  We use the Aquarius simulations to show that the most massive subhalos in
galaxy-mass dark matter halos in LCDM are grossly inconsistent with the
dynamics of the brightest Milky Way dwarf spheroidal galaxies. While the
best-fitting hosts of the dwarf spheroidals all have 12 < Vmax < 25 km/s, LCDM
simulations predict at least ten subhalos with Vmax > 25 km/s. These subhalos
are also among the most massive at earlier times, and significantly exceed the
UV suppression mass back to z ~ 10. No LCDM-based model of the satellite
population of the Milky Way explains this result. The problem lies in the
satellites' densities: it is straightforward to match the observed Milky Way
luminosity function, but doing so requires the dwarf spheroidals to have dark
matter halos that are a factor of ~5 more massive than is observed. Independent
of the difficulty in explaining the absence of these dense, massive subhalos,
there is a basic tension between the derived properties of the bright Milky Way
dwarf spheroidals and LCDM expectations. The inferred infall masses of these
galaxies are all approximately equal and are much lower than standard LCDM
predictions for systems with their luminosities. Consequently, their implied
star formation efficiencies span over two orders of magnitude, from 0.2% to 20%
of baryons converted into stars, in stark contrast with expectations gleaned
from more massive galaxies. We explore possible solutions to these problems
within the context of LCDM and find them to be unconvincing. In particular, we
use controlled simulations to demonstrate that the small stellar masses of the
bright dwarf spheroidals make supernova feedback an unlikely explanation for
their low inferred densities.
