Magnesium isotope evidence that accretional vapour loss shapes planetary compositions

Abstract

It has long been recognized that Earth and other differentiated planetary bodies are chemically fractionated compared to primitive, chondritic meteorites and, by inference, the primordial disk from which they formed. However, it is not known whether the notable volatile depletions of planetary bodies are a consequence of accretion or inherited from prior nebular fractionation. The isotopic compositions of the main constituents of planetary bodies can contribute to this debate. Here we develop an analytical approach that corrects a major cause of measurement inaccuracy inherent in conventional methods, and show that all differentiated bodies have isotopically heavier magnesium compositions than chondritic meteorites. We argue that possible magnesium isotope fractionation during condensation of the solar nebula, core formation and silicate differentiation cannot explain these observations. However, isotopic fractionation between liquid and vapour, followed by vapour escape during accretionary growth of planetesimals, generates appropriate residual compositions. Our modelling implies that the isotopic compositions of magnesium, silicon and iron, and the relative abundances of the major elements of Earth and other planetary bodies, are a natural consequence of substantial (about 40 per cent by mass) vapour loss from growing planetesimals by this mechanism.

Extended Data Figure 1

Magnesium isotope compositions of carbonaceous chondrites plotted against their average literature oxygen isotope compositions. These mass-dependent oxygen isotope measurements reflect parent body hydrothermal alteration, so the correlation (R² = 0.78) between Mg and O isotopes (as well as with petrographic group; indicated in brackets under sample names) implies that the Mg isotope compositions of some carbonaceous chondrites have been altered by hydrothermal processes. The most altered samples, to the upper right of this diagram, are excluded from our chondrite Mg isotope means.

Extended Data Figure 2

Magnesium isotope compositions of peridotites plotted against whole rock MgO (panel a) and Al₂O₃ (panel b) contents. The absence of correlations of Mg isotope compositions with MgO or Al₂O₃ indicates absence of discernible Mg isotope fractionation during partial melting.

Extended Data Figure 3

Comparison between modelled compositions of a vapour depleted liquid and observed planetary compositions. As Figure 3 in main text, but additionally including observed isotope compositions for Mars, and eucrite and angrite parents bodies as well as including elemental and isotopic Fe observations (panels b and d; Fe isotope data from [55] and references therein, all other references as in Figure 3). Comparison of observed Fe contents and isotope ratios are complicated by core formation because most Fe enters the core. In our model we assume that the iron in the core has not been affected by vaporisation, inferred to occur later. For instance, the effect of ~48% Fe loss (panel c) on the current bulk silicate Earth Fe content is dependent on the fraction of Fe that entered the core prior to collisional vaporisation and the oxygen fugacity evolution of the growing Earth. For reference, the datum labelled Fe** in panel d is therefore the Fe/Ca of the bulk Earth (calculated from [56]) instead of the Fe/Ca of the bulk silicate Earth. Similarly, Si can also enter the core, although its quantity is likely <3 wt%. Right pointing arrows in b) and d) indicate the effect of 3 wt% Si in the core (3000 K assumed for metal-silicate Si isotope fractionation factor58).

Extended Data Figure 4

Comparison between modelled compositions of a vapour depleted liquid and observed planetary compositions. Similar to Extended Data Figure 3, but for model runs with a CI chondrite initial composition. Observed Mg and Fe isotope compositions (panel b) are presented relative chondrite mean, while Si isotope observations are relative to a mean of carbonaceous and ordinary chondrites, because those chondrites have undistinguishable Si isotope compositions, yet are distinctly different from enstatite chondrites (see [4] and references therein).

Extended Data Figure 5

Magnesium isotope compositions of reference samples analysed in multiple studies. The shaded areas show the mean and 2se of the isotope compositions observed in this study. Note that the plotted composition of Murchison for Bourdon et al. is a mean of the two replicates presented in their Table 1. The value for BHVO of Chakrabarti and Jacobsen is BHVO-1, all others are BHVO-2.

Extended Data Figure 6

Variation in velocity of individual impacts (normalized by target body escape velocity) as a function of target body radius. Central line denotes median value, shaded box encompasses region spanning 25^th-75^th percentiles, upper lines denote 90th percentile. Bulk density assumed to be 3000 kg m^-3.

Extended Data Figure 7

Fractional mass loss in Grand Tack simulation as a function of final body radius for direct vapour outflow model to illustrate results both with (white boxes, as Figure 2b) and without (shaded boxes) the inclusion of inheritance effects (see Methods). Boxes denote the median value, bars denote the 25^th and 75^th quartiles.

Figure 1

Magnesium isotope compositions. a) Probability density plots of Mg isotope compositions from previous standard-sample bracketing work, highlighting the results of individual studies,– that presented numerous analyses of both terrestrial and chondritic samples using the same methodology. These data show systematic subtle differences (0.02-0.05‰) between the Earth and primitive meteorites. Typically authors refrained from interpreting such small differences. b) Samples from this study (measured by critical mixture double spiking) ordered according to sample-type. Lines and shaded bars indicate means and 2se. Samples displayed with pale symbols are excluded from means (see main text). c) Earth and chondrite analyses from b) shown as probability plot to compare with a).

Figure 2

Median cumulative vapour fractions produced as a function of final planetary mass (in Earth masses M_⊕) determined from high-resolution N-body simulations of planetary accretion. The N-body simulations encompassed two scenarios: a calm disk without gas drag (“calm”) and a disk that is disturbed by a Grand Tack motion of Jupiter (“GT”). a) Vapour loss fractions calculated for impact vaporisation parameterised to impact velocity. b) Vapour loss fractions produced by direct outflow above exposed magma ponds/oceans. In a Grand Tack scenario, Jupiter’s motions cause higher eccentricities and hence higher impact velocities for such small bodies, which explains their high vapour fractions.

Figure 3

Comparison between modelled compositions of a vapour depleted liquid and observed terrestrial compositions. a) Changes in isotope compositions (‰/amu) against total relative vapour loss (F_Total, in mole fractions) calculated in our model. b) Observed terrestrial Mg (this study), and Si (from [4] and references therein) isotope compositions relative to enstatite chondrites (EH). Errors are 2se. c) Loss (mole fraction) of a given element (X), f_X, versus F_Total. d) Molar element/Ca of the terrestrial mantle, normalised to EH. Shaded bands give error bounds for F_Total inferred from Mg isotope data and the intersection of different curves with this field indicates the range of terrestrial depletions predicted for our vapour loss model. Comparison of these values to those calculated for the Earth relative to an enstatite chondrite starting composition (b and d) is generally good, despite uncertainties in model input parameters (see Methods) and additional influences on observed values from nebular and core formation processes,. Left pointing arrows show the effect of post-volatile loss accretion of 20% chondrite (EH).