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$_{vir} = 5 \times 10^9$ M$_{\odot} \times$ N$_{GC}$ fits the data perfectly from M$_{vir} = 10^{10}$ M$_{\odot}$ to M$_{vir} = 2 \times 10^{15}$ M$_{\odot}$. This result is independent of galaxy morphology and extends statistically into the dwarf galaxy regime with M$_{vir} = 10^8 - 10^{10}$ M$_{\odot}$, 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 $5 \times 10^8$ M$_{\odot}$ 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 $\delta N_{GC}/N_{GC} \sim M_{vir}^{-1/2}$ 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.