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

Applying the mean surface density of companions, Sigma(r), to the dynamical evolution of star clusters is an interesting approach to quantifying structural changes in a cluster. It has the advantage that the entire density structure, ranging from the closest binary separations, over the core-halo structure through to the density distribution in moving groups that originate from clusters, can be analysed coherently as one function of the stellar separations r. This contribution assesses the evolution of Sigma(r) for clusters with different initial densities and binary populations. The changes in the binary, cluster and halo branches as the clusters evolve are documented using direct N-body calculations, and are correlated with the cluster core 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.