Rocky super-Earth interiors

Structure and internal dynamics of CoRoT-7b and Kepler-10b

¹ Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin-Adlershof, Germany
² Institute for Planetology, Westphalian Wilhelms-University (WWU), Wilhelm-Klemm-Strasse 10, 48149 Münster, Germany
³ Department of Geodesy, Technical University of Berlin (TUB), Strasse des 17. Juni 135, 10623 Berlin, Germany
⁴ Center of Astronomy and Astrophysics, Technical University of Berlin (TUB), Hardenbergstrasse 36, 10623 Berlin, Germany

Received: 11 November 2011
Accepted: 28 February 2012

Abstract

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 R_p = (1.58 ± 0.10) R_⊕, a revised total mass of M_p = (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 ρ_avg = (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.