Rheological Properties of�Super-Earth’s Mantle

Shun-ichiro Karato

Yale University

Department of Geology and Geophysics

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LEAPS workshop, Pasadena, 2010

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How does a super-Earth evolve?

mantle convection, thermal evolution

Plate tectonics is a key to habitable surface

environment.

Does plate tectonic operate on super-Earths?

tidal heating

orbital evolution

How much have exo-planets migrated since their formation?

🡪 Rheological properties

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Tidal dissipation and evolution of super-Earths

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(low viscosity 🡪 higher heating rate, faster orbital evolution)

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Could plate tectonics operate on a super-Earth?

How does the resistance and driving force for plate tectonics change with planetary mass?

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resistance: plate thickness 🡨 Rayleigh number

driving force: convective stress 🡨 Rayleigh number

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A large Rayleigh number 🡪 high stress, thin plate 🡪 promote plate tectonics

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How does the Rayleigh number change with planetary mass?

(Valencia et al., 2007)

P-effect on viscosity is often ignored. Is it justifiable?

T-P conditions

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P to ~1 TPa (1000 GPa)

T to 5000 K

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Viscosity of planetary materials depends strongly on T and P.

P-effect is potentially very large!

(H*=300-600 kJ/mol, V*=3-10 cc/mol for typical mantle minerals)

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Mass dependence of P: P~M

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energy balance

T-mass relationship

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Viscosity-mass relationship

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A model of a super-Earth (Earth-like composition)

A: upper mantle

B: lower mantle

C: core

Internal structure of a super-Earth

(B1🡪 B2 transition)

(dissociation of post-perovskite)

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A linear approximation, H*=E*+PV* is not valid at high-P.

V* decreases with depth (pressure) (smaller P-effect), but viscosity increases with P at a given T.

(Karato, 2010)

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interstitial mechanism

vacancy mechanism

Viscosity changes when mechanisms of atomic motion change.

V*vacancy >0

V*interstitial <0

(from (Ito and Toriumi, 2007)) (from Karato (1978))

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Viscosity changes also with crystal structure.

normalize viscosity

normalized temperature

B1

In most of super-Earth’s mantle, MgO

is the softest phase.

MgO changes its structure from B1 to

B2 at ~0.5 TPa.

(modified from Karato (1989))

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B1

B2

Materials with B2 structure are softer than those with B1 structure.

Dissociation of post-perovskite (MgSiO3=MgO+SiO2) increases the

volume fraction of a weak MgO.

(data from Franssen (1994) and Heard-Kirby (1981)) (data from Rowell-Sanger (1981))

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I: mechanism change in diffusion

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II: B1🡪 B2 transition

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III: dissociation of post-perovskite

(+ metallization?)

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Conclusions

• Effects of pressure on rheological properties are large.

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• If a conventional parameterization is used, viscosity increases so much with planetary mass and plate tectonics would be difficult for a large super-Earths.

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• Viscosity of the mantle of a super-Earth likely decreases with pressure and hence decreases with planetary mass.

🡪 plate tectonics is possible in large planets.

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• Low viscosity of the deep mantle 🡪 high tidal dissipation 🡪 rapid orbital migration + substantial heating.

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(effects of tidal dissipation is much larger for rocky planets than for gaseous planets: influence of tidal dissipation on orbital migration of super-Earths will be important to 1-2 AU)