Helffrich et al. Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-019-0312-z(2019) 6:66

Progress in Earth andPlanetary Science

RESEARCH ARTICLE

Open Access

The chemical case for Mercury mantle
stripping
George Helffrich1*, Ramon Brasser1 and Anat Shahar2

Abstract
Mercury, the Solar System’s innermost planet, has an unusually massive core prompting speculation that the planet
lost silicate after it formed. Using the unusually high sulfur and low iron composition of its surface and space geodetic
constraints on its core composition, we show Mercury’s chemistry to be compatible with formation in a larger planetat minimum 1.4–2.5 times Mercury’s present mass and possibly 2–4 times its mass by similarity with other rocky Solar
System bodies. To do this, we apply an experimentally determined metal-silicate partitioning model for sulfur to
Mercury’s silicate. The model is validated by applying it to Vesta, which, when evaluated at the conditions of Vestan
self-differentiation, yields sulfur contents in its silicate in the range of HED meteorites. Mercury could have lost a
substantial fraction of its rocky material through impacts or by being itself a remnant impactor. Independent of any
stripping, because a significant amount of silicon resides in Mercury’s core, silicate meteoritic debris from Mercury
would likely be characterized by 30 Si isotopic enrichment > + 0.10 relative to parent sources that could aid
identification of a new meteorite class.
Keywords: Mercury, Vesta, Sulfur, Silicon, N-body simulation, Meteorites, Stable isotopes

Introduction
Mercury is essentially a metal core draped with a thinsilicate mantle. Detailed models of its interior structure(Rivoldini et al. 2009; Rivoldini and Van Hoolst 2013;
Hauck II et al. 2013; Dumberry and Rivoldini 2015) indicate core radii of 2000–2060 km and a core proportionately 58–70% of the planetary mass (M , 3.302 ×1023
kg (Rivoldini et al. 2009)). By comparison, Earth’s core is
32% of the planetary mass (Stacey 1992), Venus 24–32%(Fegley 2014), Mars’ and Vesta’s cores are 21 and 18%,
respectively, of the planetary mass (Rivoldini et al. 2011;
Russell et al. 2012), and the fractional mass of metallic
elements in chondritic meteorites is ∼ 30% (McDonoughand Sun 1995). These facts suggest that Mercury might
have lost part of its original mantle at some point in the
Solar System’s history through impacts with other bodies,
stripping it of its silicate and leaving metal (Benz et al.
1988; Benz et al. 2007; Asphaug and Reufer 2014). Moreover, spectroscopic observations of Mercury’s surface by*Correspondence: george@elsi.jp
Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1 Ookayama,
Meguro-ku, Tokyo, 152-8550 Japan
Full list of author information is available at the end of the article
1

the MESSENGER mission (Nittler et al. 2011; Zolotov
et al. 2013; Weider et al. 2014) indicate high concentrations of sulfur (1–6 wt%) and low concentrations of FeO(< 1.9 wt%). From a planetological perspective, this rather
weird chemical imprint compared to either the Earth or
to CI carbonaceous chondrites (Earth: ∼ 0.03 wt% S,∼ 8 wt% FeO; CI 5.4 wt% S, 15.1 wt% FeO (McDonoughand Sun 1995)) suggests that it may have arisen underunusual conditions. Chabot et al. (2014) showed that itis difficult to reconcile the observed surface FeO content
with equilibrium between silicate and metal at pressures
up to that of Mercury’s present core-mantle boundary(CMB). Other studies showed plausible ways to build
Mercury from chondritic and non-chondritic precursors(Ebel et al. 2018; Cartier and Wood 2019). Here weapproach the problem via accretion modeling. Accretion
models for the Earth and other rocky planets use experimentally determined metal/silicate partition coefficients
to constrain the physical conditions during formation (Liand Agee 1996; Wood et al. 2006; Rubie et al. 2015). Thesemodels assume that the composition of the metal and silicate is set by equilibrium partitioning of elements at therheologically solid base of liquid silicate when a planet’s
surface is partly or completely molten due to impact© The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to theCreative Commons license, and indicate if changes were made.

(2019) 6:66

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heating (Kaula 1979; Rubie et al. 2015). Under these
conditions, the liquid metal separates from the liquid silicate and accumulates in the core of the planet, ceasing
to be in chemical equilibrium with silicate. Consequently,
we use a model for sulfur, silicon, oxygen, carbon, andiron partitioning between metal and silicate to evaluate whether there are feasible conditions for Mercury
that simultaneously satisfy the composition of the silicate mantle while yielding core compositions that satisfy
space geodetic constraints. Our objective is to show that
Mercury’s surface chemistry is compatible with the formation in an originally larger body from which the mass
was lost by impact processing.

below. To obtain the rest, we use thermodynamic constraints on metal/silicate partitioning of Si, O, and C fromvarious sources, assuming a single-stage core formation
model. To obtain the oxygen content of the metal, we use
Frost et al.’s (2010) model for Fe + O equilibrium between
metal and silicate and the specified silicate mantle
content. This gives the activity of an “FeO” component in
the metal from which the O and Fe concentrations may beobtained by

Helffrich et al. Progress in Earth and Planetary Science

Methods
Sulfur partitioning model

We use Boujibar et al.’s (2014) S partitioning model todetermine the pressure- (P) and temperature- (T) dependent joint S and FeO content of the silicate. This reads,
met/sillog10 DS
= log10 XSmet /XSsil =sillog10 WFeO
− log10 Cs + b/T + cP/T
met
met
met
+ dlog10 (1 − XSi) + elog10 2 (1 − XSi) + f log10 3 (1 − XSi
)
met
met
) + ilog10 (1 − XNi)+ glog10 (1 − XCmet ) + hlog10 (1 − XFemet+ jlog10 (1 − XO
)+k .

(1)
b − k are experimentally determined model coefficients,
listed in Table 1. The metal concentrations Ximet and XS sil
are weight fractions, whereas silicate FeO concentration
sil is weight percent. C is the sulfur carrying capacity,
WFeO
S
given bylog10 CS = − 5.704 + 3.15 × XFeO + 2.65 × XCaO + 0.12 × XMgO +0.77 × XTiO2 + 0.75 × (XNa2 O + XK2 O ) .

(2)
Here, by contrast with (1), the oxide concentrations Xi
are mole fractions in the silicate.
In order to evaluate these expressions, we need thecomposition of core metal, in particular its concentrations of Fe, Ni, O, C, Si, and S. S is fixed by a family ofsolutions to the Mercury planetary geodesy data and by
estimated mantle compositions which will be reviewed
Table 1 Sulfur solubility model parameters
Symbol bcde

405 13632±

150 25

5.5 45

K

g

h

i

j

k

181 305 30.2 1.13 10.7 31.4 − 3.72

Value

Units

f

380 6

K GPa-1

Used in Eq. (1). Source: Boujibar et al. (2014)0.14 2.5

18

0.07

met
met
× XO
=
XFe

aFeO
met × γ met .
γFe
O

(3)

Ni is obtained by assuming a chondritic mass ratio
XNi /XFe = 0.06 (McDonough and Sun 1995). C is obtainedby assuming saturation in the metal. We justify this choicebased on the quite large C concentrations implied with
Marcyr’s high S abundances using the chondritic C/S ratio(0.648) (McDonough and Sun 1995), because models of
Mercury formation invoke an early graphite crust (Kaaden
and McCubbin 2016; Cartier and Wood 2019), andbecause graphite appears to be present on Mercury’s surface (Peplowski et al. 2015). We use Wood’s (1993) parameterization for C saturation in metal, and use the pressureof the depth of the base of the magma ocean to set the
P and T conditions; see Additional file 1: Figure S1 for aplot of C saturation vs pressure. Si is obtained from Hirose
et al.’s (2017) model for joint Si and O metal/silicate
partitioning. The metal activity coefficients γi are evaluated using the  formalism (Ma 2001) with interaction parameters given in Table 2. An iterative method
is used to solve consistently for Si concentration andmetal activity coefficients given the Si and O KD s and C
concentration. Table 3 gives metal Si content at 2 wt% S.
Peridotite solidus and liquidus temperatures are from
Fiquet et al. (2010), whose mean provides the temperature as a function of pressure, eliminating an independent variable. Pressures in the proto-Mercurys arecalculated assuming an adiabatic temperature profile withthe metal-silicate equilibration pressure fixed at 12 PCMB
and no temperature discontinuity at the CMB. Internal
Table 2 Metal interaction parametersjji = i

i→

Ni

Si

C

O

S
− 5.66j↓S− 0.05

9.16

6.12

0

O

1.4

7.73

− 20.08− 9.16

C

2.31

9.70

12.83

Si

7.5

0

Ni

0.12

Sources: O-O, O-Si, Si-Si (Hirose et al. 2017); S-Ni, Si-Ni, S-S, Ni-Ni (Wade et al. 2012);
Ni-O (Tuff et al. 2011). C-C, C-S, C-O, C-Si, C-Ni MetalAct Website, http://www.earth.
ox.ac.uk/~expet/metalact/, accessed 2018/01/04 (Wade and Wood 2005)

Helffrich et al. Progress in Earth and Planetary Science(2019) 6:66

Table 3 Mercury and Vesta mantle compositions
Oxide

Zolotova

Chabotb

Nittlerc

Vestad

SiO2

56.90

49.02

52.83

44.47

TiO2

0.89

1.07

0.22

0.12

Al2 O3

14.10

11.72

4.41

2.76

FeO

3.42

0

0.03

21.02

MnO

0.69

0

0

0

MgO

17.90

29.84

37.27

28.92

CaO

5.02

8.36

3.05

2.27

Na2 O

0.18

0

1.63

0.08

K2 O

0.15

0

0.04

0.01

S

1.90

–

–

–

log10 CS

− 5.446− 5.435− 5.560− 5.091

XSisil wt%e

26.60

22.91

24.69

20.79

XSimet wt%f

28.5

28.5

27.9

–

All oxide values are wt%. a Mean of Zolotov et al. (2013) northern volcanic plains andintercrater plains compositions; b Chabot et al. (2014) experimental starting material;c Nittler et al. (2018) mean estimated mantle composition; d Average of H-chondriteand H+CM chondrite mix (Toplis et al. 2013) and OIM and BD compositions(Lodders 2000). Average Vesta metal composition (wt%): Fe 76.32, Ni 9.63, Co 0.096,
S 12.98; e Mean value is 24.73 wt%; f At 2 wt% S in metal

structure is calculated using the methodology and material properties of metal and silicate described elsewhere(Helffrich 2017). The choice of 12 PCMB is motivated byvarious studies of moderately siderophile element concentrations in the mantle (Tuff et al. 2011; Rubie et al.
2011) that find a best fit if magma ocean pressure PBMO is
2/7 ≤ PBMO /PCMB ≤ 2/3; 12 is a useful approximation to
the mean pressure.
Because they are cast as exchange reactions, our models are not explicitly dependent on oxygen fugacity ( fO2 ),which, on Mercury, is quite low relative to the iron-wüstite
buffer (Namur et al. 2016). The major element content,
rather, implies an fO2 . On the Earth, the variation in equilibrium partitioning conditions for various moderately
siderophile elements leads one to invoke a change in thecomposition of accreting material (or, equivalently, fO2 )(Wood et al. 2006; Rubie et al. 2011), but we lack theinformation required to evaluate this for Mercury. For the
Earth, there was an evolution to + 1 or + 1.5 log units moreoxidizing conditions through accretion, but at all times
was more oxidizing than Mercury’s present conditions(Wood et al. 2006; Namur et al. 2016).
In order to test the model and demonstrate its suitability for other silicate bodies, we recruit Vesta. Its
total and core mass are known from the Dawn mission,and the silicate composition is represented by the HED
meteorite suite, thought to represent Vesta fragments;
Vesta is also believed to have self-differentiated and was
not subject to significant mass loss by impact erosion(Russell et al. 2012) (but see Consolmagno et al. (2015)

Page 3 of 10

for an alternative view). Various efforts to model Vesta’s
differentiation using HED meteorites provide Vesta silicate and core compositions (Toplis et al. 2013; Mandler
and Elkins-Tanton 2013) whose average is given in Table 3.
We use the sulfur partitioning model to calculate theequilibrium sulfur content of Vestan silicate. We modify the solution method slightly for this case and fix themetal’s carbon concentration to the low-pressure saturation value in metal, 3.5 wt% (Tafwidli and Kang 2017). The
differentiation pressure is the CMB pressure (Fig. 1) andtemperature is midway between the peridotite solidus andliquidus. Figure 1 shows the results. At Vestan differentiation pressures (< 0.1 GPa), XSsil is limited to 0.47–0.55
wt% depending on the core’s Si concentration, which isconstrained by Si partitioning experiments between metaland silicate (Fischer et al. 2015). The sulfur contents ofindividual eucrite analyses (Kitts and Lodders 1998) is
0.21 ± 0.22 wt% (ranging from 0.03–1.02 wt%). Hence,
metal-silicate equilibration in Vesta may be demonstrated
at the 2σ level with the model. A further comparison,though requiring further inferences that weaken its verdict, may be made using the estimated S content of thewhole HED meteorite suite (Steenstra et al. 2019). They
estimate S in HED silicate to be 0.13 ± 0.04 wt%. The
depletion of volatile lithophile elements in HED meteorites appears to be 3–4 times relative to chondrites(Ruzicka et al. 2001). Hence, from these values, 3–4 times
0.13 wt% meteorite S yields 0.39–0.52 wt% S in bulk Vesta
silicate, which is within our model estimate’s range. Thisvalidates the model against the composition of a relatively
well-known protoplanetary body.
Isotopic model

The 30 Si isotope balance for bulk Mercury (subscript b)
may be written in terms of its partitioning between thecore’s metal (subscript c) and the mantle’s silicate (subscript m)
δ 30 Sib = fc δ 30 Sic + (1 − fc )δ 30 Sim ,(4)

where fc is the Si mass fraction of the core relative tothe planet (reckoned as 0.2918 for proto-Mercury coremass fraction of 0.26). To account for the silicate-metal
partitioning during core formation, we use temperaturedependent fractionation factors 30 Si(T). Hence,δ 30 Sic = 30 Si(T) + δ 30 Sim .

(5)

The fractionation factor expressions 30 Si(T) are either

30 Si(T) = − 7.45(± 0.41) × 106 /T 2 (Shahar et al.
2011) or a composite value derived from various fractionation factor studies: Shahar et al. (2011), Ziegler etal. (2010), Georg et al. (2007), and Hin et al. (2014). To
form the composite fractionation factor, we average using

(2019) 6:66

b)

0.7

0.65

1

0.25

a)

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2

Helffrich et al. Progress in Earth and Planetary Science

.5

0.5

.01

0.00

0.05

.05

.1

met
, wt%
XSi

0.15
0.10

P (GPa)

0.20

0.6
0.55

0

50

100

150

200

250

300

R (km)

0.45
0.0

0.5

0.4
1.0

1.5

Xmet
C sat.
2.0

2.5

P (GPa)Fig. 1 a Internal pressure within Vesta, using geodetic data from Russell et al. (2012) and methods from Helffrich (2017). Core-mantle boundary(CMB) pressure is evident in knickpoint in P(R) curve. b Sulfur model applied to Vesta, using average estimates of bulk Vesta composition. Contours
show wt% S in Vesta silicate assuming metal-silicate equilibrium at indicated pressure (P) and sulfur content of silicate XSsil . Dashed vertical line is
Vestan CMB pressure from a. Sloped horizontal line is XSimet calculated from metal-silicate equilibrium at the given pressure. For equilibrationpressures at or below the Vestan CMB (lower left), silicate sulfur content is 0.47 ≤ XSsil ≤ 0.55 wt%. For measured eucrites, 0.03 ≤ XSsil ≤ 1.02 wt%(Kitts and Lodders 1998)

1/σ 2 weights with reported uncertainties, where available.
Georg et al.’s (2007) calculations yielded two separate fractionation factor values that we average and adopt half of
their difference as the uncertainty. The uncertainty estimation procedure for the value derived from Hin et al.’s(2014) experiments is not clearly described, so we took
a weighted average of their values at the two experimental temperatures and fit those two values to a 106 /T 2
model to obtain an estimated value and uncertainty. The
individual values (and uncertainties) divided by 106 are,respectively, − 7.64 ± 0.47, − 7.45 ± 0.41, − 5.65 ± 0.15,
and − 5.05 ± 1.58, which yield a composite fractionation
factor of 30 Si(T) = − 6.00(± 1.21) × 106 /T 2 .
The mean values for various chondrite classes provideδ 30 Sib . Combining (4) and (5), δ 30 Si for the silicate of the
proto-Mercury isδ 30 Sim = δ 30 Sib − fc × 30 Si(T) .

(6)

Results
The experimentally determined metal-silicate partition
coefficient for sulfur (1) may be written assil
DS = f (P, T, CS , WFeO
, X met ) ,(7)

where f is a function of pressure (P), temperature (T),the sulfur carrying capacity of the silicate CS (2), the FeO
concentration in the silicate, and the metal composition
X met . Mercury’s silicate composition (Table 3) may thenbe used to find the P–T conditions where metal-silicate
equilibrium is achieved if the metal composition is known.

The three silicate compositional estimates are derived
in various ways from surface spectroscopic observations(Table 3). The most straightforward is to assume that thesurface represents bulk Mercury. Zolotov et al.’s (2013)
estimates of the composition of crustal lavas on Mercury
provides this compositional choice. It neglects any differentiation that arises from partial melting of the mantle—
melt fractions are thought to be 25–40% (Nittler et al.
2018)—but has the virtue of being purely observationally based. Chabot et al. (2014) attempted to reproduce
Mercury’s surface composition experimentally by melting
mixtures of silicate and metal. We use the experimental starting silicate as a second estimate of the mantle
composition. A virtue of this choice is that there is nomodel underlying it except for being a plausible parental
source composition. However, the composition is simplified, lacking alkalis (Table 3). The final estimate is by aformal back-calculation from the surface composition of
the mantle’s composition assuming that it was formed bybatch decompression melting as solid convectively rosealong an adiabat (Nittler et al. 2018). For fidelity withthe modeling assumptions, we use the model’s reported
output composition (0.02–0.04 wt% FeO, Table 3) rather
than the one augmented by the addition of 1 wt% FeO
reported by those authors. There is no significant difference in the results no matter which compositionalmodel is used, so the results shown in Fig. 2 are using
Nittler et al.’s (2018) estimate; see Additional file 1: Figure
S2 for the results using the other starting compositions.
Based on an assumption of an enstatite chondrite origin
for Mercury and the content of its surface lavas, Namur
et al. (2016) estimated the fO2 of formation conditions

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−4

wt%
0.1

25
30
35
40
75

−8

45
50

35

1

−4
30

40
45

35

2

60

4

55

6

8

Xsil
S , wt%

0.01

65

−9

0.01
0

50
70

10095 90

0

2

85

80

75

4

−9

55
60
65

45
75

−8

50

−8

40

85

−7

35

30

80

ΔIW

25

−7

25

20

−5

15

0.1

20

8

Xmet
S, C = 7, sat. wt%

−4
ΔIW

15

−9

6

−3

4
Xsil
S , wt%

−6

2

65

−5

4
5
6
7
8
9
10

70

wt%

1

80

N’18

0

8

Xmet
S, C = 2, sat. wt%

0.1

sil
XFeO
, wt%

0.01

−9

6

Xsil
S , wt%95 90 85

−3

4

45

−6

2

50

55
60

Xsil
FeO,

0

55

N’18

0.01

40
60

−8

25

70 65

ΔIW

20

−7

20

−5

15

−6

1
−5

9
10

−7

15

−3

N’18

Xmet
S, C = 5, sat. wt%

−4

30

2
3
4
5
6
7
8
9
10

−6

2

sil
,
XFeO

1

ΔIW

1

Xmet
S, C = 1, sat. wt%

0.1

sil
XFeO
, wt%

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N’18

Helffrich et al. Progress in Earth and Planetary Science

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6

8

Xsil
S , wt%Fig. 2 Compatibility of S and FeO content of Mercury’s mantle with pressure of metal/silicate equilibration for various core S contents (1, 2, 5, and 7wt%). Label on each panel gives the core metal S content at C saturation conditions (see text). Lines are contours of the pressure (GPa) ofmetal/silicate equilibrium. Colored box depicts limits on S and FeO in silicate discussed in text (see Table 3 for compositions). Lines of constant FeO
content across box indicate estimates of Mercury compositions from two sources: Nittler et al. (2018) mantle composition (0.04 wt%) and Namur etal. (2016) ( IW = − 5.4). Equivalent oxygen fugacity in log units relative to the iron-wüstite buffer on right assuming 70 wt% Fe in metal. Hatchedregions flag pressures outside Mercury’s 2/7 ≤ P/PCMB ≤ 2/3 limits. Liquid immiscibility in Fe-Si-S (Morard and Katsura 2010) potentially affects only
the lowest pressures at XSmet = 2, but does not substantially affect the resultsas − 5.4 log10 units relative to iron-wüstite, which constrains FeO to ∼ 0.3 wt%. We use this as an upper boundon the range of possible silicate FeO content. The sameauthors also analyzed Mercury surface spectroscopic data
to estimate the surface S content, finding terrane mean
ranges from 1.6 to 2.5 wt%. From melt modeling, they
reckon the source of the surface lavas contains 2–12 wt% S,
but favor 7–11 wt% on the basis of their fO2 estimate andsulfur saturation model. The FeO estimates provided by
the two studies are not mutually compatible; we adopt an
inclusive range of 0.01–0.3 wt% for FeO (but show values
up to 1 wt%) and, for S, adopt a narrower 1–7 wt% range
because we do not assume S saturation in the silicate as
Namur et al. (2016) does.

Studies of Mercury’s gravity field and spin state provide
limits on the sulfur content of its core through their compatibility with the planet’s polar moment of inertia andits mantle’s moment of inertia. Dumberry and Rivoldini(2015), extending Rivoldini and Van Hoolst’s (2013) work,
explored a range of ∼ 1–15 wt% for the sulfur content
of the core, but commonly found contents ∼ 5 wt% compatible with the geodetic data. Hauck II et al. (2013) also
explored compositional constraints on Mercury’s core but
used only a moment of inertia rotational data which do
not provide as tight constraints. We therefore examinecompositions with XSmet of 1, 2, 5, and 7 wt%. For each ofthese sulfur compositions, Fig. 2 shows the feasible pressure and compositional ranges that simultaneously satisfy

(2019) 6:66

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the S, Fe, Si, and O partitioning between core metal andmantle silicate at C saturation.
The pressure for metal-silicate equilibrium in Mercury
depends on the core sulfur content (Fig. 2). At low
values (1 wt%), the pressure is ∼ 7–75 GPa and increases
to ∼ 11–103 GPa at 7 wt%. For most of the core’s sulfur composition range, the equilibrium pressure exceeds
the present CMB pressure, ∼ 6 GPa (Rivoldini et al.
2009; Rivoldini and Van Hoolst 2013), suggesting that themetal-silicate equilibrium took place in a larger planet.
Some insights into how large the earlier planet may
have been may be derived from planetary metal proportions fmetal (= Mcore / Mbody ) and the planetary
Fe/Mg mass ratio. Figure 3 shows the relations for the
rocky planets, Vesta, and for enstatite and carbonaceouschondrites. Mercury is a clear outlier, even compared
to metal-rich CB chondrites that are not thought tobe viable Mercury building blocks (Cartier and Wood2019). However, by adding back silicate with the composition of Mercury’s bulk silicate, we see a trend leading
back to the cluster that the Solar System’s other rocky
bodies define. Between 1 and 3 additional M of silicate would place it within the solar system’s terrestrial
grouping.

To explore the additional silicate added to Mercury
needed to permit metal-silicate equilibrium, we adopt an
approach used in many simulations of major- and traceelement partitioning between the metal and silicate during planetary accretion (Wade and Wood 2005; Rubie etal. 2011). We assume a planet-wide magma ocean whosebase is at 12 PCMB and calculate the mass of the planet
required to achieve the equilibration pressure, which may
be viewed as equivalent to a single-stage core formation
model or a continuous core formation model for elements
whose metal/silicate concentration ratios do not change
significantly during accretion (principally the lithophileelements, but also some moderately siderophile elements,
e.g., Tuff et al. (2011)).
Figure 4 shows the results. The pressure at themagma ocean’s base, PBMO = 12 PCMB , is the anticipated equilibration pressure whose uncertainty istaken from various accretion scenarios, showing that
2/7 ≤ PBMO /PCMB ≤ 2/3 (Tuff et al. 2011; Rubie et al.
2011). Thus the intersection of the PBMO curve with theminimum equilibration pressure for each core sulfur
content yields the range of the minimum added silicate
mass required to allow metal-silicate equilibrium. All
XS ranges explored entail added silicate: 0.4–1.5 M(1 wt%), 0.8–3.2 M (2 wt%), and > 1.8 M (5, 7 wt%).
Thus, from a bulk chemistry standpoint alone, at least 0.4
M was lost from Mercury. An additional constraint is theplanetary Fe/Mg ratio and its comparison to the ratio interrestrial solar system bodies and chondritic precursors(Fig. 4). At low core S content (1 wt%), the Fe/Mg range
lies outside the range, rendering it infeasible on compositional grounds. Only at a core sulfur content of ∼ 2 wt%
and higher does metal/silicate sulfur partitioning alsosatsify Fe/Mg constraints. A core sulfur content of ∼ 2
wt% yields planetary Fe/Mg and metal ratios in the
known range of the other rocky bodies. A minimumof 0.8–3.3 × M added silicate is required to yield a
Mercury bulk silicate composition controlled by metalsilicate equilibrium for this core composition. MoreS-rich cores for Mercury require higher equilibrationpressures (Fig. 2) and suggest larger sizes for the protoMercury. Added silicate amounts of ∼ 1–3 M yield both
Fe/Mg ratios in the chondritic range and metal massfractions compatible with the other terrestrial planets.
It is worth highlighting some limitations of ourapproach. Firstly, we have no direct samples or observations of Mercury’s mantle composition, so it is inferred.
The surface compositions, from which all Mercury silicate estimates are derived, are obtained from re-emissionof energy radiated during solar flares (Nittler et al. 2011),
and strictly sample only the top tens of micrometersof Mercury’s surface. If the surface were completely
mantled by a late veneer, its bulk composition would

0.8

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Helffrich et al. Progress in Earth and Planetary Science

Mercury (N)Mercury (Z)0.4

f metal0.6

Mercury (C) 1

0.2

Venus (high)

5

0.0

6

Earth 2EC Venus (mean)
Venus
(low)
CC
3
Mars
4 Vesta

0.5

1.0

2.0

5.0

10.0

20.0

Fe/Mg (wt)Fig. 3 Metal weight fraction ( fmetal ) versus planetary Fe/Mg mass
ratio for various rocky bodies and chondritic meteorite classes (EC,enstatite; CC, carbonaceous). Bulk Mercury estimates from Nittler et al.
(2018), Chabot et al. (2014), and Zolotov et al. (2013). Mercury is asingular outlier from the cluster defined by the other objects. Dashedline is trend from silicate added to Mercury with the composition ofits bulk silicate (Table 3); points on line show total body mass in unitsof M . An original mass 2–4 × M would put it within the rocky bodycluster. Data are from Fegley (2014), Dumoulin et al. (2017),
McDonough and Sun (1995), Rivoldini et al. (2011), Javoy et al. (2010),
and Table 3

0.7

PCMB

0.6

CC
ECL

ECH

1.18 Fe/Mg

0.5

40

1.40

0.4

2 wt%

0.3

7 wt%
5 wt%

0.2

C
C

(m
ea
n)
Ve
nu
s

1 wt%

0

fmetal 0.1

10

PBMO

Ve
M nus
ar
s (low
)
Ve
st
a

30

Ve
nu
E
EC arth s (
hi

gh
)

fmetal20

P (GPa)1.74
OCH CI

2.39

M
er
cu
ry

4.01

50

60

15.79

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Helffrich et al. Progress in Earth and Planetary Science

1

2

3

4

5

6

M Mmerc

Fig. 4 Pressure at CMB (PCMB ) and at base of liquid silicate (PBMO ) for
Mercury grown by addition of silicate to its mantle. Four lines show
the range of minimum feasible pressures based on metal-silicate
equilibrium at Mercury IW = − 5.4 (Namur et al. 2016). Verticaldashed lines show range of proto-Mercury sizes suggested byplanetary metal and Fe/Mg (Fig. 3). Top axis shows Fe/Mg mass ratio
for the added amounts of silicate and Fe/Mg ratios for classes ofchondritic meteorites (carbonaceous, enstatite, OC ordinary, and L or
H for low and high iron groups (McDonough and Sun 1995)). Dashedlines around PBMO curve show a range of pressures used in different
magma ocean models, 2/7 ≤ PBMO /PCMB ≤ 2/3 (Tuff et al. 2011;
Rubie et al. 2011). fmetal curve (right axis) shows mass fraction of corewhen silicate is added to Mercury’s mantle. Labels on fmetal curve
indicate metal fraction of carbonaceous chondrites (McDonough andSun 1995), enstatite chondrites (Javoy et al. 2010), Venus (Dumoulin
et al. 2017), Earth (Stacey 1992), Mars (Rivoldini et al. 2011) and Vesta(Russell et al. 2012) for comparison

be masked. Mercury imaging shows extensive volcanic
formations, however, whose compositions are individually
distinct (Zolotov et al. 2013; Namur et al. 2016), making
any overall mantling unlikely, but possible still.
Our modeling is essentially driven by the surface silicate composition, from which the core composition isderived consistent with thermodynamic and experimental data and models. If Mercury is chondritic, some key
major element ratios obtained by proportionally combining the silicate and core compositions should also bechondritic. In particular, Fe/Si and Mg/Si should be. With
Additional file 1: Figure S3, one can see that the comparison is imperfect but encouraging. Either the silicate
estimates are insufficiently rich in Mg relative to Si or
the modeled core metal Si content is too high. It is
unclear where the problem lies, but, again, the surface
composition estimate relies on more model-dependentassumptions than does the sulfur partitioning model.
The sulfur partitioning model we use is experimentally calibrated to only 23 GPa, yet we employ it to highPage 7 of 10pressures; the extrapolation is questionable. However, theconstraints it provides are essentially low-pressure ones:for Vesta (< 1 GPa) and for the lowest pressures of metalsilicate equilibration (5–25 GPa). Hence, the main results
derive from pressures within the model’s applicability
range.
We rely on geodetic studies that assume that S is themain constituent of Mercury’s core. This is certainly
wrong from a chemical perspective, because our models
demand knowledge of the core’s Ni, Si, O, and C contents too. Whether density profiles for chemically realistic
Mercury core compositions would change the compositional constraints the geodetic studies provide is an open
question.

Discussion
From N-body and SPH impact simulations, Benz et al.
(1988, 2007) reckoned that Mercury’s original mass musthave been ∼ 2.25 × M , whereas Asphaug and Reufer(2014) found that impactors between 2.7–5.4×M , striking a proto-Venus- or proto-Earth-sized target at glancing
incidence (> 30°) shed sufficient mass to yield Mercurylike residues. These limits overlap with the chemical equilibration for XSmet of 2–5 wt% (Fig. 4). Though chemical
equilibrium imposes no useful upper limit to Mercury’s
original size, similarity to the Solar System’s other rocky
bodies does. A Mercury constructed from added silicate
could have had no more than about three masses added
to it before it would exceed the Solar System’s rocky body
Fe/Mg ratios (Fig. 3).
The estimated compositions also place limits on themet , which is shown in
Si content of Mercury’s core, XSi
metFig. 5a. The mean XSi depends on the pressure, though
Si solubility in metal is not strictly pressure-dependent(Fischer et al. 2015; Hirose et al. 2017) but other metalcomponents are (e.g., O) that affect γSi (Table 2). The
variation shown in Fig. 5a shows a further dependence
on core sulfur content, justifying, post hoc, the geodetic
modeling approach (Rivoldini et al. 2009; Rivoldini and
Van Hoolst 2013; Hauck II et al. 2013; Dumberry and
Rivoldini 2015). If so much silicate was lost from Mercury, there might be some as yet unidentified meteorite
material derived from the debris of its stripped mantle(Gladman and Coffey 2009); Cartier and Wood (2019)note that aubrites would be good candidates for Mercury
surface fragments. As an identification aid for Mercuryderived meteorites, stable silicon isotope analyses might
be a useful discriminant due to silicon isotope fractionation during core formation (Georg et al. 2007; Fitoussi
and Bourdon 2012; Hin et al. 2014). To draw up a siliconisotope budget, we need the core and silicate masses forthe planet, and the concentration of silicon in the metaland silicate. We use the silicate composition from Table 3
to obtain the elemental Si content (24.73 wt%) and use(2019) 6:66

Helffrich et al. Progress in Earth and Planetary Science

Page 8 of 10

a)

15

20

25

30

35

40

45

50 P/GPa

b)

20

40

60

80

100

P (GPa)−0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1

20
0

10

Xmet
Si , wt%

30

7
5
2
1

δ30Sim, per mil

0.0

0.1

1 wt%
2 wt%
5 wt%
7 wt%

40

10

0.2

5

average (ordinary & carbonaceous)enstatite
1976 2132 2276 2409 2535 2653 2765 2872 2975 3074 3169
2441 2749 2991 3195 3372 3529 3672 3802 3923 4036 4142
Magma ocean T range (K)Fig. 5 a Silicon content of Mercury’s core assuming metal-silicate equilibration at pressures prior to mantle stripping. Points show XSimet for coreformation at specified pressure for different metal S content (1, 2, 5, and 7 wt%). Horizontal dashed lines show the mean for each assumed coresulfur content. b Calculated δ 30 Sim for fractionation at various temperatures corresponding to the depth of a magma ocean and growing core mass
on proto-Mercury. Colored bands show mean and ± 2σ uncertainties for δ 30 Si for major chondritic meteorite classes. Points show predicted
fractionation in silicate for ∼ 2 wt% S content if δ 30 Sib corresponds to enstatite or ordinary and carbonaceous classes, and would be the predicted
δ 30 Si for meteorites derived from fragments of Mercury’s stripped mantle. All estimates are ∼ 0.1 higher than their chondritic parents’ means.
Circles and squares are from experimentally determined fractionation factors of Shahar et al. (2011) and the composite estimate (see the “Methods”
section), respectively

the mean core Si content to calculate the silicate-metal
partitioning of 30 Si during core formation. Lacking knowledge of the bulk Mercury δ 30 Si, we use the mean values
for various chondrite classes reported by Armytage et al.
(2011): enstatite chondrites − 0.63 ordinary and carbonaceous chondrites − 0.45Ṫhe results are shown in
Fig. 5b. We find that offsets of + 0.10 or more in δ 30 Si
relative to any chondritic parent would be characteristic of meteorites derived from the proto-Mercury body
if either Shahar et al.’s (2011) fractionation factor is usedor a composite factor derived from all sources. Due to
Mercury’s similarity to enstatite chondrites (Cartier andWood 2019), these would be the likely parent material,
and at low (15–20 GPa) magma ocean pressures corresponding to 2.5–3×M proto-Mercurys, δ 30 Si offsets
would be ∼ + 0.20 (Fig. 5b). The trend with lower
pressures also suggests that even if no stripping occurred,Mercury-derived meteorites would have significant δ 30 Si
offsets > + 0.3. Hence, the S and FeO content of thesilicate, along with the δ 30 Si offset from enstatite chondrites, might prove to be a useful signature of Mercury
provenance.
If Mercury was originally a few times its current mass
and its mantle was lost through a giant impact (Benz etal. 1988; Benz et al. 2007; Asphaug and Reufer 2014),
where did this material go? Benz et al. (1988) concluded

that the large impact scenario could only work if theejected material was not subsequently re-accreted by
Mercury. From N-body simulations of the ejecta, Benz etal. (2007) concluded that only a small fraction of ejectedmaterial would collide with Venus or be removed from
Mercury-crossing orbits through secular perturbations.
Even if launch speeds of ejecta from Mercury are highenough to place them on Venus- and Earth-crossing
orbits, only a few percent of this material collides withthe other two planets (Gladman and Coffey 2009). Only
if the debris was centimeter-sized and thus affected by
Poynting-Robertson drag could material be efficiently
removed from this region in a few million years (Benz et al.
2007; Gladman and Coffey 2009). Benz et al. (2007) compute that the size of ejecta material has a peak below 1 cm,
making Poynting-Robertson an attractive way to remove
material before most of it reaccretes onto Mercury.
Asphaug and Reufer (2014) proposed solving the problem of ejecta re-accretion onto Mercury by making
Mercury the impactor rather than the target. If protoMercury formed in the outer, volatile-rich regions of the
protoplanetary disc and, additionally, suffered multiple,
lower speed collisions with other targets, it could also
retain volatile sulfur (Hauck II et al. 2013; Asphaug andReufer 2014; Cartier and Wood 2019), solving yet another
Hermean chemical conundrum.

Helffrich et al. Progress in Earth and Planetary Science(2019) 6:66

Conclusions
In this study, we used the concept of metal-silicate partitioning in magma ocean conditions to constrain thepressure at which Mercury’s silicate and metal could havebeen in equilibrium. An experimentally derived modelof partitioning for sulfur provided the required pressurecomposition relationship. The structure of Vesta andcandidate Vestan silicate compositions provided a demonstration of the suitability of the model by showing that ityields, at Vestan equilibration pressures, silicate S content
equivalent to Vesta’s.
Applying the same model to Mercury, using its observed
surface silicate composition and estimates of its core composition from space geodetic studies, we find that equilibration may be achieved if Mercury was originally alarger planet 1.4–2.5 times more massive, and possibly
2–4 times so. Hence Mercury’s surface chemistry andgeodetic parameters are compatible with silicate mass loss
through collision with other objects, or by it having been
an impactor itself.
We used the estimated compositions of Mercury’score to calculate the stable silicon isotope fractionation
between core metal and mantle silicate. δ 30 Si offsets of+ 0.10 relative to ordinary, enstatite or carbonaceouschondrite precursors would arise, and, if Mercury’s original mass was 2.5–3 × M , the shifts would be ∼ + 0.20.
Even if no mantle stripping occurred, the fractionation
trend implies offsets in excess of + 0.30. These offsets could fingerprint meteorite fragments derived from
Mercury.
The future mission to the asteroid Psyche (Lord et al.
2017) may yield data to decide whether the body represents the end-point of a silicate stripping process. If there
is sufficient mantling silicate for estimating its mantle’s
composition and if the silicate retains sufficient sulfur, achemical approach similar to that used here may reveal
Psyche’s original mass as well.

Supplementary information
Supplementary information accompanies this paper athttps://doi.org/10.1186/s40645-019-0312-z.

Additional file 1: Discussion of fmetal for chondritic meteorites. Figure S1
Carbon saturation as a function of pressure. Figure S2a Compatibility of S
and FeO content of Mercury’s mantle with pressure of metal/silicate
equilibration for various core S contents (1, 2, 5 and 7 wt%), using Chabot
bulk silicate composition. Figure S2b Compatibility of S and FeO content
of Mercury’s mantle with pressure of metal/silicate equilibration for various
core S contents (1, 2, 5 and 7 wt%), using Zolotov bulk silicate composition.
Figure S3 Comparison of modeled bulk Mercury Fe, Mg and Si against
various chondritic meteorite classes.
Acknowledgements
Thanks to S. Ida and H. Genda for the discussions about planetary accretion, tothe reviewers of earlier versions of this paper for improving the approach, andto the handling editor for spotting and remediating flaws of text and concept.
Figures and calculations are made using R (R Core Team 2017).

Page 9 of 10

Authors’ contributions
GH designed the study, performed all calculations, and drafted the paper. RB
and AS discussed the methods used and contributed to the submitted
version’s text. All authors read and approved the final manuscript.
Funding
MEXT Kakenhi grant 15H05832 partially supported this work.
Availability of data and materials
All data used are in this paper; there are no additional experimental materials
associated with the work.
Competing interests
The authors have no competing interests regarding the Hermean
composition or resource exploitation nor in narratives of Mercury’s history.
Author details
1 Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1 Ookayama,

Meguro-ku, Tokyo, 152-8550 Japan. 2 Geophysical Laboratory, Carnegie
Institution for Science, 5251 Broad Branch Road NW, Washington, DC, 20015
USA.
Received: 11 December 2018 Accepted: 12 November 2019

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