We present new accurate measurements of the physical properties of a statistically significant sample of 103 galaxies at z~2 using near-infrared spectroscopy taken as part of the 3D-HST survey. We derive redshifts, metallicities and star formation rates (SFRs) from the [OII], [OIII] and Hbeta nebular emission lines and exploit the multi-wavelength photometry available in CANDELS to measure stellar masses. We find the mass-metallicity relation (MZR) derived from our data to have the same trend as previous determinations in the range 0<z<3, with lower mass galaxies having lower metallicities. However we find an offset in the relation compared to the previous determination of the z~2 MZR by Erb et al. 2006b, who measure metallicities using the [NII]/Halpha ratio, with metallicities lower at a given mass. Incorporating our SFR information we find that our galaxies are offset from the Fundamental Metallicity Relation (FMR) by ~0.3 dex. We investigate the photoionization conditions and find that our galaxies are consistent with the elevated ionization parameter previously reported in high-redshift galaxies. Using the BPT diagram we argue that, if this is the case, metallicity indicators based on [NII] and Halpha may not be consistent with the ones obtained via oxygen lines and Hbeta. Using a recent determination of the theoretical evolution of the star forming sequence in the BPT diagram we convert our measured [OIII]/Hbeta line ratios to [NII]/Halpha ratios. From the [NII]/Halpha ratio we infer systematically higher metallicities in better agreement with the FMR. Our results thus suggest the evolution of the FMR previously reported at z~2-3 may be an artifact of the differential evolution in metallicity indicators, and caution against using locally calibrated metallicity relations at high redshift which do not account for evolution in the physical conditions of star-forming regions.
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