The Mass-Metallicity and the Fundamental Metallicity Relation revisited
  on a fully Te-based abundance scale for galaxies
  The relationships between stellar mass, gas-phase metallicity and star
formation rate (i.e. the Mass-Metallicity, MZR, and the Fundamental Metallcity
Relation, FMR) in the local Universe are revisited by fully anchoring the
metallicity determination for SDSS galaxies on the Te abundance scale defined
exploiting the strong-line metallicity calibrations presented in Curti et al.
(2017). Self-consistent metallicity measurements allow a more unbiased
assessment of the scaling relations involving M, Z and SFR, which provide
powerful constraints for the chemical evolution models. We parametrise the MZR
with a new functional form which allows us to better characterise the turnover
mass. The slope and saturation metallicity are in good agreement with previous
determinations of the MZR based on the Te method, while showing significantly
lower normalisation compared to those based on photoionisation models. The Z-
SFR dependence at fixed stellar mass is also investigated, being particularly
evident for highly star forming galaxies, where the scatter in metallicity is
reduced up to a factor of ~30%. A new parametrisation of the FMR is given by
explicitly introducing the SFR-dependence of the turnover mass into the MZR.
The residual scatter in metallicity for the global galaxy population around the
new FMR is 0.054 dex. The new FMR presented in this work represents a useful
local benchmark to compare theoretical predictions and observational studies
(of both local and high-redshift galaxies) whose metallicity measurements are
tied to the abundance scale defined by the Te method, hence allowing to
properly assess its evolution with cosmic time.
