Spatial distribution of crystalline silicates in protoplanetary disks: How to interpret mid-infrared observations

Abstract

Context. Crystalline silicates are an important tracer of the evolution of dust, the main building block of planet formation. In an inner protoplanetary disk, amorphous silicates are annealed because of the high temperatures that prevail there. These crystalline silicates are radially and vertically distributed by a disk turbulence and/or radial transport. Mid-infrared spectrographs are sensitive to the presence and temperature of micron-sized silicates, and the dust temperature can be used to infer their spatial distribution. Aims. We aim to model the spatial distribution of crystalline silicate dust in protoplanetary disks taking into account thermal annealing of silicate dust and radial transport of dust in the midplane. Using the resulting spatial distribution of crystalline and amorphous silicates, we calculated mid-infrared spectra to study the effect on dust features and to compare these to observations. Methods. We modeled a Class II T-Tauri protoplanetary disk and defined the region where crystallization happens by thermal annealing process from the comparison between crystallization and residence timescales (τcryst < τres). Radial mixing and drift were also compared to find a vertically well mixed region (τver < τdrift). We used the DISKLAB code to model the radial transport in the mid-plane and obtained the spatial distribution of the crystalline silicates for different grain sizes. We used MCMax, a radiative transfer code, to model the mid-infrared spectrum. Results. In our modeled T-Tauri disk, different grain sizes get crystallized in different radial and vertical ranges within 0.2 au. Small dust gets vertically mixed up efficiently, so crystallized small dust in the disk surface is well mixed with the midplane. Inward of 0.075 au, all grains are fully crystalline irrespective of their size. We also find that the crystallized dust is distributed out to a few au by radial transport, smaller grains more so than larger ones. Our fiducial model shows different contributions of the inner and outer disks to the dust spectral features. The 10 µm forsterite feature has an ~30% contribution from the innermost disk (0.07–0.09 au) and <1% from the disk beyond 10 au while the 33 µm feature has an ~10% contribution from both innermost and outer disks. We also find that feature strengths change when varying the spatial distribution of crystalline dust. Our modeled spectra qualitatively agree with observations from the Spitɀer Space Telescope, but the modeled 10 µm feature is strongly dominated by crystalline dust, unlike observations. Models with reduced crystallinity and depletion of small crystalline dust within 0.2 au show a better match with observations. Conclusions. Mid-infrared observations of the disk surface represent the radial distribution of small dust grains in the midplane and provide us with abundances of crystalline and amorphous dust, size distribution, and chemical composition in the inner disk. The inner and outer disks contribute more to shorter and longer wavelength features, respectively. In addition to the crystallization and dynamical processes, amorphization, sublimation of silicates, and dust evolution have to be taken into account to match observations, especially at λ = 10 µm, where the inner disk mostly contributes. This study could interpret spectra of protoplanetary disks taken with the Mid-Infrared Instrument on board the James Webb Space Telescope.