Star cluster demographics. I. A general framework and application to the antennae galaxies

We present a framework for understanding the demographics of star cluster systems and develop a toy model that incorporates a universal initial power-law mass function, selected formation histories, selected disruption laws, and a convolution with common artifacts and selection effects found in observational data. A wide variety of observations can be explained by this simple model, including the observed correlation between the brightest young cluster in a galaxy and the total number of young clusters. The model confirms that this can be understood as a statistical size-of-sample effect rather than a difference in the physical process responsible for the formation of the clusters, suggesting that active mergers have the brightest clusters simply because they have the most clusters. A comparison is made of different cluster disruption laws, and it is shown that the break in the dN/d tau diagram used to determine the parameters in the Boutloukos & Lamers model may be produced by incompleteness near the break point. A model of the Antennae galaxies is developed and compared with the observational data; this extends the mass-age range for cluster comparison over previous studies. An important component of our model is the use of a two-stage'' disruption process, with a very high infant mortality'' rate for the clusters with ages less than similar to 10(8) yr ( i.e., roughly 80%-90% are lost each factor of 10 in time, tau, independent of mass), and two-body relaxation, which becomes the dominant disruption mechanism at older ages, preferentially removing the lower mass clusters. Hence, in our model, stars from the dissolved clusters form the field population. We note that a 90% infant mortality rate for each factor of 10 in tau (i.e., dN/d tau proportional to tau(-1)) is consistent with all measured young cluster populations, including those in the Antennae, the Small Magellanic Cloud, and the Milky Way. In fact, the population of clusters in the Antennae can be viewed as a scaled-up version of the Milky Way in many respects, with a scale factor of roughly 1000 times the Lada & Lada sample of embedded star clusters in the local Milky Way. We find no evidence for a truncation of the Antennae cluster mass function at the high-mass end.