Rheological Properties of Super-Earth’s Mantle 1 Shun-ichiro Karato Yale University Department of Geology and Geophysics LEAPS workshop, Pasadena, 2010

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 2

Tidal dissipation and evolution of super-Earths 3 (low viscosity  higher heating rate, faster orbital evolution)

4 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 number driving 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?

T-P conditions 5 P to ~1 TPa (1000 GPa) T to 5000 K

6 Viscosity of planetary materials depends strongly on T and P. P-effect is potentially very large! (H*= kJ/mol, V*=3-10 cc/mol for typical mantle minerals)

7 Mass dependence of P: P~M 2/3 energy balance T-mass relationship

8 Viscosity-mass relationship

9 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)

10 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)

11 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))

12 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))

13 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))

14 I: mechanism change in diffusion II: B1  B2 transition III: dissociation of post-perovskite (+ metallization?)

15 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)