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.
