摘要
Star-forming galaxies display a close relation among stellar mass, metallicity, and star formation rate (or molecular-gas mass). This is known as the fundamental metallicity relation (FMR) (or molecular-gas FMR), and it has a profound implication on models of galaxy evolution. However, there still remains a significant residual scatter around the FMR. We show here that a fourth parameter, the surface density of stellar mass, reduces the dispersion around the molecular-gas FMR. In a principal component analysis of 29 physical parameters of 41 338 star-forming galaxies, the surface density of stellar mass is found to be the fourth most important parameter. The new 4D fundamental relation forms a tighter hypersurface that reduces the metallicity dispersion to 50 per cent of that of the molecular-gas FMR. We suggest that future analyses and models of galaxy evolution should consider the FMR in a 4D space that includes surface density. The dilution time-scale of gas inflow and the star-formation efficiency could explain the observational dependence on surface density of stellar mass.