Self-organisation in protoplanetary discs Global, non-stratified Hall-MHD simulations

Context. Recent observations have revealed organised structures in protoplanetary discs, such as axisymmetric rings or horseshoe concentrations, evocative of large-scale vortices. These structures are often interpreted as the result of planet-disc interactions. However, these discs are also known to be unstable to the magneto-rotational instability (MRI) which is believed to be one of the dominant angular momentum transport mechanism in these objects. It is therefore natural to ask whether the MRI itself could produce these structures without invoking planets. Aims. The nonlinear evolution of the MRI is strongly affected by the low ionisation fraction in protoplanetary discs. The Hall effect in particular, which is dominant in dense and weakly ionised parts of these objects, has been shown to spontaneously drive self-organising flows in local, shearing box simulations. Here, we investigate the behaviour of global MRI-unstable disc models dominated by the Hall effect and characterise their dynamics. Methods. We validated our implementation of the Hall effect into the PLUTO code with predictions from a spectral method in cylindrical geometry. We then performed 3D unstratified Hall-MHD simulations of Keplerian discs for a broad range of Hall, Ohmic, and ambipolar Elsasser numbers. Results. We confirm the transition from a turbulent to an organised state as the intensity of the Hall effect is increased. We observe the formation of zonal flows, their number depending on the available magnetic flux and on the intensity of the Hall effect. For intermediate Hall intensity, the flow self-organises into long-lived magnetised vortices. Neither the addition of a toroidal field nor Ohmic or ambipolar diffusion change this picture drastically in the range of parameters we have explored. Conclusions. Self-organisation by the Hall effect is a robust phenomenon in global non-stratified simulations. It is able to quench turbulent transport and spontaneously produce axisymmetric rings or sustained vortices. The ability of these structures to trap dust particles in this configuration is demonstrated. We conclude that Hall-MRI driven organisation is a plausible scenario that could explain some of the structures found in recent observations.