http://arxiv.org/abs/1805.10530
More than a third of all exoplanets can be classified as super-Earths based on radius (1-2 $R_{\bigoplus}$) and mass (< 10 $M_{\bigoplus}$). Here we model mass-radius relations based on silicate mantle and iron core equations of state to infer to first order the structure and composition range of rocky super-Earths assuming insignificant gas envelopes. We develop a new equation of state of hexagonal close packed (hcp) iron for super-Earth conditions (SEOS) based on density functional theory results for pressures up to 137~TPa. A comparison of SEOS and extrapolated equations of state for iron from the literature reveals differences in density of up to 4% at 1~TPa and up to 20% at 10~TPa. Such density differences change the derived mass by up to 10\% for Earth-like super-Earths (core radius fraction of 0.5) and 20% for Mercury-like super-Earths (core radius fraction of 0.8). We find that the effect of temperature on mass (< 5%) is smaller than that resulting from the extrapolation of the equations of state of iron and lower mantle temperatures are too low to allow for rock and iron miscibility for R<1.75 $R_{\bigoplus}$. We find that modeling uncertainties dominate over observational uncertainties for many observed super-Earths. We illustrate these uncertainties explicitly for Kepler-36b with well-constrained mass and radius. Assuming a core composition of 0.8$\rho$ Fe (equivalent to 50 mol% S) instead of pure Fe leads to an increase of the core radius fraction from 0.53 to 0.64. Using a mantle composition of Mg${0.5}$Fe${0.5}$SiO$_3$ instead of MgSiO$_3$ leads to a decrease of the core radius fraction to 0.33. Effects of thermal structure and the choice of equation of state for the core material on the core radius of Kepler-36b are small but non-negligible, reaching 2% and 5%, respectively.
K. Hakim, A. Rivolidini, T. Hoolst, et. al.
Tue, 29 May 18
16/73
Comments: 24 pages, 12 figures
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