Comparison of the modeled T_e as a function of the T_e measured within PHANGS-MUSE using the [N ii] λ5755 auroral line. Each panel makes different assumptions about how the values of f_ion or 12+log(O/H) are calculated. For each panel we show a one-to-one relation (solid line) and 1σ relative scatter (dotted lines), as well as the Spearman’s rank correlation coefficient (ρ). Top left: demonstration of our adopted method (Sect. 4.3), where we use our empirical prescription for f_ion (Eq. (15)) and metallicities calculated from the strong line Scal method. We recover high correlations (ρ = 0.79) and systematic agreement within 6 K, with a scatter of 546 K. Relaxing various assumptions in our model increases the scatter. Top right: assuming a fixed f_ion = 0.94 (the median for the PHANGS-MUSE sample), which produces significantly higher scatter (~755 K) and clear deviations from the one-to-one relation. Bottom panels: with variable f_ion applied but our derivation of 12+log(O/H) relaxed, with either a linear radial gradient (left) or a fixed metallicity adopted for each galaxy (right). Both recover high correlation coefficients with moderately increased scatter (~600 K). This demonstrates the relative insensitivity to the input metallicity for this charge-exchange method of deriving T_e.