δ"17O of -1 +/- 5ppm (2se). Based on these data and our new planet formation simulations that include a realistic model for oxygen isotopic reservoirs, our results favor vigorous mixing during the giant impact and therefore a high-energy high- angular-momentum impact. The results indicate that the late veneer impactors had an average Δ"17O within approximately 1 per mil of the terrestrial value, suggesting that these impactors were water rich.

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arXiv2015

Mechanisms and Geochemical Models of Core Formation

The formation of the Earth's core is a consequence of planetary accretion and processes in the Earth's interior. The mechanical process of planetary differentiation is likely to occur in large, if not global, magma oceans created by the collisions of planetary embryos. Metal-silicate segregation in magma oceans occurs rapidly and efficiently unlike grain scale percolation according to laboratory experiments and calculations. Geochemical models of the core formation process as planetary accretion proceeds are becoming increasingly realistic. Single stage and continuous core formation models have evolved into multi-stage models that are couple to the output of dynamical models of the giant impact phase of planet formation. The models that are most successful in matching the chemical composition of the Earth's mantle, based on experimentally-derived element partition coefficients, show that the temperature and pressure of metal-silicate equilibration must increase as a function of time and mass accreted and so must the oxygen fugacity of the equilibrating material. The latter can occur if silicon partitions into the core and through the late delivery of oxidized material. Coupled dynamical accretion and multi-stage core formation models predict the evolving mantle and core compositions of all the terrestrial planets simultaneously and also place strong constraints on the bulk compositions and oxidation states of primitive bodies in the protoplanetary disk.

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arXiv2015

Highly Siderophile Elements in the Earth's Mantle as a Clock for the Moon-forming Impact

According to the generally accepted scenario, the last giant impact on the Earth formed the Moon and initiated the final phase of core formation by melting the Earth's mantle. A key goal of geochemistry is to date this event, but different ages have been proposed. Some argue for an early Moon-forming event, approximately 30 million years (Myr) after the condensation of the first solids in the Solar System, whereas others claim a date later than 50 Myr (and possibly as late as around 100 My) after condensation. Here we show that a Moon-forming event at 40 Myr after condensation, or earlier, is ruled out at a 99.9 per cent confidence level. We use a large number of N-body simulations to demonstrate a relationship between the time of the last giant impact on an Earth-like planet and the amount of mass subsequently added during the era known as Late Accretion. As the last giant impact is delayed, the late-accreted mass decreases in a predictable fashion. This relationship exists within both the classical scenario and the Grand Tack scenario of terrestrial planet formation, and it holds across a wide range of disk conditions. The concentration of highly siderophile elements (HSEs) in Earth's mantle constrains the mass of chondritic material added to Earth during Late Accretion. Using HSE abundance measurements, we determine a Moon-formation age of 95 +/- 32 Myr since condensation. The possibility exists that some late projectiles were differentiated and left an incomplete HSE record in Earth's mantle. Even in this case, various isotopic constraints strongly suggest that the late-accreted mass did not exceed 1 per cent of Earth's mass, and so the HSE clock still robustly limits the timing of the Moon-forming event to significantly later than 40 My after condensation.

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arXiv2014

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 planetary accretion and differentiation scenarios, we integrated a multistage core-mantle differentiation model with N-body accretion simulations. Impacts between embryos and planetesimals 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. The primary constraint on the combined model is the composition of the Earth's primitive mantle, 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 equilibrium pressure and 1-4 parameters that define the starting compositions of primitive bodies. This integrated model has been applied to 6 Grand Tack simulations. Investigations of a broad parameter space indicate that: accretion of Earth was heterogeneous, metal-silicate equilibration pressures increase as accretion progresses and are 60-70% of core-mantle boundary pressures at the time of each impact, and a large fraction (70-100%) of the metal of impactor cores equilibrates with a small fraction of the silicate mantles of protoplanets during each core formation event. Acceptable fits to the Earth's mantle composition are obtained only when bodies that originated close to the Sun, at <0.9-1.2 AU, are highly reduced and those beyond this distance are increasingly oxidized. 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 8-9 wt% silicon, 2-4 wt% oxygen and 10-60 ppm hydrogen, whereas the Martian core is predicted to contain low concentrations (<1 wt%) of Si and O.

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