We present deep Herschel -PACS spectroscopy of far-infrared water lines from a sample of four protoplanetary disks around solar-mass stars , selected to have strong water emission at mid-infrared wavelengths .
By combining the new Herschel spectra with archival Spitzer -IRS spectroscopy , we retrieve a parameterized radial surface water vapor distribution from 0.1-100 AU using two-dimensional dust and line radiative transfer modeling .
The surface water distribution is modeled with a step model comprising of a constant inner and outer relative water abundance and a critical radius at which the surface water abundance is allowed to change .
We find that the four disks have critical radii of \sim 3 - 11 AU , at which the surface water abundance decreases by at least 5 orders of magnitude .
The measured values for the critical radius are consistently smaller than the location of the surface snow line , as predicted by the observed spectral energy distribution .
This suggests that the sharp drop-off of the surface water abundance is not solely due to the local gas-solid balance , but may also be driven by the de-activation of gas-phase chemical pathways to water below 300 K. Assuming a canonical gas-to-dust ratio of 100 , as well as coupled gas and dust temperatures T _ { gas } = T _ { dust } , the best-fit inner water abundances become implausibly high ( 0.01-1.0 { H _ { 2 } } ^ { -1 } ) .
Conversely , a model in which the gas and dust temperatures are decoupled leads to canonical inner disk water abundances of \sim 10 ^ { -4 } H _ { 2 } ^ { -1 } , while retaining gas-to-dust ratios of 100 .
That is , the evidence for gas-dust decoupling in disk surfaces is stronger than for enhanced gas-to-dust ratios .