Impact of dust diffusion on the rim shape of protoplanetary disks

Abstract

Context. Multiple mechanisms are known to give rise to turbulence in protoplanetary disks, which facilitates the accretion onto the central star. Small dust particles that are well coupled to the gas undergo diffusion due to this turbulent motion. Aims. This paper investigates the influence of turbulence-induced dust diffusion on the equilibrium of protoplanetary disks. Methods. The model accounts for dust sublimation, radiative transfer with the flux-limited diffusion approximation, and dust diffusion. It predicts the density and temperature profiles as well as the dust-to-gas ratio of the disk. Results. It is shown that dust diffusion can have a large impact: Assuming the dust survives for 104 s or longer before it can be evaporated, this leads the dust diffusion to widen the inner disk considerably. This effect is generated through a feedback mechanism as the diffusion length is much shorter than the disk width. With increasing dust diffusion, the inclination of the inner rim toward the stellar radiation becomes steeper until it is almost vertical. The temperature range of evaporation and condensation, which is linked to the dust composition, has no influence on this effect. Conclusions. For realistic parameters, dust diffusion cannot be neglected when determining the equilibrium of the disk. Stronger turbulence inside the disk induces more dust diffusion. Therefore, the dust density grows more gradually over a greater distance and less radiation reaches the disk surface. The new equilibrium shape of the disk is more inclined toward the star. This effect is universal and independent of the specific dust composition.