The Binary Zoo: The Calculation of Production Rates of Binaries Through 2+1 Encounters in Globular Clusters

In studying encounters between binaries and single stars, one is interested in three classes of events: exchanges of stars, hardening of the original binary by a third star, and the production of merged objects. We present a means for computing cross sections for these three outcomes for an arbitrary binary and single star as might be found in the core of a globular cluster. The cross sections for a number of binaries in various stellar populations are then computed. We consider multiple encounters and the ultimate fate of a population of binaries fed into the cores of different globular cluster models. We see that the presence of only a relatively small number of binaries (containing 10\% of the stars) will boost the production rate of astrophysically-interesting objects by a factor of at least a few over the rates expected from encounters between single stars. In particular, the ratio of smothered neutron stars to low-mass X-ray binaries (LMXBs) may be greatly increased, possibly explaining, in part, the excess of millisecond pulsars compared to LMXBs.