Peter Woitke

Radiation thermo-chemical models of protoplanetary disks - I. Hydrostatic disk structure and inner rim

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

Benchmark problems for continuum radiative transfer. High optical depths, anisotropic scattering, and polarisation

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. 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. 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.

Dust in brown dwarfs II. The coupled problem of dust formation and sedimentation

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 amax ≈1 µm(upper regions) .. .100 µm(lower regions) exists, which depends on the condensate and the stellar parameters, be- yond 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 tem- perature 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 at- mospheres 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 ve- locities 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.

The 2D continuum radiative transfer problem : Benchmark results for disk configurations

We present benchmark problems and solutions for the continuum radiative transfer (RT) in a 2D disk configuration. The reliability of three Monte-Carlo and two grid-based codes is tested by comparing their results for a set of well-defined cases which differ for optical depth and viewing angle. For all the configurations, the overall shape of the resulting temperature and spectral energy distribution is well reproduced. The solutions we provide can be used for the verification of other RT codes. We also point out the advantages and disadvantages of the various numerical techniques applied to solve the RT problem.

An icy Kuiper belt around the young solar-type star HD 181327

Context. HD 181327 is a young main sequence F5/F6 V star belonging to the beta Pictoris moving group (age similar to 12 Myr). It harbors an optically thin belt of circumstellar material at radius similar to 90 AU, presumed to result from collisions in a population of unseen planetesimals. Aims. We aim to study the dust properties in the belt in details, and to constrain the gas-to-dust ratio. Methods. We obtained far-infrared photometric observations of HD 181327 with the PACS instrument onboard the Herschel Space Observatory(star), complemented by new 3.2 mm observations carried with the ATCA(star star) array. The geometry of the belt is constrained with newly reduced HST/NICMOS scattered light images that allow the degeneracy between the disk geometry and the dust properties to be broken. We then use the radiative transfer code GRATER to compute a large grid of models, and we identify the grain models that best reproduce the spectral energy distribution (SED) through a Bayesian analysis. We attempt to detect the oxygen and ionized carbon fine-structure lines with Herschel/PACS spectroscopy, providing observables to our photochemical code ProDiMo. Results. The HST observations confirm that the dust is confined in a narrow belt. The continuum is detected with Herschel/PACS completing nicely the SED in the far-infrared. The disk is marginally resolved with both PACS and ATCA. A medium integration of the gas spectral lines only provides upper limits on the [OI] and [CII] line fluxes. We show that the HD 181327 dust disk consists of micron-sized grains of porous amorphous silicates and carbonaceous material surrounded by an important layer of ice, for a total dust mass of similar to 0.05 M-circle plus. (in grains up to 1 mm). We discuss evidences that the grains consists of fluffy aggregates. The upper limits on the gas atomic lines do not provide unambiguous constraints: only if the PAH abundance is high, the gas mass must be lower than similar to 17 M-circle plus. Conclusions. Despite the weak constraints on the gas disk, the age of HD 181327 and the properties of the dust disk suggest that it has passed the stage of gaseous planets formation. The dust reveals a population of icy planetesimals, similar to the primitive Edgeworth-Kuiper belt, that may be a source for the future delivery of water and volatiles onto forming terrestrial planets.

Consistent dust and gas models for protoplanetary disks I. Disk shape, dust settling, opacities, and PAHs

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 H2, 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.

CONSISTENT SIMULATIONS OF SUBSTELLAR ATMOSPHERES AND NONEQUILIBRIUM DUST CLOUD FORMATION

We aim to understand cloud formation in substellar objects. We combined the non-equilibrium, stationary cloud model of Helling, Woitke & Thi (2008; seed formation, growth, evaporation, gravitational settling, element conservation) with the general-purpose model atmosphere code Phoenix (radiative transfer, hydrostatic equilibrium, mixing length theory, chemical equilibrium) in order to consistently calculate cloud formation and radiative transfer with their feedback on convection and gas phase depletion. We calculate the complete 1D model atmosphere structure and the chemical details of the cloud layers. The DriftPhoenix models enable the first stellar atmosphere simulation that is based on the actual cloud formation process. The resulting (T, p) profiles differ considerably from the previous limiting Phoenix cases Dusty and Cond. A tentative comparison with observations demonstrates that the determination of effective temperatures based on simple cloud models has to be applied with care. Based on our new models, we suggest a mean Teff = 1800K for the L-dwarf twin-binary system DENIS J0205-1159 which is up to 500K hotter than suggested in the literature. We show transition spectra for gas-giant planets which form dust clouds in their atmospheres and evaluate photometric fluxes for a WASP-1 type system.

Dust in brown dwarfs. III. Formation and structure of quasi-static cloud layers

In this paper, first solutions of the dust moment equations developed in (Woitke & Helling 2003) for the description of dust formation and precipitation in brown dwarf and giant gas planet atmospheres are presented. We consider the special case of a static brown dwarf atmosphere, where dust particles continuously nucleate from the gas phase, grow by the accre- tion of molecules, settle gravitationally and re-evaporate thermally. Mixing by convective overshoot is assumed to replenish the atmosphere with condensable elements, which is necessary to counterbalance the loss of condensable elements by dust formation and gravitational settling (no dust without mixing). Applying a kinetic description of the relevant microphysical and chemical processes for TiO2-grains, the model makes predictions about the large-scale stratification of dust in the atmosphere, the depletion of molecules from the gas phase, the supersaturation of the gas in the atmosphere as well as the mean size and the mass fraction of dust grains as function of depth. Our results suggest that the presence of relevant amounts of dust is re- stricted to a layer, where the upper boundary (cloud deck) is related to the requirement of a minimum mixing activity (mixing time-scale τmix ≈ 10 6 s) and the lower boundary (cloud base) is determined by the thermodynamical stability of the grains. The nucleation occurs around the cloud deck where the gas is cool, strongly depleted, but nevertheless highly supersaturated (S � 1). These particles settle gravitationally and populate the warmer layers below, where the in situ formation (nucleation) is ineffective or even not possible. During their descent, the particles grow and reach mean radii of ≈30 µm ... 400 µm at the cloud base, but the majority of the particles in the cloud layer remains much smaller. Finally, the dust grains sink into layers which are sufficiently hot to cause their thermal evaporation. Hence, an effective transport mechanism for condensable elements exists in brown dwarfs, which depletes the gas above and enriches the gas below the cloud base of a considered solid/liquid material. The dust-to-gas mass fraction in the cloud layer results to be approximately given by the mass fraction of condensable elements in the gas being mixed up. Only for artificially reduced mixing we find a self-regulation mechanism that approximately installs phase equilibrium (S ≈ 1) in a limited region around the cloud base.

2D models for dust-driven AGB star winds

New axisymmetric (2D) models for dust-driven winds of C-stars are presented which include hydrodynamics with radiation pressure on dust, equilibrium chemistry and time-dependent dust formation with coupled grey Monte Carlo radiative transfer. Considering the simplest case without stellar pulsation (hydrostatic inner boundary condition) these models reveal a more complex picture of the dust formation and wind acceleration than earlier published spherically symmetric (1D) models. The so-called exterior κ-mechanism causes radial oscillations with short phases of active dust formation between longer phases without appreciable dust formation, just like in the 1D models. However, in 2D geometry, the oscillations can be out-of-phase at different places above the stellar atmosphere which results in the formation of dust arcs or smaller caps that only occupy a certain fraction of the total solid angle. These dust structures are accelerated outward by radiation pressure, expanding radially and tangentially like mushroom clouds, while dust-poor matter is falling back towards the star at other places. A highly dynamical and turbulent dust formation zone is created in this way, which again leads to inhomogeneous dust production. Further away from the star, flow instabilities (e.g. Rayleigh-Taylor) have time to fragment the outward moving arcs and shells to produce numerous small-scale cloud-like sub-structures.

GASPS—A Herschel survey of gas and dust in protoplanetary disks: summary and initial statistics

We describe a large-scale far-infrared line and continuum survey of protoplanetary disk through to young debris disk systems carried out using the ACS instrument on the Herschel Space Observatory. This Open Time Key program, known as GASPS (Gas Survey of Protoplanetary Systems), targeted similar to 250 young stars in narrow wavelength regions covering the [OI] fine structure line at 63 mu m the brightest far-infrared line in such objects. A subset of the brightest targets were also surveyed in [OI]145 mu m, [CII] at 157 mu m, as well as several transitions of H2O and high-excitation CO lines at selected wavelengths between 78 and 180 mu m. Additionally, GASPS included continuum photometry at 70, 100 and 160 mu m, around the peak of the dust emission. The targets were SED Class II-III T Tauri stars and debris disks from seven nearby young associations, along with a comparable sample of isolated Herbig AeBe stars. The aim was to study the global gas and dust content in a wide sample of circumstellar disks, combining the results with models in a systematic way. In this overview paper we review the scientific aims, target selection and observing strategy of the program. We summarise some of the initial results, showing line identifications, listing the detections, and giving a first statistical study of line detectability. The [OI] line at 63 mu m was the brightest line seen in almost all objects, by a factor of similar to 10. Overall [OI]63 mu m detection rates were 49%, with 100% of HAeBe stars and 43% of T Tauri stars detected. A comparison with published disk dust masses (derived mainly from sub-mm continuum, assuming standard values of the mm mass opacity) shows a dust mass threshold for [OI] 63 mu m detection of similar to 10(-5) M-circle dot. Normalising to a distance of 140 pc, 84% of objects with dust masses >= 10(-5) M-circle dot can be detected in this line in the present survey; 32% of those of mass 10(-6)-10(-5) M-circle dot, and only a very small number of unusual objects with lower masses can be detected. This is consistent with models with a moderate UV excess and disk flaring. For a given disk mass, [OI] detectability is lower for M stars compared with earlier spectral types. Both the continuum and line emission was, in most systems, spatially and spectrally unresolved and centred on the star, suggesting that emission in most cases was from the disk. Approximately 10 objects showed resolved emission, most likely from outflows. In the GASPS sample, [OI] detection rates in T Tauri associations in the 0.3-4 Myr age range were similar to 50%. For each association in the 5-20 Myr age range, similar to 2 stars remain detectable in [OI]63 mu m, and no systems were detected in associations with age >20 Myr. Comparing with the total number of young stars in each association, and assuming a ISM-like gas/dust ratio, this indicates that similar to 18% of stars retain a gas-rich disk of total mass similar to 1 M-Jupiter for 1-4 Myr, 1-7% keep such disks for 5-10 Myr, but none are detected beyond 10-20 Myr. The brightest [OI] objects from GASPS were also observed in [OI]145 mu m, [CII]157 mu m and CO J = 18 - 17, with detection rates of 20-40%. Detection of the [CII] line was not correlated with disk mass, suggesting it arises more commonly from a compact remnant envelope.