The first adiabatic exponent in a partially ionized prominence plasma: Effect on the period of slow waves

Partially ionized plasmas are found in many different astrophysical environments. The study of partially ionized plasmas is of great interest for solar physics because some layers of the solar atmosphere (photosphere and chromosphere) as well as solar structures, such as spicules and prominences, are made of these kinds of plasmas. To our knowledge, despite it being known that the adiabatic coefficient, γ , or the first adiabatic exponent, Γ 1 , depend on the ionization degree, this fact has been disregarded in all the studies related to magnetohydrodynamic waves in solar partially ionized plasmas. However, in other astrophysical areas, the dependence of γ or Γ 1 on the plasma ionization degree has been taken into account. Therefore, our aim here is to study how, in a plasma with prominence physical properties, the joint action of the temperature, density, and ionization degree modifies the numerical values of the first adiabatic exponent Γ 1 which affects the adiabatic sound speed and the period of slow waves. In our computations, we have used two different approaches; first of all, we assume local thermodynamic equilibrium (LTE) and, later, we consider a non-local thermodynamic equilibrium (non-LTE) model. When comparing the results in the LTE and non-LTE cases, the numerical values of Γ 1 are clearly different for both and they are probably strongly dependent on the assumed model which determines how the ionization degree evolves with temperature. Finally, the effect of the ionization degree dependence of Γ 1 on the period of slow waves has been determined showing that it can be of great importance for seismological studies of partially ionized solar structures.