Planetary Ices and the Linear Mixing Approximation

TL;DR

This study evaluates the accuracy of the linear mixing approximation for planetary ices' equations of state at high pressures and temperatures, using ab initio simulations to inform models of Uranus and Neptune's interiors.

Contribution

It provides new EOS data for methane, ammonia, water mixtures, and assesses the approximation's validity, developing a consistent Uranus interior model.

Findings

Deviations of the linear mixing approximation are generally small, within 4%.

Diffusion coefficients in mixtures match pure compounds within 20%.

A new Uranus interior model suggests a cold core around 4000 K.

Abstract

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 ($\mathrm{T_{core}} \mathtt{\sim}$ 4000 K).