The rock-star relationship: assessing the probability that a rocky planet’s composition reflects its host star

Abstract:

The bulk density of a planet is a result of its structure and composition. Relative proportions of iron core, rocky mantle, and gaseous envelopes, however, are degenerate for a given density. This degeneracy is reduced for rocky planets without significant gaseous envelopes when the structure is assumed to be a differentiated iron core and rocky mantle, in which the core mass fraction (CMF) is a first-order description of a planet's bulk composition. A rocky planet's CMF may be derived both from bulk density and by assuming the planet reflects the host star's major refractory element abundances (Fe, Mg, and Si). When the density- and stellar- CMF values differ, this sheds light on the outcome diversity of planet formation from processes like mantle stripping, out-gassing, and/or late-stage volatile delivery. We present a statistically rigorous analysis of the consistency of these two CMF measures accounting for observational uncertainties of planet mass and radius and host star chemical abundances. Applied to a sample of 11 probable rocky exoplanets, Kepler-107c has a CMF as inferred from bulk density that is significantly greater than the inferred CMF from its host star (2σ) and is, therefore, an iron-enriched super-Mercury. K2-229b, previously described as a super-Mercury, however, does not meet the threshold for a super-Mercury at a 1- or 2- σ level. We further explore the use of planet surface gravity as a more rigorous constraint of the CMF in rocky planets.