Structure and evolution of super-Earth to super-Jupiter exoplanets

I. Heavy element enrichment in the interior

¹ École normale supérieure de Lyon, CRAL (CNRS), 46 allée d'Italie, 69007 Lyon; Université de Lyon, France e-mail: [ibaraffe;chabrier]@ens-lyon.fr
² Lowell observatory, 1400 West Mars Hill Road, Flagstaff, AZ 86001, USA e-mail: barman@lowell.edu

Received: 22 December 2007
Accepted: 11 February 2008

Abstract

Aims. We examine the uncertainties in current planetary models and quantify their impact on the planet cooling histories and mass-radius relationships.

Methods. 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.

Results. 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 substantially affects the evolution and thus the radius at a given age. For planets with large core mass fractions (50%), such as the Neptune-mass transiting planet GJ 436b, the contribution of the gravitational and thermal energy from the core to the planet cooling history is not negligible, yielding a ~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  of heavy material in the interior, at the edge of what is currently predicted by the core-accretion model for planet formation. As an alternative avenue for massive planet formation, we suggest that this planet, and similarly HD 17156b, may have formed from collisions between one or several other massive planets. This would explain these planets unusually high density and high eccentricity. We show that if planets as massive as ~25 M_J 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 high as ~100 . Such a result highlights the confusion provided by a definition of a planet based on the deuterium-burning limit.

Conclusions. We provide extensive grids of planetary evolution models from 10 to 10 M_Jup, with various fractions of heavy elements. These models provide a reference for analyzing the transit discoveries expected from the CoRoT and Kepler missions and for inferring the internal composition of these objects.