The Mass-Metallicity Relation for Giant Planets

Exoplanet discoveries of recent years have provided a great deal of new data for studying the bulk compositions of giant planets. Here we identify 47 transiting giant planets (20 M _⊕ < M < 20 M _J) whose stellar insolations are low enough (F _* < 2 × 10⁸ erg s^-1 cm^-2, or roughly T _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 47 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 previously been reported from studies with smaller sample sizes. We confirm a strong relationship between the planetary metal-enrichment relative to the parent star Z _planet/Z _star and the planetary mass, but see no relation in Z _planet/Z _star with planet orbital properties or stellar mass. The large heavy element masses of many planets (>50 M _⊕) suggest significant amounts of heavy elements in H/He envelopes, rather than cores, such that metal-enriched giant planet atmospheres should be the rule. We also discuss a model of core-accretion planet formation in a one-dimensional disk and show that it agrees well with our derived relation between mass and Z _planet/Z _star.