A Proposed Functional Form for the Upper Mass Spectrum of Old Globular Cluster Systems

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Abstract
The bright end of the luminosity function of old globular cluster systems in five E and spiral galaxies is fitted with an underlying mass spectrum of the form dN/dm ∝ m-3/2 exp(-m/mc) under the assumption that the mass-to-light ratio is a constant within each system. The globular cluster systems studied are those of M87, NGC 5846, NGC 4472, the Milky Way, and M31. In contrast to young cluster systems with power-law mass distributions, all of the old globular cluster systems are well fitted by a distribution function with an exponential cutoff as described by the above equation. The cutoff mass is in the range of 106 M☉ ≤ mc ≤ 5 × 106 M☉ and varies with the mass of the galaxy and/or the cluster environment. The different shapes of the luminosity functions of old and young cluster systems suggest that they formed in different environments. The proposed mass spectrum for the old cluster systems has the same form as that expected for an ensemble of interacting gas clouds that follow a mass-radius relation of the form M ∝ R2, as is observed in galaxies such as the Milky Way, and whose masses are governed by the process of cloud coalescence and coagulation. If globular cluster protoclouds were built up by this mechanism and if the clusters formed on short timescales, with masses that reflected the mass spectrum of their parent clouds, then the bright end of old globular cluster luminosity functions can naturally be accounted for.