How Internal Structure Shapes the Metallicity of Giant Exoplanets

TL;DR

This work quantifies how interior-structure assumptions influence the inferred bulk metallicity and its mass dependence for 44 giant exoplanets, using CEPAM evolutionary models under Core+Envelope, Dilute Core, and Fully Mixed configurations. A root-find retrieval inverts radius, mass, and age to recover metallicity distributions for each structure, including DC variants with composition gradients and atmosphere-enrichment cases. The results show a robust positive $M_Z$–$M$ relation and a negative $Z$–$M$ trend across structures, with FM generally yielding higher metallicities due to envelope-opacity effects, while DC remains close to CE; atmospheric metallicity and non-adiabatic gradients can boost inferred $Z$ by up to ~35%. The findings imply diverse formation histories for gas giants and highlight the importance of improved convective and atmospheric constraints, with upcoming PLATO and Ariel data expected to tighten interior inferences and formation pathways.

Abstract

The composition and internal structure of gas giant exoplanets encode key information about their formation and subsequent evolution. We investigate how different interior structure assumptions affect the inferred bulk metallicity and its correlation with planetary mass. For a sample of 44 giant exoplanets (0.12-5.98 MJ), we compute evolutionary models with CEPAM and retrieve their bulk metallicities under three structural hypotheses: Core+Envelope (CE), Dilute Core (DC), and Fully Mixed (FM). Across all structures, we recover a significant positive correlation between total heavy-element mass (M_Z) and planetary mass (M), and a negative correlation between metallicity (Z) and M (also for Z/Z_star vs. M). DC structures yield metallicities comparable to CE models, regardless of the assumed gradient extent. Increasing atmospheric metallicity raises the inferred bulk metallicity, as enhanced opacities slow planetary cooling. Non-adiabatic DC models can further increase the retrieved metallicity by up to 35%. Sensitivity analyses show that the mass-metallicity anti-correlation is primarily driven by low-mass, metal-rich planets, while massive planets exhibit unexpectedly high metallicities. Improved constraints on convective mixing, combined with upcoming precise measurements of planetary masses, radii, and atmospheric compositions from missions such as PLATO and Ariel, will enable more robust inferences of interior structures and formation pathways for gas giant planets.

Figures (8)

• Figure 1: Three main internal structures tested in this study, with their respective heavy elements structure profiles: Core+Envelope (CE): all the heavy elements situated in a well defined core, Dilute Core, a gradient applied to the planet's core, and Fully Mixed: an homogeneous envelope throughout the planet.
• Figure 3: Retrieved curves for CE, FM, Core+Envelope + Stellar atmospheric composition (CEA), Dilute Core with 1 and 3 $Z_{\star}$ (DCA and DCA3), in vinaccia and orange colour respectively. Dashed lines (in wine colour and orange colour) show the atmospheric abundance assumed for DCA and DCA3 models respectively. Such lines will act as a lower threshold for these models as the assumed $R_{\text{atm}}$ will be kept fixed for each planet case.
• Figure 4: Relationship between the retrieved heavy element mass $M_{Z}$ and planetary mass $M$, shown for the four main structures tested (CE, FM, DCA, and DCA3). Shown as dashed lines in gray gradient are the different curves showing how the trend looks for fixed planetary compositions (0%, 50%, 90%, and 99% gas composition respectively). Bayesian fits have been shown using a power law function $M_{Z} = \beta \, M^{\alpha}$. Median values of $\beta$ are respectively 59.57 for FM, 56.02 for DCA3, 43.11 for DCA, and 35.9 for CE. Values for $\alpha$ are 0.653 for FM, 0.718 for DCA3, 0.700 for DCA, and 0.667 for CE. Posterior uncertainties $\sigma_{\alpha}$ and $\sigma_{\beta}$ are respectively 0.068 and 4.5 for FM, 0.074 and 4.3 for DCA3, 0.098 and 4.4 for DCA, and 0.113 and 4.5 for CE.
• Figure 5: Relationship between the retrieved heavy element mass $Z$ and planetary mass $M$, shown for the four main structures tested (CE, FM, DCA, and DCA3). Bayesian fits have been shown using a power law function $Z = \beta \, M^{\alpha}$. Median values of $\beta$ are respectively 0.187 for FM, 0.176 for DCA3, 0.136 for DCA, and 0.113 for CE. Values for $\alpha$ are -0.347 for FM, -0.282 for DCA3, -0.3 for DCA, and -0.333 for CE. Posterior uncertainty $\sigma_{\alpha}$ and $\sigma_{\beta}$ are respectively 0.069 and 0.014 for FM, 0.073 and 0.014 for DCA3, 0.097 and 0.015 for DCA, and 0.115 and 0.014 for CE.
• Figure 6: Top: Four panels using the retrieved method explained in Section \ref{['sec:rootfind']}. Retrieved metallicity curves for a DCA model with the assumption of adiabaticity are compared with superadiabatic cases where the $R_\rho$ scaling factor is either 0.1 or 0.4. This is shown for four different planetary cases. Bottom: Corresponding temperature profiles for the same four planets, using the median metallicity of the DCA model at a fixed age of 4 Gyr. The different heat transport scenarios show a linear increase of heat retention (and thus deviation from adiabaticity) according to the $R_\rho$ value defined in Eq. \ref{['eq.3']}. The $x$-axis shows the bulk metallicity $Z$.