Planetary Accretion Models and the Mineralogy of Planetary InteriorsMineralogy of Planetary Interiors

Dan Frost & Dave Rubie – Bayerisches GeoinstitutDan Frost & Dave Rubie Bayerisches Geoinstitut

John Hernlund – Earth‐Life Science Institute, Institute of TechnologyTokyo 

Alessandro Morbidelli &Seth Jacobson – Observatoire de la Cote d’Azur, Nice, France

b h & d b ll f hRebecca Fischer & Andy Campbell – University of Chicago

Structure and dynamics of Earth-like planets

Chemical State of Mantle/CoreModel incorporates:‐

‐Partitioning of siderophile elementsMantle/Core mass ratio

FeO content of mantle

Partitioning of siderophile elements

‐Dynamic/ astrophysical  constraints on accretion processes

Mg/Si ratio of mantle‐Constrain success of the model by comparison with Earth mantle composition

Volatile content/H2O‐ Provide robust indicators for ranges of plausible conditions

Heterogeneous Formation of Earth and Moon

Reduced Moon formingImpact of (FeO rich)

Volatile free(FeO poor Fe rich)

Impact of (FeO rich)

CI type materialMoonMoon

Late Veneer ofSulphur richliquid stripsHSE to core

Late Veneer of1% chondriticmaterialHSE to core

(Hadean Matte)

O‘Neill (1991) GCA 55, 1159.Complicated‐ can it really be tested?

Homogeneous accretion: Metal segregation at the base of a deepmagma ocean

Constrain a single set of P,T and fo2 for core formationg , f 2

(Li & Agee, 1996; Righter & Drake 1997)

Model of continuous core formation with step-wise increases in foin fo2

(Wade & Wood 2005)(Wade & Wood, 2005)

Terrestrial Accretion under oxidising conditions

Siebert et al. (2013)

"N-body simulations" dynamic system of particles, under gravity

25-125 embryos (0.05-0.1Me), 1000-5500 planetesimals (0.0003-0.002 Me)

(e.g. O'Brien et al., 2006; Walsh et al., 2011)

Location and composition of final terrestrial planets

Combine N‐body simulations withCore/mantle differentiation for each accretion event

Earth depleted in volatiles like all chondrites relative to CI

Li

NaK

CsZn

FKEarth’s Mantle

Palme (2000)

Volatile depletion based on models for condensation

H2O + Fe ‐> FeO + H2

FeO

Preferred composition-distance model

1.0alInitial oxidation state of primitive bodies

0.8Fe/(Fe+FeO)in

met

a

0.6 Highly reduced Partially

Fe/(Fe+FeO)

emen

t

0.4

Oxidized orFully oxidized

20 t%

Partially oxidized

n of

ele

0 0

0.2Oxidized or almost fully

oxidized

+ 20 wt% water iceSi

Frac

tion

0 2 4 6 8 10 12

0.0F

Heliocentric distance (AU)Rubie et al. 2014

Mass balance approach to core formation modeling

1) bulk composition of accreting material – solar system (CI) ratios of non-volatile elements but with oxygen contents varying over a radial gradient

2) Determine equilibrium compositions of co-existing silicate and metal liquids at high P-T:q g

[(FeO)x (NiO)y (SiO2)z (Mgu Alm Can)O] + [Fea Nib Oc Sid]silicate liquid metal liquidq q

3) Maintain a mass balance- no assumed oxygen fugacity

Proportion of a target’s mantle/magma ocean that equilibrates with the impactor's coreequilibrates with the impactor s core

where Ф is the volume fraction of metal in the metal-silicate mixture

Fraction of equilibrating mantle:

• 0.35-1.7% for planetesimal impacts

2 10% f b i t• 2-10% for embryo impacts

(Deguen et al., 2011, EPSL)

Metal/Silciate partition coefficents at high P/T

Laser heated diamond anvil cell Multianvil

Up to 100 GPa

Multistage Homogeneous Core formation

2Fe  + SiO2 =  Si  +  2FeO

Metal    Silicate     Metal    Silicate

Accretion history of Grand Tack simulation

1.0 SA154_767

0.8d

#4 "Mercury" #5 "Venus" #6 "Earth"#30 "Mars"

0.4

0.6

ass

accr

eted #30 Mars

0.2

0

Ma

0 50 100 1500.0

Time (Myr)

Each accretion event (collision) results in an episode of coreformationCore formation and the evolving mantle and core chemistryare modelled in all the terrestrial planets simultaneously

Homogeneous accretion models

Evolution of Earth's mantle composition based on two homogeneous accretion models

Evolution of Earth's mantle composition based on two homogeneous accretion modelshomogeneous accretion models

16

18

20

HM-1HM-2

48

49

50

SiO2 2000

2500

3000

Ni

8

10

12

14

FeO

HM-2Fe

O (w

t%)

43

44

45

46

47

HM-1 HM-2

SiO

2 (w

t%)

500

1000

1500

2000

HM-1 HM-2

Ni (

ppm

)

0.0 0.2 0.4 0.6 0.8 1.0Mass accreted (Me)

0.0 0.2 0.4 0.6 0.8 1.042

Mass accreted (Me)0.0 0.2 0.4 0.6 0.8 1.0

0

Mass accreted (Me)

140

160

180

Co HM-1 HM-2 700

50

Ta HM-1HM-2

20

40

60

80

100

120Co

Co

(ppm

)

500

600

HM-1 HM-2

NbNb

(ppb

)

40

HM 2

Ta (p

pb)

0.0 0.2 0.4 0.6 0.8 1.0

20

Mass accreted (Me)0.0 0.2 0.4 0.6 0.8 1.0

Mass accreted (Me)

0.0 0.2 0.4 0.6 0.8 1.030

Mass accreted (Me)

120

125

1304500

19

20

90

95

100

105

110

115

V HM-1 HM-2

V (p

pm)

3000

3500

4000

HM-1 HM-2

Cr

Cr (

ppm

)

14

15

16

17

18

Nb/Ta

HM-1 HM-2

Nb/

Ta0.0 0.2 0.4 0.6 0.8 1.0

80

85

Mass accreted (Me)0.0 0.2 0.4 0.6 0.8 1.0

2500

Mass accreted (Me)

0.0 0.2 0.4 0.6 0.8 1.013

14

Mass accreted (Me)

H2O content of the mantle

H2O + Fe ‐> FeO + H2

(Deguen et al., 2011, EPSL)

Composition of Venus

Composition of Martian Mantle

Evolution of a layered structure – results of 100 N-body simulations

(wt.%

)entration 

Fe con

ce

% of core

Summary

• Combining N-body accretion and core formation models enables the evolution of core and mantle compositions to be modelledmodelled

• H2O could have been accreted relatively earlyU i thi h th f E th d V• Using this approach, the cores of Earth and Venus are predicted to contain 7 wt% silicon and 3 wt% oxygenPartitioning of oxygen and silicon into liquid Fe is enhanced by• Partitioning of oxygen and silicon into liquid Fe is enhanced by high temperature and batches of core-forming metal contain high concentrations of these elements during late accretiong g

• Development of a density stratification is inevitable in Earth-mass planets but may be destroyed by a giant impact

• The lack of a magnetic field on Venus may indicate a stratified core which has survived due to an absence of late giant i timpacts

Evolution of the concentration of light elements in Earth’s core

15

14

15nt

s (w

t%)

13

ht e

lem

en

11

12

on o

f lig

h

10

11

ncen

tratio

9

Tota

l co

0.0 0.2 0.4 0.6 0.8 1.0

Mass accreted (Me)

Metal/Silciate partition coefficents at high P/T2

2

2

( , ) 2

Met SilciateSi FeO

D P T Met SilicateFe SiO

X XK

X X

Evolution of Earth's mantle composition based on preferred composition distance modelpreferred composition-distance model

6

7

8

9

47

48

1500

2000

Ni

0

1

2

3

4

5

6

FeO

FeO

(wt%

)

44

45

46

47

SiO2SiO

2 (w

t%)

0

500

1000

Ni

Ni (

ppm

)

0.0 0.2 0.4 0.6 0.8 1.00

Mass accreted (Me)0.0 0.2 0.4 0.6 0.8 1.0

44

Mass accreted (Me)0.0 0.2 0.4 0.6 0.8 1.0

Mass accreted (Me)

80

100

120

Co

)

500

600

700

Nb

) 42

44

46

Ta

)

0.0 0.2 0.4 0.6 0.8 1.0

0

20

40

60

Co

(ppm

)

0.0 0.2 0.4 0.6 0.8 1.00

100

200

300

400

Nb

(ppb

)0.0 0.2 0.4 0.6 0.8 1.0

36

38

40Ta (p

pb

Mass accreted (Me) Mass accreted (Me) Mass accreted (Me)

75

80

85

90

95

m)

2500

3000

m) 0.06

0.08

0.10

0.12

wt%

)

H2O

0.0 0.2 0.4 0.6 0.8 1.050

55

60

65

70VV

(ppm

Mass accreted (Me)0.0 0.2 0.4 0.6 0.8 1.0

1500

2000Cr

Cr (

ppm

Mass accreted (Me)

0.0 0.2 0.4 0.6 0.8 1.0-0.02

0.00

0.02

0.04

H2O

(w

Mass accreted (Me)Mass accreted (Me) Mass accreted (Me) Mass accreted (Me)

Final core composition: 82 wt% Fe, 5 wt% Ni, 9 wt% Si, 3 wt% O, 48 ppm H

Evolution of mantle compositions of Mercury and Mars based on preferred composition distance modelbased on preferred composition-distance model

0.15

0.20

MarsMercury

20

MarsM

0.10

2O (w

t%)

y

10

15

eO (w

t%)

Mercury

0.00

0.05

H2

0

5

Fe

0.0 0.1 0.2 0.3 0.4 0.5

Mass accreted (Me)0.0 0.1 0.2 0.3 0.4 0.5

0

Mass accreted (Me)

Constraints on core-formation modelingEarth-mantle concentrations of the non-volatile siderophile elements:siderophile elements: Fe, Si, Ni, Co, Nb, Ta, V and Cr + Nb/Ta

(F O f l f M & M )(FeO contents of mantles of Mars & Mercury)

2 5 l t fitti t2-5 least-squares fitting parameters:• 1-4 parameters that define the composition of• 1-4 parameters that define the composition of

primitive bodies as a function of their heliocentric distances of origindistances of origin

• Metal-silicate equilibration pressure – as a fraction oft l t ' CMB (t i ll 0 5 0 6)a proto-planets's CMB pressure (typically 0.5-0.6).

Cause of oxidation• Oxygen fugacities of a solar gas are orders of magnitude more 

reducing than the intrinsic oxygen fugacities at which the terrestrial l t f d b t i t t ith th i f hi hl d dplanets formed but are consistent with the region of highly‐reduced 

compositions at <1.3 AU postulated here. Thus oxidation is required.

• Due to the inward net flow of material in the solar nebula, ice-covered dust moves inwards from beyond the snow linecovered dust moves inwards from beyond the snow line.

• Inside the snow line, water ice sublimes, adding H2O to the vaporphase As temperatures continue to rise and material continues tophase. As temperatures continue to rise and material continues to move inward, H2O-rich vapour reacts with Fe-bearing dust, resulting in oxidation. g

• Inward still, vapour is H2O‐poor because the products of sublimed water ice have not mixed all the way to the inner‐most solar system. Here Fe y yremains largely free of oxidation.

Evolution of the concentration of light elements in Earth’s core

15

14

15nt

s (w

t%)

13

ht e

lem

en

11

12

on o

f lig

h

10

11

ncen

tratio

9

Tota

l co

0.0 0.2 0.4 0.6 0.8 1.0

Mass accreted (Me)

Tested composition-distance models for primitive bodies

0.8

1.0 Homogeneous accretion modelsm

etal

(a)

HM-10 8

1.0 Highly reduced

(b) "Step model" HT-1

met

al

0.4

0.6

tion

of F

e in

m

HM-2

0.4

0.6

0.8

tion

of F

e in

m

Reduced chi squared = 80

0 2 4 6 8 10 120.0

0.2Frac

t

0 2 4 6 8 10 120.0

0.2 Partially oxidized

Frac

t

Reduced chi squared = ≥72

(d)

Heliocentric distance (AU) Heliocentric distance (AU)

(c)

0 6

0.8

1.0

( )

"Gradient model" HT-3

men

t in

met

al0 6

0.8

1.0

(c)"Step model" HT-2

Fe

nt in

met

al

Reduced chi squared= 3 1 Reduced chi squared

0.2

0.4

0.6

Si

Fera

ctio

n of

ele

m

0.2

0.4

0.6

Partially oxidized

Highly reduced

Sition

of e

lem

en = 3.1 Reduced chi squared = 1.5

0 2 4 6 8 10 12

0.0SiFr

Heliocentric distance (AU)(1) (2)0 2 4 6 8 10 12

0.0Si

Frac

t

Heliocentric distance (AU)

Lower mantle seismic observations

Karason & van der Hilst 2000

A peridotitic lower mantle

BSE e.gMcDonough & Sun 1995

72 mole % (Mg,Fe)(Al,Si)O3Bridgmanite

Pressure (GPa)6 l %C SiO P kit

22 mole % (Mg,Fe)O Ferropericlase

72 mole % (Mg,Fe)(Al,Si)O3Bridgmanite

Murakami et al. 2012

6 mole %CaSiO3 Perovskite

Brillouin scattering

Laser light interacts with phonons and is scattered with Doppler shifted frequency frequency

Vi = / 2n*sin (/2)

Fabry-Perot

qIncident Scattered

Laser Fabry-Perot interferometer

Incident Laser

Scattered Light

Diamond anvil cell and Brillouin scattering

Brillouin scattering X‐ray diffraction lab

Brillouin optics

MgSiO3 Bridgmanite- room temperature

(Mg0.96Fe0.04)SiO3 Bridgmanite- room temperature

MgSiO3

(Mg0.96Fe0.04)SiO3

MgSiO3

(Mg0.96Fe0.04)SiO3

Ultrasonic measurements at high pressure and temperature

Chantel et al. (2012) GRL 39,L19307

Thermo-elastic properties of mantle end-members

Thermo-elastic paramaters of the mantle phases used for calculating the sound wave velocities and densities as a function of pressure and temperature in the transition zone and lower mantle.

h l V0 KT0 K' G0 G 'Phase Formula V0(cm3/mol)

KT0(GPa) K'T0

qoG0

(GPa) G0' s0

Wadsleyite Mg2SiO4 4.052 169 4.3 853 1.21 2 112 1.4 2.6 Wadsleyite Fe2SiO4 4.28 169 4.3 719 1.21 2 72 1.4 1.1

Ringwoodite Mg2SiO4 3.949 185 4.2 891 1.11 2.4 123 1.4 2.3 Ringwoodite Fe2SiO4 4.186 213 4.2 652 1.26 2.4 92 1.4 1.8

Ca-Perovskite CaSiO3 10.98 236 3.9 802 1.89 0.9 157 2.2 1.3

Stishovite SiO2 1.402 314 3.8 1055 1.35 2.9 220 1.9 4.6 Perovskite MgSiO3 2.445 250.3 4.02 901 1.44 1.4 176.8 1.75 2.6 Perovskite FeSiO3 2.54 250.3 4.02 765 1.44 1.4 162.8 1.5 1.9 Perovskite FeAlO3 2.54 220 4.1 765 1.44 1.4 132 1.7 1.9 Perovskite AlAlO3 2.549 228 4.1 886 1.44 1.4 157 1.7 2.8 Periclase MgO 1.124 161 3.9 772 1.48 1.6 130 2.3 2.3 Wüstite FeO 1.226 149 4.9 454 1.54 1.6 47 0.7 0.6

values in italics are taken from Stixrude and Lithgow-Bertelloni (2011); values for perovskite are from Boffa Ballaran et al. (2012); Chantel et al. (2012); Kurnosov et al. (in preparation)

A peridotitic lower mantle

72 mole % (Mg,Fe)(Al,Si)O3Bridgemanite

6 l %C SiO P kit

22 mole % (Mg,Fe)O Ferropericlase

72 mole % (Mg,Fe)(Al,Si)O3Bridgemanite

6 mole %CaSiO3 Perovskite

Irifune et al. 2010

Fe and Mg exchchange between Bridgmanite and ferropericlase

Irifune et al. 2010

Mineral-physics model for a BSE deep mantle

Influence of Fe-Mg exchange

Murakami et al. 2012

High ferric iron in Bridgmanite

Irifune et al. 2010

Fe3+/TFe

Fe3+ content of Bridgmanite in equilibrium with Fe metal

FeODisproportionation‐ constantBSEbulkoxygen

3FeO = Fe0 + Fe2O3

<3 % Fe3+/ΣFe3 % Fe /ΣFe

~40 % Fe3+/ΣFe

MineralphysicsmodelwithconstantBSEbulkoxygen

Summary

- This model does not include Al in perovskite- however previous ultrasonic measurments indicate a limited influence which is currently being tested with Brillouin measurments.

V d V ti t d f BSE iti i l bl i th t 1000 k f- Vs and Vp estimated for a BSE composition mineral assemblage in the top 1000 km of the lower mantle match seimsic observations.

- Seismic properties of LLSVPs do not match Fe enrichment in a perovskite dominated i l blmineral assemblage.

Conclusions• Combining N-body accretion and core formation modeling

provides new constraints on both processes.

• Accretion of Earth and Venus was heterogeneous• For Earth, Mars and Venus, excellent results are obtained when embryos and planetesimals

that form close to the Sun, at <1‐1.5 AU, are highly reduced and bodies that form further from the Sun are partially‐ to fully‐oxidized. Other composition‐distance models fail badly.

• H2O‐bearing bodies in the SA154_767 model originate at >8.5 AU and result in ~1000 ppm H2O in the mantle

• Results are based on impactor cores equilibrating completely, but with a very limited fraction of a proto‐planet′s mantle at average pressures of 50‐60% of CMB pressuresfraction of a proto‐planet s mantle, at average pressures of 50‐60% of CMB pressures.

Accretion, heating & metal delivery byimpactsimpacts

Core formation and accretion are multistageprocesses that cannot be separated

Grand Tack accretion model

• Classical models (e g O'Brien et al 2006)• Classical models (e.g. O Brien et al 2006) consistently result in a model Mars that ist itoo massive

• The Grand Tack model (Walsh et al., 2011) ( , )is based on the inward and then outwardmigration of Jupiter and Saturn thatmigration of Jupiter and Saturn thattruncates the planetesimal disk at ~1 AU and

lt i li ti ll ll f Mresults in a realistically small mass for Mars.

Modeling planetary accretiong p y• Late stage accretion of terrestrial planets is

modeled using "N body simulations" Themodeled using N-body simulations . The "Grand Tack" model (Walsh et al., 2011) has been especially successful in reproducing thebeen especially successful in reproducing the small size of Mars.

• Start with ~40 embryos (0.07 Me) and ~1500 l l ( ) llplanetesimals (0.0003‐0.0035 Me), initially 

dispersed between 0.7 AU and 13 AU, and collide/accrete to form larger bodies.

• Combine core mantle differentiation with N body• Combine core‐mantle differentiation with N‐body accretion models

Accretion history of Grand Tack simulation SA154 767SA154_767

SA154 767

0.8

1.0 SA154_767

#4 "Mercury" #5 "Venus"#6 "Earth"

0.6

s ac

cret

ed

#6 Earth #30 "Mars"

0.2

0.4

Mas

s

0 50 100 1500.0

Ti (M )Time (Myr)

Here we consider that each accretion event (collision) results in an episode of core formation and we thus model core

formation and evolving mantle and core chemistry in all the terrestrial planets simultaneously

Model for the influence of a spin transition in ferropericlase

Wu et al. 2013