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 popu lations of a large number of astrophysically relevant species. Its basic co ncept is the idea of perturbed atomic and ionic states. At high densities, when many-body effects become dominant, the concept of perturbed atoms lose s its sense. For that reason, the MHD equation of state was originally rest ricted to the plasma of stellar envelopes, that is, to relatively moderate densities, which should not exceed rho < 10(-2) g cm(-3). However, heliosei smological analysis has demonstrated that this restriction is much too cons ervative. The principal feature of the original Hummer & Mihalas paper is a n expression for the destruction probability of a bound state (ground state or excited) of a species (atomic or ionic), linked to the mean electric mi crofield of the plasma. Hummer dr Mihalas assumed, for convenience, a simpl ified form of the Holtsmark microfield for randomly distributed ions. An im proved MHD equation of state (Q-MHD) is introduced. It is based on a more r ealistic microfield distribution that includes plasma correlations. Compari son with an alternative post-Holtsmark formalism (APEX) is made, and good a greement is shown. There is a clear signature of the choice of the microfie ld distribution in the adiabatic index gamma(1), which makes it accessible to present-day helioseismological analysis. However, since these thermodyna mic 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.