Kinematics of the Milky Way disc from the RAVE survey combined with Gaia DR1

Relying on the complementarity of Gaia proper motions with radial velocities of the RAVE survey, we attempt to constrain the kinematics of the Milky Way disc. Based on the population synthesis model, we simulate the observations, applying the detailed selection functions of the observations. The dynamics is described using a global gravitational potential computed from the mass distribution of the population model, approximated by a Stäckel potential (Bienaymé et al. 2015). We explore a set of free parameters (solar motion, age - velocity dispersion of the disc as a function of age, the velocity gradients, vertex deviation) using a Markov Chain Monte Carlo method. We show that the fitted model reproduces very well the radial velocity and proper motion distributions, allowing to constrain the thin and thick disc secular evolution with time.