A model for irradiated dust disks around Herbig Ae stars is proposed. The model is based on the flaring disk model of Chiang & Goldreich (1997, henceforth CG97), but with the central regions of the disk removed. The inner rim of the disk is puffed up and is much hotter than the rest of the disk, because it is directly exposed to the stellar flux. If located at the dust evaporation radius, its reemitted flux produces a conspicuous bump in the SED which peaks at 2-3 micron. We propose that this emission is the explanation for the near-infrared bump observed in the SEDs of Herbig Ae stars. We study for which stellar parameters this bump would be observable, and find that it is the case for Herbig Ae stellar parameters but not for T-Tauri stars, confirming what is found from the observations. We also study the effects of the shadow cast by the inner rim over the rest of the flaring disk. The shadowed region can be quite large, and under some circumstances the entire disk may lie in the shadow. This shadowed region will be much cooler than an unshadowed flaring disk, since its only heating sources are radial radiative diffusion and possible indirect sources of irradiation. Under certain special circumstances the shadowing effect can suppress, or even completely eliminate, the 10 micron emission feature from the spectrum, which might explain the anomalous SEDs of some isolated Herbig Ae stars in the sample of Meeus et al. (2001). At much larger radii the disk emerges from the shadow, and continues as a flaring disk towards the outer edge. The emission from the inner rim contributes significantly to the irradiation of this flaring disk. The complete semi-analytical model, including structure of the inner edge, shadowed region and the flared outer part, is described in detail in this paper, and we show examples of the general behavior of the model for varying parameters.

Even though dust coagulation is a very important dust-processing mechanism in interstellar space and protoplanetary disks, there are still important parts of the physics involved that are poorly understood. This imposes a serious problem for model calculations of any kind. In this paper, we attempt to improve the situation by including the e †ects of tangential forces on the contact in some detail. These have been studied in recent papers. We summarize the main results from these papers and apply them to detailed simulations of the coagulation process and of collisions between dust aggregates. Our results show the following : (1) the growth of aggregates by monomers will normally not involve major restructuring of the aggregates, (2) the classical hit-and-stick assumption is reasonably valid for this case, (3) collisions of aggregates with each other or with large grains can lead to signiÐcant compaction, and (4) the results can be easily understood in terms of critical energies for di †erent restructuring processes. We also derive a short summary that may be used as a recipe for determining the outcome of collisions in coagulation calculations. It is shown that turbulent velocity Ðelds in interstellar clouds are capable of producing considerably compressed aggregates, while the small aggregates forming early on in the solar nebula will not be compacted by collisions. However, compaction provides an important energy sink in collisions of larger aggregates in the solar nebula.

Abstract.We model the process of dust coagulation in protoplanetary disks and calculate how it affects their observational appearance. Our model involves the detailed solution of the coagulation equation at every location in the disk. At regular time intervals we feed the resulting 3D dust distribution functions into a continuum radiative transfer code to obtain spectral energy distributions. We find that, even if only the very basic -and well understood -coagulation mechanisms are included, the process of grain growth is much too quick to be consistent with infrared observations of T Tauri disks. Small grains are removed so efficiently that, long before the disk reaches an age of 10 6 years typical of T Tauri stars, the SED shows only very weak infrared excess. This is inconsistent with observed SEDs of most classical T Tauri stars. Small grains must be replenished, for instance by aggregate fragmentation through high-speed collisions. A very simplified calculation shows that when aggregate fragmentation is included, a quasi-stationary grain size distribution is obtained in which growth and fragmentation are in equilibrium. This quasi-stationary state may last 10 6 years or even longer, depending on the circumstances in the disk, and may bring the time scales into the right regime. If this is indeed the case, or if other processes are responsible for the replenishment of small grains, then the typical grain sizes inferred from infrared spectral features of T Tauri disks do not necessarily reflect the age of the system (small grains → young, larger grains → older), as is often proposed. Indeed, there is evidence reported in the literature that the typical inferred grain sizes do not correlate with the age of the star. Instead, it is more likely that the typical grain sizes found in T Tauri star (and Herbig Ae/Be star and Brown Dwarf) disks reflect the state of the disk in some more complicated way, e.g. the strength of the turbulence, the amount of dust mass transformed into planetesimals, the amount of gas lost via evaporation etc. A simple evolutionary scenario in which grains slowly grow from pristine 0.1 µm grains to larger grains over a period of a few Myr is most likely incorrect.

Abstract. Isolated Herbig Ae stars can be divided into two groups (Meeus et al. 2001): those with an almost flat spectral energy distribution in the mid-infrared ("group I"), and those with a strong decline towards the far-infrared ("group II"). In this paper we show that the group I vs. II distinction can be understood as arising from flaring vs. self-shadowed disks. We show that these two types of disks are natural solutions of the 2D radiation-hydrostatic structure equations. Disks with high optical depth turn out to be flaring and have a strong far-IR emission, while disks with an optical depth below a certain threshold drop into the shadow of their own puffed-up inner rim and are weak in the far-IR. In spite of not having a directly irradiated surface layer, self-shadowed disks still display dust features in emission, in agreement with observations of group II sources. We propose an evolutionary scenario in which a disk starts out with a flaring shape (group I source), and then goes through the process of grain growth, causing the optical depth of the disk to drop and the disk to become self-shadowed (group II source). We show that this scenario predicts that the (sub-)millimeter slope of the disk changes from steep (small grains) to Rayleigh-Jeans-like (large grains) in the early stages of evolution, so that all group II sources are expected to have Rayleigh-Jeans-like slopes, while some group I sources may still have steep (sub-)millimeter slopes.

Abstract. We analyze how the process of dust settling affects the spectral energy distribution and optical appearance of protoplanetary disks. Using simple analytic estimates on the one hand, and detailed 1+1-D models on the other hand, we show that, while the time scale for settling down to the equator may exceed the life time of the disk, it takes much less time for even small grains of 0.1 µm to settle down to a few pressure scale heights. This is often well below the original location of the disk's photosphere, and the disk therefore becomes effectively "flatter". If turbulent stirring is included, a steady state solution can be found, which is typically reached after a few ×10 5 years. In this state, the downward settling motion of the dust is balanced by vertical stirring. Dependent on the strength of the turbulence, the shape of the disk in such a steady state can be either fully flaring, or flaring only up to a certain radius and self-shadowed beyond that radius. These geometries are similar to the geometries that were found for disks around Herbig Ae/Be stars in our previous papers (Dullemond 2002, A&A, 395, 853; Dullemond & Dominik 2004, A&A, 417, 159, henceforth DD04). In those papers, however, the reason for a disk to turn self-shadowed was by loss of optical depth through dust grain growth. Here we show that dust settling can achieve a similar effect without loss of vertical optical depth, although the self-shadowing in this case only affects the outer regions of the disk, while in DD04 the entire disk outside of the puffed-up inner rim was shadowed. In reality it is likely that both grain growth and grain settling act simultaneously. The spectral energy distributions of such self-shadowed -or partly self-shadowed -disks have a relatively weak far-infrared excess (in comparison to flaring disks). We show here that, when dust settling is the cause of self-shadowing, these self-shadowed regions of the disk are also very weak in resolved images of scattered light. A reduction in the brightness was already predicted in DD04, but we find that dust settling is far more efficient than grain growth at dimming the scattered light image of the disk. Settling is also efficient in steepening the spectral energy distribution at mid-to far-infrared wavelengths. From the calculations with compact grains it follows that, after about 10 6 years, most disks should be self-shadowed. The fact that some older disks are still observed with the characteristics of flaring disks therefore seems somewhat inconsistent with the time scales predicted by the settling model based on compact grains. This suggests that perhaps even the small grains ( < ∼ 0.1 µm) have a porous or fractal structure, slowing down the settling. Alternatively, it could mean that the different geometries of observed disks is merely a reflection of the turbulent state of these disks.

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.

We present the first part of our Disks ARound TTauri Stars with SPHERE (DARTTS-S) survey: observations of eight TTauri stars that were selected based on their strong (sub-)mm excesses using SPHERE / IRDIS polarimetric differential imaging (PDI) in the J and H bands. All observations successfully detect the disks, which appear vastly different in size, from ≈ 80 au in scattered light to >400 au, and display total polarized disk fluxes between 0.06% and 0.89% of the stellar flux. For five of these disks, we are able to determine the three-dimensional structure and the flaring of the disk surface, which appears to be relatively consistent across the different disks, with flaring exponents α between ≈ 1.1 and ≈ 1.6. We also confirm literature results with regard to the inclination and position angle of several of our disks and are able to determine which side is the near side of the disk in most cases. While there is a clear trend of disk mass with stellar ages (≈ 1 Myr to > 10 Myr), no correlations of disk structures with age were found. There are also no correlations with either stellar mass or sub-mm flux. We do not detect significant differences between the J and H bands. However, we note that while a high fraction (7/8) of the disks in our sample show ring-shaped substructures, none of them display spirals, in contrast to the disks around more massive Herbig Ae/Be stars, where spiral features are common.

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.