The Star-Planet Connection I: Using Stellar Composition to Observationally Constrain Planetary Mineralogy for the Ten Closest Stars

Abstract: The compositions of stars and planets are connected, yet, the definition of "habitability" and the "habitable zone" only take into account the physical relationship between the star and planet. Planets, however, are made truly habitable by both chemical and physical processes which regulate climatic and geochemical cycling between atmosphere, surface, and interior reservoirs. Despite this, "Earth-like" is often defined as a planet made of a mixture of rock and Fe that is roughly 1 Earth-density. To understand the interior of a terrestrial planet, the stellar abundances of planet-building elements (e.g. Mg, Si, and Fe) can be utilized as a proxy for the planet's composition. We explore the planetary mineralogy and structure for fictive planets around the 10 closest stars to the Sun using stellar abundances from the Hypatia Catalog. Despite our sample containing stars both sub- and super-solar in their abundances, we find that the mineralogies are very similar for all 10 planets -- since the error or spread in the stellar abundances create significant degeneracy in the models. We show that abundance uncertainties need to be on the order of [Fe/H] < 0.02 dex, [Si/H] < 0.01 dex, [Al/H] < 0.002 dex, while [Mg/H] and [Ca/H] < 0.001 dex, in order to distinguish two unique planetary populations in our sample of 10 stars. While these precisions are high, we believe they are possible given certain abundance techniques, in addition to methodological transparency, recently demonstrated in the literature. However, without these precisions, the uncertainty in planetary structures will be so high that we will be unable to say confidently that a planet is like the Earth, or unlike anything we've ever seen.