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
1
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
2
Internal structure of a super-Earth
P to ~ 1 TPa (1000 GPa)
T to ~5000 K
3
Viscosity of planetary materials depends strongly on T and P.
P-effect is potentially very large!
h = h0 exp
*
H*
=
h
exp
( E*+PV
)
(
0
RT
RT )
4
Viscosity-mass relationship
Viscosity of solids increases with P at low P.
Is this valid at higher P in super-Earths?
5
h µ T -q Py
conventional models
new model
6
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.
7
h = h0 exp
*
( HRT* ) = h0 exp ( E*+PV
RT )
MgO
(V* decreases with depth (pressure))
8
Viscosity changes also with crystal structure.
normalize viscosity
normalized temperature
B1
MgO (B1 or B2) is the
softest mineral in the
deep mantle.
9
Materials with B1 structure are the softest among various oxides.
Materials with B2 structure are even softer than those with B1 structure.
10-4
10-5
stress=1 MPa
B2
sC
C
10-7
l
10-8
aC
N
l
strain-rate, s -1
10-6
10-9
B1
10-10
10-11
-12
10 1
1.2
1.4
1.6
1.8
2
Tm/T
Fig. 3a (Karato)
10
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))
11
B1
12
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
13
14
1
Q
µ h,
1
()
1
a
h
(low viscosity  higher heating rate, faster orbital evolution)
15
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
Ra =
r ga (T -Ts ) d 3
kh
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)
16
P to ~1 TPa (1000 GPa)
T to 5000 K
17