Galaxy metallicities depend primarily on stellar mass and molecular gas mass

Aims. We present an analysis of the behaviour of galaxies in a four-dimensional parameter space defined by stellar mass, metallicity, star formation rate, and molecular gas mass. We analyse a combined sample of 227 galaxies that draws from a number of surveys across the redshift range 0 z 90% of the sample at z ~ 0) and covers >3 decades in stellar mass. Methods. Using principal component analysis, we demonstrate that galaxies in our sample lie on a 2D plane within this 4D parameter space, which is indicative of galaxies that exist in an equilibrium between gas inflow and outflow. Furthermore, we find that the metallicity of galaxies depends only on stellar mass and molecular gas mass. In other words, gas-phase metallicity has a negligible dependence on star formation rate once the correlated effect of molecular gas content is accounted for. Results. The well-known fundamental metallicity relation which describes a close and tight relationship between metallicity and SFR (at fixed stellar mass) is therefore entirely a by-product of the underlying physical relationship with molecular gas mass (through the Schmidt-Kennicutt relation).