Equations of State for Opacity Calculations

Radiative opacities are important quantities that contribute to the prediction of radiation transport in astrophysical objects. Calculation of these opacities requires a knowledge of all electron energy level populations that can contribute significantly to photoabsorption and photon scattering in the mostly plasma environments of these objects. This can be a daunting task. Unlike a conventional equation of state that relates thermodynamic variables to uniquely describe the macroscopic state of an equilibrium solid, liquid, or gas, an "opacity equation of state" requires all the statistical thermodynamic details that are the ultimate basis of that conventional equation of state. The range of temperatures and densities required for these opacity calculations can also be extraordinarily large, so robust models are necessary. We will give a short overview of two approaches to equations of state that are currently used to produce opacities for astrophysical applications, and will go into some detail on the particular approach used for the recently updated Los Alamos National Laboratory opacity tables that cover elements from hydrogen through zinc. Our method uses a chemical picture with occupation probabilities that depend on the plasma environment to construct a free-energy function that we then minimize to obtain the equilibrium populations of ionic species and energy levels. This method guarantees thermodynamic consistency.