Abstract
Abstract 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 . 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 ϵ 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 toward the vortex center, ϵ 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 two. We also show that the inclusion of the dust scattering opacity substantially changes the disks images.
Highlights
There is not yet a full theory that successfully explains the formation of solid planet that starts with the concentration and growth of dust particles in protoplanetary disks from millimeter to planetesimal sizes
The strong disk asymmetry comes from the enhancement of the dust to gas mass ratio due to size segregation inside the vortex, the opacity is increased by a factor of 10 at the vortex center
Dust emission of vortices in protoplanetary disks is studied using the Lyra-Lin model for the concentration of dust grains towards the vortex center. Their analytic model gives the dust surface density for a single particle size. We have extended this model to the case of a dust size distribution n(a) ∝ a−p
Summary
There is not yet a full theory that successfully explains the formation of solid planet that starts with the concentration and growth of dust particles in protoplanetary disks from millimeter to planetesimal sizes. One of the main problems is the fast radial migration of millimeter and micrometer dust particles toward the central star, which prevents the formation of large bodies during the disk lifetime (e.g., Testi et al 2014; Johansen et al 2014). Barge et al 2016) in the outer edge of the dead zone, where turbulence due to the Magneto Rotational Instability (MRI) is depressed due to the low ionization state of the disk material These structures can survive over a hundred rotation periods (measured at the radius of the center of the vortex) and increase the dust to gas mass ratio one order of magnitude (Inaba & Barge 2006). This large concentration of dust mass could become gravitationally unstable, and start the formation of planetesimals
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