On the Mass-Metallicity-Star Formation Rate Relation for Galaxies at $z\sim 2$

Recent studies have shown that the local mass-metallicity (M-Z) relation depends on the specific star formation rate (SSFR). Whether such a dependence exists at higher redshifts, and whether the resulting M-Z-SFR relation is redshift invariant, is debated. We re-examine these issues by applying the non-parametric techniques of Salim et al. (2014) to ~130 $z\sim2.3$ galaxies with N2 and O3 measurements from KBSS (Steidel et al. 2014). We find that the KBSS M-Z relation depends on SSFR at intermediate masses, where such dependence exists locally. KBSS and SDSS galaxies of the same mass and SSFR ("local analogs") are similarly offset in the BPT diagram relative to the bulk of local star-forming galaxies, and thus we posit that metallicities can be compared self-consistently at different redshifts as long as the masses and SSFRs of the galaxies are similar. We find that the M-Z-SFR relation of $z\sim2$ galaxies is consistent with the local one at $\log M_*<10$, but is offset up to -0.25 dex at higher masses, so it is altogether not redshift invariant. This high-mass offset could arise from a bias that high-redshift spectroscopic surveys have against high-metallicity galaxies, but additional evidence disfavors this possibility. We identify three causes for the reported discrepancy between N2 and O3N2 metallicities at $z\sim2$: (1) a smaller offset that is also present for SDSS galaxies, which we remove with new N2 calibration, (2) a genuine offset due to differing ISM condition, which is also present in local analogs, (3) an additional offset due to unrecognized AGN contamination.