The California Legacy Survey III. On The Shoulders of (Some) Giants: The Relationship between Inner Small Planets and Outer Massive Planets

We use a high-precision radial velocity survey of FGKM stars to study the conditional occurrence of two classes of planets: close-in small planets (0.023--1 au, 2--30 Earth masses) and distant giant planets (0.23--10 au, 30--6000 Earth masses). We find that $41^{+15}_{-13}\%$ of systems with a close-in, small planet also host an outer giant, compared to $17.6^{+2.4}_{-1.9}\%$ for stars irrespective of small planet presence. This implies that small planet hosts may be enhanced in outer giant occurrence compared to all stars with $1.7\sigma$ significance. Conversely, we estimate that $42^{+17}_{-13}\%$ of cold giant hosts also host an inner small planet, compared to $27.6^{+5.8}_{-4.8}\%$ of stars irrespective of cold giant presence. We also find that more massive and close-in giant planets are not associated with small inner planets. Specifically, our sample indicates that small planets are less likely to host outer giant companions more massive than approximately 120 Earth masses and within 0.3--3 au than to host less massive or more distant giant companions, with $\sim$2.2$\sigma$ confidence. This implies that massive gas giants within 0.3--3 au may suppress inner small planet formation. Additionally, we compare the host-star metallicity distributions for systems with only small planets and those with both small planets and cold giants. In agreement with previous studies, we find that stars in our survey that only host small planets have a metallicity distribution that is consistent with the broader solar-metallicity-median sample, while stars that host both small planets and gas giants are distinctly metal-rich with $\sim$2.3$\sigma$ confidence.