tokens: that the following correction terms are subtracted from the metallicity determined from H ii calibration given in Section 3.2 : Combining these with equations ( 5 ) and ( 7 ), they result into the following final calibrations: where x and x are determined from equations ( 5 ) and ( 7 ), respectively. We apply the above corrections to the DIG/LIER-dominated spaxels (i.e. those with emission line ratios beyond the Kauffmann line) to all galaxies in sample. Fig. 3 (bottom row) shows metallicity maps of NGC 1042 obtained from O3N2 (left-hand panel) and O3S2 (middle-panel) after correction, while the corresponding maps for all other galaxies are shown in figures (bottom rows) in the supplementary online material (Appendix A). 4.3 Residual differential metallicity after correction The metallicity maps obtained using these new calibrations for the DIG/LIER regions already show an improvement, especially in terms of much reduced metallicity contrast between H ii regions and nearby DIG/LIER regions. In this subsection, we quantify such improvement. From the corrected O3N2 and O3S2 metallicity maps of each galaxy, we estimate representative values of metallicities for H ii –DIG/LIER pairs using the same methodology described in Section 3.1.1 , and study the distribution of differential metallicities in Fig. 9 . Left-hand panel shows the distribution for [S ii ]-BPT selected H ii –DIG/LIER pairs, while right-hand panel corresponds to [N ii ]-BPT selected H ii –DIG/LIER pairs. By construction, mean differential metallicity is zero for each of the two metallicity diagnostic and for both samples. A comparison of dispersions before and after applying corrections can be found in Table 1 . Figure 9. Distribution of corrected differential metallicity (Δlog Z) of H ii –DIG/LIER pairs selected on the basis of the [S ii ]-BPT (left-hand panel) and [N ii ]-BPT (right-hand panel) diagrams. In each panel, the brown and cyan histograms represent the differential metallicity distribution from O3S2, and O3N2, respectively, after applying the correction to the DIG/LIER/Seyfert spaxels presented in Section 4.2 (equations 10 , 11 , 14 , and 15 ). σ(Δlog( Z )) denotes the standard deviation of the differential metallicity distribution. In each case, the average offsets of the distribution are zero by construction. O3N2 shows comparable metallicity dispersions for H ii –DIG/LIER samples obtained from both selection criterion, i.e. 0.04 dex for [S ii ]-BPT selection and 0.03 dex for [N ii ]-BPT selection. The dispersions are smaller than the scatter in differential metallicities before applying correction (i.e. 0.05 dex). Like O3N2, O3S2 also shows comparable metallicity dispersion for H ii –DIG/LIER samples obtained from both selection criterion, i.e. 0.06 dex for [S ii ]-BPT selection and 0.07 dex for [N ii ]-BPT selection. Although the dispersions after correction are still larger than those obtained from O3N2, the improvement is significant with respect to the dispersions
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