[Paper Review] Structure and evolution of super-Earth to super-Jupiter exoplanets: I. heavy element enrichment in the interior

I. Baraffe, G. Chabrier+1 more|arXiv (Cornell University)|Feb 13, 2008

Stellar, planetary, and galactic studiesPhysics and Astronomy52 references192 citations

TL;DR

This paper investigates the impact of heavy element enrichment on the structure and evolution of super-Earth to super-Jupiter exoplanets, using detailed planetary models that incorporate varying equations of state, core distributions, and thermal contributions. It finds that core mass fractions above ~50% significantly affect planetary cooling and radius, with up to ~10% radius variation after 1 Gyr, and shows that massive planets like Hat-P-2b require at least 200 M⊕ of heavy elements—suggesting formation via giant impacts rather than standard core accretion.

ABSTRACT

We examine the uncertainties in current planetary models and we quantify their impact on the planet cooling histories and mass-radius relationships. These uncertainties include (i) the differences between the various equations of state used to characterize the heavy material thermodynamical properties, (ii) the distribution of heavy elements within planetary interiors, (iii) their chemical composition and (iv) their thermal contribution to the planet evolution. Our models, which include a gaseous H/He envelope, are compared with models of solid, gasless Earth-like planets in order to examine the impact of a gaseous envelope on the cooling and the resulting radius. We find that for a fraction of heavy material larger than 20% of the planet mass, the distribution of the heavy elements in the planet's interior affects substantially the evolution and thus the radius at a given age. For planets with large core mass fractions ($\simgr$ 50%), such as the Neptune-mass transiting planet GJ436b, the contribution of the gravitational and thermal energy from the core to the planet cooling history is not negligible, yielding a $\sim$ 10% effect on the radius after 1 Gyr. We show that the present mass and radius determinations of the massive planet Hat-P-2b require at least 200 $\mearth$ of heavy material in the interior, at the edge of what is currently predicted by the core-accretion model for planet formation. We show that if planets as massive as $\sim$ 25 $\mjup$ can form, as predicted by improved core-accretion models, deuterium is able to burn in the H/He layers above the core, even for core masses as large as $\sim$ 100 $\mearth$. We provide extensive grids of planetary evolution models from 10 $\mearth$ to 10 M$_{ m Jup}$, with various fractions of heavy elements.

Motivation & Objective

• To quantify uncertainties in planetary models related to heavy element enrichment and their impact on exoplanet cooling and mass-radius relationships.
• To assess how variations in equations of state, chemical composition, distribution, and thermal energy of heavy elements affect planetary evolution.
• To compare models with gaseous envelopes to gasless, Earth-like planets to isolate the influence of H/He atmospheres on radius and cooling.
• To evaluate the implications of high metallicity for planet formation mechanisms, especially for massive, dense planets like Hat-P-2b and HD 149026b.
• To provide a comprehensive grid of models (10 M⊕ to 10 MJ) for interpreting future CoRoT and Kepler transit data and inferring internal compositions.

Proposed method

• Constructs planetary evolution models spanning 10 M⊕ to 10 MJ, incorporating H/He envelopes and varying fractions of heavy elements.
• Uses multiple equations of state (EOS) for heavy materials (e.g., silicates, ices) to assess thermodynamic uncertainties in the interior.
• Varying the distribution of heavy elements (central core vs. uniform or mixed) to evaluate structural and thermal impacts.
• Incorporates gravitational and thermal energy release from heavy elements into cooling models to assess their contribution to planetary radius evolution.
• Compares models with and without gaseous envelopes to isolate the effect of H/He atmospheres on radius and cooling timescales.
• Applies models to observed exoplanets (e.g., GJ436b, Hat-P-2b, HD 149026b) to infer required internal compositions and formation pathways.

Experimental results

Research questions

• RQ1 How do uncertainties in equations of state for heavy elements affect the predicted mass-radius relationships of super-Earths to gas giants?
• RQ2 To what extent does the distribution of heavy elements (core vs. mixed) influence planetary cooling and radius evolution over time?
• RQ3 What is the thermal and gravitational contribution of heavy elements to the cooling history of planets with high core mass fractions (>50%)?
• RQ4 Can the high density and eccentricity of massive planets like Hat-P-2b and HD 17156b be explained by core-accretion alone, or do alternative formation mechanisms like giant impacts better explain their properties?
• RQ5 Under what conditions can deuterium burning occur in H/He envelopes of massive planets, and what does this imply for the planet/brown dwarf distinction?

Key findings

• For planets with core mass fractions >~50%, such as GJ436b, the gravitational and thermal energy from the core contributes up to ~10% to the radius evolution after 1 Gyr.
• The present mass and radius of Hat-P-2b require at least 200 M⊕ of heavy elements in its interior, exceeding current core-accretion model predictions.
• Giant impacts between massive planets or planetesimals may explain the high density and high eccentricity of planets like Hat-P-2b and HD 17156b.
• If planets of ~25 MJ can form via improved core-accretion models, deuterium burning can occur in H/He envelopes even for cores as massive as ~100 M⊕.
• The deuterium-burning limit is not a valid criterion to distinguish planets from brown dwarfs, as massive planets can ignite deuterium fusion.
• The study provides a complete grid of planetary evolution models from 10 M⊕ to 10 MJ with varying heavy element fractions, available for public use to interpret CoRoT and Kepler transit data.