Missing Satellites Problem: Completeness Corrections to the Number of Satellite Galaxies in the Milky Way are Consistent with Cold Dark Matter Predictions

A critical challenge to the cold dark matter (CDM) paradigm is that there are fewer satellites observed around the Milky Way than found in simulations of dark matter substructure. We show that there is a match between the observed satellite counts corrected by the detection efficiency of the Sloan Digital Sky Survey (for luminosities L greater than or similar to 340 L-circle dot) and the number of luminous satellites predicted by CDM, assuming an empirical relation between stellar mass and halo mass. The "missing satellites problem," cast in terms of number counts, is thus solved. We also show that warm dark matter models with a thermal relic mass smaller than 4 ke V are in tension with satellite counts, putting pressure on the sterile neutrino interpretation of recent x-ray observations. Importantly, the total number of Milky Way satellites depends sensitively on the spatial distribution of satellites, possibly leading to a "too many satellites" problem. Measurements of completely dark halos below 10(8) M-circle dot, achievable with substructure lensing and stellar stream perturbations, are the next frontier for tests of CDM.