The mean surface density of companions in a stellar-dynamical context

Applying the mean surface density of companions, Sigma (r), to the dynamica l evolution of star clusters is an interesting approach to quantifying stru ctural changes in a cluster. It has the advantage that the entire density s tructure, ranging from the closest binary separations, over the core-halo s tructure through to the density distribution in moving groups that originat e from clusters, can be analysed coherently as one function of the stellar separation r. This contribution assesses the evolution of Sigma (r) for clu sters with different initial densities and binary populations. The changes in the binary, cluster and halo branches as the clusters evolve are documen ted using direct N-body calculations, and are correlated with the cluster c ore and half-mass radius. The location of breaks in the slope of Sigma (r) and the possible occurrence of a binary gap can be used to infer dynamical cluster properties.