  We study the luminosity function and the radial distribution of satellite
galaxies within Milky Way sized haloes as predicted in Cold Dark Matter based
models of galaxy formation, making use of numerical N-body techniques as well
as three different semi-analytic model (SAMs) galaxy formation codes. We
extract merger trees from very high-resolution dissipationless simulations of
four Galaxy-sized DM haloes, and use these as common input for the
semi-analytic models. We present a detailed comparison of our predictions with
the observational data recently obtained on the Milky Way satellite luminosity
function (LF). We find that semi-analytic models with rather standard
astrophysical ingredients are able to reproduce the observed luminosity
function over six orders of magnitude in luminosity, down to magnitudes as
faint as M_V=-2. We also perform a comparison with the actual observed number
of satellites as a function of luminosity, by applying the selection criteria
of the SDSS survey to our simulations instead of correcting the observations
for incompleteness. Using this approach we again find good agreement for both
the luminosity and radial distributions of MW satellites. We investigate which
physical processes in our models are responsible for shaping the predicted
satellite LF, and find that tidal destruction, suppression of gas infall by a
photo-ionizing background, and supernova feedback all make important
contributions. We conclude that the number and luminosity of Milky Way
satellites can be naturally accounted for within the (Lambda) Cold Dark Matter
paradigm, and this should no longer be considered a problem.
