Equations of State, Thermodynamics, and Miscibility Curves for Jovian Planet and Giant Exoplanet Evolutionary Models

Abstract: The equation of state of hydrogen-helium (H-He) mixtures plays a vital role in the evolution and structure of gas giant planets and exoplanets. Recent equations of state that account for hydrogen-helium interactions, coupled with hydrogen-helium immiscibility curves, can now produce more physical evolutionary models, such as accounting for helium rain with greater fidelity than in the past. In this work, we present a set of tools for planetary evolution\footnote{All tables of thermodynamic quantities and derivatives are available at \url{https://github.com/Rob685/hhe_eos_misc}, along with a unified Python interface. Tutorials demonstrating the interface are also available in the repository.} that provides a Python interface for existing tables of useful thermodynamic quantities, state-of-the-art H-He equations of state, and pressure-dependent H-He immiscibility curves. In particular, for a collection of independent variable choices, we provide scripts to calculate the variety of thermodynamic derivatives used to model convection and energy transport. These include the chemical potential derived from the internal energy, which is a modeling necessity in the presence of composition gradients when entropy is the other primary variable. Finally, an entropy-based convection formalism is presented and fully described that highlights the physical differences between adiabatic and isentropic interior models. This centralized resource is meant to facilitate both giant planet structural and evolutionary modeling and the entry of new research groups into the field of giant planet modeling.