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      The Mass-Metallicity Relation for Giant Planets

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          Abstract

          Exoplanet discoveries of recent years have provided a great deal of new data for studying the bulk compositions of giant planets. Here we identify 38 transiting giant planets (\(20 M_\oplus < M < 20 M_{\mathrm{J}}\)) whose stellar insolation is low enough (\(F_* < 2\times10^8\; \text{erg}\; \text{s}^{-1}\; \text{cm}^{-2}\), or roughly \(T_\text{eff} < 1000\)) that they are not affected by the hot Jupiter radius inflation mechanism(s). We compute a set of new thermal and structural evolution models and use these models in comparison with properties of the 38 transiting planets (mass, radius, age) to determine their heavy element masses. A clear correlation emerges between the planetary heavy element mass \(M_z\) and the total planet mass, approximately of the form \(M_z \propto \sqrt{M}\). This finding is consistent with the core accretion model of planet formation. We also study how stellar metallicity [Fe/H] affects planetary metal-enrichment and find a weaker correlation than has been previously reported from studies with smaller sample sizes. Our results suggest that planets with large heavy element masses are more common around stars with a high iron abundance, but are not found there exclusively. We confirm a strong relationship between the planetary metal-enrichment relative to the parent star \(Z_{\rm planet}/Z_{\rm star}\) and the planetary mass, but see no relation in \(Z_{\rm planet}/Z_{\rm star}\) with planet orbital properties or stellar mass. Suggestively, circumbinary planets are more enriched in heavy elements than similar mass single-star planets, but with only four such planets the effect is not yet significant. The large heavy element masses of many planets (\(>50 M_\oplus\)) suggest significant amounts of heavy elements in H/He envelopes, rather than cores, such that metal-enriched giant planet atmospheres should be the rule.

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          Planetary astrophysics

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