Radial flow of dust particles in accretion disks

We study the radial migration of dust particles in accreting protostellar disks analogous to the primordial solar nebula. Our main objective is to determine the retention efficiency of dust particles, which are the building blocks of the much larger planetesimals. This study takes account of the two-dimensional ( radial and normal) structure of the disk gas, including the effects of the variation in the gas velocity as a function of distance from the midplane. It is shown that the dust component of disks accretes slower than the gas component. At high altitude from the disk midplane (higher than a few disk scale heights), the gas rotates faster than the particles because of the inward pressure gradient force, and its drag force causes particles to move outward in the radial direction. Viscous torque induces the gas within a scale height from the disk midplane to flow outward, carrying small (size less than or similar to 100 mum at 10 AU) particles with it. Only particles at intermediate altitude or with sufficiently large sizes (greater than or similar to 1 mm at 10 AU) move inward. When the particles radial velocities are averaged over the entire vertical direction, the particles have a net inward flux. The magnitude of their radial motion depends on their distance from the central star. At large distances, particles migrate inward with a velocity much faster than the gas accretion velocity. However, their inward velocity is reduced below that of the gas in the inner regions of the disk. The rate of velocity decrease is a function of the particles size. While larger particles retain fast accretion velocity until they approach closer to the star, 10 mum particles have slower velocity than the gas in the majority of the disk (r less than or similar to 100 AU). This differential migration of particles causes size fractionation. Dust disks composed mostly of small particles (size less than or similar to 10 mum) accrete slower than gas disks, resulting in an increase in the dust-gas ratio during the gas accretion phase. If the gas disk has a steep radial density gradient or if dust particles sediment effectively to the disk midplane, the net vertically averaged flux of particles can be outward. In this case, the accretion of the dust component is prevented, leading to the formation of residual dust disks after their gas component is severely depleted.