Scaling K2. VI. Reduced Small Planet Occurrence in High Galactic Amplitude Stars

In this study, we performed a homogeneous analysis of the planets around FGK dwarf stars observed by the Kepler and K2 missions, providing spectroscopic parameters for 310 K2 targets -- including 239 Scaling K2 hosts -- observed with Keck/HIRES. For orbital periods less than 40 days, we found that the distribution of planets as a function of orbital period, stellar effective temperature, and metallicity was consistent between K2 and Kepler, reflecting consistent planet formation efficiency across numerous ~1 kpc sight-lines in the local Milky Way. Additionally, we detected a 3X excess of sub-Saturns relative to warm Jupiters beyond 10 days, suggesting a closer association between sub-Saturn and sub-Neptune formation than between sub-Saturn and Jovian formation. Performing a joint analysis of Kepler and K2 demographics, we observed diminishing super-Earth, sub-Neptune, and sub-Saturn populations at higher stellar effective temperatures, implying an inverse relationship between formation and disk mass. In contrast, no apparent host-star spectral-type dependence was identified for our population of Jupiters, which indicates gas-giant formation saturates within the FGK mass regimes. We present support for stellar metallicity trends reported by previous Kepler analyses. Using GAIA DR3 proper motion and RV measurements, we discovered a galactic location trend: stars that make large vertical excursions from the plane of the Milky Way host fewer super-Earths and sub-Neptunes. While oscillation amplitude is associated with metallicity, metallicity alone cannot explain the observed trend, demonstrating that galactic influences are imprinted on the planet population. Overall, our results provide new insights into the distribution of planets around FGK dwarf stars and the factors that influence their formation and evolution.