Collisional hardening of compact binaries in globular clusters

We consider essential mechanisms for orbit shrinkage or 'hardening' of compact binaries in globular clusters (GCs) to the point of Roche lobe contact and X-ray emission phase, focusing on the process of collisional hardening due to encounters between binaries and single stars in the cluster core. The interplay between this kind of hardening and that due to emission of gravitational radiation produces a characteristic scaling of the orbit-shrinkage time with the single-star binary encounter rate gamma in the cluster which we introduce, clarify and explore. We investigate possible effects of this scaling on populations of X-ray binaries in GCs within the framework of a simple 'toy' scheme for describing the evolution of pre-X-ray binaries in GCs. We find the expected qualitative trends sufficiently supported by data on X-ray binaries in Galactic GCs to encourage us towards a more quantitative study.