The kinematics of late type stars in the solar cylinder studied with
  SDSS data
  We study the velocity distribution of Milky Way disk stars in a
kiloparsec-sized region around the Sun, based on ~ 2 million M-type stars from
DR7 of SDSS, which have newly re-calibrated absolute proper motions from
combining SDSS positions with the USNO-B catalogue. We estimate photometric
distances to all stars, accurate to ~ 20 %, and combine them with the proper
motions to derive tangential velocities for this kinematically unbiased sample
of stars. Based on a statistical de-projection method we then derive the
vertical profiles (to heights of Z = 800 pc above the disk plane) for the first
and second moments of the three dimensional stellar velocity distribution. We
find that <W> = -7 +/- 1 km/s and <U> = -9 +/- 1 km/s, independent of height
above the mid-plane, reflecting the Sun's motion with respect to the local
standard of rest. In contrast, <V> changes distinctly from -20 +/- 2 km/s in
the mid-plane to <V> = -32 km/s at Z = 800 pc, reflecting an asymmetric drift
of the stellar mean velocity that increases with height. All three components
of the M-star velocity dispersion show a strong linear rise away from the
mid-plane, most notably \sigma_{ZZ}, which grows from 18 km/s (Z = 0) to 40
km/s (at Z = 800 pc). We determine the orientation of the velocity ellipsoid,
and find a significant vertex deviation of 20 to 25 degrees, which decreases
only slightly to heights of Z = 800 pc. Away from the mid-plane, our sample
exhibits a remarkably large tilt of the velocity ellipsoid towards the Galactic
plane, which reaches 20 deg. at Z = 800 pc and which is not easily explained.
Finally, we determine the ratio \sigma^2_{\phi\phi}/\sigma^2_{RR} near the
mid-plane, which in the epicyclic approximation implies an almost perfectly
flat rotation curve at the Solar radius.
