A Recalibration of Strong Line Oxygen Abundance Diagnostics via the Direct Method and Implications for the High Redshift Universe

We use direct method oxygen abundances in combination with strong optical emission lines, stellar masses ($M_{\star}$), and star formation rates (SFRs) to recalibrate the N2, O3N2, and N2O2 oxygen abundance diagnostics. We stack spectra of $\sim$200,000 star-forming galaxies from the Sloan Digital Sky Survey in bins of $M_{\star}$ and SFR offset from the star forming main sequence to measure the weak emission lines needed to apply the direct method. All three new calibrations are reliable to within $\pm 0.10$ dex from $\log(M_{\star}/M_{\odot}) \sim 7.5 - 10.5$ and up to at least $200~M_{\odot}$ yr$^{-1}$ in SFR. The N2O2 diagnostic is the least subject to systematic biases. We apply the diagnostics to galaxies in the local universe and investigate the $M_{\star}$-$Z$-${\rm SFR}$ relation. The N2 and O3N2 diagnostics suggest the SFR dependence of the $M_{\star}$-$Z$-${\rm SFR}$ relation varies with both $M_{\star}$ and $\Delta \log(SSFR)$, whereas the N2O2 diagnostic suggests a nearly constant dependence on SFR. We apply our calibrations to a sample of high redshift galaxies from the literature, and find them to be metal poor relative to local galaxies with similar $M_{\star}$ and SFR. The calibrations do reproduce direct method abundances of the local analogs. We conclude that the $M_{\star}$-$Z$-${\rm SFR}$ relation evolves with redshift.