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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,τ). In particular, we derive formulae for g(M,τ) 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: τ\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,τ) \propto M^{-2} τ^{-1}, with power-law mass and age distributions, dN/dM propto M^{-2} and dN/dτ\proptoτ^{-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, τ\la 10^7$ yr; (2) continued stellar mass loss, 10^7 yr \la τ\la 10^8 yr; (3), tidal disturbances by passing molecular clouds, τ\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.