A comparative study of the fundamental metallicity relation: The impact of methodology on its observed evolution

Aims. We aim to investigate the influences on the evolution of the fundamental metallicity relation of different selection criteria. Methods. We used 5 487 star-forming galaxies at a median redshift of z ≈ 0.63 extracted from the VIMOS Public Extragalactic Redshift Survey (VIPERS) and 143 774 comparison galaxies in the local Universe from the GALEX-SDSS-WISE Legacy Catalog. We employed two families of methods: parametric and nonparametric. In the parametric approaches, we compared the fundamental metallicity relation projections plagued by observational biases on differently constructed control samples at various redshifts. Then, we compare the metallicity difference between different redshifts in stellar mass-star formation rate bins. In the nonparametric approach, we related the metallicity and the normalized specific star formation rate (sSFR). To compare galaxies with the same physical properties, we normalized the sSFR of our samples according to the median value at median redshift z ≈ 0.09. Then, the galaxies with the same distance from the star-forming main sequence at their respective redshifts were compared when the sSFR is normalized according to the expected values from their respective star-forming main sequences. Results. The methodologies implemented to construct fair, complete samples for studying the mass-metallicity relation and the fundamental metallicity relation produced consistent results showing a small but still statistically significant evolution of both relations up to z ≈ 0.63. In particular, we observed a systematic trend where the median metallicity of the sample at z = 0.63 is lower than that of the local sample at the same stellar mass and star formation rate. The average difference in the metallicity of the low and intermediate redshifts is approximately 1.8 times the metallicity standard deviation of the median of the intermediate redshift sample in stellar mass-star formation rate bins. We confirmed this result using the Kolmogorov-Smirnov test. When we applied the stellar mass-completeness criterion to catalogs, the metallicity difference in redshifts decreased to approximately 0.96 times the metallicity standard deviation of the median, and thus it was not statistically significant. The limited area of the FMR surface explored once the stellar mass-completeness criterion is applied might dominate this difference reduction, leaving out the area where the difference between the two samples is the highest. A careful reading of the results and their underlying selection criteria is crucial in studies of the mass-metallicity and fundamental metallicity relations. Conclusions. When studying the mass-metallicity and fundamental metallicity relations, we recommend using the nonparametric approach, which provides similar results compared to parametric prescriptions, is easier to use, and is clear to interpret. The nonparametric methodology provides a convenient way to compare physical properties, with a smaller impact on observational selection biases.