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 parametrized by the Oort constants A and B - depend on the local gradient of the rotation curve as well as its absolute value (Oo), and the Sun's distance to the Galactic Centre (Ro) 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 0.9R(0) and 1.2R(0) the Oort functions A(R) and B(R) differ significantly from the general similar to Theta(0)/R dependence. Various previously inexplicable observations are shown to be consistent with these new predictions. For example, these models may explain the similar to 40 per cent difference between the values for 2AR(0) derived from radial velocity data originating in the inner and outer Galaxy. 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 (R-0 = 7.1 +/- 0.4 kpc) and local circular speed (Theta(0) = 184 +/- 8 km s(-1)). With these Galactic constants the rotation curve of the Milky Way declines slowly in the outer Galaxy; V-rot(20 kpc) = 166 km s(-1). Our low value for the distance to the Galactic Centre agrees well with the only direct determination of Ro (7.2 +/- 0.7 kpc). Using these Galactic constants, we also find that the proper motion of Sgr A* is consistent with the observational constraints. Simple analytic arguments as well as detailed calculations show that the radial velocities and proper motions of our best-fitting model are entirely consistent with the radial velocities of Cepheids and the Hipparcos measurements of their proper motions.