Mathematics – Logic
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008agufm.p14b..03t&link_type=abstract
American Geophysical Union, Fall Meeting 2008, abstract #P14B-03
Mathematics
Logic
5430 Interiors (8147), 5455 Origin And Evolution, 5475 Tectonics (8149), 8120 Dynamics Of Lithosphere And Mantle: General (1213), 8147 Planetary Interiors (5430, 5724, 6024)
Scientific paper
The discovery of extra-solar super-Earths has prompted interest in their possible mantle dynamics and evolution, and in whether their lithospheres are most likely to be undergoing plate tectonics like on Earth, or be stagnant lids like on Mars and Venus. The origin of plate tectonics is poorly understood for the Earth, likely involving a complex interplay of rheological, compositional, melting and thermal effects, which makes it impossible to make reliable predictions for other planets. Nevertheless, as a starting point it is common to parameterize the complex processes involved as a simple yield stress that is either constant or has a linear "Byerlee's law" dependence on pressure (e.g., [Tackley, GCubed 2000ab] in 3D cartesian geometry; [van Heck and Tackley, GRL 2008] in 3D spherical geometry). For such a simple description, scaling with planet size is expected to depend on heating mode (internal versus basal) and lithospheric strength profile. Simple "back of the envelope" scaling laws (e.g., following Moresi and Solomatov, GJI 1998) ignoring the pressure- dependence of physical properties such as density and thermal expansivity, suggest that the threshold for plate tectonics (i.e., yield stress or friction coefficient) does not depend strongly on planet size, and plate tectonics is equally likely or more likely for larger planets. Scalings that take into account pressure-related changes in physical properties [Valencia et al., Astrophys. J., 2007] make a similar prediction for predominantly internally-heated convection. Because the simplifying assumptions made in developing analytical scalings may not be valid over all parameter ranges, numerical simulations are needed; the one numerical study on super-Earths to date (O'Neill and Lenardic, GRL 2007) finds that plate tectonics is less likely on a larger planet, in apparent contradiction of analytical results. To try and understand this we here present new calculations of yielding- induced plate tectonics as a function of planet size, focusing on the idealized endmembers of internal heating or basal heating as well as different strength profiles, and compare to analytical scalings. The temperature- dependence of viscosity is based on laboratory values, i.e., stronger than previously modelled. Preliminary results indicate some first order similarity to simple scalings although some differences exist. In Earth, physical properties such as density, thermal expansivity, thermal conductivity and viscosity change strongly with pressure so that their values change substantially between the surface and the CMB, and many modelling studies have shown that this has a strong effect on convection. On super-Earths this will be even more accentuated. Thus, in a second set of calculations, we include reasonable variations of physical properties with pressure for planets up to twice Earth radius, studying their effect on convection with rigid lids or plate tectonics.
Tackley Paul J.
van Heck H. J.
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