Convective mixing in giant planets: When does the atmospheric composition represent the planetary bulk composition?

The advent of more accurate atmospheric abundance measurements opens a new window into giant planet characterization.  Linking atmospheric measurements to the bulk planetary composition and the planetary origin is a key objective in planetary science. Typically, the observed atmospheric abundances are interpreted using rather simplified evolution and internal structure models. These models assume either a core+envelope or a homogeneous interior. However, we now know from the Solar System that the internal structure of giant planets is more complex. In addition, formation models clearly indicate that composition gradients are expected to form in the deep interior. 

In this talk, we will present results from evolution simulations that account for composition gradients and convective mixing during the planetary evolution. For the planetary evolution, we use the Modules for Experiments in Stellar Astrophysics (MESA) code with state-of-the-art equations of state (EoS) for hydrogen, helium, water, and rock. Based on mixing length theory, we improved the treatment of convective boundaries in MESA to allow a comprehensive investigation of the long-term evolution of convective mixing in giant planets.

We consider a range of planetary masses (0.3-2 M_J), initial entropies (8-11 k_b/m_u) and heavy-element profiles. We will highlight trends of convection and dependencies between different planetary parameters, such as primordial entropy, composition profile and planetary mass. In addition, we test the influence of using different EoSs and the consideration of stellar irradiation. We find that convective mixing is most efficient at early times (the first 10⁷ years of evolution) and that primordial composition gradients can be eroded. 

The efficiency of convection is primarily driven by the underlying entropy profile. If the primordial entropy is sufficiently low, convective mixing can be inhibited and composition gradients can persist over evolutionary timescales. Moreover, since the primordial entropy increases with planetary mass, more massive planets will mix more effectively. Furthermore, we show that the EoS used plays a crucial role for the long-term evolution with primordial composition gradients: heavier elements are harder to mix and therefore lead to more stable configurations, also differences in the EoS of hydrogen and helium can alter the outcome, underlining the importance of using accurate EoSs. 

Finally, we present a new analytical model that predicts convective mixing under the existence of composition (and entropy) gradients. We show that in most cases our analytical model reproduces well the results from the numerical simulations. It disentangles the key factors for convective mixing and allows to estimate the fraction of atmospheric-to-bulk metallicity without needing to model the evolution numerically.

Overall, we show that in several cases, the atmospheric composition can differ widely from the planetary bulk composition, with the exact outcome depending on the details. Our findings are critical for the interpretation of atmospheric abundance measurements and linking them to the planetary bulk composition and formation history.