The influence of composition gradients on giant planet radii

Abstract

The radius of a giant planet is a key physical property. It encapsulates the outcome of its mass, composition, and thermal state, serving as a critical link between observations and the theory of planetary interiors. While traditional interior models assume distinct core-envelope structures, recent gravity measurements of Jupiter and Saturn reveal complex interiors with deep composition gradients. Here, we combine an analytic framework with numerical evolution simulations to elucidate how internal structures with composition gradients affect the planetary radius. We demonstrate that the spatial redistribution of heavy elements does not inherently alter the planetary size; rather, it is the resulting difference in total entropy over time that drives observable radius variations. We show that this mechanism naturally establishes two distinct evolutionary regimes. During the first few gigayears of evolution, composition gradients trap thermal energy deep within the interior, significantly affecting the planetary evolution and internal structure. However, as the planet cools and contracts, this ``thermal memory'' fades and the total entropy no longer depends on the primordial conditions. Consequently, the planetary radius decouples from the internal distribution of heavy elements, becoming solely a function of the total mass and bulk composition. Our results present the physical origin of the mass-radius-composition relation and suggest that the use of simplified interior models for giant exoplanets is legitimate only after the planet has surpassed this evolutionary threshold. Our analysis establishes a thermodynamic constraint on the planetary structure: while composition gradients can temporarily modulate cooling, they cannot permanently sustain radius inflation, as the addition of heavy elements, regardless of their distribution, inevitably leads to planetary contraction.