THE SIZES AND LUMINOSITIES OF MASSIVE STAR CLUSTERS

The masses of star clusters range over seven decades, from ten up to one hundred million solar masses. Remarkably, clusters with masses in the range 10(4)-10(6) M-circle dot show no systematic variation of radius with mass. However, recent observations have shown that clusters with M-cl greater than or similar to 3 x 10(6) M-circle dot do show an increase in size with increasing mass. We point out that clusters with M-cl greater than or similar to 10(6) M-circle dot were optically thick to far-infrared radiation when they formed, and explore the hypothesis that the size of clusters with M-cl greater than or similar to 3 x 10(6) M-circle dot is set by a balance between accretion powered radiation pressure and gravity when the clusters formed, yielding a mass-radius relation r(cl) similar to 0.3(M-cl/10(6) M-circle dot)(3/5) pc. We show that the Jeans mass in optically thick objects increases systematically with cluster mass. We argue, by assuming that the break in the stellar initial mass function (IMF) is set by the Jeans mass, that optically thick clusters are born with top heavy IMFs; it follows that they are overluminous compared to optically thin clusters when young, and have a higher mass-to-light ratio. Gamma(V) = M-cl/L-V when older than similar to 1 Gyr. Old, optically thick clusters have. Gamma(V) similar to M-cl(0.1-0.3). It follows that L-V similar to sigma(beta), where sigma is the cluster velocity dispersion, and 3.6 less than or similar to beta less than or similar to 4.5. It appears that Y-V is an increasing function of cluster mass for compact clusters and ultracompact dwarf galaxies. We show that this is unlikely to be due to the presence of nonbaryonic dark matter, by comparing clusters to Milky Way satellite galaxies, which are dark matter dominated. The satellite galaxies appear to have a fixed mass inside a fiducial radius, M(r = r(0)) = constant.