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 Suns 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_{phiphi}/sigma^2_{RR} near the mid-plane, which in the epicyclic approximation implies an almost perfectly flat rotation curve at the Solar radius.