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.

Accurate measurements of the physical structure of protoplanetary discs are critical inputs for planet formation models. These constraints are traditionally established via complex modelling of continuum and line observations. Instead, we present an empirical framework to locate the CO isotopologue emitting surfaces from high spectral and spatial resolution ALMA observations. We apply this framework to the disc surrounding IM Lupi, where we report the first direct, i.e. model independent, measurements of the radial and vertical gradients of temperature and velocity in a protoplanetary disc. The measured disc structure is consistent with an irradiated self-similar disc structure, where the temperature increases and the velocity decreases towards the disc surface. We also directly map the vertical CO snow line, which is located at about one gas scale height at radii between 150 and 300 au, with a CO freeze-out temperature of 21 ± 2 K. In the outer disc (> 300 au), where the gas surface density transitions from a power law to an exponential taper, the velocity rotation field becomes significantly sub-Keplerian, in agreement with the expected steeper pressure gradient. The sub-Keplerian velocities should result in a very efficient inward migration of large dust grains, explaining the lack of millimetre continuum emission outside of 300 au. The sub-Keplerian motions may also be the signature of the base of an externally irradiated photo-evaporative wind. In the same outer region, the measured CO temperature above the snow line decreases to ≈ 15 K because of the reduced gas density, which can result in a lower CO freeze-out temperature, photo-desorption, or deviations from local thermodynamic equilibrium.

Context. In protoplanetary disks micron-size dust grains coagulate to form larger structures with complex shapes and compositions. The coagulation process changes the absorption and scattering properties of particles in the disk in significant ways. To properly interpret observations of protoplanetary disks and to place these observations in the context of the first steps of planet formation, it is crucial to understand the optical properties of these complex structures. Aims. We derive the optical properties of dust aggregates using detailed computations of aggregate structures and compare these computationally demanding results with approximate methods that are cheaper to compute in practice. In this way we wish to understand the merits and problems of approximate methods and define the context in which they can or cannot be used to analyze observations of objects where significant grain growth is taking place. Methods. For the detailed computations we used the discrete dipole approximation (DDA), a method able to compute the interaction of light with a complexly shaped, inhomogeneous particle. We compared the results to those obtained using spherical and irregular, homogeneous and inhomogeneous particles. Results. While no approximate method properly reproduces all characteristics of large dust aggregates, the thermal properties of dust can be analyzed using irregularly shaped, porous, inhomogeneous grains. The asymmetry of the scattering phase function is a good indicator of aggregate size, while the degree of polarization is probably determined by the size of the constituent particles. Optical properties derived from aggregates significantly differ from the most frequently used standard ("astronomical silicate" in spherical grains). We outline a computationally fast and relatively accurate method that can be used for a multiwavelength analysis of aggregate dust in protoplanetary disks.

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 define a small and large chemical network which can be used for the quantitative simultaneous analysis of molecular emission from the near-IR to the submm. We revise reactions of excited molecular hydrogen, which are not included in UMIST, to provide a homogeneous database for future applications. Methods. We use the thermo-chemical disk modeling code ProDiMo and a standard T Tauri disk model to evaluate the impact of various chemical networks, reaction rate databases and sets of adsorption energies on a large sample of chemical species and emerging line fluxes from the near-IR to the submm wavelength range. Results. We find large differences in the masses and radial distribution of ice reservoirs when considering freeze-out on bare or polar ice coated grains. Most strongly the ammonia ice mass and the location of the snow line (water) change. As a consequence molecules associated to the ice lines such as N 2 H + change their emitting region; none of the line fluxes in the sample considered here changes by more than 25% except CO isotopologues, CN and N 2 H + lines. The three-body reaction N+H 2 +M plays a key role in the formation of water in the outer disk. Besides that, differences between the UMIST 2006 and 2012 database change line fluxes in the sample considered here by less than a factor 2 (a subset of low excitation CO and fine structure lines stays even within 25%); exceptions are OH, CN, HCN, HCO + and N 2 H + lines. However, different networks such as OSU and KIDA 2011 lead to pronounced differences in the chemistry inside 100 au and thus affect emission lines from high excitation CO, OH and CN lines. H 2 is easily excited at the disk surface and state-to-state reactions enhance the abundance of CH + and to a lesser extent HCO + . For sub-mm lines of HCN, N 2 H + and HCO + , a more complex larger network is recommended. Conclusions. More work is required to consolidate data on key reactions leading to the formation of water, molecular ions such as HCO + and N 2 H + as well as the nitrogen chemistry. This affects many of the key lines used in the interpretation of disk observations. Differential analysis of various disk models using the same chemical input data will be more robust than the interpretation of absolute fluxes.