Title:The Kinematics of the Ultra-Faint Milky Way Satellites: Solving the Missing Satellite Problem

Abstract: We present Keck/DEIMOS spectroscopy of stars in 8 of the newly discovered ultra-faint dwarf galaxies around the Milky Way. We measure the velocity dispersions of Canes Venatici I and II, Ursa Major I and II, Coma Berenices, Hercules, Leo IV and Leo T from the velocities of 18 - 214 stars in each galaxy and find dispersions ranging from 3.3 to 7.6 km/s. The 6 galaxies with absolute magnitudes M_V < -4 are highly dark matter-dominated, with mass-to-light ratios approaching 1000. The measured velocity dispersions are inversely correlated with their luminosities, indicating that a minimum mass for luminous galactic systems may not yet have been reached. We also measure the metallicities of the observed stars and find that the 6 brightest of the ultra-faint dwarfs extend the luminosity-metallicity relationship followed by brighter dwarfs by 2 orders of magnitude in luminosity; several of these objects have mean metallicities as low as [Fe/H] = -2.3 and therefore represent some of the most metal-poor known stellar systems. We detect metallicity spreads of up to 0.5 dex in several objects, suggesting multiple star formation epochs. Having established the masses of the ultra-faint dwarfs, we re-examine the missing satellite problem. After correcting for the sky coverage of the SDSS, we find that the ultra-faint dwarfs substantially alleviate the discrepancy between the predicted and observed numbers of satellites around the Milky Way, but there are still a factor of ~4 too few dwarf galaxies over a significant range of masses. We show that if galaxy formation in low-mass dark matter halos is strongly suppressed after reionization, the simulated circular velocity function of CDM subhalos can be brought into approximate agreement with the observed circular velocity function of Milky Way satellite galaxies. [slightly abridged]