Valencia et al. (2006) have calculated the internal structure of exoplanets of terrestrial type (i.e., rocky) with radii appropriate for a range of one and ten Earth masses, taking as their point of departure the Earth's internal structure. The density, gravity, mass, and pressure are expressed as a function of the distance from the centre of the planet. By analogy with the Earth, various regions are specified (upper mantle, transition zone, lower mantle, outer core, and inner core). The mineral phases considered are olivine for the mantle and iron (with 8 per cent silicon) for the core. Still by analogy with the Earth, the model takes account of convection in the upper mantle, lower mantle, and the core, and conduction at the surface and across the boundary zones.
First of all, a simple model without any phase transition (i.e., with just a mantle and a core) enables us to establish an initial temperature profile. This profiles enables an initial determination of the location of the various phase transitions that are present in the Earth's interior. Subsequently, the thickness of each transition zone, the temperature profile and the locations of the phase transitions are adjusted by successive iterations. Figure 7.7 shows the density and temperature obtained for ex-oplanets of 1-10 Earth masses ('Super-Earths'), assuming terrestrial composition. Different compositions are also considered. In the case of the Super-Earths, the authors obtain the following power law (Valencia et al., 2006):
Similar modelling has been carried out by Valencia et al. (2006) for exoplanets less massive than the Earth ('Super-Mercurys', Fig. 7.8). Their composition is assumed similar to that of the Earth, but the mass fraction in the core is higher (60 per cent, corresponding to the internal structure of Mercury). In this case, the scale law becomes:
In parallel with these studies, Sotin et al. (2007) carried out modelling of exoplanets of the terrestrial type, basing this on the terrestrial planets and outer-planet satellites in the Solar System. The parameters entered into the models were the composition of the star, the magnesium content of the mantle, the mass fraction of water, and the overall mass of the planet.
The models by Sotin et al. (2007) are based on 5 layers: at the centre, a core rich in iron, assumed to be fluid and consisting of an Fe-FeS mixture with 80 per cent pure iron; a silicate lower mantle, consisting of mixed silicates at high pressure, rich in iron and magnesium; an upper mantle consisting of olivine and enstatite; a layer of water ice at high pressure; and a hydrosphere, where water might be in for form of a liquid or ice.
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