2007ApJ...660.1246S

LMXBs form efficiently in GCs. By combining Chandra and HST ACS observations of 11 massive early-type galaxies in the Virgo Cluster, we use the most accurate identification of LMXBs and GCs to date to explore the optical properties of 270 GCs with LMXBs and 6488 GCs without detectable X-ray emission. More massive, redder, and more compact GCs are more likely to contain LMXBs. Unlike Galactic GCs, a large number of GCs with LMXBs have half-mass relaxation times >2.5 Gyr; GCs need not survive for more than five relaxation timescales to produce LMXBs. By fitting the dependence of the expected number of LMXBs per GC, λ_t, on the GC mass M, color (g-z), and half-mass radius r_h,cor, we find that λ_t∝M^1.24±0.08x10^0.9+0.2-0.1_(g–z)r^–2.2±0.2_h,cor. This rules out that the number of LMXBs per GC is linearly proportional to GC mass (99.89% confidence limit) and leads us to predict that most GCs with high X-ray luminosities contain a single LMXB. The detailed dependence of λ_t on GC properties appears mainly due to a dependence on the encounter rate Γ_h and the metallicity Z, λ_t∝Γ^0.82±0.05_hZ^0.39±0.07. Our analysis provides strong evidence that dynamical formation and metallicity play the primary roles in determining the presence of an LMXB in extragalactic GCs. The shallower than linear encounter rate dependence requires an explanation by theories of dynamical binary formation. A metallicity-dependent variation in the number of neutron stars and black holes per unit GC mass, effects from irradiation-induced winds, or suppression of magnetic braking in metal-poor stars may all be consistent with our abundance dependence; all three scenarios require further development.