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High-precision Dark Halo Virial Masses from Globular Cluster Numbers: Implications for Globular Cluster Formation and Galaxy Assembly

We confirm that the number of globular clusters (GCs), NGC, is an excellent tracer of their host galaxy’s halo virial mass, Mvir. The simple linear relation Mvir = 5 × 109 M⊙ × NGC fits the data perfectly from Mvir = 1010 M⊙ to Mvir = 2 × 1015 M⊙. This result is independent of galaxy morphology and extends statistically into the dwarf galaxy regime with Mvir = 108–1010 M⊙, including the extreme ultra diffuse galaxy DF44. As this correlation does not depend on GC mass, it is ideally suited for high-precision determinations of Mvir. The linearity is most simply explained by cosmological merging of a high-redshift halo seed population that hosted on average one GC per 5 × 108 M⊙ of dark matter. We show that hierarchical merging is also extremely powerful in restoring a linear correlation and erasing signatures of even a strong secular evolution of GC systems. The cosmological merging scenario also implies a strong decline of the scatter in NGC with increasing virial mass in contrast with the observations that show a roughly constant scatter, independent of virial mass. This discrepancy can be explained if errors in determining virial masses from kinematical tracers and gravitational lensing are on the order of a factor of 2. GCs in dwarf satellite galaxies pose a serious problem for high-redshift GC formation scenarios; the dark halo masses of dwarf galaxies hosting GCs therefore might need to be an order of magnitude larger than currently estimated.