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The fundamental metallicity relation (FMR) states that galaxies of the samestellar mass but larger star formation rate (SFR) tend to have smallergas-phase metallicity (<Zg>). It is thought to be fundamental because itnaturally arises from the stochastic feeding of star-formation from externalmetal-poor gas accretion, a process extremely elusive to observe but essentialaccording the cosmological simulations of galaxy formation. In this letter, weshow how the FMR emerges from the local anti-correlation between SFR surfacedensity and Zg recently observed to exist in disk galaxies. We analyticallyderive the global FMR from the local law, and then show that both relationsagree quantitatively when considering the star-forming galaxies of the MaNGAsurvey. Thus, understanding the FMR becomes equivalent to understanding theorigin of the anti-correlation between SFR and metallicity followed by the setof star-forming regions of any typical galaxy. The correspondence between localand global laws is not specific of the FMR, so that a number of local relationsshould exist associated with known global relations.

the astrophysical journal. letters

The fundamental metallicity relation emerges from the local  anti-correlation between star formation rate and gas-phase metallicity  existing in disk galaxies