What determines the maximum stellar surface density of galaxies?

Observationally, it has been reported that the densest stellar system in the Universe does not exceed a maximum stellar surface density, \(\Sigma^{\max}_{*}\) = \(3\times10^5\)M\(_{\odot}\)pc\(^{-2}\), throughout a wide physical scale ranging from star cluster to galaxy. This suggests there exists a fundamental physics which regulates the star formation and stellar density. However, factors that determine this maximum limit are not clear. In this study, we show that \(\Sigma^{\max}_{*}\) of galaxies is not a constant as previous work reported, but actually depends on the stellar mass. We select galaxy sample from the Sloan Digital Sky Survey Data Release 12 at \(z=0.01-0.5\). In contrast to a constant maximum predicted by theoretical models, \(\Sigma^{\max}_{*}\) strongly depends on stellar mass especially for less massive galaxies with \(\sim10^{10}\)M\(_{\odot}\). We also found that a majority of high-\(\Sigma_{*}\) galaxies show red colours and low star-formation rates. These galaxies probably reach the \(\Sigma^{\max}_{*}\) as a consequence of the galaxy evolution from blue star forming to red quiescent by quenching star formation. One possible explanation of the stellar-mass dependency of \(\Sigma^{\max}_{*}\) is a mass dependent efficiency of stellar feedback. The stellar feedback could be relatively more efficient in a shallower gravitational potential, which terminates star formation quickly before the stellar system reaches a high stellar density.