Hydrogen Ionization Inside the Sun

TL;DR

This paper investigates hydrogen ionization in the solar plasma, modeling excited states with temperature-dependent partition functions, revealing significant effects on the adiabatic exponent and implications for helium ionization.

Contribution

It introduces a novel approach to modeling hydrogen ionization using specific partition functions, highlighting their impact on solar plasma properties.

Findings

Hydrogen ionization causes a deep lowering of $$ over the solar convective zone.

Different partition functions shift ionization profiles and affect helium ionization.

Excited state modeling can alter $$ by up to 0.01, influencing solar structure understanding.

Abstract

Hydrogen is the main chemical component of the solar plasma, and H-ionization determines basic properties of the first adiabatic exponent $\Gamma_1$. Hydrogen ionization remarkably differs from the ionization of other chemicals. Due to the large number concentration, H-ionization causes a very deep lowering of $\Gamma_1$, and the lowering profile appears to be strongly asymmetric and extends over almost the entire solar convective zone. The excited states in the hydrogen atom are modelled with the help of a partition function, which accounts the internal degrees of freedom of the composed particle. A temperature-dependent partition function with an asymptotic cut-off tail is deduced from a solution of the quantum mechanical problem of the hydrogen atom in the plasma. We present a numerical simulation of hydrogen ionization, calculated with two expressions for the partition function, Planck-Larkin (PL) and Starostin-Roerich (SR), respectively. The Hydrogen ionization is shifted toward higher temperature in the SR-case compared to the PL-case. Different models for excited states of the hydrogen atom may change $\Gamma_1$ by as much as $10^{-2}$. The behavior of the $\Gamma_1$ profiles for pure hydrogen resembles `twisted ropes' for the two considered models. This significantly affects the helium ionization and the position of the helium hump. This entanglement of H and He effect gives us a chance to study a role of excited states in the solar plasma.