Velocity-Anisotropy-Driven Bending Instability in the Galactic Stellar Disk

Motivated by the results of a recent ultra-high-resolution simulation, which discovers the disk bending instability in a regime conventional thought to be stable, we analyze an idealized galactic stellar disk against such an instability, and obtain a reasonable agreement with the simulation results. The nature of this unstable bending perturbations differs from that predicted by Toomre, in that they tend to be of long wavelength. The success of our analysis relies fundamentally on the determination of two equations of states pertaining to two adiabatic invariants of the three-dimensional stellar motion in a disk. We find that the disk can be subject to the bending instability when β/Q is greater than unity, where β is the velocity anisotropy and the Toomre Q represents the ratio of disk kinetic energy to gravitational potential energy.

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