Measuring Sizes of Marginally Resolved Young Globular Clusters with the Hubble Space Telescope

We present a method for deriving sizes of marginally resolved star clusters from Hubble Space Telescope/WFPC2 observations by fitting King models to observations. We describe results both on simulated images and on observations of young compact clusters in NGC 3597 and NGC 1275. From the simulations, we find that we can measure King model concentrations (c) to an accuracy of about a factor of 2 for all combinations of c and King radius (r₀) of interest if the data have high signal-to-noise ratio (S/N) (>~500 for the integrated brightness). If the concentration is accurately measured, we can measure the King radius accurately. For lower S/N, marginally resolved King profiles suffer from a degeneracy; different values of the concentration give different r₀ but have comparable reduced χ² values. In this case, neither the core radius nor the concentration can be constrained individually, but the half-light radius can be recovered accurately. In NGC 3597, we can differentiate between concentrations only for the very brightest clusters; these suggest a concentration of ~2. Assuming a concentration of 2 for the rest of the objects, we find an average King radius for the clusters in NGC 3597 of 0.7 pc, while the clusters in NGC 1275 have an average radius of 1.1 pc. These are similar to the average core radii for Galactic globular clusters, 0.92 pc. We find average half-light radii of 5.4 and 6.2 pc for the young clusters in NGC 3597 and NGC 1275, respectively, while the average half-light radii of Galactic globular clusters is 3.4 pc. The spread in the derived radial parameters in each cluster system is comparable to that observed in the Galactic globular cluster system. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, operated by the Association of Universities for Research in Astronomy, Inc., under contract to NASA.