The Mass-Metallicity Relation for Giant Planets

TL;DR

This study analyzes 47 transiting giant exoplanets with low stellar insolation to uncover a mass-metallicity relation, supporting core accretion models and revealing insights into planetary composition and formation processes.

Contribution

It establishes a clear mass-metallicity relation for giant planets and compares observed data with core accretion formation models, expanding understanding of planetary composition.

Findings

Heavy element mass scales with the square root of planetary mass.

Weak correlation between stellar metallicity and planetary metal enrichment.

Most giant planets contain significant heavy elements in their atmospheres.

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 47 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 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 been previously reported from studies with smaller sample sizes. 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. 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. 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 $Z_{\rm planet}/Z_{\rm star}$.