Mid-IR water and silicate relation in protoplanetary disks

Context. Mid-IR water lines from protoplanetary disks around T Tauri stars have a detection rate of 50%. Models have identified multiple physical properties of disks such as dust-to-gas mass ratio, dust size power law distribution, disk gas mass, disk inner radius, and disk scale height as potential explanations for the current detection rate. Aims. In this study, we aim to break degeneracies through constraints obtained from observations. We search for a connection between mid-IR water line fluxes and the strength of the 10 mu m silicate feature. Methods. We analyze observed water line fluxes from three blends at 15.17, 17.22 and 29.85 mu m published earlier and compute the 10 mu m silicate feature strength from Spitzer spectra to search for possible trends. We use a series of published ProDiMo thermochemical models, to explore disk dust and gas properties, and also the effects of different central stars. In addition, we produced two standard models with different dust opacity functions, and one with a parametric prescription for the dust settling. Results. Our series of models that vary properties of the grain size distribution suggest that mid-IR water emission anticorrelates with the strength of the 10 mu m silicate feature. The models also show that the increasing stellar bolometric luminosity simultaneously enhance the strength of this dust feature and the water lines fluxes. No correlation is found between the observed mid-IR water lines and the 10 mu m silicate strength. Two-thirds of the targets in our sample show crystalline dust features, and the disks are mainly flaring. Our sample shows the same difference in the peak strength between amorphous and crystalline silicates that was noted in earlier studies, but our models do not support this intrinsic difference in silicate peak strength. Individual properties of our models are not able to reproduce the most extreme observations, suggesting that more complex dust properties (e.g., vertically changing) are required to reproduce the strongest 10 mu m silicate features. A parametrized settling prescription is able to boost the peak strength by a factor of 2 for the standard model. Water line fluxes are unrelated to the composition of the dust. The pronounced regular trends seen in the model results are washed out in the data due to the larger diversity in stellar and disk properties compared to our series of model. Conclusions. The independent nature of the water line emission and the 10 mu m silicate strength found in observations, and the modeling results, leave as a possible explanation that the disks with weaker mid-IR water line fluxes are depleted in gas or enhanced in dust in the inner 10 au. In the case of gas depleted disks, settling produces very strong 10 mu m silicate features with strong peak strength. Observations of larger unbiased samples with JWST/MIRI and ALMA are essential to verify this hypothesis.