Revisiting the Relationship Between Rocky Exoplanet and Stellar Compositions: Reduced Evidence for a Super-Mercury Population

Planets and the stars they orbit are born from the same cloud of gas and dust, and the primordial compositions of rocky exoplanets have been assumed to have iron and refractory abundance ratios consistent with their host star. To test this assumption, we modeled the interior iron-to-rock ratio of 20 super-Earth sized (1-1.8R$_{\oplus}$) exoplanets around stars with homogeneously measured stellar parameters. We computed the core mass fraction for each planet and an equivalent ``core mass fraction'' for each host star based on its Fe and Mg abundances. We then fit a linear correlation using two methods (Ordinary Least Squares and Orthogonal Distance Regression) between planetary and stellar core mass fraction, obtaining substantially different slopes between these two methods (m=1.3 $\pm$ 1.0 and m=5.6 $\pm$ 1.6, respectively). Additionally, we find that 75$\%$ of planets have a core mass fraction consistent with their host star to within 1$\sigma$, and do not identify a distinct population of high-density super-Mercuries. Overall, we conclude that current uncertainties in observational data and differences in modeling methods prevent definitive conclusions about the relationship between between planet and host star chemical compositions.