Complete process for defining the S line. (a) shows the long-bin[19]. The contours with levels shown with colors from the color table of RED TEMPERATURE and from the color table of green-to-white LINEAR represent the results for the classified Seyferts and LINERs, respectively. The corresponding number densities of the contour levels are shown in the colorbars on both sides of the panel. The huge magenta asterisks represent the central points of the two contours. The magenta line represents the baseline. Two sets of parallel cyan lines divide the contour maps into 27 × 15 rectangle-bins. The boundaries of long-bin[19] are highlighted in blue. The boundaries of wider long-bins are highlighted in red. The red cross represents the intersection point of the Seyfert and LINER distributions within the long-bin[19]. (b) shows the rectangle-bin[19, 9]. The boundaries of rectangle-bin[19, 9] are highlighted in blue. The triangles in orange and the diamonds in dark green represent the Seyferts and LINERs classified in the [S II] BPT diagram, respectively. The red cross has the same meaning as that in panel (a). (c) shows the couple of histograms that depict the dependence of the percentage of Seyfert (orange) and LINER (dark green) counts within each rectangle-bin in long-bin[19] relative to their total counts in long-bin[19] on the displacement of each rectangle-bin in long-bin[19] from the bottom of long-bin[19]. The red arrow corresponds to the intersection point in long-bin[19], which matches the location of the thick red crosses in the previous two panels. (d) shows the final result of the S line (solid blue line) and its confidence bands (dashed blue lines). Magenta asterisks represent the collected intersection points from all the long-bins and wider long-bins. The solid red line is the Ke01 line. The dashed green line is the Ka03 line.