Frank W. Wagner

Rocky super-Earth interiors - Structure and internal dynamics of CoRoT-7b and Kepler-10b

Aims. We present interior structure models of the recently discovered exoplanets CoRoT-7b and Kepler-10b addressing their bulk compositions, present thermal states, and internal dynamics. We investigate how mantle convection patterns are influenced by the depth-dependence of thermodynamic parameters (e.g., thermal expansivity and conductivity) caused by the extended pressure and temperature ranges within rocky super-Earths. Methods. To model the interior of rocky exoplanets, we construct a four-layer structural model solving the mass and energy balance equations in conjunction with a generalized Rydberg equation of state providing the radial density distribution within each layer. The present thermal state is calculated according to a modified mixing-length approach for highly viscous fluids. Furthermore, the obtained internal structure is used to carry out two-dimensional convection simulations to visualize the mantle convection pattern within massive exoplanets such as CoRoT-7b and Kepler-10b. Results. Both CoRoT-7b and Kepler-10b most likely have large iron cores and a bulk composition similar to that of Mercury. For a planetary radius of Rp = (1.58 ± 0.10) R⊕, a revised total mass of Mp = (7.42 ± 1.21) M⊕, and the existence of a third planet in the CoRoT-7 planetary system, calculations suggest that an iron core of 64 wt-% and a silicate mantle of 36 wt-% is produced owing to the relatively high average compressed density of ρavg = (10.4±1.8) g cm −3 . Kepler-10b’s planetary radius and total mass yield an iron core of 59.5 wt-%, which complements the silicate mantle of 40.5 wt-%. An enhanced radiogenic heating rate owing to CoRoT-7b’s young age (1.2−2.3 Gyr) raises the radial distribution of temperature by only a few hundred Kelvin, but reduces the viscosity by an order of magnitude. The planform of mantle convection is found to be strongly modified for depth-dependent material properties, with hot plumes rising across the whole mantle and cold slabs, which stagnate in the mid-mantle because of the loss of buoyancy. Conclusions. We use a new model approach to determine the detailed interior structures and present thermal states of CoRoT-7b and Kepler-10b. Both planets are found to be enriched in iron. The results imply that modest radiogenic heating does not play a significant role in determining the internal structure of rocky exoplanets. The depth-dependence of thermodynamic properties, however, strongly influences the mantle convection patterns within exoplanets such as CoRoT-7b and Kepler-10b. This may have a significant effect on the thermal evolution and magnetic field generation of close-in super-Earths.

Interior structure models of terrestrial exoplanets and application to CoRoT-7 b

In this study, we model the internal structure of CoRoT-7b as a type example for a terrestrial extrasolar planet using mass and energy balance constraints. Our results suggest that the deep interior is predominantly composed of dry silicate rock, similar to the Earth’s Moon. A central iron core, if present, would be relatively small and less massive (< 15 wt.% of the planet’s total mass) as compared to the Earth’s (core mass fraction 32.6 wt.%). Furthermore, a partly molten near-surface magma ocean could be maintained, provided surface temperatures were sufficiently high and the rock component was mainly composed of Earth-like mineral phase assemblages.

Physical state of the deep interior of the CoRoT-7b exoplanet

The present study takes the CoRoT-7b exoplanet as an analogue for massive terrestrial planets to investigate conditions, under which intrinsic magnetic fields could be sustained in liquid cores. We examine the effect of depth-dependent transport parameters (e.g., activation volume of mantle rock) on a planets thermal structure and the related heat flux across the core mantle boundary. For terrestrial planets more massive than the Earth, our calculations suggest that a substantial part of the lowermost mantle is in a sluggish convective regime, primarily due to pressure effects on viscosity. Hence, we find substantially higher core temperatures than previously reported from parameterized convection models. We also discuss the effect of melting point depression in the presence of impurities (e.g., sulfur) in iron-rich cores and compare corresponding melting relations to the calculated thermal structure. Since impurity effects become less important at the elevated pressure and temperature conditions prevalent in the deep interior of CoRoT-7b, iron-rich cores are likely solid, implying that a self-sustained magnetic field would be absent.