Accretion disk's magnetic field controlled the composition of the terrestrial planets
AAccretion disk’s magnetic field controlled thecomposition of the terrestrial planets
William F. McDonough ∗ and Takashi Yoshizaki Department of Geology, University of Maryland, College Park, MD20742, USA Department of Earth Science, Graduate School of Science, TohokuUniversity, Sendai, Miyagi 980-8578, Japan Research Center of Neutrino Sciences, Tohoku University, Sendai,Miyagi 980-8578, JapanSeptember 10, 2020
Chondrites, the building blocks of the terrestrial planets, have mass and atomicproportions of oxygen, iron, magnesium, and silicon totaling ≥
90% and variableMg/Si ( ∼ ≥ ≥ ∗ Corresponding author. E-mail: [email protected] a r X i v : . [ a s t r o - ph . E P ] S e p nce these final bulk compositions. Here we predict terrestrial planet compositionsand show that their core mass fractions and uncompressed densities correlate withtheir heliocentric distance, and follow a simple model of the magnetic field strengthin the protoplanetary disk. Our model assesses the distribution of iron in terms ofincreasing oxidation state, aerodynamics, and a decreasing magnetic field strengthoutward from the Sun, leading to decreasing core size of the terrestrial planets withradial distance. This distribution would enhance habitability in our solar system, andwould be equally applicable to exo-planetary systems. The formation of metallic cores in terrestrial planets greatly influences the thermal andbiological evolution of a planet. Core formation concentrates the heat producing elements(i.e., potassium, thorium and uranium) into the insulating, outer silicate shell and producesa conductive fluid, which can create a planetary magnetic field. The mass fraction ofmetallic core in Mercury, Venus, Earth, and Mars decreases with heliocentric distance fromabout 2/3, to 1/3 (Venus and Earth), to 1/5, respectively (Sohl and Schubert, 2015). Whatchemical and/or physical process produced the large variation observed in Fe/O values inchondrites and the terrestrial planets, particularly for Mercury? The presence of a long-lived, internally convecting metallic core results in dynamo action and the generation ofa planet’s surrounding protective magnetosphere that nurtures life. These differentiatedplanets represent the most likely home for life and its evolution.The compositions of the terrestrial planets and chondritic asteroids record, on average,an outward increase in oxygen fugacity, potentially a decrease in the nebular condensationtemperature, and decreasing amounts of metallic iron contributing to planet building. Theredox and temperature gradients leads to less metallic iron and more H- and O-rich solids2i.e., phyllosilicates) outward in the solar system. Importantly, nebular condensates donot reach the high Fe/Si values of Mercury even with strongly reduced, high-temperatureconditions (Ebel and Alexander, 2011). Thus, further metal-oxide separation processesare needed.Compositional models for the terrestrial planets are constructed from the followingdata sets: composition of the Sun (i.e., >
99% mass of the solar system), chemical trendsfor samples from a planet, satellite observations, and compositions of chondritic meteorites(i.e., the solar system’s building blocks of undifferentiated rock and metal mixtures). Im-portantly, the chondrites that we have, however, are those leftover from planet building.Here we use our earlier compositional models for the Earth (McDonough, 2014) and Mars(Yoshizaki and McDonough, 2020b) and model the recent data from the MESSENGERmission to Mercury to predict its bulk composition (Table 1), which is consistent withknown physical and chemical constraints (Methods). Given limited data for Venus, whichis consistent with an Earth-like analog (Surkov et al., 1987; Dumoulin et al., 2017), weassume it has a bulk Earth composition.Chondrites are geologically unprocessed materials, with their chemical compositionsreflecting the local nebular conditions. However, chondrites differ markedly in their redoxstates and major element compositions (Figures 1 and 2). The redox state, mineralogies,and isotopic compositions of chondrites and other meteorites demonstrate that the earlysolar system was not compositionally homogeneous (Warren, 2011). Significantly, theless oxidized Non-Carbonaceous (NC) meteorites, including the enstatite and ordinarychondrites (Figure 2), are viewed as coming from inner solar system regions closer to theSun (i.e., mostly 2 to 3 AU) than the oxidized Carbonaceous Chondrites (CC) and related3eteorites (Kruijer et al., 2017). The redox state and a dozen or so isotopic systems nowlink enstatite chondrites and Earth and equally, ordinary chondrites and Mars (Warren,2011).The Fe content of chondrites typically ranges from 1/5 to < ± ∼
93% of its mass, with the addition of the minor elements,Ca, Al, Ni, and S, bringing the total to 99 wt% (Figure 1). A planet’s mantle Mg ∼ B = µ I πr (1)where B is magnetic flux density (Tesla, or kg s − A − ), µ is the magnetic constant (Hm − or N A − ), I is current (A), r is position in 3D-space (m) (Methods and Supplemen-tary Figure 1). Azimuthal magnetic fields are likely to be strongest in the midplane (War-dle, 2007), the site of planetary accretion. The magnetic field strength of protoplanetarydisk is recognized as a constantly evolving 4 dimensional phenomena that have been ex-tensively treated by sophisticated MHD modeling (e.g., (Wardle, 2007)). Our perspectivesimply takes as a set of average conditions for the midplane of the disk at 4 critical dis-tances: Mercury (500 µ T, assumes a saturation field (Levy, 1978)), Earth (100 µ T (Wardle,2007)), and Vesta ( ∼ µ T (Wang et al., 2017)), with interpolations for Mars (60 µ T). Thissimple model (Figure 1) appeals to a fundamental scaling relationship ( B ∝ r − . ) thatviews the magnetic field strength at the disk’s midplane decreasing with distance from thecentral current moment of the evolving Sun. MHD modeling predicts B ∝ r − . (Wardle,2007; Bai, 2015). With mT magnetic field strength of the disk at ∼ τ accretion age that is restrictedto when a nebular envelope existed. Accretion in the presence of nebular gas is consis-tent with pebble accretion models of planetary formation, which may have contributed tothe early formation of Mars and the iron meteorite parent bodies (Johansen et al., 2015).Therefore, a key implication of our model is an early formation age ( ∼ ± Methods
Model description
The bulk composition of Mercury was defined to be consistent with its geodetic observ-ables: mass, density, and MOI (moment of inertia) (Margot et al., 2018). Assuming athermal gradient in the protoplanetary disk and the higher condensation temperature forforsterite (Mg SiO ) versus enstatite (Mg Si O ), then we predict a gradient in atomicMg/Si (1.4) and Al/Si (0.12) values projecting from the values for Mars and Earth (Fig-ure 2). The assumed Fe/Si (2.7) was established from a mass fraction of silicate to metal8o be consistent with Mercury’s uncompressed density (Figure 3), assuming proportions(40:53:7) and densities of silicates, metals, and sulfides (3,100, 7,100, and 4,600 kg m − ,respectively) as nominal values and with the metal alloy being a Fe-Ni-Si mixture. It isalso likely that core-mantle differentiation add some fraction of silicon into the core underreducing conditions (Nittler et al., 2018). The atomic Ca/Al (0.73) and Fe/Ni (18.3) val-ues are those seen in chondrites (Alexander, 2019a,b). The sulfur content was based onthe planetary volatility trend established from Mercury’s measured K/Th value and an ex-trapolation to the condensation temperature, following the practice used in (McDonoughand Sun, 1995; Yoshizaki and McDonough, 2020b). Ratios of alkali metals to refractoryelements provide a constraint on a planet’s volatile element depletion trend, however, thissimple model can be influenced by redox conditions and core formational processes. Fi-nally, the oxygen content was set to make the total equal to 100%. This model establishesthe bulk properties of Mercury, but it does not specify the distribution of elements betweenthe core and mantle. Data sources
Data sources for Figures 1 and 2 are as following: chondrites (Urey and Craig, 1953;Alexander, 2019a,b; McCall, 1968; Ivanova et al., 2008; Gosselin and Laul, 1990; Wassonand Kallemeyn, 1990; Bischoff et al., 1993); Mercury (this study); Earth (McDonough,2014); Mars (Yoshizaki and McDonough, 2020b). For Figure 3, density of planetary bod-ies are from (Russell et al., 2012; Park et al., 2019; Sierks et al., 2011; Consolmagnoet al., 2006; Macke et al., 2010, 2011; Britt and Consolmagno, 2003; Lewis, 1972; Stacey,2005); heliocentric distances of chondrite parent bodies are from (Desch et al., 2018).9 eferences
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We thank many our colleagues who have listened to various versions of this project andgiven helpful comments. WFM gratefully acknowledges NSF support (EAR1650365). TYacknowledges supports from the Japanese Society for the Promotion of Science (JP18J20708)and the GP-EES and DIARE programs.
Author contributions
WFM and TY proposed and conceived various portions of this study and together calcu-lated the compositional models. The manuscript was written by WFM, with edits, discus-sions, and revisions by TY & WFM. Both authors read and approved the final manuscript.17 ompeting interests
The authors declare no competing interests.
Data and materials availability
Correspondence and requests for materials should be addressed to WFM.
Supplementary information
Supplementary information is available for this paper.18able 1:
Composition of the terrestrial planets.
Atomic% Mercury Earth & Venus Mars CI chondrite(see Methods) (McDonough, 2014) (Yoshizaki and McDonough, 2020b) (volatile-free)(Alexander, 2019a)O 36.8 49.0 55.3 48.2Mg 15.6 16.7 15.3 15.1Si 11.0 15.1 15.1 14.7Fe 30.0 15.1 10.3 12.8Ni 1.64 0.82 0.57 0.70Al 1.38 1.56 1.41 1.20Ca 1.00 1.13 1.03 0.88S 2.49 0.52 0.92 6.43Fe/Si 2.72 1.00 0.69 0.87Fe/Al 21.8 9.7 7.3 10.6Fe/O 0.82 0.31 0.19 0.26Mg/Si 1.42 1.11 1.02 1.03Al/Si 0.12 0.10 0.09 0.08Mean Z igure 1: (a) Atomic abundances of major elements and (b) Fe/O values in the solarsystem bodies. Data sources are given in supplementary materials.20igure 2:
Ratios of major cations in the terrestrial planets and chondrites. (a) Mag-nesium/Si versus Al/Si. (b) Abundances of reduced (metal and sulfide) and oxidized Fenormalized to Si. Data sources are given in supplementary materials. Red symbols identifythe inner solar system, NC chondrites; see text for details.21igure 3:
Density of the solar system bodies.
Uncompressed and solid densities areshown for terrestrial planets and chondrites (grey), respectively. Bulk planetary densitiesare shown for asteroids (blue). For 1 Ceres, its bulk density is a lower limit of its soliddensity, given its high ice abundance and porosity. The red line shows a fit curve for theplanets ( ρ = 4 , r − . ). Data sources are given in supplementary materials.22 upplementary information Supplementary Figure 1: A simple Biot-Savart type model for the average magnetic fieldstrength versus accretion position of the terrestrial planets in the protoplanetary disk. Atop x-axis shows the correlation between uncompressed density and heliocentric distance.See text for details and data. A prediction for Venus is shown with a bar; its uncompresseddensity is 4,100 kg m −3