An Analytical Model of Radial Dust Trapping in Protoplanetary Disks

Abstract

We study dust concentration in axisymmetric gas rings in protoplanetary disks. Given the gas surface density, we derived an analytical total dust surface density by taking into account the differential concentration of all grain sizes. This model allows us to predict the local dust-to-gas mass ratio and the slope of the particle size distribution, as a function of radius. We test this analytical model by comparing it with a 3D magnetohydrodynamical simulation of dust evolution in an accretion disk. The model is also applied to the disk around HD 169142. By fitting the disk continuum observations simultaneously at λ  = 0.87, 1.3, and 3.0 mm, we obtain a global dust-to-gas mass ratio and a viscosity coefficient α  = 1.35 × 10 −2 . This model can be easily implemented in numerical simulations of accretion disks.