The stability of accretion tori. V - Unstable modes and avoided crossings in extended, self-gravitating annuli

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Abstract
The dynamical evolution of 2D, differentially rotating, self-gravitating annuli is studied by investigating systems having arbitrarily large radial thickness and orbiting around a central mass. Such extended annuli are idealized models of thick, pressure-supported accretion disks. Linear growth rates and eigenfunction characteristics of the different modes are calculated through a solution of the linearized fluid and Poisson equations. In contrast to the results obtained for slender annuli, the I mode instability survives in purely self-gravitating extended annuli without a central mass. This mode is not symmetric across the pressure maximum but has corotation only in the vicinity of the outer edge. Neutral acoustic modes and neutral gravity modes undergo deflections called 'avoided crossings' right outside the outer edge.

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