The formation of higher–order hierarchical systems in star clusters

We simulate open clusters containing up to 182 stars initially in the form of singles, binaries and triples. Due to the high interaction rate a large number of stable quadruples, quintuples, sextuples, and higher-order hierarchies form during the course of the simulations. For our choice of initial conditions, the formation rate of quadruple systems after about 2 Myr is roughly constant with time at ∼ 0.008 per cluster per Myr. The formation rate of quintuple and sextuple systems are about half and one quarter, respectively, of the quadruple formation rate, and both rates are also approximately constant with time. We present reaction channels and relative probabilities for the formation of persistent systems containing up to six stars. The reaction networks for the formation and destruction of quintuple and sextuple systems can become quite complicated, although the branching ratios remain largely unchanged during the course of the cluster evolution. The total numbers of quadruples is about a factor of three smaller than observed in the solar neighborhood.