MASS-RADIUS RELATIONSHIPS FOR EXOPLANETS

For planets other than Earth, particularly exoplanets, interpretation of the composition and structure depends largely on comparing the mass and radius with the composition expected given their distance from the parent star. The composition implies a mass-radius relation which relies heavily on equations of state calculated from electronic structure theory and measured experimentally on Earth. We lay out a method for deriving and testing equations of state, and deduce mass-radius and mass-pressure relations for key, relevant materials whose equation of state (EOS) is reasonably well established, and for differentiated Fe/rock. We find that variations in the EOS, such as may arise when extrapolating from low-pressure data, can have significant effects on predicted mass-radius relations and on planetary pressure profiles. The relations are compared with the observed masses and radii of planets and exoplanets, broadly supporting recent inferences about exoplanet structures. Kepler-10b is apparently Earth-like, likely with a proportionately larger core than Earth's, nominally 2/3 of the mass of the planet. CoRoT-7b is consistent with a rocky mantle over an Fe-based core which is likely to be proportionately smaller than Earth's. GJ 1214b lies between the mass-radius curves for H2O and CH4, suggesting an icy composition with a relatively large core or a relatively large proportion of H2O. CoRoT-2b is less dense than the hydrogen relation, which could be explained by an anomalously high degree of heating or by higher than assumed atmospheric opacity. HAT-P-2b is slightly denser than the mass-radius relation for hydrogen, suggesting the presence of a significant amount of matter of higher atomic number. CoRoT-3b lies close to the hydrogen relation. The pressure at the center of Kepler-10b is 1.5(-1.0)(+1.2) TPa. The central pressure in CoRoT-7b is probably close to 0.8 TPa, though may be up to 2 TPa. These pressures are accessible by planar shock and ramp-loading experiments at large laser facilities. The center of HAT-P-2b is probably around 210 TPa, in the range of planned National Ignition Facility experiments, and that of CoRoT-3b around 1900 TPa.