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.
