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 o bservations. We describe results both on simulated images and on observatio ns 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 (r(0)) of interest if the data have high signal-to-noise ratio (S/N) (greater than or similar to 500 for the integrated brightness). If the concentration is acc urately measured, we can measure the King radius accurately. For lower S/N, marginally resolved King profiles suffer from a degeneracy; different valu es of the concentration give different r(0) but have comparable reduced chi (2) values. In this case, neither the core radius nor the concentration ca n be constrained individually, but the half-light radius can be recovered a ccurately. In NGC 3597, we can differentiate between concentrations only for the very brightest clusters; these suggest a concentration of 2. Assuming a concentr ation 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 G alactic 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 comp arable to that observed in the Galactic globular cluster system.