Mass-radius curve for extrasolar Earth-like planets and ocean planets

By comparison with the Earth-like planets and the large icy satellites of the Solar System, one can model the internal structure of extrasolar planets. The input parameters are the composition of the star (Fe/Si and Mg/Si), the Mg content of the mantle (Mg# = Mg/[Mg + Fe]), the amount of H₂O and the total mass of the planet. Equation of State (EoS) of the different materials that are likely to be present within such planets have been obtained thanks to recent progress in high-pressure experiments. They are used to compute the planetary radius as a function of the total mass. Based on accretion models and data on planetary differentiation, the internal structure is likely to consist of an iron-rich core, a silicate mantle and an outer silicate crust resulting from magma formation in the mantle. The amount of H₂O and the surface temperature control the possibility for these planets to harbor an ocean. In preparation to the interpretation of the forthcoming data from the CNES led CoRoT (Convection Rotation and Transit) mission and from ground-based observations, this paper investigates the relationship between radius and mass. If H₂O is not an important component (less than 0.1%) of the total mass of the planet, then a relation (R/REarth)=ab(M/MEarth) is calculated with (a,b)=(1,0.306) and (a,b)=(1,0.274) for ¹⁰⁻²MEarth<M<MEarth and MEarth<M<10MEarth, respectively. Calculations for a planet that contains 50% H₂O suggest that the radius would be more than 25% larger than that based on the Earth-like model, with (a,b)=(1.258,0.302) for ¹⁰⁻²MEarth<M<MEarth and (a,b)=(1.262,0.275) for MEarth<M<10MEarth, respectively. For a surface temperature of 300 K, the thickness of the ocean varies from 150 to 50 km for planets 1 to 10 times the Earth's mass, respectively. Application of this algorithm to bodies of the Solar System provides not only a good fit to most terrestrial planets and large icy satellites, but also insights for discussing future observations of exoplanets.