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Table 1

Dependence of the planetary properties as a function of stellar [Fe/H] derived from the synthetic NG76Longshot population.

Synthetic results Comparison with observations
Sect. 4: occurrence rate vs. [Fe/H]
Giant planets (Fig. 2) Positively correlated as F ∝ 10~1.3×[Fe/H] Quantitatively consistent
Neptune-sized (Fig. 3) Positively correlated as F ∝ 10~0.5–1×[Fe/H] Quantitatively consistent
Small planets (1–3.5 R) (Fig. 4) First increase before [Fe/H] ≲ 0.1 dex and then decrease Qualitatively consistent
Sub-Earths (Fig. 6) Anti-correlated as F ∝ 10−1.9×[Fe/H] Awaiting further observational results
Sect. 5: radius valley morphology vs. [Fe/H] (Figs. 8, 9, 10)
CValley (Eq. (6)) Positively correlated (Eq. (11))
CValley (Eq. (7)) Positively correlated (Eq. (11))
RValley+$\[R_{\text {Valley}}^{+}\]$ (Eq. (8)) Positively correlated (Eq. (13)) All quantitatively consistent
RValley$\[R_{\text {Valley}}^{-}\]$ (Eq. (9)) Not correlated (Eq. (14))
fNP (Eq. (10)) Positively correlated (Eq. (15))
Sect. 6: orbital periods vs. [Fe/H]
All planets Higher [Fe/H] at short period (Δ[Fe/H] = 0.05 ± 0.01, Fig. 12)
Large planets No significant [Fe/H] variation (Δ[Fe/H] = −0.05 ± 0.04, Fig. 13) All qualitatively consistent but quantitatively weaker
Sub-Neptunes Higher [Fe/H] at short period (Δ[Fe/H] = 0.02 ± 0.01)
Terrestrial planets Significantly higher [Fe/H] at short period (Δ[Fe/H] = 0.07 ± 0.01)
Sect. 7: orbital eccentricity vs. [Fe/H]
Giant planets Positively correlated (Figs. 17, 18) Qualitatively consistent but less significant
Small planets with OGPs Positively correlated (Fig. 22, Eq. (23)) Quantitatively consistent
Small planets w/o OGPs Not correlated Inconsistent (Potential reasons in Sect. 7.2)

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