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. Solving the continuum radiative transfer equation in high opacity media requires sophisticated numerical tools. In order to test the reliability of such tools, we present a benchmark of radiative transfer codes in a 2D disc configuration. Methods. We test the accuracy of seven independently developed radiative transfer codes by comparing the temperature structures, spectral energy distributions, scattered light images, and linear polarisation maps that each model predicts for a variety of disc opacities and viewing angles. The test cases have been chosen to be numerically challenging, with midplane optical depths up 10 6 , a sharp density transition at the inner edge and complex scattering matrices. We also review recent progress in the implementation of the Monte Carlo method that allow an efficient solution to these kinds of problems and discuss the advantages and limitations of Monte Carlo codes compared to those of discrete ordinate codes. Results. For each of the test cases, the predicted results from the radiative transfer codes are within good agreement. The results indicate that these codes can be confidently used to interpret present and future observations of protoplanetary discs.

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.

We introduce a fast and versatile computer code, GGchem, to determine the chemical composition of gases in thermo-chemical equilibrium down to 100 K, with or without equilibrium condensation. We review the data for molecular equilibrium constants, k p (T ), from several sources and discuss which functional fits are most suitable for low temperatures. We benchmark our results against another chemical equilibrium code. We collect Gibbs free energies, ∆G• − f , for about 200 solid and liquid species from the NIST-JANAF database and the geophysical database SUPCRTBL. We discuss the condensation sequence of the elements with solar abundances in phase equilibrium down to 100 K. Once the major magnesium silicates Mg 2 SiO 4 [s] and MgSiO 3 [s] have formed, the dust/gas mass ratio jumps to a value of about 0.0045 which is significantly lower than the often assumed value of 0.01. Silicate condensation is found to increase the carbon/oxygen ratio (C/O) in the gas from its solar value of ∼ 0.55 up to ∼ 0.71, and, by the additional intake of water and hydroxyl into the solid matrix, the formation of phyllosilicates at temperatures below ∼ 400 K increases the gaseous C/O further to about 0.83. Metallic tungsten (W) is the first condensate found to become thermodynamically stable around 1600 − 2200 K (depending on pressure), several hundreds of Kelvin before subsequent materials like zirconium dioxide (ZrO 2 ) or corundum (Al 2 O 3 ) can condense. We briefly discuss whether tungsten, despite its low abundance of ∼ 2 × 10 −7 times the silicon abundance, could provide the first seed particles for astrophysical dust formation. The GGchem code is publicly available at https://github.com/pw31/GGchem.

Abstract. In this paper, we quantify and discuss the physical and surface chemical processes leading to the formation, temporal evolution and sedimentation of dust grains in brown dwarf and giant gas planet atmospheres: nucleation, growth, evaporation and gravitational settling. Considering dust particles of arbitrary sizes in the different hydrodynamical regimes (free molecular flow, laminar flow, turbulent flow), we evaluate the equilibrium drift velocities (final fall speeds) and the growth rates of the particles due to accretion of molecules. We show that a depth-dependent maximum size of the order of a max ≈ 1 µm (upper regions) . . . 100 µm (lower regions) exists, which depends on the condensate and the stellar parameters, beyond which gravitational settling is faster than growth. Larger particles can probably not be formed and sustained in brown dwarf atmospheres. We furthermore argue that the acceleration towards equilibrium drift is always very fast and that the temperature increase of the grains due to the release of latent heat during the growth process is negligible. Based on these findings, we formulate the problem of dust formation coupled to the local element depletion/enrichment of the gas in brown dwarf atmospheres by means of a system of partial differential equations. These equations state an extension of the moment method developed by Gail & Sedlmayr (1988) with an additional advective term to account for the effect of size-dependent drift velocities of the grains. A dimensionless analysis of the new equations reveals a hierarchy of nucleation → growth → drift → evaporation, which characterises the life cycle of dust grains in brown dwarf atmospheres. The developed moment equations can be included into hydrodynamics or classical stellar atmosphere models. Applications of this description will be presented in a forthcoming paper of this series.

Aims. It is commonly assumed that the massive winds of AGB stars are dust-driven and pulsation-enhanced. However, detailed frequency-dependent dynamical models that can explain the observed magnitudes of mass loss rates and outflow velocities have been published so far only for C-stars. This letter reports on first results of similar models for oxygen-rich AGB stars. The aim is to provide a better understanding of the wind driving mechanism, the dust condensation sequence, and the role of pulsations. Methods. New dynamical models for dust-driven winds of oxygen-rich AGB stars are presented which include frequency-dependent Monte Carlo radiative transfer by means of a sparse opacity distribution technique and a time-dependent treatment of the nucleation, growth and evaporation of inhomogeneous dust grains composed of a mixture of Mg 2 SiO 4 , SiO 2 , Al 2 O 3 , TiO 2 , and solid Fe. Results. The frequency-dependent treatment of radiative transfer reveals that the gas is cold close to the star (700−900 K at 1.5−2 R ) which facilitates the nucleation process. The dust temperatures are strongly material-dependent, with differences as large as 1000 K for different pure materials, which has an important influence on the dust formation sequence. Two dust layers are formed in the dynamical models: almost pure glassy Al 2 O 3 close to the star (r > ∼ 1.5 R ) and the more opaque Fe-poor Mg-Fe-silicates further out. Solid Fe and Fe-rich silicates are found to be the only condensates that can efficiently absorb the stellar light in the near IR. Consequently, they play a key role in the wind driving mechanism and act as a thermostat. Only small amounts of Fe can be incorporated into the grains, because otherwise the grains become too hot. Thus, the models reveal almost no mass loss, and no dust shells. Conclusions. The observed dust sequence Al 2 O 3 → Fe-poor Mg-Fe-silicates for oxygen-rich AGB stars having low → high mass loss rates is in agreement with the presented model and can be understood as follows: Al 2 O 3 is present in the extended atmosphere of the star below the wind acceleration region, also without mass loss. The Mg-Fe-silicates form further out and, therefore, their amount depends on the mass loss rate. The driving mechanism of oxygen-rich AGB stars is still an unsolved puzzle.

Context. Observations of exoplanet atmospheres have revealed the presence of cloud particles in their atmospheres. 3D modelling of cloud formation in atmospheres of extrasolar planets coupled to the atmospheric dynamics has long been a challenge. Aims. We investigate the thermo-hydrodynamic properties of cloud formation processes in the atmospheres of hot Jupiter exoplanets. Methods. We simulate the dynamic atmosphere of HD 189733b with a 3D model that couples 3D radiative-hydrodynamics with a kinetic, microphysical mineral cloud formation module designed for RHD/GCM exoplanet atmosphere simulations. Our simulation includes the feedback effects of cloud advection and settling, gas phase element advection and depletion/replenishment and the radiative effects of cloud opacity. We model the cloud particles as a mix of mineral materials which change in size and composition as they travel through atmospheric thermo-chemical environments. All local cloud properties such as number density, grain size and material composition are time-dependently calculated. Gas phase element depletion as a result of cloud formation is included in the model. In situ effective medium theory and Mie theory is applied to calculate the wavelength dependent opacity of the cloud component. Results. We present a 3D cloud structure of a chemically complex, gaseous atmosphere of the hot Jupiter HD 189733b. Mean cloud particle sizes are typically sub-micron (0.01−0.5 µm) at pressures less than 1 bar with hotter equatorial regions containing the smallest grains. Denser cloud structures occur near terminator regions and deeper (∼1 bar) atmospheric layers. Silicate materials such as MgSiO 3 [s] are found to be abundant at mid-high latitudes, while TiO 2 [s] and SiO 2 [s] dominate the equatorial regions. Elements involved in the cloud formation can be depleted by several orders of magnitude. Conclusions. The interplay between radiative-hydrodynamics and cloud kinetics leads to an inhomogeneous, wavelength dependent opacity cloud structure with properties differing in longitude, latitude and depth. This suggests that transit spectroscopy would sample a variety of cloud particles properties (sizes, composition, densities).