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 \ga 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 ( \sim 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 < 100 K are found to originate partly from region 2 .
We conclude that observations of rotational water lines from Herbig Ae disks probe first and foremost the conditions in region 3 , where water is predominantly formed via neutral-neutral reactions and the gas is thermally decoupled from the dust T _ { \hskip { -0.86 pt } gas } > T _ { \hskip { -0.86 pt } 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 % .