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

## TL;DR

This paper demonstrates that the fundamental metallicity relation in galaxies naturally arises from a local anti-correlation between star formation rate surface density and gas-phase metallicity, linking local galaxy physics to global properties.

## Contribution

It analytically derives the global FMR from local anti-correlations, showing their quantitative agreement in MaNGA survey galaxies, revealing the local origin of the FMR.

## Key findings

- Global FMR can be derived from local anti-correlation laws.
- The local SFR surface density and metallicity anti-correlation explains the FMR.
- The local-global relation correspondence is likely common in galaxy physics.

## Abstract

The fundamental metallicity relation (FMR) states that galaxies of the same stellar mass but larger star formation rate (SFR) tend to have smaller gas-phase metallicity (<Zg>). It is thought to be fundamental because it naturally arises from the stochastic feeding of star-formation from external metal-poor gas accretion, a process extremely elusive to observe but essential according the cosmological simulations of galaxy formation. In this letter, we show how the FMR emerges from the local anti-correlation between SFR surface density and Zg recently observed to exist in disk galaxies. We analytically derive the global FMR from the local law, and then show that both relations agree quantitatively when considering the star-forming galaxies of the MaNGA survey. Thus, understanding the FMR becomes equivalent to understanding the origin of the anti-correlation between SFR and metallicity followed by the set of star-forming regions of any typical galaxy. The correspondence between local and global laws is not specific of the FMR, so that a number of local relations should exist associated with known global relations.