1. Department of Geology and Geophysics
Rheological Structure of the Mantle of Super-Earths: Insights from Mineral Physics
Shun-ichiro Karato
Yale University
Department of Geology and Geophysics
New Haven, CT, USA

2. Dynamics of a super-Earth
mantle convection, thermal evolution
Does plate tectonic operate on super-Earths?
Does dynamo operate in super-Earths?
tidal heating
orbital evolution
How much have exo-planets migrated since their formation?
 Rheological properties

3. Internal structure of a super-Earth
P to ~ 1 TPa (1000 GPa)
T to ~5000 K

4. P-effect is potentially very large!
Viscosity of planetary materials depends strongly on T and P.
P-effect is potentially very large!

5. Viscosity-mass relationship
Viscosity of solids increases with P at low P.
Is this valid at higher P in super-Earths?

6. conventional models
new model

7. Internal structure of a super-Earth
(B1 B2 transition)
(dissociation of post-perovsktie (?),
Metallization (?))
MgO is the softest phase in a super-Earth’s mantle.

8. MgO
(V* decreases with depth (pressure))

9. Viscosity changes also with crystal structure.
normalized temperature
MgO (B1 or B2) is the
softest mineral in the
deep mantle.
normalize viscosity B1

10. Materials with B1 structure are the softest among various oxides.
Materials with B2 structure are even softer than those with B1 structure. B2 B1

11. Viscosity changes when mechanisms of atomic motion change.
V*vacancy >0
V*interstitial <0
vacancy mechanism
interstitial mechanism
(from (Ito and Toriumi, 2007)) (from Karato (1978))

12. B1

13. Conclusions
Viscosity of the deep mantle of a super-Earth might decrease with pressure.
the Rayleigh number increases with planetary mass
reduces plate thickness, increases convective stress with planetary mass making plate tectonics possible in large planets, which would otherwise be difficult.
high tidal energy dissipation

15. (low viscosity  higher heating rate, faster orbital evolution)

16. Could plate tectonics operate on a super-Earth?
How does resistance and driving force for plate tectonics change with planetary mass?
resistance: plate thickness  Rayleigh number
driving force: convective stress  Rayleigh number
A large Rayleigh number  high stress, thin planet  promote plate tectonics
How does the Rayleigh number change with planetary mass?
P-effect on viscosity is often ignored. Is it justifiable?
(Valencia et al., 2007)

17. P to ~1 TPa (1000 GPa)
T to 5000 K