Accounting for non-ideal mixing effects in the hydrogen-helium equation of state

Abstract

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.

References in corpus (9)

• Hydrogen-Helium Mixtures in the Interiors of Giant Planets
• New models of Jupiter in the context of Juno and Galileo
• A new equation of state for dense hydrogen-helium mixtures
• Phase separation in hydrogen-helium mixtures at Mbar pressures
• Jupiter internal structure: the effect of different equations of state
• Jupiter's inhomogeneous envelope
• A new equation of state for dense hydrogen-helium mixtures II: taking into account hydrogen-helium interactions
• Understanding Jupiter's Interior
• Benchmarking the ab initio hydrogen equations of state for the interior structure of Jupiter

Cited by in corpus (18)

• Jupiter's interior from Juno: Equation-of-state uncertainties and dilute core extent
• On the mass of gas giant planets: Is Saturn a failed gas giant?
• Evolution of Jupiter and Saturn with helium rain
• TOI-5005 b: A super-Neptune in the savanna near the ridge
• GASTLI: An open-source coupled interior-atmosphere model to unveil gas giant composition
• Revising the Giant Planet Mass-Metallicity Relation: Deciphering the Formation Sequence of Giant Planets
• Giant exoplanet composition: Why do the hydrogen-helium equation of state and interior structure matter?
• The bulk metallicity of giant planets around M stars
• The Possibility of Hydrogen-Water Demixing in Uranus, Neptune, K2-18b and TOI-270d
• Breaking degeneracies in exoplanetary parameters through self-consistent atmosphere-interior modelling
• Three Warm Jupiters orbiting TOI-6628, TOI-3837, TOI-5027 and one sub-Saturn orbiting TOI-2328
• NeuralCMS: A deep learning approach to study Jupiter's interior
• Conditions for radiative zones in the molecular hydrogen envelope of Jupiter and Saturn: The role of alkali metals
• Characterizing Jupiter's interior using machine learning reveals four key structures
• GEMS JWST: Transmission spectroscopy of TOI-5205b reveals significant stellar contamination and a metal-poor atmosphere
• How Internal Structure Shapes the Metallicity of Giant Exoplanets
• Alkali Metallicity, Mineral Clouds, and Deep Atmospheric Variability on Jupiter
• A Validated Low-to-Intermediate Mass Planetary Interior Structure Model and New Mass-Radius Relations