Abstract
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 $0.10$ dex from
$łog(M_\star/M_ødot) 7.5 - 10.5$ and up to at least $200~M_ødot$
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 $M_\star$-$Z$-$SFR$ relation. The N2 and O3N2
diagnostics suggest the SFR dependence of the $M_\star$-$Z$-$SFR$
relation varies with both $M_\star$ and $\Delta łog(SSFR)$, 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 $M_\star$-$Z$-$SFR$ relation evolves with
redshift.
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