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Hot and cool water in Herbig Ae protoplanetary disks. A challenge for Herschel

The spatial origin and detectability of rotational H2O emission lines from Herbig Ae type protoplanetary disks beyond 70 micron is discussed. We use the recently developed disk code ProDiMo to calculate the thermo-chemical structure of a Herbig Ae type disk and apply the non-LTE line radiative transfer code Ratran to predict water line profiles and intensity maps. The model shows three spatially distinct regions in the disk where water concentrations are high, related to different chemical pathways to form the water: (1) a big water reservoir in the deep midplane behind the inner rim, (2) a belt of cold water around the distant icy midplane beyond the snow-line r>20AU, and (3) a layer of irradiated hot water at high altitudes z/r=0.1...0.3, extending from about 1AU to 30AU, where the kinetic gas temperature ranges from 200K to 1500K. Although region 3 contains only little amounts of water vapour (~3x10^-5 M_Earth), we find this warm layer to be almost entirely responsible for the rotational water emission lines, execpt for the 3 lowest excitation lines. Thus, Herschel will probe first and foremost the conditions and radial extension of region 3, where water is predominantly formed via neutral-neutral reactions and the gas is thermally decoupled from the dust T_gas>T_dust. The observations do not allow for a determination of the snow-line, because the snow-line truncates the radial extension of region 1, whereas the lines originate from region 3. Different line transfer approximations (LTE, escape probability, Monte Carlo) are discussed. A non-LTE treatment is required in most cases, and the results obtained with the escape probability method are found to underestimate the Monte Carlo results by 2%...45%.