Core radius and density measurements in N-body experiments Connections with theoretical and observational definitions

Observers, numerical experimenters, and theorists use a misleadingly similar language when describing star clusters, although the operational definitions of quantities such as core radius and central density differ considerably. These differences are investigated, and a class of coordinate-independent, scale-free measurements for local and global quantities, particularly suited to small N-body systems, are introduced. It is shown, by means of analytical estimates and Monte Carlo experiments, that the quantities measured are closely related to independently defined global parameters, such as the core radius and the core density. Similarities and differences between these and the definitions for corresponding quantities which are used for observations and for theoretical models, considering finite-number effects as well as those systematic discrepancies which persist in the continuum limit, are discussed. This discussion applies both to star clusters and to clusters of galaxies.