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Rheological Properties ofSuper-Earth’s Mantle
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Shun-ichiro KaratoYale University
Department of Geology and Geophysics
LEAPS workshop, Pasadena, 2010
How does a super-Earth evolve?
mantle convection, thermal evolutionPlate tectonics is a key to habitable surfaceenvironment.Does plate tectonic operate on super-Earths?
tidal heating orbital evolution
How much have exo-planets migrated since their formation?
Rheological properties2
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?
resistance: plate thickness Rayleigh numberdriving force: convective stress Rayleigh number
A large Rayleigh number high stress, thin plate promote plate tectonics
How does the Rayleigh number change with planetary mass?
(Valencia et al., 2007)
P-effect on viscosity is often ignored. Is it justifiable?
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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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A model of a super-Earth (Earth-like composition)A: upper mantleB: lower mantleC: 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 >0V*interstitial <0
(from (Ito and Toriumi, 2007)) (from Karato (1978))
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Viscosity changes also with crystal structure.
norm
aliz
e vi
scos
itynormalized 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 thevolume 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
II: B1 B2 transition
III: dissociation of post-perovskite (+ metallization?)
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Conclusions
• Effects of pressure on rheological properties are large.
• If a conventional parameterization is used, viscosity increases so much with planetary mass and plate tectonics would be difficult for a large super-Earths.
• 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.
• Low viscosity of the deep mantle high tidal dissipation rapid orbital migration + substantial heating.
(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)
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