The fundamental metallicity relation from SDSS (z ∼ 0) to VIPERS (z ∼ 0.7). Data selection or evolution

International audienceContext. Our knowledge of galaxy metallicity - the result of the integrated star formation history and the evolution of the interstellar medium - is important for constraining the description of galaxy evolution. As such, it has been widely studied in the local Universe, in particular, using data from the Sloan Digital Sky Survey (SDSS). The VIMOS Public Extragalactic Redshift Survey (VIPERS) allows us to extend such studies up to redshift of z ∼ 0.7 and to quantify a possible evolution of the galaxy metallicity with high statistical precision. Aims: We focus on how to homogenize the comparison between galaxy samples having different characteristics. We check the projections of the fundamental metallicity relation (FMR) and the evolution of these projections between a sample selected at z ∼ 0 (SDSS) and z ∼ 0.7 (VIPERS). We check, in particular, whether and to what extent selection criteria can affect the results. Methods: We checked the influence of different biases introduced either by physical constraints (evolution of the luminosity function and differences in the fraction of blue galaxies) or data selection (the signal-to-noise ratio and quality of the spectra) on the FMR and its projections. To separate the differences occurring due to the physical evolution of galaxies with redshift from the false evolution mimed by these biases, we first analyzed the effects of these biases individually on the SDSS sample, and next, starting from the SDSS data, we built a VIPERS-equivalent z ∼ 0 sample, replicating the main characteristics of VIPERS sample at z ∼ 0.7 for a fair comparison. Results: We found that the FMR projections are all sensitive to biases introduced by the selection on S/N and the quality flags of the emission line measurements in the spectra, especially the [O III]λ4959 line. The exception is the metallicity versus the sSFR plane which is insensitive to these biases. The evolution of the luminosity function introduces a bias only in the plane metallicity versus the star formation rate (SFR) while the fraction of blue galaxies has no impact on results. Conclusions: With the applied methodology, the median metallicities estimated in each stellar mass-SFR bin of the samples at z ∼ 0 and z ∼ 0.7 agree within the uncertainties between SDSS and VIPERS samples (Δ log(O/H) ∼ 0.6⟨sVIPERS⟩ = 0.08 dex, where sVIPERS stands for the metallicity standard deviation, without taking into account the biases). This difference can be reduced to ∼0.4⟨sVIPERS⟩ = 0.06 dex taking into account the biases, in particular the evolution of the luminosity function. We find a shift of the FMR projections towards lower metallicity which can be mimicked by a conservative selection on the S/N of emission lines. We also find either an overselection of high-metal galaxies at low stellar mass or an overestimation of the metallicity for the same sources at z ∼ 0.7. Any bias taken into account in this study cannot mimic this overselection or overestimation at low redshift