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21 orders of magnitude for an isotherm of 2000
K). The increase is higher for larger activation
volumes (i.e. for 10 cc/mol, the increase is more
than 100 orders of magnitude for an isotherm of
4000 K!), and lower when considering that the
mantle's temperature increases between 100 and
1000 Gpa. This simple exercise shows that the
viscosity of rocks can change dramatically inside
of a large Earth-like planet. It should be noted
that because of the high sensitivity of viscosity
on temperature, the internal temperature of
a planet is closely related to the rheological
properties of materials. For a detailed discussion
including the feedback between pressure and
temperature-dependent viscosity and interior
temperature see Karato (2011). Rocky super-
Earths are therefore interesting planets to test
theories about convection as they have hotter
interiors under large compressive forces.
Several groups have studied whether or not
plate tectonics is a viable heat loss mechanism for
super-Earths. Valencia et al . (2007) and Valencia
and O'Connell (2009) used simple parameter-
ized convection scalings to suggest that mas-
sive terrestrial analogs may maintain subduc-
tion and hence plate tectonics. They include a
temperature-dependent viscosity and changes in
bulk density due to compression effects. They
find that plates become thinner while the shear
stress beneath the plate available from convec-
tion becomes larger with increasing mass. Despite
larger gravities that may strengthen the faults
where deformation towards subduction occurs,
the shear stress on the fault is large enough to
overcome the yield stress.
Four other models use a numerical approach
that also includes a temperature-dependent vis-
cosity (not pressure) and a condition to simulate
failure based on a plastic yield stress criterion.
O'Neill and Lenardic (2007) scale a nondimen-
sional numerical model by Moresi and Soloma-
tov (1998), developed to explain plate tectonics
on Earth, where they find that at most rocky
super-Earths are in an episodic regime. Van Heck
and Tackley (2011) use a similar numerical model
(StagYY) under the same conditions for inter-
nally and basally heated planets. Their numerical
results compare well to their analytical scaling
findings where they find that in most cases larger
planets are equally likely to have plate tectonics
(expressed as a constant ratio between convective
stress to yield stress), except for the case in which
the planets are basally heated and the yield stress
is constant (as opposed to pressure dependent)
where mobile lid regime is more favorable for
larger planets. In their scaling analysis, they also
find that once pressure dependency on density is
incorporated, that larger planets are more likely
to have plate tectonics (in agreement with Valen-
cia et al ., 2007). In addition, they propose that
the reason for the discrepant result of O'Neill
and Lenardic (2007) perhaps lies in an inconsis-
tent scaling on the non-dimensional convective
parameters. On the other hand, Korenaga (2010)
used his numerical model to propose a condi-
tion for the transition between plate tectonics
and stagnant lid based on the lithospheric viscos-
ity contrast, which he finds to be proportional
to the square root of the Rayleigh number. He
finds that although the conditions are slightly
better for planets with more mass, the essential
factor is to have a very low coefficient of fric-
tion (that determines the yield stress), which can
only be achieved through a weakening agent such
as water.
On the other hand, Foley et al . (2012) imple-
ment a treatment for modeling subduction based
on damage-grainsize feedback, where the condi-
tion for subduction is achieved when the viscosity
contrast between the plate and the underlying
mantle is negligible, which is different from all
others models that use the plastic yield stress
criterion. They also find that rocky super-Earths
exhibit plate tectonics.
The studies mentioned so far share one
shortcoming: pressure effects are not included,
which affect mostly viscosity but also other
thermal parameters such as thermal expansivity,
conductivity and diffusivity. One end-member
approach is to argue based on physical grounds
that the top boundary layer is affected by local
conditions and that physical parameters at depth
do not significantly affect its behavior (adopted by
Valencia et al ., 2007; Valencia & O'Connell, 2009
to
justify
having
only
temperature-dependent
viscosity).
Another
end-member
approach
is
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