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On the non-axisymmetric fragmentation of rings generated by the Secular Gravitational Instability

Ringed structures have been observed in a variety of protoplanetary discs. Among the processes that might be able to generate such features, the Secular Gravitational Instability (SGI) is a possible candidate. It has also been proposed that the SGI might lead to the formation of planetesimals during the non-linear phase of the instability. In this context, we employ two-fluid hydrodynamical simulations with self-gravity to study the non-axisymmetric, non-linear evolution of ringed perturbations that grow under the action of the SGI. We find that the non-linear evolution outcome of the SGI depends mainly on the initial linear growth rate. For SGI growth rates smaller than typically $σ\gtrsim 10^{-4}-10^{-5}Ω$, dissipation resulting from dust feedback introduces a $m=1$ spiral wave in the gas, even for Toomre gas stability parameters $Q_g>2$ for which non-axisymmetric instabilities appear in a purely gaseous disc. This one-armed spiral subsequently traps dust particles until a dust-to-gas ratio $ε\sim 1$ is achieved. For higher linear growth rates, the dust ring is found to undergo gravitational collapse until the bump in the surface density profile becomes strong enough to trigger the formation of dusty vortices through the Rossby Wave Instability (RWI). Enhancements in dust density resulting from this process are found to scale with the linear growth rate, and can be such that the dust density is higher than the Roche density, leading to the formation of bound clumps. Fragmentation of axisymmetric rings produced by the SGI might therefore appear as a possible process for the formation of planetesimals.