Helioseismic constraints on the chemical composition and the equation of state

The intrinsic γ₁ difference is defined as the discrepancy in the adiabatic exponent γ₁, resulting from the discrepancies in the equation of state and the chemical composition. The other part of the γ₁ difference, "induced" by the discrepancy in the internal structure (i.e., pressure, density or temperature) is excluded. Our examination of solar models revealed that the discrepancy in the heavy-element composition and the discrepancy in the equation of state result in different and independent features in the functional form of the intrinsic γ₁ difference. Therefore, the two discrepancies can be distinguished by looking for the features that do not change when only either the equation of state or the chemical composition is being varied. The possibility of such a strategy was already discussed in an earlier study (Gong, Däppen and Nayfonov 2001), although only theoretically. Our inversion tests demonstrate the potential of its realization. In this paper, we present our initial inversion results between the Sun and various solar models and discuss the strengths and limits of our inversion code.