“ Consider the comparison of Fe I and Fe II lines in the spectrum of the sun and in the spectrum of a star with a very similar Teff but much lower gravity—for example, the supergiant β Draconis. From the similar temperature of these stars, we expect the level excitation as described by the Boltzmann equation to be similar. However, as described by the Saha equation, the ionization ratio Fe I/Fe II will be different because of the different pressures in the two stars' atmospheres. Therefore, in the solar spectrum the line ratio Fe I/Fe II should be larger because of the high densities and the greater possibility of ion–electron recombination.”
The above quote states that if a star of the same spectral type has a similar temperature, the intensity of the line spectrum changes due to the influence of the Saha equation, not the Boltzmann equation.
How can you estimate 'similar temperature'? I understand that the line profile strength changes due to the difference in surface gravity. Many textbooks that explain the luminosity effect do not explain why similar temperature differences occur. I want to know how to estimate the surface temperature using the Saha equation. For example, if the electron density is greater, can the Saha equation explain why the temperature is higher?
