Helioseismic Analysis of the Hydrogen Partition Function in the Solar Interior

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Abstract
The difference in the adiabatic gradient γ1 between inverted solar data and solar models is analyzed. To obtain deeper insight into the issues of plasma physics, the so-called intrinsic difference in γ1 is extracted, that is, the difference due to the change in the equation of state alone. Our method uses reference models based on two equations of state currently used in solar modeling, the Mihalas-Hummer-Däppen (MHD) equation of state and the OPAL equation of state (developed at Livermore). Solar oscillation frequencies from the SOI/MDI instrument on board the SOHO spacecraft during its first 144 days in operation are used. Our results confirm the existence of a subtle effect of the excited states in hydrogen that was previously studied only theoretically (Nayfonov & Däppen). The effect stems from an internal partition function of hydrogen, as is used in the MHD equation of state. Although it is a pure hydrogen effect, it takes place in somewhat deeper layers of the Sun, where more than 90% of hydrogen is ionized, and where the second ionization zone of helium is located. Therefore, the effect will have to be taken into account in reliable helioseismic determinations of the astrophysically relevant helium abundance of the solar convection zone.