The Role of Equation-of-State Uncertainties in Solar and Stellar Modeling

University Of Southern California, Los Angeles CA

Investigators

Abstract

Accurate solar and stellar models crucially depend on the underlying equation of state and the associated thermodynamic properties. First, the equation of state determines the hydrostatic stratification. Second, the adiabatic sound speed is the key thermodynamic property in any analysis of helioseismic data. The modulation of the equation of state by the chemical composition makes it a natural helioseismic method for the determination of the helium and heavy-element abundance in the solar interior. The accuracy of the method is governed on the one hand by the reliability of the equation of state itself, on the other hand by uncertainties in the other physical ingredients. Fortunately, at least in deeper layers of the solar convection zone, the influence of the other ingredients is greatly suppressed, since there, by virtue of the nearly adiabatic convection, the entire stratification is mainly determined by the equation of state. However, the uncertainty in the equation of state itself severely limits any helioseismic abundance determination. Therefore, to answer the need for an improved equation of state and to examine the heavy element composition of the Sun, Dr. Dappen and collaborators will continue development and application of accurate equations of state for use in the computation of solar and stellar interior models. These equations of state will have the accuracy of the best available formalisms, such as the OPAL Astrophysical Opacity Tables from the Lawrence Livermore National Laboratory, but will be sufficiently flexible to be used directly in stellar models, even when the chemical composition is locally varying (OPAL results are currently only available in tabular form and only for selected compositions). This is particularly important given the recent suggested revision in the solar oxygen and sodium abundances, which these new equations of state will help verify. To estimate the absolute accuracy of the equations of state, the Feynman-Kac formalism, based on path integrals, will also be applied and extended. It is noted this formalism will likely always be limited to the deeper solar interior, where matter is nearly fully ionized. However, in its domain of applicability, it has the potential to become the most accurate theory, so that it can serve as a benchmark for the more general equation of state formalism which can cover the entire Sun. The Sun is a laboratory for studying the properties of Coulomb systems under conditions that cannot be achieved on Earth, and therefore, indirectly this work will address a wider range of plasmas (lower mass stars, brown dwarfs, giant planets, and terrestrial laser shock experiments). The new equations of state will also improve solar models which will help tackle future problems such as the seat of the solar cycle, solar variability, etc. Towards this end, the equations of state and opacity tables constructed here will be made publicly available. Three graduate students will be supported and trained per year during the execution of this project.