The luminosity function of the Milky Way satellites

We quantify the detectability of stellar MilkyWay satellites in the Sloan Digital Sky Survey (SDSS) Data Release 5. We show that the effective search volumes for the recently discovered SDSS satellites depend strongly on their luminosity, with their maximum distance, D-max, substantially smaller than the Milky Way halo's virial radius. Calculating the maximum accessible volume, V-max, for all faint detected satellites allows the calculation of the luminosity function for Milky Way satellite galaxies, accounting quantitatively for their detectability. We find that the number density of satellite galaxies continues to rise toward low luminosities, but may flatten at M-V similar to -5; within the uncertainties, the luminosity function can be described by a single power law dN/dM(V) = 10 x 10(0.1( MV+5)), spanning luminosities from M-V = 2 all the way to the luminosity of the Large Magellanic Cloud. In comparing these results to several semianalytic galaxy formation models, we find that their predictions differ significantly from the data: either the shape of the luminosity function or the model's surface brightness distribution does not match.