2009ApJ...691..946M

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 10⁴-10⁶ M_☉ show no systematic variation of radius with mass. However, recent observations have shown that clusters with M_cl≳ 3 x10⁶ M_☉ do show an increase in size with increasing mass. We point out that clusters with M_cl≳ 10⁶ M_☉ were optically thick to far-infrared radiation when they formed, and explore the hypothesis that the size of clusters with M_cl≳ 3x10⁶ M_☉ is set by a balance between accretion powered radiation pressure and gravity when the clusters formed, yielding a mass-radius relation r_cl∼ 0.3(M_cl/10⁶ M_☉)^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 Υ_V= M_cl/L_V when older than ∼1 Gyr. Old, optically thick clusters have Υ_V∼ M ^0.1–0.3_cl. It follows that L_V∼ σ^β, where σ is the cluster velocity dispersion, and 3.6 ≲ β ≲ 4.5. It appears that Υ_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 = r₀) = constant.