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Vortices have long been speculated to play a role in planet formation, viathe collection of dust in the pressure maxima that arise at the cores ofvortices in protoplanetary discs. The question remains however: as dustcollects in the core of a vortex, when does that vortex remain stable and ableto collect further dust, and when and why does it break up? We study thisquestion by running high resolution 2D simulations of dust laden vortices. Byusing the terminal velocity approximation in a local shearing box it waspossible to efficiently run simulations of back-reacting dust in a gas at highresolution. Our results show how the stability of 2D dust laden vortices inprotoplanetary discs depends on their size relative to the disc scale height,as well as the dust coupling. We find small vortices with semiminor axis muchsmaller than the scale height to be stable for the duration of the simulations($t>2000$ orbits). Larger vortices, with semiminor axis smaller than but oforder of the scale height, exhibit a drag instability after undergoing a longperiod of contraction where the core becomes progressively more dust rich. Thelifetime of these vortices depends on the dust size, with larger dust grainscausing the instability to occur sooner. For the size ranges tested in thispaper, $\mu$m to mm sized grains, vortices survived for several hundreds oforbits. The result implies that the stability of vortices formed by verticalshear instability and zombie vortex instability, or the breakup of largervortices through hydrodynamic instabilities, is affected by the presence ofdust in the disc. The lifetimes observed in this paper, while shortened by thepresence of dust for larger vortices, were still long enough to lead toconsiderable dust enrichment in the vortex cores.

Dynamics of Dusty Vortices II: Stability of 2D dust laden vortices