Thermal and transport properties of mantle rock at high pressure: Applications to Super-Earths

Kurzfassung

In the present study, the temperature- and pressure-dependent transport and thermal properties, i.e., viscosity, phonon thermal conductivity, thermal expansivity and heat capacity, 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 elaborate on an addition of periclase MgO and incorporated Fe. 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 Lindeman-Stacey scaling law and fit it to available experimental data. The best data fitting melting temperature for pv reaches 5700K at 135GPa and increases to 20’000K at 1.1TPa, corresponding to the core mantle boundary of a 10 Earth mass super-Earth (10MEarth). We find the adiabatic temperature (with a potential temperature of 1700K) to reach 2570K at 135GPa and 5000K at 1.1TPa. 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 decreases from 2.8cm3/mol at 25GPa to 1.4cm3/mol at 1.1TPa resulting in a viscosity increases by ∼15 orders of magnitude along our reference adiabat. Furthermore, the thermal expansivity decreases by a factor of 8 and the total thermal conductivity (phonon, radiative and electronic) increases by a factor of 7 through an adiabatic mantle of a 10MEarth super-Earth. At higher temperatures, i.e., for super-adiabatic temperature profiles, the electronic and radiative thermal transport strongly increases and dominates the thermal conductivity. 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.