A fundamental relation between mass, star formation rate 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 <it>M</it><inf>★</inf>, gas-phase metallicity and star formation 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 metallicity, i.e. ∼12 per cent. 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 <it>z</it>∼ 2.5 are found to follow the same FMR defined by local Sloan Digital Sky Survey (SDSS) galaxies, with no…