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Star-forming galaxies display a close relation among stellar mass,metallicity and star-formation rate (or molecular-gas mass). This is known asthe fundamental metallicity relation (FMR) (or molecular-gas FMR), and it has aprofound implication on models of galaxy evolution. However, there stillremains a significant residual scatter around the FMR. We show here that afourth parameter, the surface density of stellar mass, reduces the dispersionaround the molecular-gas FMR. In a principal component analysis of 29 physicalparameters of 41,338 star-forming galaxies, the surface density of stellar massis found to be the fourth most important parameter. The new four-dimensional(4D) fundamental relation forms a tighter hypersurface that reduces themetallicity dispersion to 50% of that of the molecular-gas FMR. We suggest thatfuture analyses and models of galaxy evolution should consider the FMR in a 4Dspace that includes surface density. The dilution time scale of gas inflow andthe star-formation efficiency could explain the observational dependence onsurface density of stellar mass. AKARI is expected to play an important role inshedding light on the infrared properties of the new 4D FMR.

Surface density: a new parameter in the fundamental metallicity relation of star-forming galaxies