The equation of state for stellar envelopes. II - Algorithm and selected results

Abstract

A free-energy-minimization method for computing the dissociation and ionization equilibrium of a multicomponent gas is discussed. The adopted free energy includes terms representing the translational free energy of atoms, ions, and molecules; the internal free energy of particles with excited states; the free energy of a partially degenerate electron gas; and the configurational free energy from shielded Coulomb interactions among charged particles. Internal partition functions are truncated using an occupation probability formalism that accounts for perturbations of bound states by both neutral and charged perturbers. The entire theory is analytical and differentiable to all orders, so it is possible to write explicit analytical formulas for all derivatives required in a Newton-Raphson iteration; these are presented to facilitate future work. Some representative results for both Saha and free-energy-minimization equilibria are presented for a hydrogen-helium plasma with N(He)/N(H) = 0.10. These illustrate nicely the phenomena of pressure dissociation and ionization, and also demonstrate vividly the importance of choosing a reliable cutoff procedure for internal partition functions.