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The mid-IR water and silicate relation in protoplanetary disks

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 explanation for the current detection rate. We search for a connection between mid-IR water line fluxes and the strength of the 10~$μ$m silicate feature. We analyse observed water line fluxes from three blends and compute the 10~$μ$m silicate feature strength from Spitzer spectra. We use a series of published models, exploring disk dust and gas properties, and the effects of different stars. The models also show that the increasing stellar luminosity enhance simultaneously 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~$μ$m silicate. 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 model series are not able to reproduce the most extreme observations, suggesting that more complex dust properties are required. A parametrized settling prescription is able to boost the peak strength by a factor 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 model series. The disks with 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~$μ$m silicate features, with strong peak strength.