Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010agufm.p21a1582s&link_type=abstract
American Geophysical Union, Fall Meeting 2010, abstract #P21A-1582
Astronomy and Astrophysics
Astrophysics
[5430] Planetary Sciences: Solid Surface Planets / Interiors, [5440] Planetary Sciences: Solid Surface Planets / Magnetic Fields And Magnetism, [5460] Planetary Sciences: Solid Surface Planets / Physical Properties Of Materials, [6296] Planetary Sciences: Solar System Objects / Extra-Solar Planets
Scientific paper
The recent dicscovery of extrasolar planets with radii of about twice the Earth radius and masses of several Earth masses such as e.g., Corot-7b (approx 5Mearth and 1.6Rearth, Queloz et al. 2009) has increased the interest in the properties of rock at extremely high pressures. While the pressure at the Earth’s core-mantle boundary is about 135GPa, pressures at the base of the mantles of extraterrestrial rocky planets - if these are at all differentiated into mantles and cores - may reach Tera Pascals. Although the properties and the mineralogy of rock at extremely high pressure is little known there have been speculations about mantle convection, plate tectonics and dynamo action in these “Super-Earths”. We assume that the mantles of these planets can be thought of as consisting of perovskite but we discuss the effects of the post-perovskite transition and of MgO. We use the Keane equation of state and the Slater relation (see e.g., Stacey and Davies 2004) to derive an infinite pressure value for the Grüneisen parameter of 1.035. To derive this value we adopted the infinite pressure limit for K’ (pressure derivative of the bulk modulus) of 2.41 as derived by Stacey and Davies (2004) by fitting PREM. We further use the Lindeman law to calculate the melting curve. We gauge the melting curve using the available experimental data for pressures up to 120GPa. The melting temperature profile reaches 6000K at 135GPa and increases to temperatures between 12,000K and 24,000K at 1.1TPa with a preferred value of 21,000K. We find the adiabatic temperature increase to reach 2,500K at 135GPa and 5,400K at 1.1TPa. To calculate the pressure dependence of the viscosity we assume that the rheology is diffusion controlled and calculate the partial derivative with respect to pressure of the activation enthalpy. We cast the partial derivative in terms of an activation volume and use the semi-empirical homologous temperature scaling (e.g., Karato 2008). We find that the activation volume decreases from 2.4cm^3/mol at 135GPa to 1.6cm^3/mol at 1.1TPa. An estimate of the viscosity increase across the mantle to a pressure of 1.1TPa using the adiabat calculated above results in an increase of the viscosity of 19 orders of magnitude. This value raises questions about the differentiation of these planets, heat transfer in their deep interiors, and magnetic field generation.(Ref.: Karato, S. 2008. Deformation of Earth Materials, Cambridge University Press.; Stacey, F.D., Davies, P.M. 2004. PEPI 142: 137; Queloz, D. et al., 2009. Astronomy and Astrophysics 506: 303.)
Breuer Doris
Spohn Tilman
Stamenkovic Vlada
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