Kinematic Modeling of the Milky Way Using the RAVE and GCS Stellar Surveys

We investigate the kinematic parameters of the Milky Way disk using the Radial Velocity Experiment (RAVE) and Geneva-Copenhagen Survey (GCS) stellar surveys. We do this by fitting a kinematic model to the data and taking the selection function of the data into account. For stars in the GCS we use all phase-space coordinates, but for RAVE stars we use only (l, b, v los). Using the Markov Chain Monte Carlo technique, we investigate the full posterior distributions of the parameters given the data. We investigate the age-velocity dispersion relation for the three kinematic components (σ R , σphi, σ z ), the radial dependence of the velocity dispersions, the solar peculiar motion (U ⊙, V ⊙, W ⊙), the circular speed Θ0 at the Sun, and the fall of mean azimuthal motion with height above the midplane. We confirm that the Besançon-style Gaussian model accurately fits the GCS data but fails to match the details of the more spatially extended RAVE survey. In particular, the Shu distribution function (DF) handles noncircular orbits more accurately and provides a better fit to the kinematic data. The Gaussian DF not only fits the data poorly but systematically underestimates the fall of velocity dispersion with radius. The radial scale length of the velocity dispersion profile of the thick disk was found to be smaller than that of the thin disk. We find that correlations exist between a number of parameters, which highlights the importance of doing joint fits. The large size of the RAVE survey allows us to get precise values for most parameters. However, large systematic uncertainties remain, especially in V ⊙ and Θ0. We find that, for an extended sample of stars, Θ0 is underestimated by as much as 10% if the vertical dependence of the mean azimuthal motion is neglected. Using a simple model for vertical dependence of kinematics, we find that it is possible to match the Sgr A* proper motion without any need for V ⊙ being larger than that estimated locally by surveys like GCS