  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 H2O 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-LTE 2D radiative transfer
model of water lines in the 10-36 mum range that can be used to constrain the
abundance structure of water vapor, given an observed spectrum, and show that
an assumption of local thermodynamic equilibrium (LTE) does not accurately
estimate the physical conditions of the water vapor emission zones. 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 one to two orders of
magnitude higher than the canonical interstellar medium ratio of 100-200, and
3) the gas temperature must be higher than the dust temperature, and 4) the
water vapor abundance in the disk surface must be truncated beyond ~ 1 AU. A
low efficiency of water formation below ~ 300 K may naturally result in a lower
water abundance beyond a certain radius. However, we find that chemistry, may
not be sufficient to produce an 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.
