The equation of state for stellar envelopes. I - an occupation probability formalism for the truncation of internal partition functions

Abstract

The authors have formulated a new equation of state for material in stellar envelopes, subject to the limits T ⪉ 107K and ρ ⪉ 10-2g cm-3. Under these conditions, the method of free energy minimization can be used to allow for nonideal effects; this method ensures thermodynamic consistency among the material properties. A chemical picture is used in which atomic and molecular particles retain their identities. An occupation probability formalism is used to represent the effects of the plasma in establishing a finite partition function, and attention is paid to representing these effects in a way that is consistent from the point of view of statistical mechanics. The use of the static screened Coulomb potential to calculate level shifts and to estimate the cutoff of the internal partition function is shown by elementary arguments to be invalid. For most of the parameter space relevant to stellar envelopes, perturbations arising from the plasma ions are shown to be dominant in establishing the internal partition functions.