Vanishing Refractories: Tracing Dust Evolution in the BP Tau Protoplanetary Disk

Context. Crystalline silicates are an important tracer of the evolution of dust, the main building block of planet formation. In an inner protoplanetary disk, amorphous silicates are annealed because of the high temperatures that prevail there. These crystalline silicates are radially and vertically distributed by a disk turbulence and/or radial transport. Mid-infrared spectrographs are sensitive to the presence and temperature of micron-sized silicates, and the dust temperature can be used to infer their spatial distribution. Aims. We aim to model the spatial distribution of crystalline silicate dust in protoplanetary disks taking into account thermal annealing of silicate dust and radial transport of dust in the midplane. Using the resulting spatial distribution of crystalline and amorphous silicates, we calculated mid-infrared spectra to study the effect on dust features and to compare these to observations. Methods. We modeled a Class II T-Tauri protoplanetary disk and defined the region where crystallization happens by thermal annealing process from the comparison between crystallization and residence timescales (τcryst < τres). Radial mixing and drift were also compared to find a vertically well mixed region (τver < τdrift). We used the DISKLAB code to model the radial transport in the mid-plane and obtained the spatial distribution of the crystalline silicates for different grain sizes. We used MCMax, a radiative transfer code, to model the mid-infrared spectrum. Results. In our modeled T-Tauri disk, different grain sizes get crystallized in different radial and vertical ranges within 0.2 au. Small dust gets vertically mixed up efficiently, so crystallized small dust in the disk surface is well mixed with the midplane. Inward of 0.075 au, all grains are fully crystalline irrespective of their size. We also find that the crystallized dust is distributed out to a few au by radial transport, smaller grains more so than larger ones. Our fiducial model shows different contributions of the inner and outer disks to the dust spectral features. The 10 µm forsterite feature has an ~30% contribution from the innermost disk (0.07–0.09 au) and <1% from the disk beyond 10 au while the 33 µm feature has an ~10% contribution from both innermost and outer disks. We also find that feature strengths change when varying the spatial distribution of crystalline dust. Our modeled spectra qualitatively agree with observations from the Spitɀer Space Telescope, but the modeled 10 µm feature is strongly dominated by crystalline dust, unlike observations. Models with reduced crystallinity and depletion of small crystalline dust within 0.2 au show a better match with observations. Conclusions. Mid-infrared observations of the disk surface represent the radial distribution of small dust grains in the midplane and provide us with abundances of crystalline and amorphous dust, size distribution, and chemical composition in the inner disk. The inner and outer disks contribute more to shorter and longer wavelength features, respectively. In addition to the crystallization and dynamical processes, amorphization, sublimation of silicates, and dust evolution have to be taken into account to match observations, especially at λ = 10 µm, where the inner disk mostly contributes. This study could interpret spectra of protoplanetary disks taken with the Mid-Infrared Instrument on board the James Webb Space Telescope.

The majority of young, low-mass stars are surrounded by optically thick accretion disks. These circumstellar disks provide large reservoirs of gas and dust that will eventually be transformed into planetary systems. Theory and observations suggest that the earliest stage toward planet formation in a protoplanetary disk is the growth of particles, from sub-micron-sized grains to centimeter- sized pebbles. Theory indicates that small interstellar grains are well coupled into the gas and are incorporated to the disk during the proto-stellar collapse. These dust particles settle toward the disk mid-plane and simultaneously grow through collisional coagulation in a very short timescale. Observationally, grain growth can be inferred by measuring the spectral energy distribution at long wavelengths, which traces the continuum dust emission spectrum and hence the dust opacity. Several observational studies have indicated that the dust component in protoplanetary disks has evolved as compared to interstellar medium dust particles, suggesting at least 4 orders of magnitude in particle- size growth. However, the limited angular resolution and poor sensitivity of previous observations has not allowed for further exploration of this astrophysical process. As part of my thesis, I embarked in an observational program to search for evidence of radial variations in the dust properties across a protoplanetary disk, which may be indicative of grain growth. By making use of high angular resolution observations obtained with CARMA, VLA, and SMA, I searched for radial variations in the dust opacity inside protoplanetary disks. These observations span more than an order of magnitude in wavelength (from sub-millimeter to centimeter wavelengths) and attain spatial resolutions down to 20 AU. I characterized the radial distribution of the circumstellar material and constrained radial variations of the dust opacity spectral index, which may originate from particle growth in these circumstellar disks. Furthermore, I compared these observational constraints with simple physical models of grain evolution that include collisional coagulation, fragmentation, and the interaction of these grains with the gaseous disk (the radial drift problem). For the parameters explored, these observational constraints are in agreement with a population of grains limited in size by radial drift. Finally, I also discuss future endeavors with forthcoming ALMA observations.

IntroductionIn recent years, the discovery of more exoplanetary systems and interstellar objects has highlighted the growing synergy between exoplanetary science and planetary science. While exoplanetary science offers statistical insights into planetary architectures and formation scenarios, planetary science provides detailed physical models essential for the characterization of exoplanets [1]. Planet formation, whether in our Solar System or around other stars, is strongly influenced by the initial conditions of protoplanetary disks (PPDs)—including masses, sizes, surface densities, and temperature profiles [10]. In addition to that, the subsequent evolution of these PPDs is governed by processes such as radial drift, vertical mixing, and, in particular, grain growth [2].One of the major challenges in planet formation is understanding how dust grains grow into millimeter- to centimeter-sized particles. Such large grains—found in comets—serve as local analogs to the solids observed in disks around young stars [3] and provide a unique opportunity to investigate early grain growth processes. However, studies of these particles, which also constitute the bulk of the total coma mass [4], remain largely unexplored. Large particles also contribute to the grain size distribution, which plays a critical role in estimating the total dust mass in PPDs. Accurate dust mass estimates are essential to evaluate the potential to form planetesimals, rocky planets, and giant planet cores [5]. However, the current dust mass estimates are highly uncertain and insufficient to explain the observed high incidence of massive exoplanets [6,7].These challenges—uncertainties in PPD dust masses and limited characterization of large particles—can be addressed through multi-frequency analysis of dust in both protoplanetary disks and comets. Although numerous studies have individually investigated dust properties in each of these environments, comparative analyses integrating exoplanetary and planetary science remain understudied. Such interdisciplinary comparisons of dust properties have the potential to significantly improve our understanding of the processes governing the evolution of planetary systems.Observations and MethodsAs part of the ODISEA project (Ophiuchus DIsk Survey Employing ALMA) [8], we combined the archival ALMA observations across Band 3 (100 GHz), Band 4 (140 GHz), Band 6 (230 GHz), Band 7 (350 GHz), and Band 8 (410 GHz). This multi-frequency approach allows us to constrain dust temperatures, surface densities, and grain size distributions as a function of radius [9]. This is in contrast to the single-frequency approach, which requires assuming a single temperature and optically thin emission. Our method is based on the radiative transfer equation under the plane-parallel slab approximation, which is given by:Iν = Bν (Td) [1 - exp (-τ0 (ν/ν0) β)]where Bν(Td) is the Planck function, Td is the dust temperature, τ0 is the optical depth of dust at frequency ν0, and β is the dust opacity spectral index. This framework, therefore, enables more robust dust mass estimates by integrating over the surface density profile.To extend this analysis to the solar system context, we apply a similar multi-frequency approach to study the dust properties in comets. Using a similar set of ALMA bands, we target the distribution of dust and the presence of large grains in the comae of the exceptionally bright Oort Cloud comets, C/2023 A3 and C/2017 K2. These long-period comets are among the least thermally processed bodies in the Solar System and are also known to be dust-rich, making them one of the best-preserved reservoirs of primitive material from the solar nebula. Our observations aim to constrain the dust mass-loss rate and model the spectral energy distribution (SED) to derive the grain size distribution and dust structure. Additionally, we obtained mid-infrared observations of comet A3 with VLT’s VISIR instrument to investigate the long-standing contradiction of detecting crystalline silicates, formed at high temperatures, in comets that originated in cold environments.I will present the analysis of dust continuum from both A3 and K2 based on our ALMA observations, alongside key results of their composition from mid-infrared spectral fitting using dust models. In parallel, I will present the statistical results on dust surface density, maximum grain size, and dust temperature profiles in PPDs, emphasizing the comparison between dust masses derived from single- versus multi-frequency analyses. This represents the first comprehensive multi-frequency study of a large sample of 44 Class I and Class II disks, corresponding to the early stages of PPD evolution, within a single molecular cloud. Finally, I will discuss how integrating findings from both cometary and disk environments through consistent multi-frequency analysis helps bridge a critical knowledge gap in our understanding of grain growth, the role of large particles, and the evolution of dust properties across different stages of planetary system formation.

Context. Mid-infrared spectra indicate considerable chemical diversity in the inner regions of protoplanetary discs, with some being H2O-dominated and others CO2-dominated. Sublimating ices from radially drifting dust grains are often invoked to explain some of this diversity, particularly with regards to H2O-rich discs. Aims. We model the contribution made by radially drifting dust grains to the chemical diversity of the inner regions of protoplanetary discs. These grains transport ices – including those of H2O and CO2 – inwards to snow lines, thus redistributing the molecular content of the disc. As radial drift can be impeded by dust trapping in pressure maxima, we also explore the difference between smooth discs and those with dust traps due to gas gaps, quantifying the effects of gap location and formation time. Methods. We used a 1D protoplanetary disc evolution code to model the chemical evolution of the inner disc resulting from gas viscous evolution and dust radial drift. We post-processed these models to produce synthetic spectra, which we analyse with 0D LTE slab models to understand how this evolution may be expressed observationally. Results. Discs evolve through an initial H2O-rich phase as a result of sublimating ices, followed by a CO2 -rich phase as H2O vapour is advected onto the star and CO2 is advected into the inner disc from its snow line. The introduction of traps hastens the transition between the phases, temporarily raising the CO2/H2O ratio. However, whether or not this evolution can be traced in observations depends on the contribution of dust grains to the optical depth. If the dust grains become coupled to the gas after crossing the H2O snow line – for example if bare grains fragment more easily than icy grains – then the dust that delivers the H2O adds to the continuum optical depth and obscures the H2O, preventing any evolution in its visible column density. However, the CO2/H2O visible column density ratio is only weakly sensitive to assumptions about the dust continuum obscuration, making it a more suitable tracer of the impact of transport on chemistry than either individual column density. This can be investigated with spectra that show weak features that probe deep enough into the disc. The least effective gaps are those that open close to the star on timescales competitive with dust growth and drift as they block too much CO2; gaps opened later or further out lead to higher CO2/H2O. This leads to a potential correlation between CO2/H2O and gap location that occurs on million-year timescales for fiducial parameters. Conclusions. Radial drift, especially when combined with dust trapping, produces CO2 -rich discs on timescales longer than the viscous timescale at the H2O snow line (while creating H2O-rich discs at earlier times). Population analyses of the relationship between observed inner disc spectra and large-scale disc structure are needed to test the predicted role of traps.

We present measurements of the longitudinal magnetic field component B ‖ of the young star BP Tau in the He I 5876 emission line formation region, i.e., in the accretion flow near the stellar surface. The values obtained (≃1.7 kG and ≃1.0 kG in 2000 and 2001, respectively) agree with the results of similar measurements by other authors. At the same time, we show that the previously obtained field strength at the magnetic pole, B p, and the inclination of the magnetic axis to the rotation axis, β, are untrustworthy. In our opinion, based on the B ‖ measurements available to date, it is not possible to conclude whether the star’s magnetic field is a dipole one or has a more complex configuration and to solve the question of whether this field is stationary. However, we argue that at least in the He I 5876 line formation region, the star’s magnetic field is not stationary and can be restructured in a time of the order of several hours. Nonstationary small-scale magnetic fields of active regions on the stellar surface and/or magnetospheric field line reconnection due to the twisting of these field lines as the star rotates could be responsible for the short-term magnetic field variability. It seems highly likely that there are no strictly periodic variations in brightness and emission line profiles in BP Tau due to the irregular restructuring of the star’s magnetic field.

ALMA observations of protoplanetary disks confirm earlier indications that there is a clear difference between the dust and gas radial extents. The origin of this difference is still debated, with both radial drift of the dust and optical depth effects suggested in the literature. In this work, the feedback of realistic dust particle distributions onto the gas chemistry and molecular emissivity is investigated, with a particular focus on CO isotopologues. The radial dust grain size distribution is determined using dust evolution models that include growth, fragmentation and radial drift. A new version of the code DALI is used to take into account how dust surface area and density influence the disk thermal structure, molecular abundances and excitation. The difference of dust and gas radial sizes is largely due to differences in the optical depth of CO lines and millimeter continuum, without the need to invoke radial drift. The effect of radial drift is primarily visible in the sharp outer edge of the continuum intensity profile. The gas outer radius probed by $^{12}$CO emission can easily differ by a factor of $\sim 2$ between the models for a turbulent $\alpha$ ranging between typical values. Grain growth and settling concur in thermally decoupling the gas and dust components, due to the low collision rate with large grains. As a result, the gas can be much colder than the dust at intermediate heights, reducing the CO excitation and emission, especially for low turbulence values. Also, due to disk mid-plane shadowing, a second CO thermal desorption (rather than photodesorption) front can occur in the warmer outer mid-plane disk. The models are compared to ALMA observations of HD 163296 as a test case. In order to reproduce the observed CO snowline of the system, a binding energy for CO typical of ice mixtures needs to be used rather than the lower pure CO value.

Context . During the evolution of protoplanetary disks, dust grains start to grow, form larger particles, settle to the midplane, and rearrange the disk, mainly by the inward radial drift. Because of this, dust pebbles with an irregular shape usually align mechanically and thus cause polarization signatures in their thermal radiation due to dichroic emission or absorption. Aims . The goal of this paper is to evaluate the potential to trace the impact of mechanical grain alignment in protoplanetary disks on the observed degree and orientation of linear polarization at millimeter wavelengths. Methods . We combined 3D radiation hydrodynamical simulations to determine the density distribution and the velocity field of gas and dust particles, Monte Carlo dust-gas interaction simulations to calculate the mechanical alignment of dust in a gas flow, and, finally, 3D Monte Carlo polarized radiative transfer simulations to obtain synthetic polarimetric observations. Results . We find that large grains, which contribute the most to the net polarization, are potentially mechanically aligned in the protoplanetary disk under the effect of the vertical shear instability (VSI). Thereby, the drift velocity is parallel to the rotational disk axis. Assuming oblate dust grains that are aligned with their short axis parallel to the direction of the drift velocity, the resulting polarization is usually along the major axis of the disk. This is in contrast to typical drift models that propose either a radial or azimuthal drift velocity component. Conclusions . If hydrodynamical instabilities, such as the VSI, dominate the kinematics in protoplanetary disks, the mechanical alignment of dust is a promising mechanism for grain alignment in these systems. In that case, the resulting millimeter polarization allows us to trace the orientation of aligned millimeter-sized grains.

T Tauri stars produce broad Lyα emission lines that contribute ∼88% of the total UV flux incident on the inner circumstellar disks. Lyα photons are generated at the accretion shocks and in the protostellar chromospheres and must travel through accretion flows, winds, and jets, the protoplanetary disks, and the interstellar medium before reaching the observer. This trajectory produces asymmetric, double-peaked features that carry kinematic and opacity signatures of the disk environments. To understand the link between the evolution of Lyα emission lines and the disks themselves, we model HST-COS spectra from targets included in Data Release 3 of the Hubble UV Legacy Library of Young Stars as Essential Standards program. We find that resonant scattering in a simple spherical expanding shell is able to reproduce the high-velocity emission line wings, providing estimates of the average velocities within the bulk intervening H i. The model velocities are significantly correlated with the K-band veiling, indicating a turnover from Lyα profiles absorbed by outflowing winds to emission lines suppressed by accretion flows as the hot inner disk is depleted. Just 30% of targets in our sample have profiles with redshifted absorption from accretion flows, many of which have resolved dust gaps. At this stage, Lyα photons may no longer intersect with disk winds along the path to the observer. Our results point to a significant evolution of Lyα irradiation within the gas disks over time, which may lead to chemical differences that are observable with ALMA and JWST.

Protoplanetary disks are a byproduct of the star formation process. In the dense mid-plane of these disks, planetesimals and planets are expected to form. The first step in planet formation is the growth of dust particles from submicrometer-sized grains to macroscopic mm-sized aggregates. The grain growth is accompanied by radial drift and vertical segregation of the particles within the disk. To understand this essential evolutionary step, spatially resolved multi-wavelength observations as well as photometric data are necessary which reflect the properties of both disk and dust. We present the first spatially resolved image obtained with NACO at the VLT in the L$_\text{p}$ band of the near edge-on protoplanetary disk FS Tau B. Based on this new image, a previously published Hubble image in H band and the spectral energy distribution from optical to millimeter wavelengths, we derive constraints on the spatial dust distribution and the progress of grain growth. For this purpose we perform a disk modeling using the radiative transfer code MC3D. Radial drift and vertical sedimentation of the dust are not considered. We find a best-fit model which features a disk extending from $2\,\text{AU}$ to several hundreds AU with a moderately decreasing surface density and $M_\text{disk}=2.8\,\times\,10^{-2}\,\text{M}_\odot$. The inclination amounts to $i=80^\circ$. Our findings indicate that substantial dust grain growth has taken place and that grains of a size equal to or larger than $1\,\text{mm}$ are present in the disk. In conclusion, the parameters describing the vertical density distribution are better constrained than those describing the radial disk structure.

Using ≈190 000 spectra from the 17th data release of the Sloan Digital Sky Survey (SDSS), we investigate the ultraviolet emission line properties in z ≈ 2 quasars. Specifically, we quantify how the shape of C iv λ1549 and the equivalent width (EW) of He ii λ1640 depend on the black hole mass and Eddington ratio inferred from Mg ii λ2800. Above L/LEdd ≳ 0.2, there is a strong mass dependence in both C iv blueshift and He ii EW. Large C iv blueshifts are observed only in regions with both high mass and high accretion rate. Including X-ray measurements for a subsample of 5000 objects, we interpret our observations in the context of AGN accretion and outflow mechanisms. The observed trends in He ii and 2 keV strength are broadly consistent with theoretical qsosed models of AGN spectral energy distributions (SEDs) for low spin black holes, where the ionizing SED depends on the accretion disc temperature and the strength of the soft excess. High spin models are not consistent with observations, suggesting SDSS quasars at z ≈ 2 may in general have low spins. We find a dramatic switch in behaviour at L/LEdd ≲ 0.1: the ultraviolet emission properties show much weaker trends, and no longer agree with qsosed predictions, hinting at changes in the structure of the broad line region. Overall, the observed emission line trends are generally consistent with predictions for radiation line driving where quasar outflows are governed by the SED, which itself results from the accretion flow and hence depends on both the SMBH mass and accretion rate.

The connection between the nature of a protoplanetary disk and that of a debris disk is not well understood. Dust evolution, planet formation, and disk dissipation likely play a role in the processes involved. We aim to reconcile both manifestations of dusty circumstellar disks through a study of optically thin Class III disks and how they correlate to younger and older disks. In this work, we collect literature and Atacama Large Millimeter/submillimeter Array archival millimeter fluxes for 85 disks (8%) of all Class III disks across nearby star-forming regions. We derive millimeter-dust masses M dust and compare these with Class II and debris disk samples in the context of excess infrared luminosity, accretion rate, and age. The mean M dust of Class III disks is 0.29 ± 0.19 M ⊕. We propose a new evolutionary scenario wherein radial drift is very efficient for nonstructured disks during the Class II phase resulting in a rapid M dust decrease. In addition, we find possible evidence for long infrared protoplanetary disk timescales, ∼8 Myr, consistent with overall slow disk evolution. In structured disks, the presence of dust traps allows for the formation of planetesimal belts at large radii, such as those observed in debris disks. We propose therefore that the planetesimal belts in debris disks are the result of dust traps in structured disks, whereas protoplanetary disks without dust traps decrease in dust mass through radial drift and are therefore undetectable as debris disks after the gas dissipation. These results provide a hypothesis for a novel view of disk evolution.

Context. Protoplanetary discs are the birthplace of planets. Studying protoplanetary discs is the key to constraining theories of planet formation. By observing dust and gas in associations at different ages we can study the evolution of these discs, their clearing timescales, and their physical and geometrical properties.The stellar association η Cha is peculiar; some members still retain detectable amounts of gas in their discs at the late age of ~7 Myr, making it one of the most interesting young stellar associations in the solar neighbourhood. Aims: We characterise the properties of dust and gas in protoplanetary and transitional discs in the η Cha young cluster, with special emphasis on explaining the peculiarities that lead to the observed high disc detection fraction and prominent IR excesses at an age of ~7 Myr. Methods: We observed 17 members of the η Cha association with Herschel-PACS in photometric mode and line spectroscopic mode. A subset of members were also observed in range spectroscopic mode. The observations trace [OI] and H2O emissions at 63.18 and 63.32 μm, respectively, as well as CO, OH, CH+, and [CII] at different wavelengths for those systems observed in range mode. The photometric observations were used to build complete spectral energy distributions (SEDs) from the optical to the far-IR. High-resolution multi-epoch optical spectra with high signal-to-noise ratios were also analysed to study the multiplicity of the sources and look for further gas (accreting) and outflow indicators. Results: We detect four out of fifteen sources observed at 70 μm, four out of six at 100 μm, and six out of sixteen at 160 μm. Only one system shows [OI] emission at 63 μm, namely RECX 15 or J0843.3-7905. None of them shows far-IR line emission at any other wavelength. The [OI] emission toward RECX 15 points to the presence of an outflow; however, the emission is not extended. We study Hα emission among η Cha members and conclude that RECX 4, 5, 9, 11, and 15 are actively accreting in at least one epoch. Conclusions: The SEDs of the discs in η Cha show a variety of shapes, from those in Taurus and in Upper Scorpius to sources showing excess over the Taurus median SED. Furthermore, the SEDs of RECX 3 and RECX 4 are typical of debris discs. The detection fraction for [OI] in η Cha is lower than younger regions like Taurus and Cha II, indicative of an evolutionary trend. The lack of [OI] emission, together with the intermediate values of the IR excess, can be explained by long-lived discs with a flattened geometry or by flared discs with a low UV flux, or by a combination of the two scenarios. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.

Context. Recent ALMA surveys of protoplanetary disks have shown that for most disks the extent of the gas emission is greater than the extent of the thermal emission of millimeter-sized dust. Both line optical depth and the combined effect of radially dependent grain growth and radial drift may contribute to this observed effect. To determine whether or not radial drift is common across the disk population, quantitative estimates of the effect of line optical depth are required. Aims. For a sample of ten disks from the Lupus survey we investigate how well dust-based models without radial dust evolution reproduce the observed 12CO outer radius, and determine whether radial dust evolution is required to match the observed gas–dust size difference. Methods. Based on surface density profiles derived from continuum observations we used the thermochemical code DALI to obtain 12CO synthetic emission maps. Gas and dust outer radii of the models were calculated using the same methods as applied to the observations. The gas and dust outer radii (RCO, Rmm) calculated using only line optical depth were compared to observations on a source-by-source basis. Results. For five disks, we find RCO, obs∕Rmm, obs > RCO, mdl∕Rmm, mdl. For these disks we need both dust evolution and optical depth effects to explain the observed gas–dust size difference. For the other five disks, the observed RCO∕Rmm lies within the uncertainties on RCO, mdl∕Rmm, mdl due to noise. For these disks the observed gas–dust size difference can be explained using only line optical depth effects. We also identify six disks not included in our initial sample but part of a survey of the same star-forming region that show significant signal-to-noise ratio (S∕N ≥ 3) 12CO J = 2−1 emission beyond 4 × Rmm. These disks, for which no RCO is available, likely have RCO∕Rmm ≫ 4 and are difficult to explain without substantial dust evolution. Conclusions. Most of the disks in our sample of predominantly bright disks are consistent with radial drift and grain growth. We also find six faint disks where the observed gas–dust size difference hints at considerable radial drift and grain growth, suggesting that these are common features among both bright and faint disks. The effects of radial drift and grain growth can be observed in disks where the dust and gas radii are significantly different, while more detailed models and deeper observations are needed to see this effect in disks with smaller differences.

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 χ2 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.

Dust growth and settling considerably affect the spectral energy distributions (SEDs) of protoplanetary disks. We investigated dust growth and settling in protoplanetary disks through numerical simulations to examine time evolution of the disk optical thickness and SEDs. In this paper we considered laminar disks as the first step in a series of papers. As a result of dust growth and settling, a dust layer forms around the midplane of a gaseous disk. After the formation of the dust layer, small dust grains remain floating above the layer. Although the surface density of the floating small grains is much less than that of the dust layer, they govern the disk optical thickness and the emission. Size distributions of the floating grains obtained from numerical simulations are well described by a universal power-law distribution, which is independent of the disk temperature, the disk surface density, the radial position in the disk, etc. The floating small grains settle onto the dust layer in a long timescale compared with the formation of the dust layer. Typically, it takes 106 yr for micron-sized grains. Rapid grain growth in the inner part of disks makes the radial distribution of the disk optical thickness less steep than that of the disk surface density, Σ. For disks with Σ ∝ R-3/2, the radial distribution of the optical thickness is almost flat for all wavelengths at t 106 yr. At t > 106 yr, the optical thickness of the inner disk (a few AU) almost vanishes, which may correspond to disk inner holes observed by Spitzer Space Telescope. Furthermore, we examined time evolution of disk SEDs, using our numerical results and the two-layer model. The grain growth and settling decrease the magnitude of the SEDs, especially at λ ≥ 100 μm. Our results indicate that grain growth and settling can explain the decrease in observed energy fluxes at millimeter/submillimeter wavelengths with timescales of 106-107 yr without depletion of the disks.