Modeling Exoplanet Interiors From Host Star Elemental Abundances

Spectroscopy is used to determine elemental abundances of a star. These abundances represent the bulk composition of the system, and are the constituents from which all bodies within a system, including any terrestrial planets, are formed. Using these abundances, interior structures of terrestrial (exo)planets can be modeled, and more accurate estimations of their radii can be found than by using mass alone. The abundances are used to estimate mantle mineralogy based on the ratios of the most abundant heavy elements: Si, Mg, and Fe. The amount of volatiles incorporated is calculated according to these ratios, yielding estimated mineral percentages, and a core mass for the planet. To model a planet the mass must be input, along with the estimated mineralogy and a speculated starting radius. Physical changes are then calculated from the surface to the center of the planet at depth increments of 1 km. Known pressure related phase changes in the minerals are used to distinguish upper and lower mantle boundaries, with physical characteristics adjusted at these transitions to match the new mineralogy, and the amount of available Fe used to estimate the core mass. Physical properties, such as densities and bulk moduli, are determined based on the selected minerals, and changes to these attributes along with pressure, gravity, and thermal expansion are calculated with increasing depth. After compressional modeling has been completed and thermal corrections applied, behavior at the center is assessed, and the radius of the planet is adjusted. Subsequent iterations are ran until an equilibrium is found when gravity at the center approaches zero. The result of this method is a best fit radius for a planet, as well as the depth of the upper and lower mantle, which is unique to that specific star system and planet mass. Results of compressional and thermal modeling showed the core mass of a terrestrial planet has a large influence on planet radii. Experiments modeled planets with a mass equal to one Earth mass (1ME) using abundance data from 15 F and G class stars. Although the overall mass was constant, the resulting radii varied by over 200 km due to differing elemental ratios. Additionally, a relationship between the Si/Fe ratios and planet radii was found which can be used to estimate a planet radius ± 25 km for a planet equal to 1ME.