Dust concentration and emission in protoplanetary disks vortices

We study the dust concentration and emission in protoplanetary disks vortices. We extend the Lyra-Lin solution for the dust concentration of a single grain size to a power-law distribution of grain sizes $n(a) \propto a^{-p}$. Assuming dust conservation in the disk, we find an analytic dust surface density as a function of the grain radius. We calculate the increase of the dust to gas mass ratio $\epsilon$ and the slope $p$ of the dust size distribution due to grain segregation within the vortex. We apply this model to a numerical simulation of a disk containing a persistent vortex. Due to the accumulation of large grains towards the vortex center, $\epsilon$ increases by a factor of 10 from the background disk value, and $p$ decreases from 3.5 to 3.0. We find the disk emission at millimeter wavelengths corresponding to synthetic observations with ALMA and VLA. The simulated maps at 7 mm and 1 cm show a strong azimuthal asymmetry. This happens because, at these wavelengths, the disk becomes optically thin while the vortex remains optically thick. The large vortex opacity is mainly due to an increase in the dust to gas mass ratio. In addition, the change in the slope of the dust size distribution increases the opacity by a factor of 2. We also show that the inclusion of the dust scattering opacity substantially changes the disks images.