Thermal evolution of terrestrial exoplanets
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The recent rapid development in the detection and characterisation of exoplanets (planets outside the Solar System) call for a systematic comparison of their thermal state and planetary history under different internal conditions. Previous studies suggest that the initial condition of the Earth's thermal history is 'forgotten' relatively early in its history and therefore does not contribute to the Earth's current thermal state. This does not hold true for large terrestrial exoplanets based on similar calculations for larger planetary sizes. In this study we use a steady state temperature profile just below the solidus as the initial condition. A series of numerical modelling experiments are performed to investigate the effects of planetary size, surface temperature, depth-dependent viscosity profiles and the core mass ratio of the planet. Both a parameterised modelling approach and a dynamical approach are applied to thermal convection models in a hierarchy of complexity. Thermal equilibrium models are performed to study the effects of planetary internal conditions on steady state temperatures and thus suitable initial conditions for the investigation of subsolidus thermal convection, while thermal evolutionary experiments study the effects of these parameters on exoplanetary thermal history. We find that larger planets in general cool slower from an initial hot state, due to larger total internal production of heat and relatively low surface-to-volume ratio. In their early history, planets with a smaller core are more likely to be in a thermal regime of periodic melting than those of an equal mass and larger core, their subsolidus cooling being accordingly delayed. This is a combined effect of larger planetary size, rapid decrease of gravitational acceleration with depth, and relatively low melting temperatures. 'Super-plumes' are observed in planets without a metal core, which efficiently transport hot materials to the surface and thereby decease the planet's internal thermal gradient. Depth-dependent viscosity profiles calculated from an Arrhenius type of formulation are found to suppress surface thermal instabilities and mobilise the low-viscosity zones in the upper part and the bottom of the mantle layer. When the depth-dependence of viscosity is considered, convective motion is propelled by warm upwellings close to the core mantle boundary while the surface is characterised by a thick boundary layer of stable conduction. This in turn changes the internal thermal structure of the planet and increases steady state temperatures.