729 research outputs found
Curvature and Acoustic Instabilities in Rotating Fluid Disks
The stability of a rotating fluid disk to the formation of spiral arms is
studied in the tightwinding approximation in the linear regime. The dispersion
relation for spirals that was derived by Bertin et al. is shown to contain a
new, acoustic instability beyond the Lindblad resonances that depends only on
pressure and rotation. In this regime, pressure and gravity exchange roles as
drivers and inhibitors of spiral wave structures. Other instabilities that are
enhanced by pressure are also found in the general dispersion relation by
including higher order terms in the small parameter 1/kr for wavenumber k and
radius r. These instabilities are present even for large values of Toomre's
parameter Q. Unstable growth rates are determined in four cases: a
self-gravitating disk with a flat rotation curve, a self-gravitating disk with
solid body rotation, a non-self-gravitating disk with solid body rotation, and
a non-self-gravitating disk with Keplerian rotation. The most important
application appears to be as a source of spiral structure, possibly leading to
accretion in non-self-gravitating disks, such as some galactic nuclear disks,
disks around black holes, and proto-planetary disks. All of these examples have
short orbital times so the unstable growth time can be small.Comment: 30 pages, 5 figures, scheduled for ApJ 520, August 1, 199
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