The origin of the vertical corrugation in rotating galactic discs of a finite thickness composed of stars

ABSTRACT The origin of the vertical corrugation of odd symmetry to the mean horizontal plane, revealed in disc galaxies, including the Milky Way Galaxy, has not yet been explained. Observationally, the corrugation can be interpreted as a wave propagating towards the outer disc. To explain the phenomenon, we study the development of collective oscillations in a galactic stellar disc using a linear theory based on the Poisson equation for the gravitational potential and the Boltzmann kinetic equation for the distribution function of stars. A 3D, differentially rotating, self-gravitating disc is considered, taking into account the effects of the noncircular motion of stars. A dispersion relation is derived to describe the dynamics of spontaneous-bending gravity perturbations that develop in the system with or without an inertial halo (dark matter), in isolation. These antisymmetric perturbations make the system ripple, compressing/dispersing the material perpendicular to the plane and propagating in the horizontal directions. The excitation of oscillatory growing bending waves via the resonant wave–star interaction, formally resembling inverse Landau damping, is proposed to be responsible for the vertically short $\sim 200\text{-}300$ pc but radially long $\sim 2\text{-}3$ kpc wavelength corrugation.