Curvature and Acoustic Instabilities in Rotating Fluid Disks

The stability of a rotating fluid disk to the formation of spiral arms isstudied in the tightwinding approximation in the linear regime. The dispersionrelation for spirals that was derived by Bertin et al. is shown to contain anew, acoustic instability beyond the Lindblad resonances that depends only onpressure and rotation. In this regime, pressure and gravity exchange roles asdrivers and inhibitors of spiral wave structures. Other instabilities that areenhanced by pressure are also found in the general dispersion relation byincluding higher order terms in the small parameter 1/kr for wavenumber k andradius r. These instabilities are present even for large values of Toomre'sparameter Q. Unstable growth rates are determined in four cases: aself-gravitating disk with a flat rotation curve, a self-gravitating disk withsolid body rotation, a non-self-gravitating disk with solid body rotation, anda non-self-gravitating disk with Keplerian rotation. The most importantapplication appears to be as a source of spiral structure, possibly leading toaccretion in non-self-gravitating disks, such as some galactic nuclear disks,disks around black holes, and proto-planetary disks. All of these examples haveshort orbital times so the unstable growth time can be small.Comment: 30 pages, 5 figures, scheduled for ApJ 520, August 1, 199