Quasi-stationary distribution function of the rotating collisionless gravitating disk

We have constructed a quasi-stationary distribution function of the rotating collisionless gravitating disk with an oblate spheroid-like structure at the center. The construction technique is based on the numerical tracking of the evolution of the initially non-stationary thin disk on time scales of dozens of rotations. We show that a distribution function can be approximated using the axially symmetric density σ(r, z) and the velocity dispersions cr(r), cφ(r), cz(r). The numerical analysis of the disk stability in the vertical direction has been made. It was found that a forced compression of the disk height implies the development of a bending instability.