A study of the accuracy of mass-radius relationships for silicate-rich and ice-rich planets up to 100 earth masses

Abstract

A mass-radius (M-R) relationship is proposed for solid planets and solid cores ranging from 1 to 100 Earth-mass planets. It relies on the assumption that solid spheres are composed of iron and silicates, around which a variable amount of water is added. The M-R law has been set up assuming that the planetary composition is similar to the averaged composition for silicates and iron obtained from the major elements ratio of 94 stars hosting exoplanets. Except on Earth for which a tremendous amount of data is available, the composition of silicate mantles and metallic cores cannot be constrained. Similarly, thermal profiles are poorly known. In this work, the effect of compositional parameters and thermal profiles on radii estimates is quantified. It will be demonstrated that uncertainties related to composition and temperature are secondary compared to the effect of the amount of water. The super-Earth family includes four classes of planets: iron-rich, silicate-rich, water-rich, or with a thick atmosphere. For a given mass, the planetary radius increases significantly from the iron-rich to the atmospheric-rich planet. Even if some overlaps are likely, M-R measurements could be accurate enough to ascertain the discovery of an Earth-like planet. The present work describes how the amount of water can be assessed from M-R measurements. Such an estimate depends on several assumptions including (1) the accuracy of the internal structure model and (2) the accuracy of mass and radius measurements. It is shown that if the mass and the radius are perfectly known, the standard deviation of the amount of water is about 4.5%. This value increases rapidly with the radius uncertainty but does not strongly depend on the mass uncertainty. © 2009. The American Astronomical Society. All rights reserved.