The Solar-Interior Equation of State with the Path-Integral Formalism I. Domain of Validity

TL;DR

This paper introduces the Feynman-Kac formalism for the solar equation of state, assesses its validity domain, and highlights its potential for improved accuracy in modeling the Sun's interior, especially where helium is highly ionized.

Contribution

It presents the FK equation of state adapted for solar conditions and evaluates its domain of validity, setting the stage for future applications and extensions.

Findings

Applicable where helium is over 90% ionized, up to 0.98 solar radius.

Potentially more accurate than current equations of state in relevant regions.

Enables study of Coulomb screening, bound states, and recombination effects.

Abstract

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. Use of the FK equation of state is limited to physical conditions for which more than 90% of helium is ionized. This incudes 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. 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.