Ionization of heavy elements and the adiabatic exponent in the solar plasma

¹ Sternberg Astronomical Institute, M.V. Lomonosov Moscow State University, 13, Universitetskij pr., 119234, Moscow, Russia
e-mail: avo@sai.msu.ru
² Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, USA
³ Institute of Problems of Chemical Physics RAS, Chernogolovka, Russia
⁴ Joint Institute for High Temperatures RAS, Moscow, Russia
⁵ Moscow Institute of Physics and Technology, Dolgoprudnyi, Russia

Received: 26 July 2021
Accepted: 31 January 2022

Abstract

Context. The adiabatic exponent Γ₁ is studied as a thermodynamic quantity in the partially ionized plasma of the solar convection zone.

Aims. The aim of this study is to understand the impact of heavy elements on the Γ₁ profile. We calculated Γ₁ with the SAHA-S equation of state for different chemical compositions of plasma, and we analyzed contributions of individual elements to Γ₁. We attempted to determine the mass fractions of the heavy elements using our analysis of the Γ₁ profile.

Methods. We studied the decrease in Γ₁ due to the ionization of heavy elements in comparison with the value obtained for a pure hydrogen-helium plasma. These types of differences are denoted as “Z contributions”, and we analyzed them for eight elements (C, N, O, Ne, Mg, S, Si, and Fe) as well as for a mixture of elements corresponding to the solar chemical composition. The contributions of the heavy elements are studied on an adiabat in the lower part of the convection zone, where the influence of hydrogen and helium to the Z contribution is minimal. The Z-contribution profiles are unique for each chemical element. We compared linear combinations of individual Z contributions with the exact Z contribution. Applying a least-squares technique to the decomposition of the full Z contribution to a basis of individual-element contributions, we obtained the mass fractions of the heavy elements.

Results. The Z contribution of heavy elements can be described by a linear combination of individual-element Z contributions with a high level of accuracy of 5 × 10⁻⁶. The inverse problem of estimating the mass fractions of heavy elements from a given Γ₁ profile was considered for the example of solar-type mixtures. In ideal numerical simulations, the mass fractions of the most abundant elements could be determined with a relative accuracy better than a few tenths of a percent. In the presence of random or systematic errors in the Γ₁ profile, abundance estimations become remarkably less accurate, especially due to unknown features of the equations of state. If the amplitude of the errors does not exceed 10⁻⁴, we can expect a determination of at least the oxygen abundance with a relative error of about 10%. Otherwise, the results of the method would not be reliable.