Generation of spiral bending waves in a rotating galactic stellar disk of finite thickness

A self-gravitating rotation-flattened galactic disk of finite thickness composed of identical stars is considered, taking into account the stellar random motions. A dispersion relation is derived to describe the dynamics of spontaneous bending gravity perturbations developing in the system by exploring a linear kinetic theory based on the Poisson and collisionless Boltzmann equations. These perturbations, or vertical corrugations, compress/disperse the medium in the direction normal to the midplane and propagate horizontally, making the disk rippled. The self-excitation of oscillatory-growing, spiral bending waves via the wave-star resonant interaction is proposed to be responsible for the vertically short ( ~ 200--300 ∼ 200 – 300 pc), still radially long ( ~ 2--3 ∼ 2 – 3 kpc) wavelength corrugation. It is a collective effect, meaning it arises from the interaction of many stars with the perturbation’s gravitational field. Self-gravity effects, acting both in the disk’s vertical dimension and in dimensions parallel to the plane, are critically important for the formation and evolution of weakly unstable waves. The free kinetic energy associated with the disk’s circular rotation is one possible source of the wave energy’s growth. Such ripple structures antisymmetric to the midplane are often observed in disk galaxies seen edge-on, even in isolation, including the Milky Way.