Refining the Oort and Galactic constants

The local stellar kinematics of the Milky Way offer a useful tool for studying the rotation curve of the Galaxy. These kinematics – usually parameterized by the Oort constants A and B – depend on the local gradient of the rotation curve as well as its absolute value (Θ0), and the Sun’s distance to the Galactic center (R0). The density of interstellar gas in the Milky Way is shown to vary non-monotonically with radius, and so contributes significantly to the local gradient of the rotation curve. We have therefore calculated mass models for the Milky Way that include this component, and have derived the corresponding radial variation in the Oort constants. Between 0.9R0 and 1.2R0 the Oort functions A(R) and B(R) differ significantly from the general ∼ Θ0/R dependence. Various previously-inexplicable observations are shown to be consistent with these new predictions. For example, these models may explain the ∼40% difference between the values for 2AR0 derived from radial velocity data originating in the inner and outer Galaxy (Merrifield 1992). They also go some way toward explaining the different shapes of the velocity ellipsoids of giant and dwarf stars in the solar neighbourhood. However, a consistent picture only emerges if one adopts small values for the radius of the solar circle (R0 = 7.1 ± 0.4 kpc) and local circular speed (Θ0 = 184 ± 8 km s). With these Galactic constants the Milky Way’s rotation curve declines slowly in the outer Galaxy; Vrot(20 kpc) = 166 km s . Our low value for the distance to the Galactic center agrees well with the only direct determination of R0 (7.2 ± 0.7 kpc, Reid 1993). Using these Galactic constants, we find that the proper motion of Sgr A∗ is consistent with the observational constraints (Backer & Sramek 1987; Backer 1996; Reid 1998). Simple analytic arguments as well as detailed calculations show that the radial velocities and proper motions of our best fit model are entirely consistent with the radial velocities of Cepheids (Pont, Mayor & Burki 1994) and the Hipparcos measurements of their proper motions (Feast & Whitelock 1997).