The Milky Way Tomography with SDSS. III. Stellar Kinematics

We study Milky Way kinematics using a sample of 18.8 million main-sequence stars with r < 20 and proper-motion measurements derived from Sloan Digital Sky Survey (SDSS) and POSS astrometry, including ~170,000 stars with radial-velocity measurements from the SDSS spectroscopic survey. Distances to stars are determined using a photometric-parallax relation, covering a distance range from ~100 pc to 10 kpc over a quarter of the sky at high Galactic latitudes (|b|>20°). We find that in the region defined by 1 kpc <Z< 5 kpc and 3 kpc <R< 13 kpc, the rotational velocity for disk stars smoothly decreases, and all three components of the velocity dispersion increase, with distance from the Galactic plane. In contrast, the velocity ellipsoid for halo stars is aligned with a spherical coordinate system and appears to be spatially invariant within the probed volume. The velocity distribution of nearby (Z < 1 kpc) K/M stars is complex, and cannot be described by a standard Schwarzschild ellipsoid. For stars in a distance-limited subsample of stars (<100 pc), we detect a multi-modal velocity distribution consistent with that seen by HIPPARCOS. This strong non-Gaussianity significantly affects the measurements of the velocity-ellipsoid tilt and vertex deviation when using the Schwarzschild approximation. We develop and test a simple descriptive model for the overall kinematic behavior that captures these features over most of the probed volume, and can be used to search for substructure in kinematic and metallicity space. We use this model to predict further improvements in kinematic mapping of the Galaxy expected from Gaia and the Large Synoptic Survey Telescope.