Seismological Comparisons of Solar Models with Element Diffusion Using the MHD, Opal, and Sireff Equations of State

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Abstract
We compare the thermodynamic and helioseismic properties of solar models evolved using three different equation of state (EOS) treatments: the Mihalas, Däppen & Hummer EOS tables (MHD); the latest Rogers, Swenson, & Iglesias EOS tables (OPAL), and a new analytical EOS (SIREFF) developed by Swenson et al. All of the models include diffusive settling of helium and heavier elements. The models use updated OPAL opacity tables based on the 1993 Grevesse & Noels solar element mixture, incorporating 21 elements instead of the 14 elements used for earlier tables. The properties of solar models that are evolved with the SIREFF EOS agree closely with those of models evolved using the OPAL or MHD tables. However, unlike the MHD or OPAL EOS tables, the SIREFF in-line EOS can readily account for variations in overall Z abundance and the element mixture resulting from nuclear processing and diffusive element settling. Accounting for Z abundance variations in the EOS has a small, but nonnegligible, effect on model properties (e.g., pressure or squared sound speed), as much as 0.2% at the solar center and in the convection zone). The OPAL and SIREFF equations of state include electron exchange, which produces models requiring a slightly higher initial helium abundance, and increases the convection zone depth compared to models using the MHD EOS. However, the updated OPAL opacities are as much as 5% lower near the convection zone base, resulting in a small decrease in convection zone depth. The calculated low-degree nonadiabatic frequencies for all of the models agree with the observed frequencies to within a few microhertz (0.1%). The SIREFF analytical calibrations are intended to work over a wide range of interior conditions found in stellar models of mass greater than 0.25 M☉ and evolutionary states from pre-main-sequence through the asymptotic giant branch (AGB). It is significant that the SIREFF EOS produces solar models that both measure up to the stringent requirements imposed by solar oscillation observations and inferences, and are more versatile than EOS tables.

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