Close Approach during Hard Binary–Binary Scattering

It is now clear that there is a substantial population of primordial binaries in galactic globular clusters and that binary interactions are a major influence on globular cluster evolution. Collisional interactions involving stars in binaries may provide a significant channel for the formation of various stellar exotica, such as blue stragglers, X–ray binaries and millisecond pulsars. We report on an extensive series of numerical experiments of binary–binary scattering, analysing the cross–section for close approach during interactions for a range of hard binary parameters of interest in globular cluster cores. We consider the implied rate for tidal interactions for different globular clusters and compare our results with previous, complementary estimates of stellar collision rates in globular clusters. We find that the collision rate for binary–binary encounters dominates in low density clusters if the binary fraction in the cluster is larger than 0.2 for wide main–sequence binaries. In dense clusters binary–single interactions dominate the collision rate and the core binary fraction must be < ∼ 0.1 per decade in semi–major axis or too many collisions take place compared to observations. The rates are consistent if binaries with semi–major axes ∼ 100AU are overabundant in low density clusters or if breakup and ejection substantially lowers the binary fraction in denser clusters. Given reasonable assumptions about fractions of binaries in the cores of low density clusters such as NGC 5053, we cannot account for all the observed blue stragglers by stellar collisions during binary encounters, suggesting a substantial fraction may be due to coalescence of tight primordial binaries.