  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.
