The mass-metallicity-star formation rate relation at z > 2 with 3D Hubble Space Telescope

We present new accurate measurements of the mass, metallicity and star-formation rate of a statistically significant sample of 93 galaxies at z greater than or similar to 2 using near-infrared spectroscopy taken as part of the 3D-Hubble Space Telescope survey. We derive a mass-metallicity relation (MZR) for our sample with metallicities based on the oxygen and Hβ nebular emission lines. We find the MZR derived from our data to have the same trend as previous determinations in the range 0 <z <3 with metallicity decreasing with stellar mass. However, we find that our MZR is offset from a previous determination at z greater than or similar to 2 which used metallicities derived from the [N ii]/Hα ratio. Incorporating star formation rate information, we find that our galaxies are also offset from the fundamental metallicity relation (FMR) by similar to 0.3 dex. Using the Baldwin-Phillips-Terlevich (BPT) diagram we argue that, if the physical conditions of star-forming regions evolve with redshift, metallicity indicators based on [N ii] and Hα, calibrated in the local Universe, may not be consistent with the ones based on oxygen lines and Hβ. Our results thus suggest that the evolution of the FMR previously reported at z similar to 2-3 may be an artefact of the differential evolution in metallicity indicators and caution against using locally calibrated empirical metallicity relations at high redshift, which do not account for evolution in the physical conditions of star-forming regions.