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 effective dust can accumulate along the
azimuthal direction. We also want to find out if the size- sorting resulting
from this can produce a detectable signatures at millimeter wavelengths.
Methods. To keep the numerical cost under control we develop a 1+1D method in
which the azimuthal variations are treated sepa- rately from the radial ones.
The azimuthal structure is calculated analytically for a steady-state between
mixing and azimuthal drift. We derive equilibration time scales and compare the
analytical solutions to time-dependent numerical simulations.
Results. We find 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 P\'eclet number, which is the relative importance
of advection and diffusion. We apply our model to transition disks and our
simulated observations show that this effect would be easily observable with
ALMA and in principle allows to put constraints on the strength of turbulence
and the local gas density.Comment: 4 pages, 4 figures, accepted for publication in A&A Letter
