The Oort constants measured from proper motions

The Oort constants describe the local spatial variations of the stellar streaming field. The classic way for their determination employs their effect on stellar proper motions. We discuss various problems arising in this procedure. A large, hitherto apparently overlooked, source of potential systematic error arises from longitudinal variations of the mean stellar parallax, caused by intrinsic density inhomogeneities and interstellar extinction. Together with the reflex of the solar motion, these variations by mode mixing create contributions to the longitudinal proper motions (mu) over bar (l)* (l) that are indistinguishable from the Oort constants at less than or similar to20% of their amplitude. Fortunately, we can correct for this mode mixing using the latitudinal proper motions mu(b)(l). We use about 10(6) stars from the ACT/Tycho-2 catalogs brighter than V approximate to 11 with median proper-motion error of approximate to3 mas yr(-1), taking every precaution to avoid or correct for the various sources of systematic error, significant deviations from expectations based on a smooth axisymmetric equilibrium, in particular nonzero C for old red giant stars. We also find variations of the Oort constants with the mean color, which correlate nicely with the asymmetric drift of the subsample considered. In addition, these correlations are different in nature than those expected for an axisymmetric galaxy. The most reliable tracers for the true Oort constants are red giants, which are old enough to be in equilibrium and distant enough to be unaffected by possible local anomalies. For these stars we find, after correction for mode mixing and the axisymmetric asymmetric-drift effects, A approximate to 16, Bapproximate to - 17, A - B approximate to 33, and C approximate to - 10 kin s(-1) kpc(-1) with internal errors of about 1-2 and external error of perhaps the same order. These values are consistent with our knowledge of the Milky Way (flat rotation curve and Omega = A - B approximate to 28 +/- 2), based on observations made with the ESA Hipparcos astrometry satellite.