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.
