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Fig. 4.

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Mass–metallicity relation with both interior structures, using the CMS19+HG23 EOS. Top panel: errorbars show the inferred range of bulk metallicity with the core+envelope (blue) or fully mixed (orange) structure, as in Fig. 3. Orange and blue lines show the best fit for both cases, while the shaded areas show the 1σ error contour. The metallicities of Jupiter and Saturn (Helled & Howard 2024) are shown in black. The solid and dashed grey lines show the best fits from Müller & Helled (2023) and Thorngren et al. (2016), respectively. The star metallicities were derived using the solar value from Asplund et al. (2021). Middle panel: absolute difference in metallicity due to either the H–He EOS (grey dots, taken from Fig. 3) or the interior structure (squares). Blue (orange) squares indicate planets where the core+envelope case gives lower (higher) metallicity than the fully mixed case. Bottom panel: absolute difference in metallicity. Pink dots show the sum of the H–He EOS and the interior structure effects. Black triangles show the range of metallicity inferred from observational uncertainties (radius and age).

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