Abstract
The European FP7 project DIANA has performed a coherent analysis of a large set of observational data of protoplanetary disks by means of thermo-chemical disk models. The collected data ...include extinction-corrected stellar UV and X-ray input spectra (as seen by the disk), photometric fluxes, low and high resolution spectra, interferometric data, emission line fluxes, line velocity profiles and line maps, which probe the dust, polycyclic aromatic hydrocarbons (PAHs) and the gas in these objects. We define and apply a standardized modeling procedure to fit these data by state-of-the-art modeling codes (
ProDiMo
,
MCFOST
,
MCMax
), solving continuum and line radiative transfer (RT), disk chemistry, and the heating and cooling balance for both the gas and the dust. 3D diagnostic RT tools (e.g., FLiTs) are eventually used to predict all available observations from the same disk model, the DIANA-standard model. Our aim is to determine the physical parameters of the disks, such as total gas and dust masses, the dust properties, the disk shape, and the chemical structure in these disks. We allow for up to two radial disk zones to obtain our best-fitting models that have about 20 free parameters. This approach is novel and unique in its completeness and level of consistency. It allows us to break some of the degeneracies arising from pure Spectral Energy Distribution (SED) modeling. In this paper, we present the results from pure SED fitting for 27 objects and from the all inclusive DIANA-standard models for 14 objects. Our analysis shows a number of Herbig Ae and T Tauri stars with very cold and massive outer disks which are situated at least partly in the shadow of a tall and gas-rich inner disk. The disk masses derived are often in excess to previously published values, since these disks are partially optically thick even at millimeter wavelength and so cold that they emit less than in the Rayleigh–Jeans limit. We fit most infrared to millimeter emission line fluxes within a factor better than 3, simultaneously with SED, PAH features and radial brightness profiles extracted from images at various wavelengths. However, some line fluxes may deviate by a larger factor, and sometimes we find puzzling data which the models cannot reproduce. Some of these issues are probably caused by foreground cloud absorption or object variability. Our data collection, the fitted physical disk parameters as well as the full model output are available to the community through an online database (
http://www.univie.ac.at/diana
).
Context
. The bulk abundances of CHNOS-bearing species of a planet have a profound effect on its interior structure and evolution. Therefore, it is key to investigate the behavior of the local ...abundances of these elements in the solid phase in the earliest stages of planet formation, where micrometer-sized dust grows into larger and larger aggregates. However, the physical and chemical processes occurring in planet-forming disks that shape these abundances are highly coupled and nonlocal.
Aims
. We aim to quantify the effects of the interplay between dynamical processes (turbulent diffusion, dust settling and radial drift), collision processes (coagulation and fragmentation), and the adsorption and desorption of ices on the abundances of CHNOS in local disk solids as a function of position throughout the planet-forming region.
Methods
. We used SHAMPOO (Stochastic Monomer Processor), which tracks the ice budgets of CHNOS-bearing molecules of a dust monomer as it undergoes nonlocal disk processing in a Class I disk. We used a large set of individual monomer evolutionary trajectories to make inferences about the properties of the local dust populations via a stochastic analysis of 64 000 monomers on a preexisting spatial grid.
Results
. We find that spatially, monomers can travel larger distances farther out in the disk, leading to a larger spread in positions of origin for a dust population at, for example,
r
= 50 AU compared to
r
= 2 AU. However, chemically, the inner disk (
r
≲ 10 AU) is more nonlocal due to the closer spacing of ice lines in this disk region. Although to zeroth order the bulk ice mantle composition of icy dust grains remains similar compared to a fully local dust population, the ice mass associated with individual chemical species can change significantly. The largest differences with local dust populations were found near ice lines where the collisional timescale is comparable to the adsorption and desorption timescales. Here, aggregates may become significantly depleted in ice as a consequence of microscopic collisional mixing, a previously unknown effect where monomers are stored away in aggregate interiors through rapid cycles of coagulation and fragmentation.
Conclusions
. Nonlocal ice processing in a diffusion-dominated, massive, smooth disk has the most significant impact on the inner disk (
r
≲ 10 AU). Furthermore, microscopic collisional mixing can have a significant effect on the amounts of ice of individual species immediately behind their respective ice lines. This suggests that ice processing is highly coupled to collisional processing in this disk region, which implies that the interiors of dust aggregates must be considered and not just their surfaces.
Context.
The analysis of spectral energy distributions (SEDs) of protoplanetary disks to determine their physical properties is known to be highly degenerate. Hence, a full Bayesian analysis is ...required to obtain parameter uncertainties and degeneracies. The main challenge here is computational speed, as one proper full radiative transfer model requires at least a couple of CPU minutes to compute.
Aims.
We performed a full Bayesian analysis for 30 well-known protoplanetary disks to determine their physical disk properties, including uncertainties and degeneracies. To circumvent the computational cost problem, we created neural networks (NNs) to emulate the SED generation process.
Methods.
We created two sets of MCFOST Monte Carlo radiative transfer disk models to train and test two NNs that predict SEDs for continuous and discontinuous disks, with 18 and 26 free model parameters, respectively. A Bayesian analysis was then performed on 30 protoplanetary disks with SED data collected by the FP7-Space DIANA project to determine the posterior distributions of all parameters. We ran this analysis twice, (i) with old distances and additional parameter constraints as used in a previous study, to compare results, and (ii) with updated distances and free choice of parameters to obtain homogeneous and unbiased model parameters. We evaluated the uncertainties in the determination of physical disk parameters from SED analysis, and detected and quantified the strongest degeneracies.
Results.
The NNs are able to predict SEDs within ~1 ms with uncertainties of about 5% compared to the true SEDs obtained by the radiative transfer code. We find parameter values and uncertainties that are significantly different from previous values obtained by
χ
2
fitting. Comparing the global evidence for continuous and discontinuous disks, we find that 26 out of 30 objects are better described by disks that have two distinct radial zones. The analysed sample shows a significant trend for massive disks to have small scale heights, which is consistent with lower midplane temperatures in massive disks. We find that the frequently used analytic relationship between disk dust mass and millimetre-flux systematically underestimates the dust mass for high-mass disks (dust mass ≥10
−4
M
⊙
). We determine how well the dust mass can be determined with our method for different numbers of flux measurements. As a byproduct, we created an interactive graphical tool that instantly returns the SED predicted by our NNs for any parameter combination.
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 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.
Context
. Stars in the solar neighbourhood have refractory element ratios slightly different from that of the Sun. It is unclear how much the condensation of solids and thus the composition of ...planets forming around these stars is affected.
Aims
. We aim to understand the impact of changing the ratios of the refractory elements Mg, Si, and Fe within the range observed in solar-type stars within 150 pc of the Sun on the composition of planets forming around them.
Methods
. We use the GGchem code to simulate the condensation of solids in protoplanetary disks with a minimum mass solar nebula around main sequence G-type stars in the solar neighbourhood. We extract the stellar elemental composition from the Hypatia Database.
Results
. We find that a lower Mg/Si ratio shifts the condensation sequence from forsterite (Mg
2
SiO
4
) and SiO to enstatite (MgSiO
3
) and quartz (SiO
2
); a lower Fe/S ratio leads to the formation of FeS and FeS
2
and few or no Fe-bearing silicates. Ratios of refractory elements translate directly from the gas phase to the condensed phase for T < 1000 K. However, ratios with respect to volatile elements (e.g. oxygen and sulphur) in the condensates – the building blocks of planets – differ from the original stellar composition.
Conclusions
. Our study shows that the composition of planets crucially depends on the abundances of the stellar system under investigation. Our results can have important implications for planet interiors, which depend strongly on the degree of oxidation and the sulphur abundance.
Context.
Spatially resolved continuum observations of planet-forming disks show prominent ring and gap structures in their dust distribution. However, the picture from gas observations is much less ...clear and constraints on the radial gas density structure (i.e. gas gaps) remain rare and uncertain.
Aims.
We want to investigate the importance of thermo-chemical processes for the interpretation of high-spatial-resolution gas observations of planet-forming disks and their impact on the derived gas properties.
Methods.
We applied the radiation thermo-chemical disk code P
RO
D
I
M
O
(PROtoplanetary DIsk MOdel) to model the dust and gas disk of HD 163296 self-consistently, using the DSHARP (Disk Substructure at High Angular Resolution) gas and dust observations. With this model we investigated the impact of dust gaps and gas gaps on the observables and the derived gas properties, considering chemistry, and heating and cooling processes.
Results.
We find distinct peaks in the radial line intensity profiles of the CO line data of HD 163296 at the location of the dust gaps. Our model indicates that those peaks are not only a consequence of a gas temperature increase within the gaps but are mainly caused by the absorption of line emission from the back side of the disk by the dust rings. For two of the three prominent dust gaps in HD 163296, we find that thermo-chemical effects are negligible for deriving density gradients via measurements of the rotation velocity. However, for the gap with the highest dust depletion, the temperature gradient can be dominant and needs to be considered to derive accurate gas density profiles.
Conclusions.
Self-consistent gas and dust thermo-chemical modelling in combination with high-quality observations of multiple molecules are necessary to accurately derive gas gap depths and shapes. This is crucial to determine the origin of gaps and rings in planet-forming disks and to improve the mass estimates of forming planets if they are the cause of the gap.
Context. The MIRI instrument on board the James Webb Space Telescope probes the chemistry and dust mineralogy of the inner regions of protoplanetary disks. The observed spectra are unprecedented in ...their detail and reveal a rich chemistry with strong diversity between objects. This complicates interpretations that are mainly based on manual continuum subtraction and 0D slab models. Aims. We investigate the physical conditions under which the gas emits in protoplanetary disks. Based on MIRI spectra, we apply a full Bayesian analysis that provides the posterior distributions of dust and molecular properties, such as column densities and emission temperatures. Methods. To do so, we introduced the Dust Continuum Kit with Line emission from Gas (DuCKLinG), a Python-based model simultaneously describing the molecular line emission and the dust continuum of protoplanetary disks without large computational cost. The model describes the dust continuum emission by dust models with precomputed dust opacities. The molecular emission is based on LTE slab models but from extended radial ranges with gradients in column densities and emission temperatures. We compare the model to observations using Bayesian analysis with linear regression techniques to reduce the dimension of the parameter space. We benchmarked this model to a complex thermo-chemical ProDiMo model of AATau and fit the MIRI spectrum of GW Lup. The latter allowed for a comparison to the previous results obtained with single slab models and hand-fitted continuum. Results. We successfully decrease the computational time of the fitting method by a factor of 80 by eliminating linear parameters, such as the emission areas, from the Bayesian run. This approach does not significantly change the retrieved molecular parameters, and only the calculated errors on the optically thin dust masses slightly decrease. For an AA Tau ProDiMo mock observation, we find that the retrieved molecular conditions from DuCKLinG (column densities from 3 × 10 18 cm −2 to 4 × 10 20 cm −2 , radial range from 0.2 au to 1.2 au, and temperature range from about 200 K to 400 K) fall within the true values from ProDiMo (column densities between 4 × 10 17 cm -2 to 5 × 10 20 cm −2 , radial extent 0.1 au to 6.6 au, and temperature range from about 120 to 1000 K). The smaller DuCKLinG ranges can be explained by the relative flux contributions of the different parts of ProDiMo. The parameter posterior of GW Lup reinforces previously found results. The previously determined column densities fall within the retrieved ranges in this study for all examined molecules (CO 2 , H 2 O, HCN, and C 2 H 2 ). Similar overlap is found for the temperatures with only the temperature range of HCN (from 570 −60 +60 to 750 −70 +90 K) not including the previously found value (875 K). This discrepancy may be due to the simultaneous fitting of all molecules compared to the step-by-step fitting of the previous study. There is statistically significant evidence for radial temperature and column density gradients for H 2 O and CO 2 compared to the constant temperature and column density assumed in the 0D slab models. Additionally, HCN and C 2 H 2 emit from a small region with near constant conditions. Due to the small selected wavelength range 13.6–16.3 µm, the dust properties are not well constrained for GW Lup. DuCKL inG can become an important tool to analyse the molecular emission and dust mineralogy of large samples based on JWST /MIRI spectra in an automated way.
Context. Anomalies in the abundance measurements of short lived radionuclides in meteorites indicate that the protosolar nebulae was irradiated by a large number of energetic particles (E ≳ 10 MeV). ...The particle flux of the contemporary Sun cannot explain these anomalies. However, similar to T Tauri stars the young Sun was more active and probably produced enough high energy particles to explain those anomalies. Aims. We aim to study the interaction of stellar energetic particles with the gas component of the disk (i.e. ionization of molecular hydrogen) and identify possible observational tracers of this interaction. Methods. We used a 2D radiation thermo-chemical protoplanetary disk code to model a disk representative for T Tauri stars. We used a particle energy distribution derived from solar flare observations and an enhanced stellar particle flux proposed for T Tauri stars. For this particle spectrum we calculated the stellar particle ionization rate throughout the disk with an accurate particle transport model. We studied the impact of stellar particles for models with varying X-ray and cosmic-ray ionization rates. Results. We find that stellar particle ionization has a significant impact on the abundances of the common disk ionization tracers HCO+ and N2H+, especially in models with low cosmic-ray ionization rates (e.g. 10-19 s-1 for molecular hydrogen). In contrast to cosmic rays and X-rays, stellar particles cannot reach the midplane of the disk. Therefore molecular ions residing in the disk surface layers are more affected by stellar particle ionization than molecular ions tracing the cold layers and midplane of the disk. Conclusions. Spatially resolved observations of molecular ions tracing different vertical layers of the disk allow to disentangle the contribution of stellar particle ionization from other competing ionization sources. Modelling such observations with a model like the one presented here allows to constrain the stellar particle flux in disks around T Tauri stars.
Context.
Direct observations of young stellar objects are important to test established theories of planet formation. PDS 70 is one of the few cases where robust evidence favours the presence of two ...planetary mass companions inside the gap of the transition disk. Those planets are believed to be going through the last stages of accretion from the protoplanetary disk, a process likely mediated by a circumplanetary disk (CPD).
Aims.
We aim to develop a three-dimensional radiative transfer model for the dust component of the PDS 70 system which reproduces the system’s global features observed at two different wavelengths: 855 μm with the Atacama large millimeter/submillimeter array (ALMA) and 1.25 μm with the Spectro-polarimetric high-contrast exoplanet research instrument at the Very large telescope (VLT/SPHERE). We use this model to investigate the physical properties of the planetary companion PDS 70 c and its potential circumplanetary disk.
Methods.
We base our modelling process on published ALMA and VLT/SPHERE observations of the dust continuum emission at 855 and 1.25 μm, respectively. We selected initial values for the physical properties of the planet and CPD through appropriate assumptions about the nature and evolutionary stage of the object. We modified the properties of the protoplanetary disk iteratively until the predictions retrieved from the model were consistent with both data sets. Simulations were carried out with the three-dimensional radiative transfer code
MCMax3D
.
Results.
We provide a model that jointly explains the global features of the PDS 70 system seen in sub-millimetre and polarised-scattered light. Our model suggests that spatial segregation of dust grains is present in the protoplanetary disk. The sub-millimetre modelling of the PDS 70 c source favours the presence of an optically thick CPD and places an upper limit on its dust mass of 0.7
M
⊕
. Furthermore, analysis of the thermal structure of the CPD demonstrates that the planet luminosity is the dominant heating mechanism of dust grains inside 0.6 au from the planet, while heating by stellar photons dominates at larger planetocentric distances.
Conclusions.
A CPD surrounding the planetary-mass companion PDS 70 c is a plausible scenario to explain the substructure observed with ALMA. The heating feedback from the protoplanetary disk has an non-negligible effect on the equilibrium temperature of dust grains in the outskirts of the CPD. The connection between the CPD properties and the planet mass still depends on a series of key assumptions. Further observations with high spatial and spectral resolution also for the gas component of the CPD are required to break the degeneracy between the properties of the planet and the disk.
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