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, , 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 and find it varies by less than a factor of 4. We find a mean value of for these different distributions of ¼ 1:7 ; 10 À8 M À1 with ¼ 1:2 ; 10 À8 M À1 . Performing a 2 test, we demonstrate could exhibit a positive slope, but that it depends on the assumed distribution in cluster ages. While the estimated uncertainties in 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.

Multiwavelength study of Chandra X-ray sources in the Antennae

“…6 shows computed for each cluster, but binned by bins of data number (DN) −1 . As can be seen, there does not appear to be a significant slope and η is consistent with a constant value of with an uncertainty of and is in agreement with the value found in Clark et al (2008).…”

“…Since any value of ΔΣχ 2 less than one indicates no significant slope, this suggests there is no slope in η. This differs from the value of ΔΣχ 2 = 1.9 when using only the 15 clusters found with associations to X‐ray sources (Clark et al 2008) and seems to strengthen the case that there is only a flat slope in the functional form of η( M c ).…”

“…Following the procedure outlined in Clark et al (2008), we computed the cluster mass relation, η, defined in that paper, but now included our extended list of clusters with X‐ray counterparts. As defined in Clark et al (2008), η relates the function of X‐ray detections per mass as a function of cluster mass and can be formalized with the following equation: …”

“…To estimate the strength of this result, we performed a χ 2 test between the mean value of η and a fitted line to the plotted values of η (Fig. 6; see Clark et al 2008). We found a ΔΣχ 2 = 0.45.…”

“…Following the work in Clark et al (2008), we explored the relationship between cluster mass and the detected number of X‐ray sources. In Clark et al (2008) we defined a function η relating the number of X‐ray detections per mass as a function of cluster mass. We found η is consistent with a mean value of .…”