The photophoretic sweeping of dust in transient protoplanetary disks

Context. Protoplanetary disks start their lives with a dust free inner region where the temperatures are higher than the sublimation temperature of solids. As the star illuminates the innermost particles, which are immersed in gas at the sublimation edge, these particles are subject to a photophoretic force. Aims. We examine the motion of dust particles at the inner edge of protoplanetary disks due to photophoretic drag. Methods. We give a detailed treatment of the photophoretic force for particles in protoplanetary disks. The force is applied to particles at the inner edge of a protoplanetary disk and the dynamical behavior of the particles is analyzed. Results. We find that, in a laminar disk, photophoretic drag increases the size of the inner hole after accretion onto the central body has become subdued. This region within the hole becomes an optically transparent zone containing gas and large dusty particles (>> 10 cm), but devoid of, or strongly depleted in, smaller dust aggregates. Photophoresis can clear the inner disk of dust out to 10 AU in less than 1 Myr. The details of this clearance depend on the size distribution of the dust. Any replenishment of the dust within the cleared region will be continuously and rapidly swept out to the edge. At late times, the edge reaches a stable equilibrium between inward drift and photophoretic outward drift, at a distance of some tens of AU. Eventually, the edge will move inwards again as the disk disperses, shifting the equilibrium position back from about 40 AU to below 30 AU in 1-2 Myr in the disk model. In a turbulent disk, diffusion can delay the clearing of a disk by photophoresis. Smaller and/or age-independent holes of radii of a few AU are also possible outcomes of turbulent diffusion counteracting photophoresis. Conclusions. This outward and then inward moving edge marks a region of high dust concentration. This density enhancement, and the efficient transport of particles from close to the star to large distances away, can explain features of comets such as high measured ratios of crystalline to amorphous silicates, and has a large number of other applications.