A recurrent spiral instability cycle in self-gravitating particle discs

We have discovered a new type of small-amplitude spiral mode in collisionless, self-gravitating discs. It is a fierce dynamical instability which appears to be driven by a trough, or 'groove', in the phase space density at a particular angular momentum. At large amplitude, the wave scatters particles at its Lindblad resonances, which are sufficiently well localized to create new grooves in phase space at which new linear instabilities of the same type can develop. Resonant scattering also leads to a general increase in non-circular motions within the disc, so the recurrent cycle ends, in the absence of cooling, when the entire disc is so hot that coherent waves can no longer be sustained. Discs that are cooled, however, should support this instability cycle indefinitely.