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We study the fragmentation of collisional ring galaxies (CRGs) using a linearperturbation analysis that computes the physical conditions of gravitationalinstability, as determined by the balance of self-gravity of the ring againstpressure and Coriolis forces. We adopt our formalism to simulations of CRGs andshow that the analysis can accurately characterise the stability and onset offragmentation, although the linear theory appears to under-predict the numberof fragments of an unstable CRG by a factor of 2. In addition, since theorthodox `density-wave' model is inapplicable to such self-gravitating rings,we devise a simple approach that describes the rings propagating as materialwaves. We find that the toy model can predict whether the simulated CRGsfragment or not using information from their pre-collision states. We alsoapply our instability analysis to a CRG discovered at a high redshift,$z=2.19$. We find that a quite high velocity dispersion is required for thestability of the ring, and therefore the CRG should be unstable to ringfragmentation. CRGs are rarely observed at high redshifts, and this may bebecause CRGs are usually too faint. Since the fragmentation can induce activestar formation and make the ring bright enough to observe, the instabilitycould explain this rarity. An unstable CRG fragments into massive clumpsretaining the initial disc rotation, and thus it would evolve into a clumpygalaxy with a low surface density in an inter-clump region.

Fragmentation of ring galaxies and transformation to clumpy galaxies