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

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 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 pv 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 of pv decreases from 2.8cm3/mol at 25GPa to 1.4cm3/mol at 1.1TPa-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.