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, $\Sigma ^{\max }_{*}$ = $3\times 10^5\, {\rm M}_{\odot }\,{\rm pc}^{-2}$ , throughout a wide physical scale ranging from star cluster to galaxy. This suggests that there exists a fundamental physics that 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 it 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 $\text{$\sim$}10^{10}\, {\rm M}_{\odot }$ . We also found that a majority of high-Σ_* 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 dependence 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.