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 deprojection 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 −1 and 〈 U 〉 = −9 ± 1 km s −1 , 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 −1 in the mid-plane to 〈 V 〉 = −32 km s −1 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 σ ZZ , which grows from 18 km s −1 ( Z = 0) to 40 km s −1 (at Z = 800 pc). We determine the orientation of the velocity ellipsoid, and find a significant vertex deviation of 20°–25°, 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 toward the Galactic plane, which reaches 20° at Z = 800 pc and which is not easily explained. Finally, we determine the ratio σ 2 ϕϕ /σ 2 RR near the mid-plane, which in the epicyclic approximation implies an almost perfectly flat rotation curve at the solar radius.