Non-linear violent disc instability with high Toomre's Q in high-redshift clumpy disc galaxies

We utilize zoom-in cosmological simulations to study the nature of violent disc instability (VDI) in clumpy galaxies at high redshift, $z=1$--$5$. Our simulated galaxies are not in the ideal state assumed in Toomre instability, of linear fluctuations in an isolated, uniform, rotating disk. There, instability is characterised by a $Q$ parameter below unity, and lower when the disk is thick. Instead, the high-redshift discs are highly perturbed. Over long periods they consist of non-linear perturbations, compact massive clumps and extended structures, with new clumps forming in inter-clump regions. This is while the galaxy is subject to frequent external perturbances. We compute the local, two-component $Q$ parameter for gas and stars, smoothed on a $\sim1~{\rm kpc}$ scale to capture clumps of $10^{8-9}~{\rm M}_\odot$. The $Q<1$ regions are confined to collapsed clumps due to the high surface density there, while the inter-clump regions show $Q$ significantly higher than unity. Tracing the clumps back to their relatively smooth Lagrangian patches, we find that $Q$ prior to clump formation typically ranges from unity to a few. This is unlike the expectations from standard Toomre instability. We discuss possible mechanisms for high-$Q$ clump formation, e.g. rapid turbulence decay leading to small clumps that grow by mergers, non-axisymmetric instability, or clump formation induced by non-linear perturbations in the disk. Alternatively, the high-$Q$ non-linear VDI may be stimulated by the external perturbations such as mergers and counter-rotating streams. The high $Q$ may represent excessive compressive modes of turbulence, possibly induced by tidal interactions.