A Maximum Stellar Surface Density in Dense Stellar Systems
  We compile observations of the surface mass density profiles of dense stellar
systems, including globular clusters in the Milky Way and nearby galaxies,
massive star clusters in nearby starbursts, nuclear star clusters in dwarf
spheroidals and late-type disks, ultra-compact dwarfs, and galaxy spheroids
spanning the range from low-mass cusp bulges and ellipticals to massive core
ellipticals. We show that in all cases the maximum stellar surface density
attained in the central regions of these systems is similar, Sigma_max ~ 10^11
M_sun/kpc^2 (~20 g/cm^2), despite the fact that the systems span 7 orders of
magnitude in total stellar mass M_star, 5 in effective radius R_e, and have a
wide range in effective surface density M_star/R_e^2. The surface density limit
is reached on a wide variety of physical scales in different systems and is
thus not a limit on three-dimensional stellar density. Given the very different
formation mechanisms involved in these different classes of objects, we argue
that a single piece of physics likely determines Sigma_max. The radiation
fields and winds produced by massive stars can have a significant influence on
the formation of both star clusters and galaxies, while neither supernovae nor
black hole accretion are important in star cluster formation. We thus conclude
that feedback from massive stars likely accounts for the observed Sigma_max,
plausibly because star formation reaches an Eddington-like flux that regulates
the growth of these diverse systems. This suggests that current models of
galaxy formation, which focus on feedback from supernovae and active galactic
nuclei, are missing a crucial ingredient.
