Super-Earths and sub-Neptunes are Insensitive to Stellar Metallicity

Kepler planets (including super-Earths and sub-Neptunes, from 1 to 4 Earth radii) are likely formed before the gaseous proto-planetary disks have dissipated, as are the Jovian planets. If the metal content in these disks resembles that in the host stars, one might expect Kepler planets to occur more frequently, and to be more massive, around metal-rich stars. Contrary to these expectations, we find that the radii of Kepler planets (a proxy for mass) are independent of host metallicity. Previous claims that larger planets prefer more metal-rich stars can be adequately explained by the combined facts that more massive stars tend to host bigger planets, and that more massive stars are also more metal rich in the Kepler sample. We interpret this independence as that the mass of a Kepler planet is not determined by the availability of solids, but is instead regulated by an as yet unknown process. Moreover, we find that the occurrence rates of Kepler planets rise only weakly with stellar metallicity, a trend that is further flattened when the influence of close stellar binaries is accounted for. We explain this weak dependence, in contrast to the strong dependence exhibited by Jovian planets, using a phenomenological model, wherein the masses of proto-planetary disks have a much larger spread than the spread in stellar metallicity, and wherein the formation of Jovian planets requires disks that contain some $5$ times more solid than that needed to form Kepler planets. This model predicts that stars more metal-poor than half-solar should rarely host any Kepler planets.