  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.
