Influence of Ionization on the Polytropic Index of the Solar Atmosphere within Local Thermodynamic Equilibrium Approximation

An initial theoretical attempt to explain the observed decrease of the polytropic/adiabatic index $\gamma$ in the solar corona has been accomplished. The chemical reactions of the ionization-recombination processes in local thermodynamic equilibrium (LTE) of a solar plasma cocktail containing heavy elements are found to cause $1.1 < \gamma \leq 5/3$ in the quiet solar atmosphere. It is also shown that the quiet solar atmosphere is in LTE justifying this theoretical study. This result is obtained by numerically solving the Saha equation and subsequently using a newly derived equation for calculation of the polytropic index from thermodynamic partial derivatives of the enthalpy and pressure with respect to density and temperature. In addition, a comparison between calculated in this way polytropic index and measured from spectroscopic observations of propagating slow magneto-hydrodynamics (MHD) waves in coronal loops shows that LTE ionization accounts for very small part of the observed decrease of $\gamma$ meaning that the solar plasma in the active region is not in LTE as expected. However, the observed dependency of higher polytropic index at higher temperatures is confirmed by the current theoretical approach. It is concluded that to account for the polytropic index decrease in the active regions of the solar corona, it is necessary kinetic non-LTE ionization calculations to be performed.