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), N_GC, is an excellent tracer of their host galaxy's halo virial mass, M_vir. The simple linear relation M_vir = 5 × 10⁹ M_⊙ × N_GC fits the data perfectly from M_vir = 10¹⁰ M_⊙ to M_vir = 2 × 10¹⁵ M_⊙. This result is independent of galaxy morphology and extends statistically into the dwarf galaxy regime with M_vir = 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 M_vir. 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 N_GC with increasing virial mass $\delta {N}_{\mathrm{GC}}/{N}_{\mathrm{GC}}\sim {M}_{\mathrm{vir}}^{-1/2}$ 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.