Perturbed distribution functions with accurate action estimates for the Galactic disc

In the Gaia era, understanding effects of perturbations Galactic disc is major importance in context dynamical modelling. this theoretical paper we extend previous work which, making use epicyclic approximation, linearized Boltzmann equation had been used to explicitly compute, away from resonances, perturbed distribution function a thin-disc population presence non-axisymmetric perturbation constant amplitude. Here improve framework two distinct ways new code that present. First, better estimates for action-angle variables quasi-circular orbits, computed AGAMA software, and present an efficient routine numerically re-express any perturbing potential these coordinates with typical accuracy at per cent level. The more accurate action allows us identify resonances such as outer 1:1 bar resonance higher azimuthal velocities than Lindblad (OLR), our results well above plane, where show how they differ approximation. particular, displacement velocity space height can principle constrain 3D structure potential. Second, allow be time dependent, thereby allowing model effect transient spiral arms or growing bar. tools presented here will useful thorough analytical modelling complex stars measured by past upcoming data releases.