The solar-interior equation of state with the path-integral formalism

Abstract

Aims. This is the first paper in a series that deals with solar-physics applications of the equation-of-state formalism based on the formulation of the so-called “Feynman-Kac (FK) representation”. Here, the FK equation of state is presented and adapted for solar applications. Its domain of validity is assessed. The practical application to the Sun will be dealt with in Paper II. Paper III will extend the current FK formalism to a higher order. Methods. A recent rigorous quantum-statistical formalism for Coulomb systems is used to compute the thermodynamical quantities for solar modeling, taking into account the necessary requirements on smoothness and accuracy. The FK formalism being a virial expansion, it suffers from the well-known deficiency that it is limited to nearly full ionization. This point is elaborated in detail, and the quantitative criterion for the domain of validity of the FK equation of state is established. Results. Use of the FK equation of state is limited to physical conditions for which more than 90% of helium is ionized. This includes the inner region of the Sun out to about .98 of the solar radius. Despite this limitation, in the parts of the Sun where it is applicable, the FK equation of state has the power to be more accurate than the equations of state currently used in solar modeling. The FK approach is especially suited to study physical effects such as Coulomb screening, bound states, the onset of recombination of fully ionized species, as well as diffraction and exchange effects. Conclusions. Despite technical difficulties in its application, there are unique features in the FK approach that promise to turn it into the most exact of the available formalisms, provided FK is restricted to the deeper layers of the Sun where more than 90% of helium is ionized. The localizing power of helioseismology allows a test of the FK equation of state. Such a test will be beneficial both for better solar models and for tighter solar constraints of the equation of state.