New Tests for Disruption Mechanisms of Star Clusters: Methods and
  Application to the Antennae Galaxies
  We present new tests for disruption mechanisms of star clusters based on the
bivariate mass-age distribution g(M,\tau). In particular, we derive formulae
for g(M,\tau) for two idealized models in which the rate of disruption depends
on the masses of the clusters and one in which it does not. We then compare
these models with our Hubble Space Telescope observations of star clusters in
the Antennae galaxies over the mass-age domain in which we can readily
distinguish clusters from individual stars: \tau\la10^7(M/10^4 M_{\odot})^{1.3}
yr. We find that the models with mass-dependent disruption are poor fits to the
data, even with complete freedom to adjust several parameters, while the model
with mass-independent disruption is a good fit. The successful model has the
simple form g(M,\tau) \propto M^{-2} \tau^{-1}, with power-law mass and age
distributions, dN/dM propto M^{-2} and dN/d\tau\propto\tau^{-1}. The predicted
luminosity function is also a power law, dN/dL \propto L^{-2}, in good
agreement with our observations of the Antennae clusters. The similarity of the
mass functions of star clusters and molecular clouds indicates that the
efficiency of star formation in the clouds is roughly independent of their
masses. The age distribution of the massive young clusters is plausibly
explained by the following combination of disruption mechanisms: (1) removal of
interstellar material by stellar feedback, \tau \la 10^7$ yr; (2) continued
stellar mass loss, 10^7 yr \la \tau \la 10^8 yr; (3), tidal disturbances by
passing molecular clouds, \tau \ga 10^8 yr. None of these processes is expected
to have a strong dependence on mass, consistent with our observations of the
Antennae clusters. We speculate that this simple picture also applies--at least
approximately--to the clusters in many other galaxies.
