Convective Mixing in Gas Giant Planets with Primordial Composition Gradients

Linking atmospheric measurements to the bulk planetary composition and ultimately the planetary origin is a key objective in planetary science. In this work, we identify the cases in which the atmospheric composition represents the bulk composition. We simulate the evolution of giant planets considering a wide range of planetary masses ($0.3-2~M_{\mathrm{J}}$), initial entropies ($8-11~k_{\mathrm{B}} m_\mathrm{u}^{-1}$), and primordial heavy-element profiles. We find that convective mixing is most efficient at early times (ages $\lesssim 10^7$ yr) and that primordial composition gradients can be eroded. In several cases, however, the atmospheric composition can differ widely from the planetary bulk composition, with the exact outcome depending on the details. We show that the efficiency of convection is primarily controlled by the underlying entropy profile: For low primordial entropies of $8-9~k_\mathrm{B} m_\mathrm{u}^{-1}$, convective mixing can be inhibited and composition gradients can persist over billions of years. The scaling of mixing efficiency with mass is governed by the primordial entropy. For the same primordial entropy, low-mass planets mix more efficiently than high-mass planets. If the primordial internal entropy would increase with mass, however, this trend could reverse. We also present a new analytical model that predicts convective mixing under the existence of composition (and entropy) gradients. Our results emphasize the complexity in the interpretation of atmospheric abundance measurements and show the great need to better understand the planetary formation process as it plays a key role in determining the planetary evolution and final structure.