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

精确的太阳和恒星模型至关重要地依赖于基本的状态方程和相关的热力学性质。首先，状态方程决定了流体静力分层。第二，绝热声速是任何日震数据分析的关键热力学性质。化学成分对状态方程的调制使它成为测定太阳内部氦和重元素丰度的天然日震法。该方法的准确性一方面取决于状态方程本身的可靠性，另一方面取决于其他物理成分的不确定性。幸运的是，至少在太阳对流区的较深层，其他成分的影响被大大抑制，因为在那里，由于几乎绝热的对流，整个分层主要是由状态方程决定的。然而，状态方程本身的不确定性严重限制了任何日震丰度的确定。因此，为了满足对改进状态方程的需求，并检查太阳的重元素组成，Dappen博士和合作者将继续开发和应用精确的状态方程，用于计算太阳和恒星内部模型。这些状态方程将具有最佳可用形式的准确性，例如劳伦斯利弗莫尔国家实验室的OPAL天体物理不透明度表，但将具有足够的灵活性，可以直接用于恒星模型，即使化学成分局部变化（OPAL结果目前仅以表格形式提供，仅用于选定的成分）。考虑到最近提出的对太阳氧和钠丰度的修正，这一点尤其重要，这些新的状态方程将有助于验证。为了估计状态方程的绝对精度，基于路径积分的费曼-卡茨形式也将被应用和扩展。值得注意的是，这种形式可能总是局限于太阳内部深处，那里的物质几乎完全电离。然而，在它的适用范围内，它有可能成为最精确的理论，因此它可以作为更一般的状态方程形式主义的基准，它可以覆盖整个太阳。太阳是在地球上无法实现的条件下研究库仑系统特性的实验室，因此，这项工作将间接地解决更广泛的等离子体（低质量恒星、褐矮星、巨行星和陆地激光冲击实验）。新的状态方程还将改进太阳模型，这将有助于解决未来的问题，如太阳周期的位置、太阳的可变性等。为此，这里构建的状态方程和不透明度表将向公众开放。在项目实施期间，每年将支持和培训三名研究生。

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.