We study the luminosity function (LF) and the radial distribution of satellite galaxies within Milky Way (MW) 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 models (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 SAMs. We present a detailed comparison of our predictions with the observational data recently obtained on the MW satellite LF. We find that SAMs with rather standard astrophysical ingredients are able to reproduce the observed LF over six orders of magnitude in luminosity, down to magnitudes as faint as MV = -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 photoionizing background, and supernova feedback all make important contributions. We conclude that the number and luminosity of MW satellites can be naturally accounted for within the (Λ)cold dark matter paradigm, and this should no longer be considered a problem.
