Rocky super-Earth interiors

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 . This may have a significant effect on the thermal evolution and magnetic field generation of close-in super-Earths.

In Situ and Ex Situ Formation Models of Kepler 11 Planets

“…That parametrization is applied in the calculations to the entire silicate mantle. For the Earth test discussed here, the dynamical viscosity (νρ) of the mantle ranges from ∼ 10 20 to ∼ 10 23 Pa s, in accord with the inferred values in the Earth's mantle (Stamenković et al 2011;Wagner et al 2012). The complex rheology of ice, especially of the low-pressure phases, (e.g., Barr & Showman 2009, and references therein), is not meant to be fully accounted for in these calculations.…”

“…For the largest planets Kepler 11c, d, e, and g, the pressure at the base of the H 2 O shell is 160 GPa, so that ppv is the only phase present in their silicate mantles. Post-post-perovskite phases are predicted for P 900 GPa (Wagner et al 2012), a value reached only at the bottom of the mantle of Kepler 11e (although the stability field of post-ppv phases is also determined by temperature, Stamenković et al 2011). The H 2 O shell is mostly in fluid/superionic phase, except for the presence of ice VII layers in the outer parts of Kepler 11c, d and f.…”

“…Here, the transition among these species is regulated by the phase diagrams of Fei et al (2004) and Tateno et al (2009). Post-postperovskite phases (e.g., see the discussion in Stamenković et al 2011;Wagner et al 2012) are neglected. The H 2 O shell is composed of several types of ice (Ih, III, V, VI, VII, and X) and water, according to the phase curves of Loubeyre et al (1999), Lin et al (2004), Lin et al (2005), and Choukroun & Grasset (2007).…”

Mass-Radius Relationships of Rocky Exoplanets

“…Whereas the low density of GJ 1214b, that has no analogue in the solar system, is attributed to the presence of an extended optically thick hydrogen atmosphere (Rogers & Seager 2011), it has been suggested that carbon-rich solids may predominate the bulk composition of 55 Cancri e (Madhusudhan et al 2012). CoRoT-7b and Kepler-10b, on the other hand, are thought to be composed of silicate rock and iron with the latter concentrated in massive metallic cores (Wagner et al 2012, Swift et al 2012. These compositional trends are roughly followed by the calculated equilibrium surface temperatures, with relatively hot planetary environments along and below the silicate line and colder but still hot environments along and above the water ice line.…”

“…where β is the scaling exponent, we first solve the structural equations for mass and momentum assuming hydrostatic equilibrium (e.g., Wagner et al 2012)…”