be insensitive to bin widths.

The left panel of Figure \[fig:BPT\] shows where ${\hbox{$M_{\star}$}}$–${\hbox{$\Delta\log$(SSFR)}}$ stacks fall on the BPT diagram relative to the galaxies in our sample (gray contours) and individual regions from @Pilyugin12 (black points). The stacks with high ${\hbox{$\Delta\log$(SSFR)}}$ are undergoing relatively intense star formation, and their line ratios closely resemble those of individual regions. The passively star forming stacks track the overall distribution of galaxies, which is not traced by the individual regions.

Naively we expect that galaxies undergoing more intense star formation have many more ionizing photons per atom. While the excitation parameter $P$ is marginally dependant on abundance, the right panel of Figure \[fig:BPT\] suggests our naive expectation is correct; stacks with high ${\hbox{$\Delta\log$(SSFR)}}$ show systematically higher values of $P$. Incorporating ${\hbox{$\Delta\log$(SSFR)}}$ accounts for some of the strong line ratios’ sensitivity to ionization conditions.

Lastly, it is easily shown that many strong line ratios (e.g. N2) are biased by SFR since they include ${\hbox{H$\alpha$}}$ flux. By grouping galaxies with similar ${\hbox{$\Delta\log$(SSFR)}}$, which is equivalent to SFR at fixed ${\hbox{$M_{\star}$}}$, our chosen stacking methodology minimizes this bias.

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Stellar Continuum Subtraction
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Many emission lines used in this study (particularly ) 