The Sizes and Luminosities of Massive Star Clusters

• Published in: The Astrophysical journal 2009-02, Vol.691 (2), p.946-962
• Main Author: Murray, Norman
• Format: Article
• Language: English
• Subjects: Astronomy; Earth, ocean, space; Exact sciences and technology
• ISSN: 0004-637X; 1538-4357
• DOI: 10.1088/0004-637X/691/2/946

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 X 106 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 3 X 106 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 V = M cl/LV when older than ~1 Gyr. Old, optically thick clusters have V ~ M 0.1-0.3 cl. It follows that LV ~ sigma beta , where sigma is the cluster velocity dispersion, and 3.6 beta 4.5. It appears that 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.