The equation of state for hydrogen and helium is fundamental for studying stars and giant planets. It has been shown that because of interactions at atomic and molecular levels, the behaviour of a mixture of hydrogen and helium cannot be accurately represented by considering these elements separately. This paper aims at providing a simple method to account for interactions between hydrogen and helium in interior and evolution models of giant planets. Using on the one hand ab initio simulations that involve a system of interacting hydrogen and helium particles and pure equations of state for hydrogen and helium on the other, we derived the contributions in density and entropy of the interactions between hydrogen and helium particles. We show that relative variations of up to 15% in density and entropy arise when non-ideal mixing is accounted for. These non-ideal mixing effects must be considered in interior models of giant planets based on accurate gravity field measurements, particularly in the context of variations in the helium-to-hydrogen ratio. They also affect the mass-radius relation of exoplanets. We provide a table that contains the volume and entropy of mixing as a function of pressure and temperature. This table is to be combined with pure hydrogen and pure helium equations of state to obtain an equation of state that self-consistently includes mixing effects for any hydrogen and helium mixing ratio and may be used to model the interior structure and evolution of giant planets to brown dwarfs. Non-linear mixing must be included in accurate calculations of the equations of state of hydrogen and helium. Uncertainties on the equation of state still exist, however. Ab initio calculations of the behaviour of the hydrogen-helium mixture in the megabar regime for various compositions should be performed in order to gain accuracy.
A new equation of state for dense hydrogen-helium mixtures II: taking into account hydrogen-helium interactions
在最近的一篇论文（Chabrier et al. 2019）中，我们推导出了一个新的稠密氢/氦混合物的状态方程（EOS），该方程涵盖了从太阳型恒星到棕矮星和气态行星的温度-密度域。该EOS基于所谓的加性体积定律，因此没有考虑氢和氦物质之间的相互作用。在本文中，我们超越这些计算考虑H/He相互作用，来自量子分子动力学模拟。这些相互作用，最终导致H/He相分离，在低温和高密度下，在棕矮星和巨行星领域变得重要。这个新的EOS的表格是公开的。
Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics
UC Berkeley（加州大学伯克利分校）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；The Institute of Science and Technology Austria（奥地利科学技术研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Bakar Institute of Digital Materials for the Planet, UC Berkeley（加州大学伯克利分校巴卡尔地球数字材料研究所）
