Inner dusty regions of protoplanetary discs – I. High-resolution temperature structure




Our current understanding of the physical conditions in the inner regions of protoplanetary discs is being increasingly challenged by more detailed observational and theoretical explorations. The calculation of the dust temperature is one of the key features that we strive to understand and this is a necessary step in image and flux reconstruction. Here, we explore the coexistence of small (0.1-μm radius) and large (2-μm radius) dust grains, which can coexist at distances from the star where small grains would not survive without large grains shielding them from the direct starlight. Our study required a high-resolution radiative transfer calculation, which is capable of resolving the large temperature gradients and disc-surface curvatures caused by dust sublimation. This method of calculation was also capable of resolving the temperature inversion effect in large grains, where the maximum dust temperature is at a visual optical depth of τV∼ 1.5. We also show disc images and spectra, with disentangled contributions from small and large grains. Large grains dominate the near-infrared flux, mainly because of the bright hot inner disc rim. Small grains populate almost the entire interior of the inner disc, but they appear at the disc’s surface at distances 2.2 times larger than the closest distance of the large grains from the star. Nevertheless, small grains can contribute to the image surface brightness at smaller radii because they are visible below the optically thin surface defined by stellar heating. Our calculations demonstrate that the sublimation temperature does not provide a unique boundary condition for radiative transfer models of optically thick discs. The source of this problem is the temperature inversion effect, which allows the survival of optically thin configurations of large grains closer to the star than the inner radius of the optically thick disc. Future attempts to derive more realistic multigrain inner disc models will need the numerical resolution shown in our study, especially if the dust dynamics is considered where grains can travel through zones of local temperature maxima.