Steady state of dust distributions in disk vortices: Observational predictions and applications to transitional disks

TL;DR

This paper develops analytical steady-state models for dust distributions in disk vortices, aiding interpretation of ALMA observations of transitional disks and providing insights into turbulence and dust trapping mechanisms.

Contribution

It introduces exact analytical solutions for dust distribution in vortices, linking observable quantities to vortex properties and turbulence strength.

Findings

Model successfully applied to Oph IRS 48 system

Derived dust contrast and trapped dust mass

Validated model against observational data

Abstract

The Atacama Large Millimeter Array (ALMA) has been returning images of transitional disks in which large asymmetries are seen in the distribution of mm-sized dust in the outer disk. The explanation in vogue borrows from the vortex literature by suggesting that these asymmetries are the result of dust trapping in giant vortices, excited via Rossby wave instability (RWI) at planetary gap edges. Due to the drag force, dust trapped in vortices will accumulate in the center, and diffusion is needed to maintain a steady state over the lifetime of the disk. While previous work derived semi-analytical models of the process, in this paper we provide analytical steady-state solutions. Exact solutions exist for certain vortex models. The solution is determined by the vortex rotation profile, the gas scale height, the vortex aspect ratio, and the ratio of dust diffusion to gas-dust friction. In principle, all these quantities can be derived from observations, which would give validation of the model, also giving constrains on the strength of the turbulence inside the vortex core. Based on our solution, we derive quantities such as the gas-dust contrast, the trapped dust mass, and the dust contrast at the same orbital location. We apply our model to the recently imaged Oph IRS 48 system, finding values within the range of the observational uncertainties.