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.

Abstract. We present spectroscopic observations of a large sample of Herbig Ae stars in the 10 µm spectral region. We perform compositional fits of the spectra based on properties of homogeneous as well as inhomogeneous spherical particles, and derive the mineralogy and typical grain sizes of the dust responsible for the 10 µm emission. Several trends are reported that can constrain theoretical models of dust processing in these systems: i) none of the sources consists of fully pristine dust comparable to that found in the interstellar medium; ii) all sources with a high fraction of crystalline silicates are dominated by large grains; iii) the disks around more massive stars (M > ∼ 2.5 M , L > ∼ 60 L ) have a higher fraction of crystalline silicates than those around lower mass stars, iv) in the subset of lower mass stars (M < ∼ 2.5 M ) there is no correlation between stellar parameters and the derived crystallinity of the dust. The correlation between the shape and strength of the 10 micron silicate feature reported by van Boekel et al. (2003) is reconfirmed with this larger sample. The evidence presented in this paper is combined with that of other studies to present a likely scenario of dust processing in Herbig Ae systems. We conclude that the present data favour a scenario in which the crystalline silicates are produced in the innermost regions of the disk, close to the star, and transported outward to the regions where they can be detected by means of 10 micron spectroscopy. Additionally, we conclude that the final crystallinity of these disks is reached very soon after active accretion has stopped.

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.

Abstract. In this paper we study the combined effects of size and shape of small solid state particles on the absorption, emission and scattering characteristics. We use the statistical approach to calculate these optical properties. In this approach the average optical properties of an ensemble of particles in random orientation are represented by the average optical properties of an ensemble of simple shapes. The validity of this approach is studied in detail for a uniform distribution of hollow spheres where the fractional volume of the central inclusion is varied. We apply the results to two different areas of interest, i) infrared spectroscopy; and ii) polarization of scattered light. The effects of particle size and shape on the optical characteristics are discussed. We compare the results using the distribution of hollow spheres with those obtained by using randomly oriented spheroids. Also we compare the results with observations and laboratory measurements. The distribution of hollow spheres is very successful in reproducing laboratory measurements of the scattering angle distribution of the degree of linear polarization for incident unpolarized light of randomly oriented irregular quartz particles. Furthermore, we show that we are able to derive the size distribution of dust grains by fitting the measured degree of linear polarization using computational result for hollow spheres. It is shown that the distribution of hollow spheres is a powerful tool for studying light scattering, absorption and emission by cosmic dust grains and in particular when large numbers of particle parameters need to be considered since the computational demand of the distribution of hollow spheres is small.