A Synoptic Comparison of the Mihalas‐Hummer‐Dappen and OPAL Equations of State

Abstract

A detailed comparison is carried out between two popular equations of state (EOSs), the Mihalas-Hummer-Däppen (MHD) and OPAL equations of state, which have found widespread use in solar and stellar modeling during the past two decades. They are parts of two independent efforts to recalculate stellar opacities: the international Opacity Project (OP) and the Livermore-based OPAL project. We examine the difference between the two EOSs in a broad sense, over the whole applicable ϱ-T range, and for three different chemical mixtures. Such a global comparison highlights both their differences and their similarities. We find that omitting a questionable hard-sphere correction, τ, to the Coulomb interaction in the MHD formulation, greatly improves the agreement between the MHD and OPAL EOSs. We also find signs of differences that could stem from quantum effects not yet included in the MHD EOS, and differences in the ionization zones that are probably caused by differences in the mechanisms for pressure ionization. Our analysis not only gives a clearer perception of the limitations of each EOS for astrophysical applications, but also serves as guidance for future work on the physical issues behind the differences. The outcome should be an improvement of both EOSs.