  Numerical simulations of Milky-Way size Cold Dark Matter (CDM) halos predict
a steeply rising mass function of small dark matter subhalos and a substructure
count that greatly outnumbers the observed satellites of the Milky Way. Several
proposed explanations exist, but detailed comparison between theory and
observation in terms of the maximum circular velocity (Vmax) of the subhalos is
hampered by the fact that Vmax for satellite halos is poorly constrained. We
present comprehensive mass models for the well-known Milky Way dwarf
satellites, and derive likelihood functions to show that their masses within
0.6 kpc (M_0.6) are strongly constrained by the present data. We show that the
M_0.6 mass function of luminous satellite halos is flat between ~ 10^7 and 10^8
M_\odot. We use the ``Via Lactea'' N-body simulation to show that the M_0.6
mass function of CDM subhalos is steeply rising over this range. We rule out
the hypothesis that the 11 well-known satellites of the Milky Way are hosted by
the 11 most massive subhalos. We show that models where the brightest
satellites correspond to the earliest forming subhalos or the most massive
accreted objects both reproduce the observed mass function. A similar analysis
with the newly-discovered dwarf satellites will further test these scenarios
and provide powerful constraints on the CDM small-scale power spectrum and warm
dark matter models.
