Cluster Mass Functions in the Large and Small Magellanic Clouds: Fading and Size-of-Sample Effects

Abstract

The properties of 939 star clusters in the Large and Small Magellanic Clouds were determined from ground-based CCD images in UBVR passbands. The areal coverage was extensive, corresponding to 11.0 sq-kpc in the LMC and 8.3 sq-kpc in the SMC. After corrections for reddening, the colors and magnitudes of the clusters were converted to ages and masses, and the resulting mass distributions were searched for the effects of fading, evaporation, and size-of-sample bias. The data show a clear signature of cluster fading below the detection threshold. The initial cluster mass function (ICMF) was determined by fitting the mass and age distributions with cluster population models. These models suggest a new method to determine the ICMF that is nearly independent of fading or disruption and is based on the slope of a correlation between age and the maximum cluster mass in equally spaced intervals of log-age. For a nearly uniform star formation rate, this correlation has a slope equal to 1/(alpha-1) for an ICMF of dn(M)/dM proportional to M^-alpha. We determine that alpha is between 2 and 2.4 for the LMC and SMC using this method plus another method in which models are fit to the mass distribution integrated over age and to the age distribution integrated over mass. The maximum mass method also suggests that the cluster formation rate in the LMC age gap between 3 and 13 Gy is about a factor of ten below that in the period from 0.1 Gy to 1 Gy. The oldest clusters correspond in age and mass to halo globular clusters in the Milky Way. They do not fit the trends for lower-mass clusters but appear to be a separate population that either had a very high star formation rate and became depleted by evaporation or formed with only high masses.