On the Probability that a Rocky Planet's Composition Reflects its Host Star

The bulk density of a planet, as measured by mass and radius, is a result of planet structure and composition. Relative proportions of iron core, rocky mantle, and gaseous envelopes 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 rock-building elemental abundances (Fe, Mg, and Si). Contrasting CMF measures, therefore, shed light on the outcome diversity of planet formation from processes including 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. We find that these two measures are unlikely to be resolvable as statistically different unless the bulk density CMF is at least 40% greater than or 50% less than the CMF as inferred from the host star. Applied to 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 (2$\sigma$) and is therefore likely 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- $\sigma$ level.