Context. Transition disks typically appear in resolved millimeter observations as giant dust rings surrounding their young host stars. More accurate observations with ALMA have shown several of these rings to be in fact asymmetric: they have lopsided shapes. It has been speculated that these rings act as dust traps, which would make them important laboratories for studying planet formation. It has been shown that an elongated giant vortex produced in a disk with a strong viscosity jump strikingly resembles the observed asymmetric rings. Aims. We aim to study a similar behavior for a disk in which a giant planet is embedded. However, a giant planet can induce two kinds of asymmetries: (1) a giant vortex, and (2) an eccentric disk. We studied under which conditions each of these can appear, and how one can observationally distinguish between them. This is important because only a vortex can trap particles both radially and azimuthally, while the eccentric ring can only trap particles in radial direction. Methods. We used the FARGO code to conduct the hydro-simulations. We set up a disk with an embedded giant planet and took a radial grid spanning from 0.1 to 7 times the planet semi-major axis. We ran the simulations with various viscosity values and planet masses for 1000 planet orbits to allow a fully developed vortex or disk eccentricity. Afterwards, we compared the dust distribution in a vortex-holding disk with an eccentric disk using dust simulations. Results. We find that vorticity and eccentricity are distinguishable by looking at the azimuthal contrast of the dust density. While vortices, as particle traps, produce very pronounced azimuthal asymmetries, eccentric features are not able to accumulate millimeter dust particles in azimuthal direction, and therefore the asymmetries are expected to be modest.
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