Context. The planet-forming region of protoplanetary disks is cold, dense, and therefore weakly ionized. For this reason, magnetohydrodynamic (MHD) turbulence is thought to be mostly absent, and another mechanism has to be found to explain gas accretion. It has been proposed that magnetized winds, launched from the ionized disk surface, could drive accretion in the presence of a large-scale magnetic field. Aims. The efficiency and the impact of these surface winds on the disk structure is still highly uncertain. We present the first global simulations of a weakly ionized disk that exhibits large-scale magnetized winds. We also study the impact of self-organization, which was previously demonstrated only in non-stratified models. Methods. We perform numerical simulations of stratified disks with the PLUTO code. We compute the ionization fraction dynamically, and account for all three non-ideal MHD effects: ohmic and ambipolar diffusions, and the Hall drift. Simplified heating and cooling due to non-thermal radiation is also taken into account in the disk atmosphere. Results. We find that disks can be accreting or not, depending on the configuration of the large-scale magnetic field. Magnetothermal winds, driven both by magnetic acceleration and heating of the atmosphere, are obtained in the accreting case. In some cases, these winds are asymmetric, ejecting predominantly on one side of the disk. The wind mass loss rate depends primarily on the average ratio of magnetic to thermal pressure in the disk midplane. The non-accreting case is characterized by a meridional circulation, with accretion layers at the disk surface and decretion in the midplane. Finally, we observe self-organization, resulting in axisymmetric rings of density and associated pressure "bumps". The underlying mechanism and its impact on observable structures are discussed.

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.