THE MINIMUM DETECTABLE CORE RADIUS OF STAR-CLUSTERS

Sampling errors limit the minimum detectable core radius of centrally condensed star clusters. A formalism is developed for calculating minumum detectable core radii which apply even to images of arbitrarily high resolution. The relative advantage of star counts over brightness profiles is analyzed in terms of typical cluster luminosity functions. The analysis considers the effects of detector limitations, dynamical evolution and image postprocessing on these errors. For a typical cusp globular cluster (such as NGC 7099 or M15 at a distance of 10 kpc), the minimum detectable core radius is approximate to 0.004 pc approximate to 0 ''.1 (from star counts) or approximate to 0.12 pc approximate to 2 ''.8 (from brightness profiles).