No Evidence for a Metallicity-dependent Enhancement of Distant Giant Companions to Close-in Small Planets in the California Legacy Survey

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Understanding the relationship between close-in small (CS) planets and distant giants (DGs) is central to understanding the formation of planetary systems like our own. Most studies of this connection have found evidence for a positive correlation, though significant statistical and systematic uncertainties remain due to differences in sample size, target selection bias, and even the definitions of CS and DG planets. Recently, M. L. Bryan & E. J. Lee conducted a study of 184 stars hosting super-Earths ( Msini=1−20M⊕ or R = 1 − 4 R ⊕) to determine the effect of stellar metallicity on the prevalence of DG companions ( Msini=0.5−20MJ , a = 1−10 au). They found that such giants are twice as common in the presence of inner planets, but only in metal-rich systems: P(DG∣CS, [Fe/H] > 0) = 28.0−4.6+4.9% versus P(DG∣[Fe/H] > 0) = 14.3−1.8+2.0% . Further, they found that this correlation disappears for metal-poor stars: P(DG∣CS, [Fe/H] ≤ 0) = 4.5−1.9+2.6% versus P(DG∣[Fe/H] ≤ 0) = 5.0−1.3+1.6% . We conducted an analogous study to test whether this effect was present in the California Legacy Survey sample. Using the same planet definitions, we did not find evidence for an enhancement in metal-rich systems: P(DG∣CS, [Fe/H] > 0) = 14−8+11% versus P(DG∣[Fe/H] > 0) = 17.9−2.4+2.5% . We also found a 2σ tension between our conditional rate and a 2x enhancement. We brought our results into closer agreement with M. L. Bryan & E. J. Lee by repeating our analysis with different planet definitions. For example, considering only CS planets with 1≤Msini≤10M⊕ and DG planets with 0.5≤Msini≤20MJ gives P(DG∣CS, [Fe/H] > 0) = 48−17+17% and P(DG∣[Fe/H] > 0) = 21.8−2.7+2.9% , consistent with a 2x enhancement. However, we find that this 2x enhancement is also present when we apply the same planet definitions to the overall sample, challenging the idea that metallicity is responsible. Our sample, though only ∼1/6 the size of M. L. Bryan & E. J. Lee, was assembled and analyzed self-consistently. The discrepancy between our findings and theirs may arise from a variety of sources, underscoring the need for large exoplanet surveys to overcome both small number statistics and sample inhomogeneities.