2013AJ....146..135A

The Andromeda galaxy, M31, has several times the number of globular clusters found in the Milky Way. It contains a correspondingly larger number of low-mass X-ray binaries (LMXBs) associated with globular clusters, and as such can be used to investigate the cluster properties that lead to X-ray binary formation. The best tracer of the spatial structure of M31 globulars is the high-resolution imaging available from the Hubble Space Telescope (HST), and we have used HST data to derive structural parameters for 29 LMXB-hosting M31 globular clusters. These measurements are combined with structural parameters from the literature for a total of 41 (of 50 known) LMXB clusters and a comparison sample of 65 non-LMXB clusters. Structural parameters measured in blue bandpasses are found to be slightly different (smaller core radii and higher concentrations) than those measured in red bandpasses; this difference is enhanced in LMXB clusters and could be related to stellar population differences. Clusters with LMXBs show higher collision rates for their mass compared to clusters without LMXBs, and collision rates estimated at the core radius show larger offsets than rates estimated at the half-light radius. These results are consistent with the dynamical formation scenario for LMXBs. A logistic regression analysis finds that, as expected, the probability of a cluster hosting an LMXB increases with increasing collision rate and proximity to the galaxy center. The same analysis finds that probability of a cluster hosting an LMXB decreases with increasing cluster mass at a fixed collision rate, although we caution that this could be due to sample selection effects. Metallicity is found to be a less important predictor of LMXB probability than collision rate, mass, or distance, even though LMXB clusters have a higher metallicity on average. This may be due to the interaction of location and metallicity: a sample of M31 LMXBs with a greater range in galactocentric distance would likely contain more metal-poor clusters and make it possible to disentangle the two effects.