A First Estimate of the X‐Ray Binary Frequency as a Function of Star Cluster Mass in a Single Galactic System

Abstract

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 Ks 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 = 1.7 × 10−8 M−1☉ with ση = 1.2 × 10−8 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.