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

It was recently discovered that the temperature in the surface layer ofexternally heated optically thick gray dust clouds increases with the opticaldepth for some distance from the surface, as opposed to the normal decrease intemperature with distance in the rest of the cloud. This temperature inversionis a result of efficient absorption of diffuse flux from the cloud interior bythe surface dust exposed to the external radiation. A micron or bigger sizegrains experience this effect when the external flux is of stellar spectrum. Weexplore what happens to the effect when dust is a mixture of grain sizes(multigrain). Two possible boundary conditions are considered: i) a constantexternal flux without constrains on the dust temperature, and ii) the maximumdust temperature set to the sublimation temperature. We find that the firstcondition allows small grains to completely suppress the temperature inversionof big grains if the overall opacity is dominated by small grains. The secondcondition enables big grains to maintain the inversion even when they are aminor contributor to the opacity. In reality, the choice of boundary conditiondepends on the dust dynamics. When applied to the physics of protoplanetarydisks, the temperature inversion leads to a previously unrecognized diskstructure where optically thin dust can exist inside the dust destructionradius of an optically thick disk. We conclude that the transition between thedusty disk and the gaseous inner clearing is not a sharp edge, but rather alarge optically thin region.Comment: 8 pages, 10 figures, Accepted for publication in the Astrophysical Journa