Understanding the water emission in the mid- and far-IR from protoplanetary disks around T Tauri stars

International audience Aims: We investigate which properties of protoplanetary disks around T Tauri stars affect the physics and chemistry in the regions where mid- and far-IR water lines originate and their respective line fluxes. We search for diagnostics for future observations. Methods: With the code ProDiMo, we build a series of models exploring a large parameter space, computing rotational and ro-vibrational transitions of water in nonlocal thermodynamic equilibrium (non-LTE). We select a sample of transitions in the mid-IR regime and the fundamental ortho and para water transitions in the far-IR. We investigate the chemistry and the local physical conditions in the line emitting regions. We calculate Spitzer spectra for each model and compare far-IR and mid-IR lines. In addition, we use mid-IR colors to tie the water line predictions to the dust continuum. Results: Parameters affecting the water line fluxes in disks by more than a factor of three are : the disk gas mass, the dust-to-gas mass ratio, the dust maximum grain size, interstellar medium (ISM) UV radiation field, the mixing parameter of Dubrulle settling, the disk flaring parameter, and the dust size distribution. The first four parameters affect the mid-IR lines much more than the far-IR lines. Conclusions: A key driver behind water spectroscopy is the dust opacity, which sets the location of the water line emitting region. We identify three types of parameters, including those (1) affecting global disk opacity and opacity function (maximum dust size and dust size distribution); (2) affecting global disk opacity (dust-to-gas mass ratio, Dubrulle settling, disk gas mass); and (3) not affecting disk opacity (flaring parameter, ISM UV radiation field, fraction of PAHs). Parameters, such as dust-to-gas ratio, ISM radiation field, and dust size distribution, affect the mid-IR lines more, while the far-IR transitions are more affected by the flaring index. The gas mass greatly affects lines in both regimes. Higher spectral resolution and line sensitivities, like from the James Webb Space Telescope, are needed to detect a statistically relevant sample of individual water lines to distinguish further between these types of parameters. Appendices are available in electronic form at http://www.aanda.org