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.