A stellar audit: the computation of encounter rates for 47 Tucanae and ω Centauri

Using King-Mitchie Models, we compute encounter rates between the variousstellar species in the globular clusters $\omega$ Cen, and 47 Tuc. We alsocompute event rates for encounters between single stars and a population ofprimordial binaries. Using these rates, and what we have learnt fromhydrodynamical simulations of encounters performed earlier, we compute theproduction rates of objects such as low-mass X-ray binaries (LMXBs), smotheredneutron stars and blue stragglers (massive main-sequence stars). If 10\% of thestars are contained in primordial binaries, the production rate of interestingobjects from encounters involving these binaries is as large as that fromencounters between single stars. For example, encounters involving binariesproduce a significant number of blue stragglers in both globular clustermodels. The number of smothered neutron stars may exceed the number of low-massX-ray binaries (LMXBs) by a factor of 5-20, which may help explain whymillisecond pulsars are observed to outnumber LMXBs in globular clusters.