The Missing Massive Satellites of the Milky Way
  Recent studies suggest that only three of the twelve brightest satellites of
the Milky Way (MW) inhabit dark matter halos with maximum circular velocity,
V_max, exceeding 30km/s. This is in apparent contradiction with the LCDM
simulations of the Aquarius Project, which suggest that MW-sized halos should
have at least 8 subhalos with V_max>30km/s. The absence of luminous satellites
in such massive subhalos is thus puzzling and may present a challenge to the
LCDM paradigm. We note, however, that the number of massive subhalos depends
sensitively on the (poorly-known) virial mass of the Milky Way, and that their
scarcity makes estimates of their abundance from a small simulation set like
Aquarius uncertain. We use the Millennium Simulation series and the invariance
of the scaled subhalo velocity function (i.e., the number of subhalos as a
function of \nu, the ratio of subhalo V_max to host halo virial velocity,
V_200) to secure improved estimates of the abundance of rare massive
subsystems. In the range 0.1<\nu<0.5, N_sub(>\nu) is approximately
Poisson-distributed about an average given by <N_sub>=10.2x(\nu/0.15)^(-3.11).
This is slightly lower than in Aquarius halos, but consistent with recent
results from the Phoenix Project. The probability that a LCDM halo has 3 or
fewer subhalos with V_max above some threshold value, V_th, is then
straightforward to compute. It decreases steeply both with decreasing V_th and
with increasing halo mass. For V_th=30km/s, ~40% of M_halo=10^12 M_sun halos
pass the test; fewer than 5% do so for M_halo>= 2x10^12 M_sun; and the
probability effectively vanishes for M_halo>= 3x 10^12 M_sun. Rather than a
failure of LCDM, the absence of massive subhalos might simply indicate that the
Milky Way is less massive than is commonly thought.
