McDonough and Yoshizaki Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-021-00429-4(2021) 8:39

Progress in Earth andPlanetary Science

REVIEW

Open AccessTerrestrial planet compositions
controlled by accretion disk magnetic field
William F. McDonough1,2,3*

and Takashi Yoshizaki2

Abstract
Terrestrial planets (Mercury, Venus, Earth, and Mars) are differentiated into three layers: a metallic core, a silicate shell(mantle and crust), and a volatile envelope of gases, ices, and, for the Earth, liquid water. Each layer has different
dominant elements (e.g., increasing iron content with depth and increasing oxygen content to the surface).
Chondrites, the building blocks of the terrestrial planets, have mass and atomic proportions of oxygen, iron,magnesium, and silicon totaling ≥ 90% and variable Mg/Si (∼ 25%), Fe/Si (factor of ≥2), and Fe/O (factor of ≥ 3). Whatremains an unknown is to what degree did physical processes during nebular disk accretion versus those during postnebular disk accretion (e.g., impact erosion) influence these planets final bulk compositions. Here we predict terrestrial
planet compositions and show that their core mass fractions and uncompressed densities correlate with their
heliocentric distance, and follow a simple model of the magnetic field strength in the protoplanetary disk. Our model
assesses the distribution of iron in terms of increasing oxidation state, aerodynamics, and a decreasing magnetic fieldstrength outward from the Sun, leading to decreasing core size of the terrestrial planets with radial distance. This
distribution enhances habitability in our solar system and may be equally applicable to exoplanetary systems.
Keywords: Planetary formation, Planetary composition, Accretionary disk, Magnetic field

1 Introduction
The formation of metallic cores in terrestrial planets
greatly influences the thermal and biological evolution ofa planet. Core formation typically concentrates the heatproducing elements (i.e., potassium, thorium, and uranium) into the insulating, outer silicate shell and produces
a conductive fluid, which can create a planetary magnetic
field. The presence of a long-lived, internally convecting
metallic core results in dynamo action and the generation of a planet’s surrounding protective magnetospherethat nurtures life. These differentiated planets represent
the most likely home for life and its evolution. Core
segregation also controls the distribution of some essential nutrients (e.g., phosphorus) (e.g., 90% of the Earth’s
P budget is in the core; McDonough, 2014). The mass
*Correspondence: mcdonoug@umd.edu
Department of Geology, University of Maryland, College Park, 8000 Regents
Drive, College Park, MD 20742, USA
2
Department of Earth Science, Tohoku University, 6-3, Aoba, Aramaki, Aoba,
Sendai 980-8578, Japan
Full list of author information is available at the end of the article1

fraction of metallic core in Mercury, Venus, Earth, andMars decreases with heliocentric distance from about 3/4,
to 1/3 (Venus and Earth), to 1/5, respectively (Sohl and
Schubert 2015). Chondrites, the building blocks of theterrestrial planets, have ≥ 93% of their mass and atomic
proportion being composed of O, Fe, Mg, and Si (Wasson and Kallemeyn 1988). The abundances of O and Fe
in chondrites typically varies by a factor of three, but insome uncommon Fe-rich examples, it approaches a factorof eight. In addition, most chondritic meteorites (except
EH, G, CB, and CH chondrite groups) have sub-solar Fe/Si
values (Urey and Craig 1953; Wood 2005). What chemical and/or physical processes produced the large variation
observed in Fe/O values in chondrites and the terrestrial planets, particularly for the dense, metal-rich planet
Mercury?
Given the compositions of the terrestrial planets andchondritic asteroids, there was, on average, an outward© The Author(s). 2021 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit
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McDonough and Yoshizaki Progress in Earth and Planetary Science

increase in oxygen fugacity during their accretion. Likewise, in space and time, there was also a decrease in nebular condensation temperatures and amounts of metallic
iron contributing to planetary building. We also note thatthe protoplanetary disk had redox and temperature gradients that lead to less metallic iron and more H- andO-rich solids (i.e., phyllosilicates) outward in the solar
system. Importantly, equilibrium nebular condensates do
not reach the high Fe/Si values of Mercury even withstrongly reduced, high-temperature conditions (Weidenschilling 1978; Cameron et al. 1988; Ebel and Alexander2011). Thus, further metal-oxide separation processes,
such as a mechanical enrichment of metal sunwards
in the protoplanetary disk (Larimer and Anders 1970;
Weidenschilling 1978; Wasson 1988; Wurm et al. 2013)and post-accretionary mantle stripping by one or multiple impacts (Benz et al. 1988; Cameron et al. 1988;
Asphaug 2014), are needed to produce a dense planet like
Mercury.

2 The protoplanetary disk
The terrestrial planets are the residua of the Sun’s accretion, given the former’s negligible mass contribution (afew parts per million) to the solar system. Stars and planets form from the gravitational collapse of a molecular
cloud (McKee and Ostriker 2007). The shared rotational
moments and prograde orbits of the Sun and planets document the solar system’s formation from a co-rotational,
accreting gas-dust cloud (i.e., a protoplanetary disk, or
solar nebula). Protoplanetary disks are rapidly evolving
systems with lifetimes of up to 10 million years (Myr)(Williams and Cieza 2011). Many physical and chemical
attributes of the disk (i.e., temperature, redox state, composition, gas and solid density, magnetic field strength)change in both time and space. The dynamics of these processes help shape the composition of the planets and wehighlight here a few critical variables that have played arole in building the terrestrial planets.
The dust comprising this molecular cloud is conventionally considered to be equivalent in composition to CI
chondrite, the seemingly most primitive undifferentiatedmeteorite, whose composition best matches that of thesolar photosphere (e.g., Asplund et al. (2009)). However,
one cannot simply take this composition to make a planet
without considering chemical fractionation accompanying the condensation process, which is well documented
in the chondrites (Larimer and Anders 1970). The gravitational collapse of the molecular cloud, the rapid inflow
of material onto the star accompanied by outflow of material to conserve the angular momentum, and the frictional
heating of the disk during these processes, collectively
produced a high-temperature gradient outwards fromthe Sun (Boss 1998). Thus, the high-temperature stateof the inner collapsing disk vaporized the pre-existing(2021) 8:39

Page 2 of 12

materials, which in turn led to their re-condensing ina specific sequence recorded in minerals in chondrites(Larimer and Anders 1970).
The mineralogical and chemical compositions of theterrestrial planets and chondritic bodies reflect timeintegrated, local nebular conditions during their formation (Figs. 1 and 2). Chondrites and other meteorites
document the spatial compositional heterogeneity in thesolar system (Larimer 1979; Kerridge 1979; Warren 2011).
Compositionally-driven models for the Earth’s accretionconclude that there was a temporal variation in the chemistry of materials added to the growing planet. Earth’s earlyaccretion (i.e., as much as 60 to 90% of its mass) was dominated by reduced materials and the remainder by oxidizedmaterials (Wänke 1981; Rubie et al. 2011; Dauphas 2017).
A redox gradient in the protoplanetary disk is documented in the chondrites (Righter et al. 2016). The more
reduced, non-carbonaceous (NC) meteorites, including
the enstatite and ordinary chondrites (Fig. 2), come fromthe inner solar system, closer to the Sun (i.e., inwardof the Jupiter’s orbit) (Kruijer et al. 2017). The moreoxidized carbonaceous chondrites (CC) and related meteorites (Figs. 1 and 2) are considered to be from more distalsources, including the outer asteroid belt (e.g., ≥ 3 AU),
Jupiter’s Trojans, and the Kuiper belt (Kruijer et al. 2017).
The redox state and a dozen or so isotopic systems now
link enstatite chondrites and the Earth and equally, ordinary chondrites and Mars (Warren 2011; Dauphas 2017).
The Earth at 1 AU is more oxidized than the enstatitechondrites, but less so than Mars at 1.5 AU and theordinary chondrites (Fig. 2b).

3 Composition of the terrestrial planets
Compositional models for the terrestrial planets are constructed from the following data sets: composition of
the Sun (i.e., > 99% mass of the solar system) (Lodders2020), chemical trends for samples from a planet, satellite
observations, and compositions of chondritic meteorites(i.e., the solar system’s building blocks of undifferentiatedrock and metal mixtures) (Wasson and Kallemeyn 1988;
Alexander 2019a; 2019b). Importantly, the chondrites
that we have, however, are leftovers from the planetary
formation. The bulk compositions of chondrites can be
broken down into main group (i.e., O, Mg, Si, and Fe;∼ 93%) and minor group elements (i.e., Al, Ca, S, andNi) and together they constitute 99% the mass and atomic
proportions of all terrestrial planetary models (Fig. 1 andTable 1).
Here we use our earlier compositional models for
the Earth (McDonough 2014) and Mars (Yoshizaki and
McDonough 2020) and model the recent data from
the MESSENGER mission to Mercury (Margot et al.
2018; Nittler et al. 2018) to predict its bulk composition (Table 1), which is verified to be consistent

McDonough and Yoshizaki Progress in Earth and Planetary Science(2021) 8:39

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Fig. 1 a Atomic abundances of major elements and b Fe/O values in the solar system bodies. Data sources: chondrites (Alexander 2019a; 2019b;
McCall 1968; Ivanova et al. 2008; Gosselin and Laul 1990; Wasson and Kallemeyn 1990; Bischoff et al. 1993); Mercury (this study); Earth (McDonough2014); Mars (Yoshizaki and McDonough 2020)

Fig. 2 Ratios of major cations in the terrestrial planets and chondrites. a Magnesium/Si versus Al/Si. b Abundances of reduced (metal and sulfide)
and oxidized Fe normalized to Si. Data sources are as in Fig. 1 and Urey and Craig (1953). Red symbols identify the inner solar system, NC chondrites;
see text for details. The Si-bearing core results in a Bulk Silicate Mercury that plots off scale at Al/Si (0.143) and Mg/Si (1.53)

McDonough and Yoshizaki Progress in Earth and Planetary Science(2021) 8:39

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Table 1 Composition of the terrestrial planets
Atomic%Mercurya

VenusaEarthbMarsc

CI chondrited(volatile-free)

O

27.5

49.0

49.0

55.3

48.2

Mg

11.1

16.7

16.7

15.3

15.1

Si

11.1

15.1

15.1

15.1

14.7

Fe

41.2

15.1

15.1

10.3

12.8

Ni

2.25

0.82

0.82

0.57

0.70

Al

1.03

1.56

1.56

1.41

1.20

Ca

0.75

1.13

1.13

1.03

0.88

S

5.07

0.52

0.52

0.92

6.43

Fe/O

1.50

0.31

0.31

0.19

0.27

Fe/Si

3.71

1.00

1.00

0.69

0.87

Mg/Si

0.99

1.11

1.11

1.02

1.03

Al/Si

0.093

0.103

0.103

0.093

0.082

Fe/Al

40.0

9.7

9.7

7.3

10.7

Mg/Al

10.7

10.8

10.8

10.9

12.6

mean Z

17.5

12.7

12.7

11.8

12.6

wt%

Mercury

Venus

Earth

Mars

CI (volatile-free)O12.0 (± 2.1)

29.7

29.7

36.3

29.1

Mg

7.31 (± 1.3)

15.4

15.4

15.3

13.9

Si

8.50 (± 1.0)

16.1

16.1

17.4

15.6

Fe

62.6 (± 4.5)

32.0

32.0

23.7

26.9

Ni

3.60 (± 0.25)

1.82

1.82

1.36

1.54

Al

0.76 (± 0.14)

1.59

1.59

1.56

1.22

Ca

0.82 (± 0.15)

1.71

1.71

1.69

1.33

S

4.42 (± 1.50)

0.64

0.64

1.21

7.78

Uncompressed ρ e5200 ± 200

4100

4200

3800

2430f

Metal mass fraction

74/100 (± 5)

1/3

1/3

1/5

0

H distance (AU)

0.39

0.72

1.00

1.52

> 15g

h (pW kg−1 )h

2.0

3.6

3.3

4.0

–

h (TW)h

0.7

18

20

2.5

–

This study. The ± values (1 standard deviation) are calculated as the differences between the high and low uncompressed density models
McDonough (2014).
c
Yoshizaki and McDonough (2020).
d
Alexander (2019a).
e
Uncompressed ρ, density, in kg/m3 (Lewis 1972; Lodders and Fegley Jr. 1998; Stacey 2005).
f
Macke et al. (2011).
g
Desch et al. (2018).
hHeat production in the bulk silicate planets are calculated from chondritic (Al/Th)mass = 2.81×105 and (Th/U)mass = 3.7, planetary (K/Th)mass = 7000, 3700, and 5300 for
Mercury, Earth, and Mars, respectively (Peplowski et al. 2011; Arevalo Jr. et al. 2009; Taylor et al. 2006), and an equation from McDonough et al. (2020). pW = 10−12 W; TW =1012 W.
ab

with known physical and chemical constraints. Given limited data for Venus, which is consistent with an Earth-likeanalog (Surkov et al. 1987; Aitta 2012; Dumoulin et al.
2017), we assume it has a bulk Earth composition.

3.1 Mercury model

The bulk composition (i.e., abundant elements O, Fe, Mg,
Si, Ni, Al, Ca, and S) of Mercury was defined to be consistent with its geodetic observables: mass, density, andMcDonough and Yoshizaki Progress in Earth and Planetary Science

MOI (moment of inertia) (Margot et al. 2018), compositional trends for Earth and Mars, and chondritic ratios
showing limited variation (≤ ± 10%). We used the density of Mercury and assumed a thermal gradient in the
protoplanetary disk outward from the accreting Sun toconstrain the model. Also, we assume chondritic proportions of Ca/Al (0.73) and Fe/Ni (18.3), which is empiricallydefined and reflects condensation conditions in the protoplanetary disk. (Unless otherwise specified, atomic ratios
are reported throughout.)
Given a thermal gradient in the protoplanetary disk andhigher condensation temperature for forsterite (Mg2 SiO4 )versus enstatite (Mg2 Si2 O6 ) (e.g., (Lodders 2003)), we predict a gradient in Mg/Si and Al/Si values from Mercury toMars for the silicate component of these planets (Fig. 2).
The major elements (Mg, Fe, and Si, plus Ni) have lower
condensation temperatures than the refractories (Ca, Al)and higher than the moderately volatiles (K and S). Prior
studies (Larimer 1979; Kerridge 1979) have observed that
NC chondrites form a distinctive array on the Mg/Si-Al/Si
plot as compared to CC meteorites (Fig. 2). Despite themarked variation in Mg/Si and Al/Si in chondrites, there
is only 15% variation in Mg/Al (11.2 ± 1.7). Consequently,
we assume a Mg/Al (10.7) value for Mercury, which iscomparable to that for Earth and Mars (10.8 ± 0.1) (Fig. 2).
We calculated Mercury’s core and mantle fractions to beconsistent with its uncompressed density (Table 1). The
observed Mg# (atomic Mg/(Mg+Fe)) of ∼ 0.99 for Mercury’s surface (Nittler et al. 2018) points to the core’s differentiation proceeding under reducing conditions. Thus,
some Si was likely added to the core (Nittler et al. 2018).
Using the Fe-Ni-Si composition of kamacite (Fe,Ni alloy)
and perryite ((Ni,Fe)8 (Si,P)2 ) in enstatite chondrites asa guide, we assume the equivalent metal in Mercury tohave Fe/Ni of 18.3, ∼ 4% atomic Si, and Ni/Si ∼0.6
(Ringwood 1961; Leitch and Smith 1982; Weisberg andKimura 2012). The contribution of Si from a schreibersite ((Fe,Ni)3 P) component is not significant, given its low
Si abundance (≤ 0.2 wt%) and minor mode proportion(≤ 1%) observed in type-3 enstatite chondrites (Weisberg and Kimura 2012). The mantle is assumed to havea composition that is approximately that of an orthosilicate (pseudo-olivine), with cations of Mg, Al, Ca, Fe, andSi, where Ca/Al = 0.73, Mg/Al = 10.7 and Mg# = 0.99 andfitting Si to the remainder.
To model Mercury’s interior we used the average densities of silicates, metals, and sulfides as 3300, 7100, and4600 kg m−3 , respectively, and obtained a mode proportion of 41:45:14, respectively. The resulting mass model
for Mercury has 26 ± 5% silicate shell and 74 ± 5%
core. This estimate compares favorably with that presented by Margot et al. (2018) for his Preliminary Reference Mercury Model (PRMM; 74% core and 26% silicate
sphere).

(2021) 8:39

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Mercury’s sulfur content was based on the planetary volatility trend established from its surface measured K/Th value (6000 to 8000) (in wt ratio; Nittler et al. (2018)), the Ni-normalized volatility trend
for the siderophile and chalcophile elements establishedby Wasson and Kallemeyn (1988), and an extrapolation
to the condensation temperature, following the practiceused in McDonough and Sun (1995) and Yoshizaki and
McDonough (2020). We adopted the 50% condensation
temperature of S in a gas of solar composition (Lodders
2003). The major carrier of S in enstatite chondrites andpossibly Mercury is troilite (FeS), which condenses at similar temperatures in both solar-like and highly reduced
redox conditions (Hutson and Ruzicka 2000; Pasek et al.
2005). We note, however, that S can become less volatile
under highly reducing conditions because of stabilizationof refractory sulfides such as oldhamite (CaS) and (MgS)
and incorporation of refractory elements (e.g., Ti, Nb)
into troilite (Hutson and Ruzicka 2000; Pasek et al. 2005;
Yoshizaki et al. 2021). We referenced Mercury’s volatile
depleted S content to the average depletion factor of K
(i.e., K/Th ∼ 7000; (K)CI− and Al−normalized ∼0.38). Ratiosof alkali metals to refractory elements provide an additional constraint on a planet’s volatile element depletion
trend, however, this simple model can be influenced byredox conditions and core formational processes. We estimate a sulfur content for Mercury of 4.4 ± 1.5 wt%. By
comparison, Namur et al. (2016) has suggested the bulk
Mercury has 3 wt% to 5 wt% S, whereas Boujibar et al.
(2019) has modeled a range of bulk S contents based upona range of plausible redox states (∼ 23 wt% S for logfO2 =IW − 7 to ∼ 2 wt% S for IW − 2.6) for the planet.
Mercury has a markedly elevated Fe and Ni abundances
relative to its budget of lithophile elements (e.g., Fe/Al= 40.0, Fe/Si = 3.7, Fe/O = 1.5; Table 1) leading to anenrichment factor of (Fe)CI− and Al−normalized of ∼ 3.7 (cf.,that for Si and Mg is 0.85). In addition, its Mg/Si (0.99)
is approximately CI-like, which is much higher than thatfor the highly reduced enstatite chondrites. This result
is a product of our modeling approach that matches theplanet’s uncompressed density to the mode of silicate, FeNi-Si metal, and troilite. Predicting Mercury’s abundancesof S and other chalcophile elements is challenging; it is
the least volatile depleted body of the terrestrial planets(i.e., highest K/Th value). Our prediction of Mercury’s S
content (Fig. 3) is consistent with either (1) an extensionof the volatile depletion trend for the siderophile elements, and/or (2) Mercury having CI relative abundancesfor elements with half-mass condensation temperatures of< 1000 K (Krähenbühl et al. 1973; Takahashi et al. 1978;
Braukmüller et al. 2019).
This temperature of 1000 K represents a limit. At lower
temperatures in a condensing nebula, depending upon its
C/O value, precipitation of MgS and CaS phases begin

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Fig. 3 Normalized abundances of the lithophile (blue) and siderophile (red) elements in the bulk Mercury. Abundances are normalized to Al and CI
chondrites and plotted against log of their 50% condensation temperatures (K) at 10 Pa (see Yoshizaki and McDonough (2020)). Volatility trend for
Mercury constrains its S content in the core. The predicted S content is consistent with either an extension of the volatile trend for the siderophile
and/or and addition of CI chondritic volatiles with 50% condensation temperatures <1000 K. See text for details(Hutson & Ruzicka, 2000). The consequence of significant
CaS fractionation would result in changes to critical chondritic ratios (e.g., Ca/Al, Ca/Ti, and Al/Ti). Observations
from the orbiting spectrometers on the MESSENGER
Mission did not find such unusual ratios (Nittler et al.,2018). In contrast, chondrules from enstatite chondrites,
which contain highly reduced silicates, are highly fractionated in both Al/Ti and Ca/Al. Above this critical temperature of 1000 K condensation of fosterite and Fe-Ni-Si
metal occurs, without accompanying sulfide precipitation.
The result of these conditions is a bulk condensate with a
Mg/Si value that is higher than in enstatite chondrites andSi-enriched metals; these are the features proposed for ourmodel Mercury composition.
In Table 2, we present compositional models for thecores and bulk silicate shells of Mercury, Earth and Mars.
The models for the Earth comes from McDonough (2014)
and Mars from Yoshizaki and McDonough (2020). The
model for Mercury is based on its bulk compositionalmodel (Table 1) along with the following constraints:(1) Mg, Al, and Ca is solely concentrated in the silicate shell, (2) Ni and S is partition between the core
(60%, including and FeS component) and silicate shell(40%) following the models of Namur et al. (2016) andBoujibar et al. (2019), (3) the silicate shell’s Mg# = 0.99,(4) the Si contents of metals in EH chondrites, and (5) Si
being partitioned between the core (35%) and the silicate
shell (65%).

3.1.1 Implications of the model

Incorporation of silicon, sulfur, and other elements into
the Fe-Ni core of Mercury influences its size, density,and solidus temperature. Lowering the solidus of the core
keeps it molten and convecting, thus providing the critically important conditions for dynamo action and magnetosphere generation (Schubert et al. 1988; Tosi et al.
2013). Magnetospheres of terrestrial planets deflect solar
wind particles. This deflection shield is important for aplanet’s atmospheric retention (i.e., losses due to radiationand solar winds), keeping water present at the surface, andprotection of its biological habitat (See et al. 2014).
Based on the compositional estimates given in Table 1,chondritic ratios of refractory elements, and planetary
K/Th values, we have calculated the present-day radiogenic heating rate (pW kg−1 ) and total planetary radiogenic power (TW) according to the method outlinedin McDonough et al. (2020). The estimated bulk uranium contents of Mercury, Earth, and Mars are 7, 13,
and 15 ppb (10−9 kg/kg). Because of its small fraction of silicate shell, Mercury has the least amountof total radiogenic power of the terrestrial planets(Table 1).

4 Distribution of Fe (and Ni) in the protoplanetary
disk
The Fe content of chondrites typically ranges from 1/5 to<1/3 of their total mass, with Fe/Si typically 0.74 ±0.12,

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Table 2 Composition of silicate shells and metallic cores of the terrestrial planets
Mercurya

Earthb

Marsc

Bulk silicate shell, atomic% (wt%)
O

55.30 (42.3)

58.5 (44.0)

59.3 (43.2)

Mg

25.93 (25.9)

20.0 (22.8)

16.9 (18.7)

Si

14.6 (19.6)

15.9 (21.0)

16.6 (21.3)

Fe

0.17 (0.46)

2.4 (6.3)

4.5 (11.4)Al

2.1 (2.7)

1.85 (2.35)

1.55 (1.90)

Ca

1.5 (2.9)

1.34 (2.53)

1.13 (2.06)S

4.1 (6.3)

–

–

Mg#

0.99

0.89

0.79

Mg/Si

1.53 (1.32)

1.26 (1.09)

1.01 (0.88)

Al/Si

0.143 (0.137)

0.117 (0.11)

0.0929 (0.089)

Fe/Si

0.0118 (0.024)

0.150 (0.30)

0.269 (0.54)

Silicate mass (kg)d

8.6 ×1022

4.04 ×1024

5.27 ×1023

6.4 (2.0)

16 (5.2)

Core, including an FeS component, atomic% (wt%)
O

–

Si

7.6 (4.1)

7.3 (4.0)–

Fe

81 (86)78 (86)68 (80)Ni

4.4 (4.9)

4.4 (5.1)

6.0 (7.4)S

6.0 (3.6)

3.0 (1.9)9.9 (6.6)

Values outside and inside parentheses are in atomic% and wt%, respectively
This study.
b
McDonough (2014).
c
Yoshizaki and McDonough (2020).
d
Planet masses from https://nssdc.gsfc.nasa.gov/planetary/factsheet/. Bulk silicate shell fractions are 0.260, 0.676, 0.820 for Mercury, Earth and Mars, respectivelyawhereas some rare chondrite groups (i.e., CB, CH, and G
types) can have Fe/Si values up to 8 (Fig. 2b). Our modelfor the terrestrial planets have Fe/Si varying from 3.7 to
0.7 from Mercury to Mars (Table 1). The ratio of metallic
iron to total iron varies from 1 (EH and EL chondrites) to
0 (CI and CM) in the chondrites, whereas the terrestrial
planets have intermediate values (Fig. 2b and Table 1).
The amount of iron accreted by a chondritic parent
body or a terrestrial planet is not set by any particular ruleand likewise the same is true for its metal to oxide fraction.
A planet’s mass fraction of metallic core to silicate shellreflects the time-integrate redox condition during accretion and core-mantle differentiation. Impact-induced erosion/evaporation can also modify a core’s mass fraction(Cameron et al. 1988). Accretion sets the relative contents of Fe/O, Fe/Si, Fe/Mg, and Mg/Si, which accounts for∼ 93% of its mass (Fig. 1).
Mercury has the largest metallic core fraction, high
Fe/Al (40) and Mg/Si (0.99) values (Table 1 and Fig. 2),
and a silicate sphere with negligible Fe (i.e., Mg# ∼ 0.99)(Nittler et al. 2018). By comparison, Mars has a smaller
metallic core, a lower Fe/Al (7.3) and Mg/Si (1.02), and asilicate shell with a low Mg# (0.79) than Mercury and theEarth (9.7, 1.11, and 0.89, respectively) (Table 1). Therefore, in relative terms the silicate shells of Mars, Earth (and
Venus), and Mercury get progressively thinner, their cores
bigger, and their mantles more Mg#-rich with decreasing
heliocentric distance.
Here we show that the uncompressed densities (Fig. 4)
and mean atomic numbers (Z, Table 1) of the terrestrial
planets increases with decreasing heliocentric distance.
These trends also extend to bodies in the asteroidal belt:
undifferentiated and differentiated asteroids are less dense
than the terrestrial planets (Fig. 4). Most chondrites havesub-solar Fe/Si (Fig. 2b) and show a marked variationin Fe/Si and metallic iron content. Thus, the outward
decrease of planetary density appears to primarily reflect
dynamic metal-oxide separation in the protoplanetarydisk, rather than post-accretionary processes.

5 Processes in the protoplanetary disk
Significantly, condensing iron-nickel grains, and othermetallic alloys, in the protoplanetary disk are distinctly
influenced by aerodynamic, gravitational, photophoretic,
and electromagnetic sorting forces, compared to silicates(Larimer and Anders 1970; Weidenschilling 1978; Wurm

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Fig. 4 Density of the rocky solar system bodies. Uncompressed and solid densities are shown for terrestrial planets and chondrites (gray),respectively. Bulk planetary densities are shown for asteroids (blue). For 1 Ceres, its bulk density is a lower limit of its solid density, given its high ice
abundance and porosity. The red line shows a fit curve for the planets (ρ = 4100r −0.21 ). Data sources: density of planetary bodies are from Russell etal. (2012); Park et al. (2019); Sierks et al. (2011); Consolmagno et al. (2006); Macke et al. (2010); Macke et al. (2011); Britt and Consolmagno (2003);
Lewis (1972); Stacey (2005); heliocentric distances of chondrite parent bodies are from Desch et al. (2018)

et al. 2013; Kruss and Wurm 2018). We highlight electromagnetic separation of magnetized micro-particles of
Fe-Ni alloys (existing below their Curie point with a stable magnetic spin) from silicates (Harris and Tozer 1967;
Larimer and Anders 1970) coupled with metal-oxide separation during chondrule formation as being effective
segregation processes (e.g., Connolly Jr. et al. (2001)).
Recently, Wurm et al. (2013) also observed that photophoretic separation enhances a metal-silicate fractionation. Thus, these physical fractionation processes likely
occurred in the protoplanetary disk and may well explain
the observed variations in Fe/O, Fe/Si, and Fe/Mg inchondrites and terrestrial planets. The degree of sunward
enrichment of magnetic micro-particles in the protoplanetary disk appears to scale radially with its magnetic fieldstrength.
Paleomagnetic measurements of meteorites and their
inclusions provide unique constraints on spatial andtemporal changes of the magnetic field in the protoplanetary disk. Meteoritic records indicate the magnetic
field intensity of ∼50 μT at 2.5 AU and ∼ 2 Myr
after the solar system initiation (t0 ) (Fu et al. 2014),
whereas at 3–4 Myr after t0 , it weakens to <20 μT
at 3–4 AU (Cournede et al. 2015; Desch et al. 2018).
Finally, the nebular gas and thus its magnetic field
deceased at ∼4 Myr after t0 , as recorded by the volcanicachondrite angrite (Wang et al. 2017). These observations document a decrease in the nebular magnetic fieldstrength with increasing heliocentric distance and timeafter t0 .

The terrestrial planets formed closer to the Sun compared to these meteorites and their components, given
their present-day distributions. Chronological studies ofplanetary materials and planetary accretion models indicate that Earth and Mars grew rapidly within the first 2
Myr after t0 , although their final accretion continued formore than 10 Myr (Kleine et al. 2009; Dauphas and Pourmand 2011). Early, rapid growth of the inner rocky planetsis envisaged at locations closer to the Sun compared tometeorites and their constituents. Thus, it is likely thatterrestrial planets formed under a stronger solar magnetic
field compared to outer, younger meteoritic materials.
We show a correlation between the metallic core fraction and heliocentric distance for the terrestrial planets(Fig. 4). This trend is interpreted as resulting from spatial
and temporal decays of magnetic field strength in the protoplanetary disk, which is consistent with paleomagnetic
intensities recorded in meteorites (Bryson et al. 2020; Fu
et al. 2020), magneto-hydrodynamic (MHD) disk models(Bai 2015), and accretion rates of stars (Wardle 2007).
Accretion rates for solar-mass stars in protoplanetarydisks can have multi-Myr timescales (∼ 10−9 to 10−7 M
yr−1 ) (Hartmann et al. 2016). Collisional accretion, protoplanetary disk winds, and electromagnetic fields may
control the evolution and dispersal of matter during theplanet formation. The magnetic field strength (B) in a
protoplanetary disk should decrease with heliocentric distance. In addition, the azimuthal magnetic fields are likely
to be strongest in the disk midplane (Bai 2017), the site ofplanetary accretion. The required B to drive gas accretion

McDonough and Yoshizaki Progress in Earth and Planetary Science

onto the central star can be determined using equation
19 of Wardle (2007): where B ∼0.1–1 × (r/au)(−1.25) mT,
assuming appropriate accretion rates. Using this equation,
the estimated time averaged magnetic field strength during the planet formation in the presence of a protoplanetary disk is ∼ 0.3–3 mT at Mercury, ∼ 0.1–1 mT at the
Earth, ∼ 3–300 μT at r = 2.5 AU (main belt asteroids), and∼ 6–60 μT at r = 10 AU. The latter two values are consistent with paleomagnetic measurements of the Semarkona
meteorite (2.3 AU) by Fu et al. (2014) and the chondrite
WIS 91600 (i.e. 10 AU, the putative initial formation location for WIS 91600, ungrouped C2 chondrite) reported by
Bryson et al. (2020).
Kruss and Wurm (2018) suggested that enhanced
growth of iron-rich dust aggregates in the inner region of
protoplanetary disks leads to an iron gradient in the solar
system. A corollary of this model is that planetary migration in the inner solar system did not disrupt this final
result and that the Fe content can help us determine where
and when an object was dominantly formed. The experiment carried out by Kruss and Wurm (2018) observed acritical magnetic field strength (∼ 2 mT) where chains ofmagnetic grains start to form (their Fig. 9) due to stronger
magnetic attraction relative to collisional repulsion. Later
experiments by Kruss and Wurm (2020) observed chainsof magnetic grains aggregating into clusters in a magnetic
field above a given mass fraction of iron (their Fig. 10).
These early experiments provide some support for forming mercury-type planets, but their results depended on
the magnetic field strength and the mass fraction of iron.
It is not clear if these experiments would only apply toregions around Mercury (where the magnetic fields arestrongest), or extend out to the orbits of Earth and Mars.
Nebular gas carries the magnetic field in the protoplanetary disk. Metal-silicate segregation by solar magnetic forces is only effective before nebular gas dissipation(Kruss and Wurm 2020; Wang et al. 2017). Mercury’s formation under reduced conditions in the presence of agas disk with a strong magnetic field implies a τaccretionage that is restricted to when a nebular envelope existed.
Accretion in the presence of nebular gas is consistent withpebble accretion models of planetary formation, which
may have contributed to the early formation of Marsand iron meteorite parent bodies (Johansen et al. 2015).
Therefore, a key implication of our model is an early formation age (∼ 2 Myr) for Mercury, comparable to thatof Mars (Dauphas and Pourmand 2011; Yoshizaki and
McDonough 2021). Furthermore, our model does not
require a giant impact event and partial loss of its silicate
shell for the origin of Mercury’s large core (Benz et al.
2007; Asphaug and Reufer 2014).
Is our model applicable to exoplanetary systems? Unfortunately the database at present is not large enough to
conduct a thorough assessment. TRAPPIST-1, our best

(2021) 8:39

Page 9 of 12

documented exoplanetary system (i.e., 7 planets with M⊕ ,R⊕ , and orbiting data), does not have a mercury-type
planet. It is, however, an unusual system in that theseplanets are (1) close in (0.01 to 0.06 AU), (2) orbiting an
ultra-cool, low mass, red dwarf star (∼ 0.09 M ), (3) theirmasses and radii are large relative to those of the star,and (4) they are predicted to have roughly similar compositional characteristics (Agol et al. 2021). The chemistryof this star is poorly understood, given its cool temperature. Thus, typical comparisons between these planets andtheir star composition cannot be completed.
Dense mercury-like exoplanets have been identified, butthey are less common and often Earth-sized and larger
objects (e.g., Santerne et al. (2018); Bonomo et al. (2019);
Price and Rogers (2020); Schulze et al. (2021)). Interestingly, K2-229 b (0.6 days year−1 , 1.2 R⊕ and 2.6 M⊕ ) has acore mass fraction (70%) equivalent to Mercury’s, and its
Fe-enrichment contrasts with its star’s chemistry (Saterne
et al. 2018). Several other Fe-rich exoplanets have been
identified (e.g., see Table S5 in Schulze et al. 2021) manyof which orbit close to their star that has a composition
similar to our Sun’s. Future exoplanetary observations will
test this hypothesis of compositional fractionation in the
protoplanetary disk by an evolving magnetic field and its
control on planetary chemistry during accretion.
The potential for a habitable zone in an exoplanetary systems may be influenced by physical and chemical
processes controlling the distribution of metal and silicate in an evolving protoplanetary disk. These processes
can control the size and composition of a planet’s core.
The chemical equilibrium during accretion and metalsilicate differentiation reflects the local redox conditions
and influences the amount of light elements partitioned
into the core. In turn, these factors influence the stability and duration of the core’s dynamo, which generates
the planet’s magnetosphere and serves to protect a yet
unrealized biosphere. These factors, plus the distributionof some critical life supporting elements (e.g., 90% of the
Earth’s phosphorus budget is in the core), are critical inestablishing a planet’s prospects for habitability.

6 Conclusions
We have developed compositional models for the terrestrial planets that takes note of their chemical differences
as a function of their heliocentric positions. The presence and size of their metallic cores depends on the redox
environment in the protoplanetary disk and the planet’s
mass fraction of accreted metal alloys, the latter of whichis controlled by electromagnetic processing in the disk.
We use the measured K/Th values of the terrestrial planets to estimate its volatile element inventory (e.g., bulk
sulfur content). The redox condition during core formation, controls the identity and amount of light elements inthe core (e.g., S, Si, O). These light elements significantly

McDonough and Yoshizaki Progress in Earth and Planetary Sciencelower the core’s solidus and extends its molten-state lifetime. Collectively, these factors contribute to convection
in a molten core and dynamo action.
These attributes of our solar system may be equallyapplicable to exoplanetary systems. The generation of aplanetary magnetosphere, which nurtures life, shapes aplanet’s habitability. It is likely that life’s sustainability
critically depends on being sited in the Goldilocks zone
and having the right amount of metallic core, which contains an appropriate amount of a light element and is notcooling too fast.
Acknowledgements
We thank many our colleagues, particularly T. Kakegawa, E. Ohtani, N. Chabot,
V. Lekic, and R. Ash, who have listened to various versions of this project andgiven helpful comments. We are very grateful to the editor and the twoanonymous reviewers who offered significant improvements to ourmanuscript.
Authors’ contributions
WFM and TY proposed and conceived various portions of this study andtogether calculated the compositional models. The manuscript was written by
WFM, with edits, discussions, and revisions by TY and WFM. Both authors readand approved the final manuscript.
Funding
This work was supported by NSF grant (EAR1650365) to WFM, and the JSPS
KAKENHI Grant (JP18J20708), the GP-EES research grant and DIARE grant to TY.
Availability of data and materials
Correspondence and requests for materials should be addressed to WFM.

Declarations
Competing interests
The authors declare that they have no competing interest.
Received: 17 December 2020 Accepted: 17 May 2021

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