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

The spatial origin and detectability of rotational H(2)O emission lines from Herbig Ae type protoplanetary disks beyond 70 mu m 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 "snowline" r greater than or similar to 20 AU, and (3) a layer of irradiated hot water at high altitudes z/r = 0.1...0.3, extending from about 1 AU to 30 AU, where the kinetic gas temperature ranges from 200 K to 1500 K. Although region 3 contains only little amounts of water vapour (similar to 10(-4) M(Earth)), it is this warm layer that is almost entirely responsible for the rotational water emission lines as observable with Herschel. Only one ortho and two para H(2)O lines with the lowest excitation energies T(dust). The observation of rotational water lines does not allow for a determination of the snowline, because the snowline truncates the radial extension of region 1, whereas the lines originate from the 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%.