The MHD equation of state with post-Holtsmark microfield distributions

The Mihalas-Hummer-Dappen (MHD) equation of state is a part of the Opacity Project (OP), where it mainly provides ionization equilibria and level populations of a large number of astrophysically relevant species. Its basic concept is the idea of perturbed atomic and ionic states. The MHD equation of state was originally restricted to the plasma of stellar envelopes, that is, to relatively moderate densities, which should not exceed rho < 10**-2 g/cm**3. However, helioseismological analysis has demonstrated that this restriction is much too conservative. The principal feature of the original Hummer & Mihalas (1988) paper was a simplified form of the Holtsmark microfield for randomly distributed ions. An improved MHD equation of state (Q-MHD) is introduced. It is based on a more realistic microfield distribution (Hooper 1966, 1968) that includes plasma correlations. Comparison with an alternative post-Holtsmark formalism (APEX) is made, and good agreement is shown. There is a clear signature of the choice of the microfield distribution in the adiabatic index gamma_1, which makes it accessible to present-day helioseismological analysis. But since these thermodynamic effects of the microfield distribution are quite small, it also follows that the approximations chosen in the original MHD equation of state were reasonable. A particular feature of the original MHD papers was an explicit list of the adopted free energy and its first- and second-order analytical derivatives. The corresponding Q-MHD quantities are given in the Appendix.