The vertical effects of disc non-axisymmetries from perturbation theory:
  the case of the Galactic bar
  Evidence for non-zero mean stellar velocities in the direction perpendicular
to the Galactic plane has been accumulating from various recent large
spectroscopic surveys. Previous analytical and numerical work has shown that a
"breathing mode" of the Galactic disc, similar to what is observed in the Solar
vicinity, can be the natural consequence of a non-axisymmetric internal
perturbation of the disc. Here we provide a general analytical framework, in
the context of perturbation theory, allowing us to compute the vertical bulk
motions generated by a single internal perturber (bar or spiral pattern). In
the case of the Galactic bar, we show that these analytically predicted bulk
motions are well in line with the outcome of a numerical simulation. The mean
vertical motions induced by the Milky Way bar are small (mean velocity of less
than 1 km/sec) and cannot be responsible alone for the observed breathing mode,
but they are existing. Our analytical treatment is valid close to the plane for
all the non-axisymmetric perturbations of the disc that can be described by
small-amplitude Fourier modes. Further work should study how the coupling of
multiple internal perturbers and external perturbers is affecting the present
analytical results.
