2008ApJ...678..798C

We use the previously identified 15 infrared star cluster counterparts to X-ray point sources in the interacting galaxies NGC 4038/4039 (the Antennae) to study the relationship between total cluster mass and X-ray binary number. This significant population of X-Ray/IR associations allows us to perform, for the first time, a statistical study of X-ray point sources and their environments. We define a quantity, η, relating the fraction of X-ray sources per unit mass as a function of cluster mass in the Antennae. We compute cluster mass by fitting spectral evolutionary models to K_s luminosity. Considering that this method depends on cluster age, we use four different age distributions to explore the effects of cluster age on the value of η and find it varies by less than a factor of 4. We find a mean value of η for these different distributions of η=1.7x10^–8 M^–1_☉ with σ_η=1.2x10^–8 M^–1_☉. Performing a χ² test, we demonstrate η could exhibit a positive slope, but that it depends on the assumed distribution in cluster ages. While the estimated uncertainties in η are factors of a few, we believe this is the first estimate made of this quantity to ``order of magnitude'' accuracy. We also compare our findings to theoretical models of open and globular cluster evolution, incorporating the X-ray binary fraction per cluster.