line is not measurable). The R$_{23}$ diagnostic is based on the electron temperature sensitivity of the oxygen spectral lines, achieved via using the ratio of the oxygen line strength to a spectral feature independent of metallicity. R$_{23}$ requires measurement of the 3727 [Å]{} \[O II\], 5007 [Å]{} \[O III\], and H$\beta$ lines.\[metal\_lines\] However as the Oxygen line strength initially increases with and then (due to infrared fine-structure lines inducing a cooling effect) decreases with increasing metallicity this method alone is only sufficient to determine a pair of degenerate upper and lower branch metallicity values. Therefore the R$_{23}$ diagnostic is typically coupled with a second metallicity diagnostic to resolve this degeneracy. Typically, and specifically for all the objects in this paper, this is done using the \[N II\] / H$\alpha$ diagnostic requiring spectral coverage of the 6584 [Å]{} \[N II\] to H$\alpha$ line ratio (or its limit). While the \[N II\] / H$\alpha$ diagnostic is not nearly as precise as R$_{23}$ it is sufficient to exclude one of the R$_{23}$ branches except when the branches are near their intersection point where the metallicity values of the two branches converge anyway.

Due to differences between metallicity diagnostics and their various calibrations, a 