No abstract

The strikingly low luminosity of Uranus (T eff ≃ T eq ) constitutes a long-standing challenge to our understanding of Ice Giant planets. Here we present the first Uranus structure and evolution models that are constructed to agree with both the observed low luminosity and the gravity field data. Our models make use of modern ab initio equations of state at high pressures for the icy components water, methane, and ammonia. Proceeding step by step, we confirm that adiabatic models yield cooling times that are too long, even when uncertainties in the ice:rock ratio (I:R) are taken into account. We then argue that the transition between the ice/rock-rich interior and the H/He-rich outer envelope should be stably stratified. Therefore, we introduce a simple thermal boundary and adjust it to reproduce the low luminosity. Due to this thermal boundary, the deep interior of the Uranus models are up to 2-3 warmer than adiabatic models, necessitating the presence of rocks in the deep interior with a possible I:R of 1× solar. Finally, we allow for an equilibrium evolution (T eff ≃ T eq ) that begun prior to the present day, which would therefore no longer require the current era to be a "special time" in Uranus' evolution. In this scenario, the thermal boundary leads to more rapid cooling of the outer envelope. When T eff ≃ T eq is reached, a shallow, subadiabatic zone in the atmosphere begins to develop. Its depth is adjusted to meet the luminosity constraint. This work provides a simple foundation for future Ice Giant structure and evolution models, that can be improved by properly treating the heat and particle fluxes in the diffusive zones.

The validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices is investigated at pressure-temperature conditions typical for the interior of Uranus and Neptune. The basis of this study are ab initio data ranging up to 1000 GPa and 20 000 K calculated via density functional theory molecular dynamics simulations. In particular, we calculate a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the linear mixing approximation from the results of the real mixture are generally small; for the thermal EOS they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior (T core ∼ 4000 K).