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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)) | |
(Eq. (8)) |
Positively correlated (Eq. (13)) | All quantitatively consistent |
(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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![$\[R_{\text {Valley}}^{+}\]$](/articles/aa/full_html/2025/09/aa55380-25/aa55380-25-eq79.png)
![$\[R_{\text {Valley}}^{-}\]$](/articles/aa/full_html/2025/09/aa55380-25/aa55380-25-eq80.png)