Test of the Accuracy of Approximate Methods to Handle Distant Binary-Single Star Encounters

In the numerical simulations of evolution of star clusters, binary-single star interactions frequently take place. Since the direct integration of them is time consuming, distant interactions between binaries and field stars are often integrated by using some approximations. Traditionally the effect of the error caused by the approximated treatment is regarded as small enough to be ignored. However, if we have a binary-dominated core, the energy drift is large. In this study, we perform numerical experiments to evaluate the effect of neglecting the weak perturbation from distant single particles. We developed an N-body integrator which can manipulate multiple precision floating point numbers.