Temperature Inversion on the Surface of Externally Heated Optically Thick Multigrain Dust Clouds

Abstract

It was recently discovered that the temperature in the surface layer of externally heated optically thick gray dust clouds increases with the optical depth for some distance from the surface, as opposed to the normal decrease in temperature with distance in the rest of the cloud. This temperature inversion is a result of efficient absorption of diffuse flux from the cloud interior by the surface dust exposed to external radiation. Grains of size 1 μm or bigger experience this effect when the external flux is of stellar spectrum. We explore what happens to the effect when dust is a mixture of grain sizes (multigrain). Two possible boundary conditions are considered: (1) a constant external flux without constrains on the dust temperature, and (2) the maximum dust temperature set to the sublimation temperature. We find that the first condition allows small grains to completely suppress the temperature inversion of big grains if the overall opacity is dominated by small grains. The second condition enables big grains to maintain the inversion even when they are a minor contributor to the opacity. In reality, the choice of boundary condition depends on the dust dynamics. When applied to the physics of protoplanetary disks, the temperature inversion leads to a previously unrecognized disk structure in which optically thin dust can exist inside the dust destruction radius of an optically thick disk. We conclude that the transition between the dusty disk and the gaseous inner clearing is not a sharp edge, but rather a large optically thin region.