The Luminosity Function of the Milky Way Satellites

We quantify the detectability of stellar Milky Way 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 towards low luminosities, but may flatten at $M_V \sim -5$; within the uncertainties, the luminosity function can be described by a single power law $dN/dM_{V}= 10 \times 10^{0.1 (M_V+5)}$, spanning luminosities from $M_V=-2$ all the way to the luminosity of the Large Magellanic Cloud. Comparing these results to several semi-analytic galaxy formation models, we find that their predictions differ significantly from the data: either the shape of the luminosity function, or the surface brightness distributions of the models, do not match.