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 discs, 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, Σ_max ~ 10¹¹ M. kpc^-2 (~20 g cm^-2), despite the fact that the systems span ~7 orders of magnitude in total stellar mass M* and ~5 in effective radius R^-_e. and have a wide range in effective surface density M*. 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 Σ_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 is important in star cluster formation. We thus conclude that feedback from massive stars likely accounts for the observed Σ_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.