Lopsided dust rings in transition disks

Context. Particle trapping in local or global pressure maxima in protoplanetary disks is one of the new paradigms in the theory of the first stages of planet formation. However, finding observational evidence for this effect is not easy. Recent work suggests that the large ring-shaped outer disks observed in transition disk sources may in fact be lopsided and constitute large banana-shaped vortices. Aims. We wish to investigate how effectively dust can accumulate along the azimuthal direction. We also want to find out if the size-sorting resulting from this accumulation can produce detectable signatures at millimeter wavelengths. Methods. To keep the numerical cost under control we developed a 1 + 1D method in which the azimuthal variations are treated separately from the radial variations. The azimuthal structure was calculated analytically for a steady-state between mixing and azimuthal drift. We derived equilibration time scales and compared the analytical solutions to time-dependent numerical simulations. Results. We found that weak, but long-lived azimuthal density gradients in the gas can induce very strong azimuthal accumulations of dust. The strength of the accumulations depends on the Peclet number, which describes the relative importance of advection and diffusion. We applied our model to transition disks and our simulated observations show that this effect would be easily observable with the Atacama Large Millimeter / submillimeter Array (ALMA) and could be used to put constraints on the strength of turbulence and the local gas density.