Surface density: a new parameter in the fundamental metallicity relation
  of star-forming galaxies
  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 four-dimensional
fundamental relation forms a tighter hypersurface that reduces the metallicity
dispersion to 50\% of that of the molecular-gas FMR. We suggest that future
analyses and models of galaxy evolution should consider the FMR in a
four-dimensional 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.
