Context. Size measurements of young star clusters are valuable tools to put constraints on the formation and early dynamical evolution of star clusters. Aims. We use HST/ACS observations of the spiral galaxy M51 in F435W, F555W and F814W to select a large sample of star clusters with accurate effective radius measurements in an area covering the complete disc ofM51.We present the dataset and study the radius distribution and relations between radius, colour, arm/interarm region, galactocentric distance, mass and age. Methods. We select a sample of 7698 (F435W), 6846 (F555W) and 5024 (F814W) slightly resolved clusters and derive their effective radii (Reff) by fitting the spatial profiles with analytical models convolved with the point spread function. The radii of 1284 clusters are studied in detail. Results. We find cluster radii between 0.5 and ∼10 pc, and one exceptionally large cluster candidate with Reff = 21.6 pc. The median Reff is 2.1 pc. We find 70 clusters in our sample which have colours consistent with being old GC candidates and we find 6 new “faint fuzzy” clusters in, or projected onto, the disc of M51. The radius distribution can not be fitted with a power law similar to the one for star-forming clouds. We find an increase in Reff with colour as well as a higher fraction of clusters with B−V >∼ 0.05 in the interarm regions. We find a correlation between Reff and galactocentric distance (RG) of the formReff ∝ R0.12±0.02 G , which is considerably weaker than the observed correlation for old Milky Way GCs. We find weak relations between cluster luminosity and radius: Reff ∝ L0.15±0.02 for the interarm regions and Reff ∝ L−0.11±0.01 for the spiral arm regions, but we do not observe a correlation between cluster mass and radius. Conclusions. The observed radius distribution indicates that shortly after the formation of the clusters from a fractal gas, the radii of the clusters have changed in a non-uniform way. We find tentative evidence suggesting that clusters in spiral arms are more compact
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