Deriving the coronal hole electron temperature: electron density dependent ionization recombination considerations

Comparison of appropriate theoretically derived line ratios with observational data can yield estimates of a plasma's physical parameters, such as electron density or temperature. The usual practice in the calculation of the line ratio is the assumption of excitation by electrons/protons followed by radiative decay. Furthermore, it is normal to use the so-called coronal approximation, i.e. one only considers ionization and recombination to and from the ground-state. A more accurate treatment is to include ionization/recombination to and from metastable levels. Here, we apply this to two lines from adjacent ionization stages, Mg IX 368 angstrom and Mg X 625 angstrom, which has been shown to be a very useful temperature diagnostic. At densities typical of coronal hole conditions, the difference between the electron temperature derived assuming the zero density limit compared with the electron density dependent ionization/recombination is small. This, however, is not the case for flares where the electron density is orders of magnitude larger. The derived temperature for the coronal hole at solar maximum is around 1.04 MK compared to just below 0.82 MK at solar minimum.