As in Fig. 1, f_ion modeled assuming the values of T_e([N ii]) measured from direct detection of auroral lines in the PHANGS-MUSE Η ii region sample (points). This forms a continuous sequence with the Η ii regions in the CHAOS sample (open circles), but with a significantly more pronounced nonlinear trend. From the PHANGS-MUSE sample, we selected only regions with a more than 50% contrast against the DIG background and with [S iii]/[S ii] > 0.5 (filled circles). We then combined the PHANGS-MUSE and CHAOS samples to construct a binned median (red circles). We fit this with the functional form described in Eq. (15) (dashed red line) to determine our empirical relation for f_ion.