A fundamental relation between mass, SFR and metallicity in local and high redshift galaxies

We show that the mass-metallicity relation observed in the local universe is due to a more general relation between stellar mass M?, gas-phase metallicity and star forma-tion rate (SFR). Local galaxies define a tight surface in this 3D space, the Fundamental Metallicity Relation (FMR), with a small residual dispersion of ∼0.05 dex in metallic-ity, i.e, ∼12%. At low stellar mass, metallicity decreases sharply with increasing SFR, while at high stellar mass, metallicity does not depend on SFR. High redshift galaxies, up to z∼2.5 are found to follow the same FMR defined by local SDSS galaxies, with no indication of evolution. In this respect, the FMR defines the properties of metal enrichment of galaxies in the last 80 % of cosmic time. The evolution of the mass-metallicity relation observed up to z=2.5 is due to the fact that galaxies with progressively higher SFRs, and therefore lower metallicities, are selected at increasing redshifts, sampling different parts of the same FMR. By introducing the new quantity µα = log(M?) − α log(SFR), with α=0.32, we define a projection of the FMR that minimizes the metallicity scatter of local galaxies