We propose a set of standard assumptions for the modelling of Class II and III protoplanetary disks, which includes detailed continuum radiative transfer, thermo-chemical modelling of gas and ice, and line radiative transfer from optical to cm wavelengths. The first paper of this series focuses on the assumptions about the shape of the disk, the dust opacities, dust settling, and polycyclic aromatic hydrocarbons (PAHs). In particular, we propose new standard dust opacities for disk models, we present a simplified treatment of PAHs in radiative equilibrium which is sufficient to reproduce the PAH emission features, and we suggest using a simple yet physically justified treatment of dust settling. We roughly adjust parameters to obtain a model that predicts continuum and line observations that resemble typical multi-wavelength continuum and line observations of Class II T Tauri stars. We systematically study the impact of each model parameter (disk mass, disk extension and shape, dust settling, dust size and opacity, gas/dust ratio, etc.) on all mainstream continuum and line observables, in particular on the SED, mm-slope, continuum visibilities, and emission lines including [OI] 63 μm, high-J CO lines, (sub-)mm CO isotopologue lines, and CO fundamental ro-vibrational lines. We find that evolved dust properties, i.e. large grains, often needed to fit the SED, have important consequences for disk chemistry and heating/cooling balance, leading to stronger near-to far-IR emission lines in general. Strong dust settling and missing disk flaring have similar effects on continuum observations, but opposite effects on far-IR gas emission lines. PAH molecules can efficiently shield the gas from stellar UV radiation because of their strong absorption and negligible scattering opacities in comparison to evolved dust. The observable millimetre-slope of the SED can become significantly more gentle in the case of cold disk midplanes, which we find regularly in our T Tauri models. We propose to use line observations of robust chemical tracers of the gas, such as O, CO, and H 2 , as additional constraints to determine a number of key properties of the disks, such as disk shape and mass, opacities, and the dust/gas ratio, by simultaneously fitting continuum and line observations.

The European FP7 project DIANA has performed a coherent analysis of a large set of observational data of protoplanetary disks by means of thermo-chemical disk models. The collected data include extinction-corrected stellar UV and X-ray input spectra (as seen by the disk), photometric fluxes, low and high resolution spectra, interferometric data, emission line fluxes, line velocity profiles and line maps, which probe the dust, polycyclic aromatic hydrocarbons (PAHs) and the gas in these objects. We define and apply a standardized modeling procedure to fit these data by state-of-the-art modeling codes (ProDiMo, MCFOST, MCMax), solving continuum and line radiative transfer (RT), disk chemistry, and the heating and cooling balance for both the gas and the dust. 3D diagnostic RT tools (e.g., FLiTs) are eventually used to predict all available observations from the same disk model, the DIANA-standard model. Our aim is to determine the physical parameters of the disks, such as total gas and dust masses, the dust properties, the disk shape, and the chemical structure in these disks. We allow for up to two radial disk zones to obtain our best-fitting models that have about 20 free parameters. This approach is novel and unique in its completeness and level of consistency. It allows us to break some of the degeneracies arising from pure Spectral Energy Distribution (SED) modeling. In this paper, we present the results from pure SED fitting for 27 objects and from the all inclusive DIANA-standard models for 14 objects. Our analysis shows a number of Herbig Ae and T Tauri stars with very cold and massive outer disks which are situated at least partly in the shadow of a tall and gas-rich inner disk. The disk masses derived are often in excess to previously published values, since these disks are partially optically thick even at millimeter wavelength and so cold that they emit less than in the Rayleigh–Jeans limit. We fit most infrared to millimeter emission line fluxes within a factor better than 3, simultaneously with SED, PAH features and radial brightness profiles extracted from images at various wavelengths. However, some line fluxes may deviate by a larger factor, and sometimes we find puzzling data which the models cannot reproduce. Some of these issues are probably caused by foreground cloud absorption or object variability. Our data collection, the fitted physical disk parameters as well as the full model output are available to the community through an online database (http://www.univie.ac.at/diana).

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 rovibrational 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.

Context. The mid-IR detection rate of water lines in disks around Herbig stars disks is about 5%, while it is around 50% for disks around T Tauri stars. The reason for this is still unclear. Aims. In this study, we want to find an explanation for the different detection rates between low mass and high mass pre-main-sequence stars in the mid-IR regime. Methods. We ran disk models with stellar parameters adjusted to spectral types B9 through M2, using the radiation thermo-chemical disk modelling code ProDiMo. We explored also a small parameter space around a standard disk model, considering dust-to-gas mass ratio, disk gas mass, mixing coefficient for dust settling, flaring index, dust maximum size, and size power law distribution index. We produced convolved spectra at the resolution of Spitzer, IRS, JWST MIRI, and VLT VISIR spectrographs. We applied random noise derived from typical Spitzer spectra for a direct comparison with observations. Results. The strength of the mid-IR water lines correlates directly with the luminosity of the central star. The models show that it is possible to suppress the water emission; however, current observations are not sensitive enough to detect mid-IR lines in disks for most of the explored parameters. The presence of noise in the spectra, combined with the high continuum flux (noise level is proportional to the continuum flux), is the most likely explanation for the non-detections towards Herbig stars. Conclusions. Mid-IR spectra with resolution higher than 20 000 are needed to investigate water in protoplanetary disks. Intrinsic differences in disk structure, such as inner gaps, gas-to-dust ratio, dust size and distribution, and inner disk scale height, between Herbig and T Tauri star disks are able to explain a lower water detection rate in disks around Herbig stars.