Thermal and transport properties of mantle rock at high pressure: Applications to super-Earths |
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| Authors: | Vlada Stamenkovi? Doris Breuer Tilman Spohn |
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| Institution: | 1. Institute of Planetology, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 10, 48149 Münster, Germany;2. Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany;3. European Space Research and Technology Centre ESTEC, SRE-PE, European Space Agency, Keplerlaan 1, Postbus 299, 2200 AG Noordwijk, The Netherlands;1. Scottish Universities Physics Alliance (SUPA), and Centre for Science at Extreme Conditions, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, UK;2. Sorbonne Universités, UPMC Univ Paris 06, UMR 7193, ISTEP, F-75005 Paris, France;3. HPCAT, Geophysical Laboratory, Carnegie Institution of Washington, USA;1. Instituto de Ciencia de Materials de Madrid (ICMM–CSIC), Campus de Cantoblanco, 28049 Madrid, Spain;2. Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, United Kingdom;1. Laboratory of Seismology and Physics of Earth''s Interior, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui, China;2. CAS Center for Excellence in Comparative Planetology, China, Anhui 233500, China;1. Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, 100029 Beijing, China;2. Key Laboratory of Computational Geodynamics, College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, 100049 Beijing, China;3. Department of Earth and Planetary Sciences, University of California, Davis, CA, 95616, USA;4. University of Chinese Academy of Science, 100049 Beijing, China;5. Innovation Academy for Earth Science, Chinese Academy of Science, 100029 Beijing, China;1. Bayerisches Geoinstitut, Universität Bayreuth, D-95440 Bayreuth, Germany;2. School of Geosciences, University of the Witwatersrand, Private Bag 3, 2050, Wits, South Africa;3. Department of Computer Science, Louisiana State University, Baton Rouge, LA 70803, United States;4. Department of Geology and Geophysics, Louisiana State University, Baton Rouge, LA 70803, United States;5. Department of Earth Sciences, University College London, Gower Street, London, WC1E 6BT, United Kingdom |
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| Abstract: | In the present study, the temperature- and pressure-dependent transport and thermal properties, i.e., viscosity, phonon thermal conductivity, thermal expansivity and heat capacities, as well as electronic and radiative thermal conductivities, have been derived for the mantles of super-Earths. These properties are necessary to understand the interior dynamics and the thermal evolution of those planets. We assume that the mantles consist of MgSiO3 perovskite (pv), but we discuss the effects of the post-perovskite transition, and we elaborate on an addition of periclase MgO and incorporated Fe. However, MgO is found to only significantly influence the phonon thermal conductivity – the viscosities, heat capacities and thermal expansivities of pv and MgO remain comparable. We use the Keane theory of solids, which takes into account the behavior of solid matter at the infinite pressure limit, adopt the Keane equations of state, and adjust for pv and MgO by comparison with experimental high-pressure and high-temperature data. We find the theory of the infinite pressure limit of Keane to be in excellent agreement with recent ab initio studies and experiments. To calculate the melting curve, we further use the Lindemann–Stacey scaling law and fit it to available experimental data. The best data fitting melting temperature for pv reaches 5700 K at 135 GPa and increases to 20,000 K at 1.1 TPa, corresponding to the core-mantle boundary of a 10 Earth mass super-Earth (10MEarth). We find the pv adiabatic temperature (with a potential temperature of 1700 K) to reach 2570 K at 135 GPa and 5000 K at 1.1 TPa. To calculate the pressure-and temperature-dependent viscosity, we use the semi-empirical homologous temperature scaling to relate enthalpy change, and hence viscosity, to the melting temperature. We find that the resulting activation volume of pv decreases from 2.8 cm3/mol at 25 GPa to 1.4 cm3/mol at 1.1 TPa-resulting in a viscosity increase by ～15 orders of magnitude through the adiabatic mantle of a 10MEarth planet. Furthermore, the thermal expansivity (of pv and MgO) decreases by a factor of eight, and the total thermal conductivity (phonon, radiative and electronic) of an Earth-like pv/MgO composite increases by a factor of seven through an adiabatic mantle of a 10MEarth super-Earth. At higher temperatures, i.e., for super-adiabatic temperature profiles, the electronic and radiative thermal conductivities strongly increase and dominate the conductive heat transport. All findings indicate an increase of heat transfer solely by conduction in the lower mantles of super-Earths. Thus our results disagree with Earth-biased full-mantle convection assumptions made by previous models for super-Earths, and additionally raise questions about the differentiation of massive rocky exoplanets and their ability to generate magnetic fields or sustain plate tectonics. |
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