Mass-Radius Relationships for Exoplanets

Abstract

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 is reasonably well established, and for differentiated Fe/rock.We find that variations in the equation of state, such as may arise when extrapolating from low pressure data, can have significant effects on predicted massradius 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 'Earthlike,' 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 H 2 O and CH 4 , suggesting an 'icy' composition with a relatively large core or a relatively large proportion of H 2 O. 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 +1.2 −1.0 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 pla--3nar 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.

Examining Tatooine: Atmospheric Models of Neptune-Like Circumbinary Planets

“…Assuming the planet is approximately Neptunelike in mass, it is not massive enough to significantly perturb the stellar orbits away from Keplerian motion over the timescales we consider. Our assumption of planet mass is based on the measured radii of known circumbinary planets, and mass-radius models and observations which do not predict a planet of this size to be dense enough to be terrestrial (Swift et al 2012;Rogers 2015;Wu & Lithwick 2013).…”

Tidal Venuses: Triggering a Climate Catastrophe via Tidal Heating

“…Their formulation is complicated, and rather than reproduce it here, the reader is referred to their paper. We do not include the recent models put forth by Swift et al (2012), as they did not include formulae, but they did find that their results are consistent with those of Fortney et al (2007) and Valencia et al (2010) for rock and iron planets.…”

Interior Structure, Composition, and Mineralogy of the Terrestrial Planets

“…For rocky exoplanets, the numerical models have to be consistent with the observed planetary masses and radii. Calculated models have been used to derive mass-radius relationships for exoplanets assuming a range of different mineralogical compositions to gain insight into the interior structure and possible bulk compositions of these planets (Fortney et al, 2007;Grasset et al, 2008;Seager et al, 2007;Sotin et al, 2007;Swift et al, 2012;Valencia et al, 2006Valencia et al, , 2007Wagner et al, 2011;Zeng and Sasselov, 2013). Principal uncertainties mainly arise from the extrapolation of an equation of state to high pressures owing to the lack of reliable experimental data in the warm dense matter regime in the pressure range of 200 GPa-10 TPa, whereas the surface temperature and internal thermal state of a massive rocky exoplanet are less important for its radial density distribution (Seager et al, 2007).…”