Radiative Transfer Models of Mid-Infrared H_2O Lines in the Planet-Forming Region of Circumstellar Disks

The study of warm molecular gas in the inner regions of protoplanetary disks is of key importance for the study of planet formation and especially for the transport of H_2O and organic molecules to the surfaces of rocky planets/satellites. Recent Spitzer observations have shown that the mid-infrared spectra of protoplanetary disks are covered in emission lines due to water and other molecules. Here, we present a non-local thermodynamic equilibrium (LTE) two-dimensional radiative transfer model of water lines in the 10-36 μm range that can be used to constrain the abundance structure of water vapor, given an observed spectrum, and show that an assumption of LTE does not accurately estimate the physical conditions of the water vapor emission zones, including temperatures and abundance structures. By applying the model to published Spitzer spectra we find that: (1) most water lines are subthermally excited, (2) the gas-to-dust ratio must be as much as 1-2 orders of magnitude higher than the canonical interstellar medium ratio of 100-200, (3) the gas temperature must be significantly higher than the dust temperature, in agreement with detailed heating/cooling models, and (4) the water vapor abundance in the disk surface must be significantly truncated beyond ~1 AU. A low efficiency of water formation below T ~ 300 K may naturally result in a lower water abundance beyond a certain radius. However, we find that chemistry, although not necessarily ruled out, may not be sufficient to produce a sharp abundance drop of many orders of magnitude and speculate that the depletion may also be caused by vertical turbulent diffusion of water vapor from the superheated surface to regions below the snow line, where the water can freeze out and be transported to the midplane as part of the general dust settling. Such a vertical cold finger effect is likely to be efficient due to the lack of a replenishment mechanism of large, water-ice coated dust grains to the disk surface