Cardinal kinematics: I. Rotation fields of the APOGEE Survey
  Correlations between stellar chemistry and kinematics have long been used to gain insight into the evolution of the Milky Way Galaxy. Orbital angular momentum is a key physical parameter and it is often estimated from three-dimensional space motions. We here demonstrate the lower uncertainties that can be achieved in the estimation of one component of velocity through selection of stars in key directions and use of line-of-sight velocity alone (i.e. without incorporation of proper motion data). In this first paper we apply our technique to stars observed in the direction of Galactic rotation in the APOGEE survey. We first derive the distribution of azimuthal velocities, $v_\phi$, then from these and observed radial coordinates, estimate the stellar guiding centre radii, $R_g$, within $6.9\leq R \leq 10$ kpc with uncertainties smaller than (or of the order of) 1kpc. We show that there is no simple way to select a clean stellar sample based on low errors on proper motions and distances to obtain high-quality 3D velocities and hence one should pay particular attention when trying to identify kinematically peculiar stars based on velocities derived using the proper motions. Using our azimuthal velocity estimations, we investigate the joint distribution of elemental abundances and rotational kinematics free from the blurring effects of epicyclic motions, and we derive the $\partial v_\phi / \partial R_g$ trends for the thin and thick discs as a function of radius. Our analysis provides further evidence for radial migration within the thin disc and hints against radial migration playing a significant role in the evolution of the thick disc. 
Georges Kordopatis, Rosemary F.G. Wyse, Cristina Chiappini, Ivan   Minchev, Friedrich Anders, Basilio Santiago
astro-ph.GA