Interior phase transformations and mass-radius relationships of silicon-carbon planets

Planets such as 55 Cancri e orbiting stars with a high carbon-to-oxygen ratio are considered to consist primarily of silicon and carbon, with successive layers of carbon, silicon carbide and iron. The behaviour of silicon-carbon materials at planetary interior pressures at the extreme pressures prevalent in planetary interiors, however, has not yet been sufficiently understood. In this work we use simulations based on density functional theory to determine high-pressure phase transitions in the silicon-carbon system, including the prediction of new stable compounds with Si2C and SiC2 stoichiometry at high pressures. We compute equations of state for these silicon-carbon compounds as a function of pressure, and hence derive interior structural models and mass-radius relationships for planets composed of silicon and carbon. Notably, we predict a substantially smaller radius for SiC planets than in previous models. We also compute a new equation of state for iron. We rederive interior models for 55 Cancri e and are able to place more stringent restrictions on its composition.