Subhalo statistics of galactic halos: beyond the resolution limit
  We study the substructure population of Milky Way (MW)-mass halos in the
$\Lambda$CDM cosmology using a novel procedure to extrapolate subhalo number
statistics beyond the resolution limit of N-body simulations. The technique
recovers the mean and the variance of the subhalo abundance, but not its
spatial distribution. It extends the dynamic range over which precise
statistical predictions can be made by the equivalent of performing a
simulation with 50 times higher resolution, at no additional computational
cost. We apply this technique to MW-mass halos, but it can easily be applied to
halos of any mass. We find up to $20\%$ more substructures in MW-mass halos
than found in previous studies. Our analysis lowers the mass of the MW halo
required to accommodate the observation that the MW has only three satellites
with a maximum circular velocity $V_{max}\ge30 km/s$ in the $\Lambda$CDM
cosmology. The probability of having a subhalo population similar to that in
the MW is $20\%$ for a virial mass, $M_{200}=1\times10^{12} M_\odot$ and
practically zero for halos more massive than $M_{200}=2\times10^{12} M_\odot$.
