Context. Emission lines from protoplanetary disks originate mainly in the irradiated surface layers, where the gas is generally warmer than the dust. Therefore, interpreting emission lines requires detailed thermo-chemical models, which are essential to converting line observations into understanding disk physics. Aims. We aim at hydrostatic disk models that are valid from 0.1 AU to 1000 AU to interpret gas emission lines from UV to sub-mm. In particular, our interest lies in interpreting far IR gas emission lines, such as will be observed by the Herschel observatory, related to the Gasps open time key program. This paper introduces a new disk code called ProDiMo. Methods. We combine frequency-dependent 2D dust continuum radiative transfer, kinetic gas-phase and UV photo-chemistry, ice formation, and detailed non-LTE heating & cooling with the consistent calculation of the hydrostatic disk structure. We include Fe ii and CO ro-vibrational line heating/cooling relevant to the high-density gas close to the star, and apply a modified escapeprobability treatment. The models are characterised by a high degree of consistency between the various physical, chemical, and radiative processes, where the mutual feedbacks are solved iteratively. Results. In application to a T Tauri disk extending from 0.5 AU to 500 AU, the models show that the dense, shielded and cold midplane (z/r < ∼ 0.1, T g ≈ T d ) is surrounded by a layer of hot (T g ≈ 5000 K) and thin (n H ≈ 10 7 to 10 8 cm −3 ) atomic gas that extends radially to about 10 AU and vertically up to z/r ≈ 0.5. This layer is predominantly heated by the stellar UV (e.g. PAH-heating) and cools via Fe ii semi-forbidden and Oi 630 nm optical line emission. The dust grains in this "halo" scatter the starlight back onto the disk, which affects the photochemistry. The more distant regions are characterised by a cooler flaring structure. Beyond r > ∼ 100 AU, T g decouples from T d even in the midplane and reaches values of about T g ≈ 2T d . Conclusions. Our models show that the gas energy balance is the key to understanding the vertical disk structure. Models calculated with the assumption T g = T d show a much flatter disk structure. The conditions in the close regions (<10 AU) with densities n H ≈ 10 8 to 10 15 cm −3 resemble those of cool stellar atmospheres and, thus, the heating and cooling is more like in stellar atmospheres. The application of heating and cooling rates known from PDR and interstellar cloud research alone can be misleading here, so more work needs to be invested to identify the leading heating and cooling processes.

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.

Aims. We present a comparison between independent computer codes, modeling the physics and chemistry of interstellar photon dominated regions (PDRs). Our goal was to understand the mutual differences in the PDR codes and their effects on the physical and chemical structure of the model clouds, and to converge the output of different codes to a common solution. Methods. A number of benchmark models have been created, covering low and high gas densities n = 10 3 , 10 5.5 cm −3 and far ultraviolet intensities χ = 10, 10 5 in units of the Draine field (FUV: 6 < h ν < 13.6 eV). The benchmark models were computed in two ways: one set assuming constant temperatures, thus testing the consistency of the chemical network and photo-processes, and a second set determining the temperature self consistently by solving the thermal balance, thus testing the modeling of the heating and cooling mechanisms accounting for the detailed energy balance throughout the clouds. Results. We investigated the impact of PDR geometry and agreed on the comparison of results from spherical and plane-parallel PDR models. We identified a number of key processes governing the chemical network which have been treated differently in the various codes such as the effect of PAHs on the electron density or the temperature dependence of the dissociation of CO by cosmic ray induced secondary photons, and defined a proper common treatment. We established a comprehensive set of reference models for ongoing and future PDR model bench-marking and were able to increase the agreement in model predictions for all benchmark models significantly. Nevertheless, the remaining spread in the computed observables such as the atomic fine-structure line intensities serves as a warning that there is still a considerable uncertainty when interpreting astronomical data with our models.

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.

Models for the structure of protoplanetary disks have so far been based on the assumption that the gas and the dust temperature are equal. The gas temperature, an essential ingredient in the equations of hydrostatic equilibrium of the disk, is then determined from a continuum radiative transfer calculation, in which the continuum opacity is provided by the dust. It has been long debated whether this assumption still holds in the surface layers of the disk, where the dust infrared emission features are produced. In this paper we compute the temperature of the gas in the surface layers of the disk in a self-consistent manner. The gas temperature is determined from a heating-cooling balance equation in which processes such as photoelectric heating, dissociative heating, dust-gas thermal heat exchange and line cooling are included. The abundances of the dominant cooling species such as CO, C, C + and O are determined from a chemical network based on the atomic species H, He, C, O, S, Mg, Si, Fe (Kamp & Bertoldi 2000). The underlying disk models to our calculations are the models of Dullemond et al. (2002). We find that in general the dust and gas temperature are equal to withing 10% for A V 0.1, which is above the location of the 'super-heated surface layer' in which the dust emission features are produced (Chiang & Goldreich 1997, e.g.). High above the disk surface the gas temperature exceeds the dust temperature and can can become -in the presence of polycyclic aromatic hydrocarbonsas high as 600 K at a radius of 100 AU. This is a region where CO has fully dissociated, but a significant fraction of hydrogen is still in molecular form. The densities are still high enough for non-negligible H 2 emission to be produced. At radii inward of 50 AU, the temperature of the gas above the photosphere can reach up to ∼ 10 4 K. In the disk surface layers, the gas temperature exceeds the virial temperature of hydrogen. Some of this material could possibly evaporate, but firm conclusions have to await the fully self-consistent disk models, where the disk structure and gas temperature determination will be solved iteratively.