Gas and dust hydrodynamical simulations of massive lopsided transition discs - II. Dust concentration

We investigate the dynamics of large dust grains in massive lopsided transition discs via 2D hydrodynamical simulations including both gas and dust. Our simulations adopt a ring-like gas density profile that becomes unstable against the Rossby-wave instability and forms a large crescent-shaped vortex. When gas self-gravity is discarded, but the indirect force from the displacement of the star by the vortex is included, we confirm that dust grains with stopping times of order the orbital time, which should be typically a few centimetres in size, are trapped ahead of the vortex in the azimuthal direction, while the smallest and largest grains concentrate towards the vortex centre. We obtain maximum shift angles of about 25 degrees. Gas self-gravity accentuates the concentration differences between small and large grains. At low to moderate disc masses, the larger the grains, the farther they are trapped ahead of the vortex. Shift angles up to 90 degrees are reached for 10 cm-sized grains, and we show that such large offsets can produce a double-peaked continuum emission observable at mm/cm wavelengths. This behaviour comes about because the large grains undergo horseshoe U-turns relative to the vortex due to the vortex's gravity. At large disc masses, since the vortex's pattern frequency becomes increasingly slower than Keplerian, small grains concentrate slightly beyond the vortex and large grains form generally non-axisymmetric ring-like structures around the vortex's radial location. Gas self-gravity therefore imparts distinct trapping locations for small and large dust grains which may be probed by current and future observations, and which suggest that the formation of planetesimals in vortices might be more difficult than previously thought.