Heavy Elements Abundances Inferred from the First Adiabatic Exponent in the Solar Envelope

The first adiabatic exponent profile, noted \({{\Gamma }_{1}}\), computed along adiabatic coordinates (\(T\), \(\rho \)), is in the focus of our study. Under conditions of almost fully ionized hydrogen and helium, the \({{\Gamma }_{1}}\) profile is quite sensitive to heavy elements ionization. \({{\Gamma }_{1}}\) decreases in regions where an element is partially ionized. The recent helioseismic structural inversion is obtained with an accuracy better than \({{10}^{-4}}\) in the most of the adiabatic convective zone that allows to study ionization variations. The aim is to determine the major heavy elements content in the solar convective zone. The method of our research is synthesis of the \(\Gamma _{1}\) profile, which is based on a linear combination of the contributions of individual heavy elements. The idea of the approach was proposed and justified by Baturin et al. (2022). We find the best approximation of the inverted profile \({{\Gamma }_{1}}\) adjusting the abundances of major elements (C, N, O, Ne), meanwhile the abundances of elements heavier than neon are fixed. We synthesize the theoretical \({{\Gamma }_{1}}\) profile using the SAHA-S equation of state, and are able to reproduce the inverted profiles with an accuracy of \((1-2)\cdot {{10}^{-5}}\). Total mass fraction of heavy elements found with this method is \(Z=0.0148\pm 0.0004\). The oxygen logarithmic abundance is \(8.70\pm 0.03\), carbon \(8.44\pm 0.04\), nitrogen \(8.12\pm 0.08\), and neon \(8.17\pm 0.09\). The obtained estimations of oxygen and carbon agree with spectroscopic abundances by Asplund, Amarsi, and Grevesse (2021).