A model for the minimum mass of bound stellar clusters and its
  dependence on the galactic environment
  We present a simple physical model for the minimum mass of bound stellar
clusters as a function of the galactic environment. The model evaluates which
parts of a hierarchically-clustered star-forming region remain bound given the
time-scales for gravitational collapse, star formation, and stellar feedback.
We predict the initial cluster mass functions (ICMFs) for a variety of galaxies
and we show that these predictions are consistent with observations of the
solar neighbourhood and nearby galaxies, including the Large Magellanic Cloud
and M31. In these galaxies, the low minimum cluster mass of
$\sim10^2~\rm{M}_{\odot}$ is caused by sampling statistics, representing the
lowest mass at which massive (feedback-generating) stars are expected to form.
At the high gas density and shear found in the Milky Way's Central Molecular
Zone and the nucleus of M82, the model predicts that a mass
$>10^2~\rm{M}_{\odot}$ must collapse into a single cluster prior to
feedback-driven dispersal, resulting in narrow ICMFs with elevated
characteristic masses. We find that the minimum cluster mass is a sensitive
probe of star formation physics due to its steep dependence on the star
formation efficiency per free-fall time. Finally, we provide predictions for
globular cluster (GC) populations, finding a narrow ICMF for dwarf galaxy
progenitors at high redshift, which can explain the high specific frequency of
GCs at low metallicities observed in Local Group dwarfs like Fornax and WLM.
The predicted ICMFs in high-redshift galaxies constitute a critical test of the
model, ideally-suited for the upcoming generation of telescopes.
