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Models of planetary core growth by either planetesimal or pebble accretion are traditionally disconnected from the models of dust evolution and formation of the first gravitationally-bound planetesimals. The state-of-the-art models typically start with massive planetary cores already present. We aim to study the formation and growth of planetary cores in a pressure bump, motivated by the annular structures observed in protoplanetary disks, starting with sub-micron-sized dust grains. We connect the models of dust coagulation and drift, planetesimal formation in the streaming instability, gravitational interactions between planetesimals, pebble accretion, and planet migration, into one uniform framework. We find that planetesimals forming early at the massive end of the size distribution grow quickly dominantly by pebble accretion. These few massive bodies grow on the timescales of ~100 000 years and stir the planetesimals formed later preventing the emergence of further planetary cores. Additionally, a migration trap occurs allowing for retention of the growing cores. Pressure bumps are favourable locations for the emergence and rapid growth of planetary cores by pebble accretion as the dust density and grain size are increased and the pebble accretion onset mass is reduced compared to a smooth-disk model., 15 pages, 11 figures. Replaced with published version

Many processes during the evolution of protoplanetary disks and during planet formation are highly sensitive to the sizes of dust particles that are present in the disk: The efficiency of dust accretion in the disk and volatile transport on dust particles, gravoturbulent instabilities leading to the formation of planetesimals, or the accretion of pebbles onto large planetary embryos to form giant planets are typical examples of processes that depend on the sizes of the dust particles involved. Furthermore, radiative properties like absorption or scattering opacities depend on the particle sizes. To interpret observations of dust in protoplanetary disks, a proper estimate of the dust particle sizes is needed. We present DustPy - A Python package to simulate dust evolution in protoplanetary disks. DustPy solves gas and dust transport including viscous advection and diffusion as well as collisional growth of dust particles. DustPy is written with a modular concept, such that every aspect of the model can be easily modified or extended to allow for a multitude of research opportunities., Accepted for publication in ApJ. Installation via "pip install dustpy"

Observations of protoplanetary disks provide information on planet formation and the reasons for the diversity of planetary systems. The key to understanding planet formation is the study of dust evolution from small grains to pebbles. Smaller grains are well-coupled to the gas dynamics, and their distribution is significantly extended above the disk midplane. Larger grains settle much faster and are efficiently formed only in the midplane. By combining near-infrared polarized light and millimeter observations, it is possible to constrain the spatial distribution of both the small and large grains. We aim to construct detailed models of the size distribution and vertical/radial structure of the dust particles in protoplanetary disks based on observational data. In particular, we are interested in recovering the dust distribution in the IM Lup protoplanetary disk. We create a physical model for the dust distribution of protoplanetary disks and simulate the radiative transfer of the millimeter continuum and the near-infrared polarized radiation. Using a Markov chain Monte Carlo method, we compare the derived images to the observations available for the IM Lup disk to constrain the best physical model for IM Lup and to recover the vertical grain size distribution. The millimeter and near-infrared emission tightly constrain the dust mass and grain size distribution of our model. We find size segregation in the dust distribution, with millimeter-sized grains in the disk midplane. These grains are efficiently formed in the disk, possibly by sedimentation-driven coagulation, in accord with the short settling timescales predicted by our model. This also suggests a high dust-to-gas ratio at smaller radii in the midplane, possibly triggering streaming instabilities and planetesimal formation in the inner disk., Comment: 15 pages, 16 figures, accepted by Astronomy & Astrophysics

Recent sub-arcsecond resolution surveys of the dust continuum emission from nearby protoplanetary disks showed a strong correlation between the sizes and luminosities of the disks. We aim to explain the origin of the (sub-)millimeter size-luminosity relation (SLR) between the $68\%$ effective radius ($r_{eff}$) of disks with their continuum luminosity ($L_{mm}$), with models of gas and dust evolution in a simple viscous accretion disk and radiative transfer calculations. We use a large grid of models ($10^{5}$ simulations) with and without planetary gaps, varying the initial conditions of the key parameters. We calculate the disk continuum emission and the effective radius for all models as a function of time. By selecting those simulations that continuously follow the SLR, we can derive constraints on the input parameters of the models. We confirm previous results that models of smooth disks in the radial drift regime are compatible with the observed SLR ($L_{mm}\propto r_{eff}^{2}$) but only smooth disks cannot be the reality. We show that the SLR is more widely populated if planets are present. However they tend to follow a different relation than smooth disks, potentially implying that a mixture of smooth and sub-structured disks are present in the observed sample. We derive a SLR ($L_{mm}\propto r_{eff}^{5/4}$) for disks with strong sub-structure. To be compatible with the SLR, models need to have an initially high disk mass ($\geq 2.5 \cdot 10^{-2}M_{\star}$) and low turbulence-parameter $\alpha$ values ($\leq 10^{-3}$). Furthermore, we find that the grain composition and porosity drastically affects the evolution of disks on the size-luminosity diagram where relatively compact grains that include amorphous carbon are favoured. Moreover, a uniformly optically thick disk with high albedo ($0.9$) that follows the SLR cannot be formed from an evolutionary procedure., Comment: Replaced with the published version in A&A. 19+11 pages, 11+10 figures

The nucleosynthetic isotope dichotomy between carbonaceous (CC) and non-carbonaceous (NC) meteorites has been interpreted as evidence for spatial separation and the coexistence of two distinct planet-forming reservoirs for several million years in the solar protoplanetary disk. The rapid formation of Jupiter's core within one million years after the formation of calcium-aluminium-rich inclusions (CAIs) has been suggested as a potential mechanism for spatial and temporal separation. In this scenario, Jupiter's core would open a gap in the disk and trap inward-drifting dust grains in the pressure bump at the outer edge of the gap, separating the inner and outer disk materials from each other. We performed simulations of dust particles in a protoplanetary disk with a gap opened by an early-formed Jupiter core, including dust growth and fragmentation as well as dust transport, using the dust evolution software DustPy. Our numerical experiments indicate that particles trapped in the outer edge of the gap rapidly fragment and are transported through the gap, contaminating the inner disk with outer disk material on a timescale that is inconsistent with the meteoritic record. This suggests that other processes must have initiated or at least contributed to the isotopic separation between the inner and outer Solar System., Comment: Accepted for publication in Astronomy & Astrophysics Letters

The mass of protoplanetary disks is arguably one of their most important quantities shaping their evolution toward planetary systems, but it remains a challenge to determine this quantity. Using the high spatial resolution now available on telescopes such as the Atacama Large Millimeter/submillimeter Array (ALMA), recent studies derived a relation between the disk surface density and the location of the "dust lines". This is a new concept in the field, linking the disk size at different continuum wavelengths with the radial distribution of grain populations of different sizes. We aim to use a dust evolution model to test the dependence of the dust line location on disk gas mass. In particular, we are interested in the reliability of the method for disks showing radial substructures, as recent high-resolution observations revealed. Our models show that the determination of the dust line location is a promising approach to the mass estimate of protoplanetay disks, but the exact relation between the dust line location and disk mass depends on the structure of the particular disk. We calibrated the relation for disks without evidence of radial structures, while for more complex structures we ran a simple dust evolution model. However, this method fails when there is evidence of strong dust traps. It is possible to reveal when dust evolution is dominated by traps, providing the necessary information for when the method should be applied with caution., 14 pages, 18 figures, accepted by Astronomy & Astrophysics

The "Disk Substructures at High Angular Resolution Project" (DSHARP) has revealed an abundance and ubiquity of rings and gaps over a large sample of young planet-forming disks, which are hypothesised to be induced by the presence of forming planets. In this context, we present the first attempt to directly image these young companions for 10 of the DSHARP disks, by using NaCo/VLT high contrast observations in L'-band instrument and angular differential imaging techniques. We report the detection of a point-like source candidate at 1.1" (174.9 au) for RU Lup, and at 0.42" (55 AU) for Elias 24. In the case of RU Lup, the proper motion of the candidate is consistent with a stationary background contaminant, based on the astrometry derived from our observations and available archival data. For Elias 24 the point-like source candidate is located in one of the disk gaps at 55 AU. Assuming it is a planetary companion, our analysis suggest a mass ranging from $0.5 M_J$ up to $5 M_J$, depending on the presence of a circumplanetary disk and its contribution to the luminosity of the system. However, no clear confirmation is obtained at this stage, and follow-up observations are mandatory to verify if the proposed source is physical, comoving with the stellar host, and associated with a young massive planet sculpting the gap observed at 55\,AU. For all the remaining systems, the lack of detections suggests the presence of planetary companions with masses lower than $5M_J$, based on our derived mass detection limits. This is consistent with predictions of both hydrodynamical simulations and kinematical signatures on the disk, and allows us to set upper limits on the presence of massive planets in these young disks., Comment: 19 pages, 10 figures; Published by AJ

Recent millimeter and infrared observations have shown that gap and ring-like structures are common in both dust thermal emission and scattered-light of protoplanetary disks. We investigate the impact of the so-called Thermal Wave Instability (TWI) on the millimeter and infrared scattered-light images of disks. We perform 1+1D simulations of the TWI and confirm that the TWI operates when the disk is optically thick enough for stellar light, i.e., small-grain-to-gas mass ratio of $\gtrsim0.0001$. The mid-plane temperature varies as the waves propagate and hence gap and ring structures can be seen in both millimeter and infrared emission. The millimeter substructures can be observed even if the disk is fully optically thick since it is induced by the temperature variation, while density-induced substructures would disappear in the optically thick regime. The fractional separation between TWI-induced ring and gap is $\Delta r/r \sim$ 0.2-0.4 at $\sim$ 10-50 au, which is comparable to those found by ALMA. Due to the temperature variation, snow lines of volatile species move radially and multiple snow lines are observed even for a single species. The wave propagation velocity is as fast as $\sim$ 0.6 ${\rm au~yr^{-1}}$, which can be potentially detected with a multi-epoch observation with a time separation of a few years., Comment: 10 pages, 8 figures, accepted for publication in ApJL

The protoplanetary disk around the T Tauri star GM Aur was one of the first hypothesized to be in the midst of being cleared out by a forming planet. As a result, GM Aur has had an outsized influence on our understanding of disk structure and evolution. We present 1.1 and 2.1 mm ALMA continuum observations of the GM Aur disk at a resolution of ~50 mas (~8 au), as well as HCO$^+$ $J=3-2$ observations at a resolution of ~100 mas. The dust continuum shows at least three rings atop faint, extended emission. Unresolved emission is detected at the center of the disk cavity at both wavelengths, likely due to a combination of dust and free-free emission. Compared to the 1.1 mm image, the 2.1 mm image shows a more pronounced "shoulder" near R~40 au, highlighting the utility of longer-wavelength observations for characterizing disk substructures. The spectral index $\alpha$ features strong radial variations, with minima near the emission peaks and maxima near the gaps. While low spectral indices have often been ascribed to grain growth and dust trapping, the optical depth of GM Aur's inner two emission rings renders their dust properties ambiguous. The gaps and outer disk ($R>100$ au) are optically thin at both wavelengths. Meanwhile, the HCO$^+$ emission indicates that the gas cavity is more compact than the dust cavity traced by the millimeter continuum, similar to other disks traditionally classified as "transitional.", Comment: 31 pages, 15 figures, accepted by ApJ. Self-calibration and imaging scripts, images, and self-calibrated visibilities available at https://zenodo.org/record/3628656#.XjEXyRNKiYV

ALMA surveys have suggested that the dust in Class II disks may not be enough to explain the averaged solid mass in exoplanets, under the assumption that the mm disk continuum emission is optically thin. This optically thin assumption seems to be supported by recent DSHARP observations where the measured optical depths of spatially resolved disks are mostly less than one. However, we point out that dust scattering can considerably reduce the emission from an optically thick region. If that scattering is ignored, the optical depth will be considerably underestimated. An optically thick disk with scattering can be misidentified as an optically thin disk. Dust scattering in more inclined disks can reduce the intensity even further, making the disk look even fainter. The measured optical depth of $\sim$0.6 in several DSHARP disks can be naturally explained by optically thick dust with an albedo of $\sim$0.9 at 1.25 mm. Using the DSHARP opacity, this albedo corresponds to a dust population with the maximum grain size ($s_{max}$) of 0.1-1 mm. For optically thick scattering disks, the measured spectral index $\alpha$ can be either larger or smaller than 2 depending on if the dust albedo increases or decreases with wavelength. Using the DSHARP opacity, $\alpha, Comment: 15 pages, 11 figures, Accepted for publication in ApJL

Context. When we wish to understand planetesimal formation, the only data set we have is our own Solar System. The Solar System is particularly interesting because so far, it is the only planetary system we know of that developed life. Understanding the conditions under which the solar nebula evolved is crucial in order to understand the different processes in the disk and the subsequent dynamical interaction between (proto-)planets after the gas disk has dissolved. Aims. Protoplanetary disks provide a plethora of different parameters to explore. The question is whether this parameter space can be constrained, allowing simulations to reproduce the Solar System. Methods. Models and observations of planet formation provide constraints on the initial planetesimal mass in certain regions of the solar nebula. By making use of pebble flux-regulated planetesimal formation, we performed a parameter study with nine different disk parameters such as the initial disk mass, the initial disk size, the initial dust-to-gas ratio, the turbulence level, and others. Results. We find that the distribution of mass in planetesimals in the disk depends on the timescales of planetesimal formation and pebble drift. Multiple disk parameters can affect the pebble properties and thus planetesimal formation. However, it is still possible to draw some conclusions on potential parameter ranges. Conclusions. Pebble flux-regulated planetesimal formation appears to be very robust, allowing simulations with a wide range of parameters to meet the initial planetesimal constraints for the solar nebula. This means that it does not require much fine-tuning.

We propose an expression for a local planetesimal formation rate proportional to the instantaneous radial pebble flux. The result --- a radial planetesimal distribution --- can be used as initial condition to study the formation of planetary embryos. We follow the idea that one needs particle traps to locally enhance the dust-to-gas ratio sufficiently such that particle gas interactions can no longer prevent planetesimal formation on small scales. The location of these traps can emerge everywhere in the disk. Their occurrence and lifetime is subject of ongoing research, thus they are implemented via free parameters. This enables us to study the influence of the disk properties on the formation of planetesimals, predicting their time dependent formation rates and location of primary pebble accretion. We show that large $\alpha$-values of $0.01$ (strong turbulence) prevent the formation of planetesimals in the inner part of the disk, arguing for lower values of around $0.001$ (moderate turbulence), at which planetesimals form quickly at all places where they are needed for proto-planets. Planetesimals form as soon as dust has grown to pebbles ($\sim\mathrm{mm}$ to $\mathrm{dm}$) and the pebble flux reaches a critical value, which is after a few thousand years at $2-3\,$AU and after a few hundred thousand years at $20-30\,$AU. Planetesimal formation lasts until the pebble supply has decreased below a critical value. The final spatial planetesimal distribution is steeper compared to the initial dust and gas distribution which helps to explain the discrepancy between the minimum mass solar nebula and viscous accretion disks.

The Disk Substructures at High Angular Resolution Project (DSHARP) provides a large sample of protoplanetary disks having substructures which could be induced by young forming planets. To explore the properties of planets that may be responsible for these substructures, we systematically carry out a grid of 2-D hydrodynamical simulations including both gas and dust components. We present the resulting gas structures, including the relationship between the planet mass and 1) the gaseous gap depth/width, and 2) the sub/super-Keplerian motion across the gap. We then compute dust continuum intensity maps at the frequency of the DSHARP observations. We provide the relationship between the planet mass and 1) the depth/width of the gaps at millimeter intensity maps, 2) the gap edge ellipticity and asymmetry, and 3) the position of secondary gaps induced by the planet. With these relationships, we lay out the procedure to constrain the planet mass using gap properties, and study the potential planets in the DSHARP disks. We highlight the excellent agreement between observations and simulations for AS 209 and the detectability of the young Solar System analog. Finally, under the assumption that the detected gaps are induced by young planets, we characterize the young planet population in the planet mass-semimajor axis diagram. We find that the occurrence rate for $>$ 5 $M_J$ planets beyond 5-10 au is consistent with direct imaging constraints. Disk substructures allow us probe a wide-orbit planet population (Neptune to Jupiter mass planets beyond 10 au) that is not accessible to other planet searching techniques., 36 pages, 22 figures, ApJ Letters, in press

We present a detailed analysis of new ALMA observations of the disk around the T-Tauri star HD 143006, which at 46 mas (7.6 au) resolution reveal new substructures in the 1.25 mm continuum emission. The disk resolves into a series of concentric rings and gaps together with a bright arc exterior to the rings that resembles hydrodynamics simulations of a vortex, and a bridge-like feature connecting the two innermost rings. Although our $^{12}$CO observations at similar spatial resolution do not show obvious substructure, they reveal an inner disk depleted of CO emission. From the continuum emission and the CO velocity field we find that the innermost ring has a higher inclination than the outermost rings and the arc. This is evidence for either a small ($\sim8^{\circ}$) or moderate ($\sim41^{\circ}$) misalignment between the inner and outer disk, depending on the specific orientation of the near/far sides of the inner/outer disk. We compare the observed substructures in the ALMA observations with recent scattered light data from VLT/SPHERE of this object. In particular, the location of narrow shadow lanes in the SPHERE image combined with pressure scale height estimates, favor a large misalignment of about $41^{\circ}$. We discuss our findings in the context of a dust-trapping vortex, planet-carved gaps, and a misaligned inner disk due to the presence of an inclined companion to HD 143006., 15 pages, 8 figures, accepted for publication at ApJ Letters

The Disk Substructures at High Angular Resolution Project (DSHARP) is the largest homogeneous high-resolution ($\sim 0.035$ arcsec, or $\sim$ 5 au) disk continuum imaging survey with ALMA so far. In the coming years, many more disks will be mapped with ALMA at similar resolution. Interpreting the results in terms of the properties and quantities of the emitting dusty material is, however, a very non-trivial task. This is in part due to the uncertainty in the dust opacities, an uncertainty which is not likely to be resolved any time soon. It is also partly due to the fact that, as the DSHARP survey has shown, these disk often contain regions of intermediate to high optical depth, even at millimeter wavelengths and at relatively large radius in the disk. This makes the interpretation challenging, in particular if the grains are large and have a large albedo. On the other hand, the highly structured features seen in the DSHARP survey, of which strong indications were already seen in earlier observations, provide a unique opportunity to study the dust growth and dynamics. To provide continuity within the DSHARP project, its follow-up projects, and projects by other teams interested in these data, we present here the methods and opacity choices used within the DSHARP collaboration to link the measured intensity $I_\nu$ to dust surface density $\Sigma_d$., Comment: ApJ Letters, in press

Young circumstellar disks are of prime interest to understand the physical and chemical conditions under which planet formation takes place. Only very few detections of planet candidates within these disks exist, and most of them are currently suspected to be disk features. In this context, the transition disk around the young star PDS 70 is of particular interest, due to its large gap identified in previous observations, indicative of ongoing planet formation. We aim to search for the presence of planets and search for disk structures indicative for disk-planet interactions and other evolutionary processes. We analyse new and archival near-infrared (NIR) images of the transition disk PDS 70 obtained with the VLT/SPHERE, VLT/NaCo and Gemini/NICI instruments in polarimetric differential imaging (PDI) and angular differential imaging (ADI) modes. We detect a point source within the gap of the disk at about 195 mas (about 22 au) projected separation. The detection is confirmed at five different epochs, in three filter bands and using different instruments. The astrometry results in an object of bound nature, with high significance. The comparison of the measured magnitudes and colours to evolutionary tracks suggests that the detection is a companion of planetary mass. We confirm the detection of a large gap of about 54 au in size within the disk in our scattered light images, and detect a signal from an inner disk component. We find that its spatial extent is very likely smaller than about 17 au in radius. The images of the outer disk show evidence of a complex azimuthal brightness distribution which may in part be explained by Rayleigh scattering from very small grains. Future observations of this system at different wavelengths and continuing astrometry will allow us to test theoretical predictions regarding planet-disk interactions, planetary atmospheres and evolutionary models., Comment: 23 pages, accepted by A&A

The canonical model for the formation of terrestrial planets and giant planet cores implicitly relies on an early and efficient phase of planetesimal growth in a gas-rich circumstellar disk. But, as theorists have known for decades now, there are some formidable obstacles to meeting that requirement. Many of these problems, and potentially their solutions, are associated with the growth and migration of "pebbles" (̃mm/cm-sized solids) in the first few million years of a disk's lifetime. That is especially fortuitous, since the thermal continuum emission from these particles in nearby disks can be readily detected and resolved with long-baseline radio interferometers. This chapter describes what is being learned about the early evolution of solids by comparing such data with sophisticated simulations. Specifically, the focus will be on the observable signatures of particle growth and migration and the mounting evidence that small-scale substructures in the (gas) disk play fundamental - and perhaps mandatory - roles in the planet formation process.

Combining hydrodynamic planet-disk interaction simulations with dust evolution models, we show that protoplanetary disks having a giant planet can reveal diverse morphology in (sub-)millimeter continuum, including a full disk without significant radial structure, a transition disk with an inner cavity, a disk with a single gap and a central continuum peak, and a disk with multiple rings and gaps. Such a diversity originates from (1) the level of viscous transport in the disk which determines the number of gaps a planet can open; (2) the size and spatial distributions of grains determined by the coagulation, fragmentation, and radial drift, which in turn affects the emmisivity of the disk at (sub-)millimeter wavelengths; and (3) the angular resolution used to observe the disk. In particular, our results show that disks having the same underlying gas distribution can have very different grain size/spatial distributions and thus appearance in continuum, depending on the interplay among coagulation, fragmentation, and radial drift. This suggests that proper treatments for the grain growth have to be included in models of protoplanetary disks concerning continuum properties and that complementary molecular line observations are highly desired in addition to continuum observations to reveal the true nature of disks. The fact that a single planet can produce diverse disk morphology emphasizes the need to search for more direct, localized signatures of planets in order to confirm (or dispute) the planetary origin of observed ringed substructures., 12 pages, 8 figures, Accepted for publication in the ApJ Letters

We present an analysis of ALMA 1.25 millimeter continuum observations of spiral structures in three protoplanetary disks from the Disk Substructures at High Angular Resolution Project. The disks around Elias 27, IM Lup, and WaOph 6 were observed at a resolution of $\sim40-60$ mas ($\sim6-7$ au). All three disks feature $m=2$ spiral patterns in conjunction with annular substructures. Gas kinematics established by $^{12}$CO $J=2-1$ observations indicate that the continuum spiral arms are trailing. The arm-interarm intensity contrasts are modest, typically less than 3. The Elias 27 spiral pattern extends throughout much of the disk, and the arms intersect the gap at $R\sim69$ au. The spiral pattern in the IM Lup disk is particularly complex-it extends about halfway radially through the disk, exhibiting pitch angle variations with radius and interarm features that may be part of ring substructures or spiral arm branches. Spiral arms also extend most of the way through the WaOph 6 disk, but the source overall is much more compact than the other two disks. We discuss possible origins for the spiral structures, including gravitational instability and density waves induced by a stellar or planetary companion. Unlike the millimeter continuum counterparts of many of the disks with spiral arms detected in scattered light, these three sources do not feature high-contrast crescent-like asymmetries or large ($R>20$ au) emission cavities. This difference may point to multiple spiral formation mechanisms operating in disks., 19 pages, 9 figures, minor typos corrected

We present an improved method to measure the rotation curves for disks with non-axisymmetric brightness profiles initially published in Teague et al. (2018a). Application of this method to the well studied AS$~$209 system shows substantial deviations from Keplerian rotation of up to $\pm 5\%$. These deviations are most likely due to perturbations in the gas pressure profile, including a perturbation located at $\approx 250~$au and spanning up to $\approx 50~$au which is only detected kinematically. Modelling the required temperature and density profiles required to recover the observed rotation curve we demonstrate that the rings observed in $\mu$m scattered light are coincident with the pressure maxima, and are radially offset from the rings observed in mm continuum emission. This suggests that if rings in the NIR are due to sub-$\mu$m grains trapped in pressure maxima that there is a vertical dependence on the radius of the pressure minima., Comment: Accepted by ApJ

Systems with tightly-packed inner planets (STIPs) are very common. Chatterjee & Tan proposed Inside-Out Planet Formation (IOPF), an in situ formation theory, to explain these planets. IOPF involves sequential planet formation from pebble-rich rings that are fed from the outer disk and trapped at the pressure maximum associated with the dead zone inner boundary (DZIB). Planet masses are set by their ability to open a gap and cause the DZIB to retreat outwards. We present models for the disk density and temperature structures that are relevant to the conditions of IOPF. For a wide range of DZIB conditions, we evaluate the gap opening masses of planets in these disks that are expected to lead to truncation of pebble accretion onto the forming planet. We then consider the evolution of dust and pebbles in the disk, estimating that pebbles typically grow to sizes of a few cm during their radial drift from several tens of AU to the inner, $\lesssim1\:$AU-scale disk. A large fraction of the accretion flux of solids is expected to be in such pebbles. This allows us to estimate the timescales for individual planet formation and entire planetary system formation in the IOPF scenario. We find that to produce realistic STIPs within reasonable timescales similar to disk lifetimes requires disk accretion rates of $\sim10^{-9}\:M_\odot\:{\rm yr}^{-1}$ and relatively low viscosity conditions in the DZIB region, i.e., Shakura-Sunyaev parameter of $��\sim10^{-4}$., 20 pages, 13 figures, accepted by ApJ, comments welcome

A large fraction of the protoplanetary disks observed with ALMA display multiple well-defined and nearly perfectly circular rings in the continuum, in many cases with substantial peak-to-valley contrast. The DSHARP campaign shows that several of these rings are very narrow in radial extent. In this paper we test the hypothesis that these dust rings are caused by dust trapping in radial pressure bumps, and if confirmed, put constraints on the physics of the dust trapping mechanism. We model this process analytically in 1D, assuming axisymmetry. By comparing this model to the data, we find that all rings are consistent with dust trapping. Based on a plausible model of the dust temperature we find that several rings are narrower than the pressure scale height, providing strong evidence for dust trapping. The rings have peak absorption optical depth in the range between 0.2 and 0.5. The dust masses stored in each of these rings is of the order of tens of Earth masses, though much ambiguity remains due to the uncertainty of the dust opacities. The dust rings are dense enough to potentially trigger the streaming instability, but our analysis cannot give proof of this mechanism actually operating. Our results show, however, that the combination of very low alpha_turb << 5e-4 and very large grains a_grain >> 0.1 cm can be excluded by the data for all the rings studied in this paper., Accepted for publication in ApJ Letters

We present a detailed analysis of the high-angular resolution (0.''037, corresponding to 5 au) observations of the 1.25 mm continuum and $^{12}$CO $2-1$ emission from the disk around the T Tauri star AS 209. AS 209 hosts one of the most unusual disks from the DSHARP sample, the first high angular resolution ALMA survey of disks (Andrews et al. 2018), as nearly all of the emission can be explained with concentric Gaussian rings. In particular, the dust emission consists of a series of narrow and closely spaced rings in the inner $\sim$60 au, two well-separated bright rings in the outer disk, centered at 74 and 120 au, and at least two fainter emission features at 90 and 130 au. We model the visibilities with a parametric representation of the radial surface brightness profile, consisting of a central core and 7 concentric Gaussian rings. Recent hydro-dynamical simulations of low viscosity disks show that super-Earth planets can produce the multiple gaps seen in AS 209 millimeter continuum emission. The $^{12}$CO line emission is centrally peaked and extends out to $\sim$300 au, much farther than the millimeter dust emission. We find axisymmetric, localized deficits of CO emission around four distinct radii, near 45, 75, 120 and 210 au. The outermost gap is located well beyond the edge of the millimeter dust emission, and therefore cannot be due to dust opacity and must be caused by a genuine CO surface density reduction, due either to chemical effects or depletion of the overall gas content., ApJ Letters, in press

Observations of multiple rotational transitions from a single molecule allow for unparalleled constraints on the physical conditions of the emitting region. We present an analysis of CS in TW~Hya using the $J=7-6$, $5-4$ and $3-2$ transitions imaged at $\sim 0.5^{\prime\prime}$ spatial resolution, resulting in a temperature and column density profile of the CS emission region extending out to 230~au, far beyond previous measurements. In addition, the 15~kHz resolution of the observations and the ability to directly estimate the temperature of the CS emitting gas, allow for one of the most sensitive searches for turbulent broadening in a disk to date. Limits of $v_{\rm turb} \lesssim 0.1 c_s$ can be placed across the entire radius of the disk. We are able to place strict limits of the local H$_2$ density due to the collisional excitations of the observed transitions. From these we find that a minimum disk mass of $3 \times 10^{-4}~M_{\rm sun}$ is required to be consistent with the CS excitation conditions and can uniquely constrain the gas surface density profile in the outer disk., Comment: Accepted by ApJ

ALMA observations of protoplanetary disks acquired by the Disk Substructure at High Angular Resolution Project (DSHARP) resolve the dust and gas emission on angular scales as small as 3 astronomical units, offering an unprecedented detailed view of the environment where planets form. In this article, we present and discuss observations of the HD 163296 protoplanetary disk that imaged the 1.25 mm dust continuum and $^{12}$CO J=2-1 rotational line emission at a spatial resolution of 4 and 10 au, respectively. The continuum observations resolve and allow us to characterize the previously discovered dust rings at radii of 67 and 100 au. They also reveal new small scale structures, such as a dark gap at 10 au, a bright ring at 15 au, a dust crescent at a radius of 55 au, and several fainter azimuthal asymmetries. The observations of the CO and dust emission inform about the vertical structure of the disk and allow us to directly constrain the dust extinction optical depth at the dust rings. Furthermore, the observed asymmetries in the dust continuum emission corroborate to the hypothesis that the complex structure of the HD 163296 disk is the result of the gravitational interaction with yet unseen planets., Comment: ApJ Letters, in press. 19 pages, 11 figures

We present a sub-arcsecond resolution survey of the 340 GHz dust continuum emission from 50 nearby protoplanetary disks, based on new and archival observations with the Submillimeter Array. The observed visibility data were modeled with a simple prescription for the radial surface brightness profile. The results were used to extract intuitive, empirical estimates of the emission "size" for each disk, $R_{\rm eff}$, defined as the radius that encircles a fixed fraction of the total continuum luminosity, $L_{\rm mm}$. We find a significant correlation between the sizes and luminosities, such that $R_{\rm eff} \propto L_{\rm mm}^{0.5}$, providing a confirmation and quantitative characterization of a putative trend that was noted previously. This correlation suggests that these disks have roughly the same average surface brightness interior to their given effective radius, ~0.2 Jy arcsec$^{-2}$ (or 8 K in brightness temperature). The same trend remains, but the 0.2dex of dispersion perpendicular to this relation essentially disappears, when we account for the irradiation environment of each disk with a crude approximation of the dust temperatures based on the stellar host luminosities. We consider two (not mutually exclusive) explanations for the origin of this size-luminosity relationship. Simple models of the growth and migration of disk solids can account for the observed trend for a reasonable range of initial conditions, but only on timescales that are much shorter than the nominal ages present in the sample. An alternative scenario invokes optically thick emission concentrated on unresolved scales, with filling factors of a few tens of percent, that are perhaps manifestations of localized particle traps., Accepted for publication in ApJ

We present the next step in a series of papers devoted to connecting the composition of the atmospheres of forming planets with the chemistry of their natal evolving protoplanetary disks. The model presented here computes the coupled chemical and dust evolution of the disk and the formation of three planets per disk model. Our three canonical planet traps produce a Jupiter near 1 AU, a Hot Jupiter and a Super-Earth. We study the dependency of the final orbital radius, mass, and atmospheric chemistry of planets forming in disk models with initial disk masses that vary by 0.02 $M_\odot$ above and below our fiducial model ($M_{disk,0} = 0.1 ~M_\odot$). We compute C/O and C/N for the atmospheres formed in our 3 models and find that C/O$_{\rm planet}\sim$ C/O$_{\rm disk}$, which does not vary strongly between different planets formed in our model. The nitrogen content of atmospheres can vary in planets that grow in different disk models. These differences are related to the formation history of the planet, the time and location that the planet accretes its atmosphere, and are encoded in the bulk abundance of NH$_3$. These results suggest that future observations of atmospheric NH$_3$ and an estimation of the planetary C/O and C/N can inform the formation history of particular planetary systems., Accepted for publication in MNRAS

Context. Ice lines are suggested to play a significant role in grain growth and planetesimal formation in protoplanetary disks. Evaporation fronts directly influence the gas and ice abundances of volatile species in the disk and therefore the coagulation physics and efficiency and the chemical composition of the resulting planetesimals. Aims. In this work we investigate the influence of the existence of the CO ice line on the particle growth and on the distribution of CO in the disk. Methods. We include the possibility of tracking the CO content and/or other volatiles in particles and in the gas in our existing dust coagulation and disk evolution model and developed a method for evaporation and condensation of CO using the Hertz-Knudsen equation. Our model does not include fragmentation, yet, which will be part of further investigations. Results. We find no enhanced grain growth just outside the ice line where the particle size is limited by radial drift. Instead we find a depletion of solid material inside the ice line which is solely due to evaporation of the CO. Such a depression inside the ice line may be observable and may help to quantify the processes described in this work. Furthermore, we find that the viscosity and diffusivity of the gas heavily influence the re-distribution of vaporized CO at the ice line and can lead to an increase in the CO abundance by up to a factors of a few in the region just inside the ice line. Depending on the strength of the gaseous transport mechanisms the position of the ice line in our model can change by up to 10 AU and consequently, the temperature at that location can range from 21 K to 23 K., Comment: Accepted to A&A. 16 pages, 11 figures

Tidal interactions between the embedded planets and their surrounding protoplanetary disks are often postulated to produce the observed complex dust substructures, including rings, gaps, and asymmetries. In this Letter, we explore the consequences of dust coagulation on the dust dynamics and ring morphology. Coagulation of dust grains leads to dust size growth which, under typical disk conditions, produces faster radial drifts, potentially threatening the dust ring formation. Utilizing 2D hydrodynamical simulations of protoplanetary disks which include a full treatment of dust coagulation, we find that if the planet does not open a gap quickly enough, the formation of an inner ring is impeded due to dust coagulation and subsequent radial drift. Furthermore, we find that a "buildup" of sub-mm sized grains often appears in the dust emission at the outer edge of the dust disk., Comment: 11 pages, 5 figures, accepted for publication in ApJL on 21 December 2019

We present long-baseline Atacama Large Millimeter/submillimeter Array (ALMA) observations of the 870 micron continuum emission from the nearest gas-rich protoplanetary disk, around TW Hya, that trace millimeter-sized particles down to spatial scales as small as 1 AU (20 mas). These data reveal a series of concentric ring-shaped substructures in the form of bright zones and narrow dark annuli (1-6 AU) with modest contrasts (5-30%). We associate these features with concentrations of solids that have had their inward radial drift slowed or stopped, presumably at local gas pressure maxima. No significant non-axisymmetric structures are detected. Some of the observed features occur near temperatures that may be associated with the condensation fronts of major volatile species, but the relatively small brightness contrasts may also be a consequence of magnetized disk evolution (the so-called zonal flows). Other features, particularly a narrow dark annulus located only 1 AU from the star, could indicate interactions between the disk and young planets. These data signal that ordered substructures on ~AU scales can be common, fundamental factors in disk evolution, and that high resolution microwave imaging can help characterize them during the epoch of planet formation., published in Astrophysical Journal Letters; image files are available at http://www.cfa.harvard.edu/~sandrews/data/twhya/

We present high spatial resolution observations of the continuum emission from the young multiple star system UZ Tau at frequencies from 6 to 340 GHz. To quantify the spatial variation of dust emission in the UZ Tau E circumbinary disk, the observed interferometric visibilities are modeled with a simple parametric prescription for the radial surface brightnesses at each frequency. We find evidence that the spectrum steepens with radius in the disk, manifested as a positive correlation between the observing frequency and the radius that encircles a fixed fraction of the emission ($R_{eff} \propto \nu^{0.34 \pm 0.08}$). The origins of this size--frequency relation are explored in the context of a theoretical framework for the growth and migration of disk solids. While that framework can reproduce a similar size--frequency relation, it predicts a steeper spectrum than is observed. Moreover, it comes closest to matching the data only on timescales much shorter ($\le 1$ Myr) than the putative UZ Tau age (~2-3 Myr). These discrepancies are the direct consequences of the rapid radial drift rates predicted by models of dust evolution in a smooth gas disk. One way to mitigate that efficiency problem is to invoke small-scale gas pressure modulations that locally concentrate drifting solids. If such particle traps reach high continuum optical depths at 30-340 GHz with a ~30-60% filling fraction in the inner disk ($r \lesssim20$ au), they can also explain the observed spatial gradient in the UZ Tau E disk spectrum., Comment: Accepted for publication in The Astrophysical Journal (13 pages, 8 figures)

We combined hydrodynamical simulations of planet-disk interactions with dust evolution models that include coagulation and fragmentation of dust grains over a large range of radii and derived observational properties using radiative transfer calculations. We studied the role of the snow line in the survival of the inner disk of transition disks. Inside the snow line, the lack of ice mantles in dust particles decreases the sticking efficiency between grains. As a consequence, particles fragment at lower collision velocities than in regions beyond the snow line. This effect allows small particles to be maintained for up to a few Myrs within the first astronomical unit. These particles are closely coupled to the gas and do not drift significantly with respect to the gas. For lower mass planets (1$M_{\rm{Jup}}$), the pre-transition appearance can be maintained even longer because dust still trickles through the gap created by the planet, moves invisibly and quickly in the form of relatively large grains through the gap, and becomes visible again as it fragments and gets slowed down inside of the snow line. The global study of dust evolution of a disk with an embedded planet, including the changes of the dust aerodynamics near the snow line, can explain the concentration of millimetre-sized particles in the outer disk and the survival of the dust in the inner disk if a large dust trap is present in the outer disk. This behaviour solves the conundrum of the combination of both near-infrared excess and ring-like millimetre emission observed in several transition disks., Accepted for publication in A&A (including acknowledgments)

The solid content of circumstellar disks is inherited from the interstellar medium: dust particles of at most a micrometer in size. Protoplanetary disks are the environment where these dust grains need to grow at least 13 orders of magnitude in size. Our understanding of this growth process is far from complete, with different physics seemingly posing obstacles to this growth at various stages. Yet, the ubiquity of planets in our galaxy suggests that planet formation is a robust mechanism. This chapter focuses on the earliest stages of planet formation, the growth of small dust grains towards the gravitationally bound "planetesimals", the building blocks of planets. We will introduce some of the key physics involved in the growth processes and discuss how they are expected to shape the global behavior of the solid content of disks. We will consider possible pathways towards the formation of larger bodies and conclude by reviewing some of the recent observational advances in the field., Comment: 43 pages, 6 figures. Chapter in International Space Science Institute (ISSI) Book on "The Disk in Relation to the Formation of Planets and their Proto-atmospheres", published in Space Science Reviews by Springer

Molecular snow lines in protoplanetary disks have been studied theoretically for decades because of their importance in shaping planetary architectures and compositions. The water snow line lies in the planet formation region at < 10 AU, and so far its location has been estimated only indirectly from spatially-unresolved spectroscopy. This work presents a proof-of-concept method to directly image the water snow line in protoplanetary disks through its physical and chemical imprint in the local dust properties. We adopt a physical disk model that includes dust coagulation, fragmentation, drift, and a change in fragmentation velocities of a factor 10 between dry silicates and icy grains as found by laboratory work. We find that the presence of a water snow line leads to a sharp discontinuity in the radial profile of the dust emission spectral index {\alpha}_mm, due to replenishment of small grains through fragmentation. We use the ALMA simulator to demonstrate that this effect can be observed in protoplanetary disks using spatially-resolved ALMA images in two continuum bands. We explore the model dependence on the disk viscosity and find that the spectral index reveals the water snow line for a wide range of conditions, with opposite trends when the emission is optically thin rather than thick. If the disk viscosity is low ({\alpha}_visc < 10^-3) the snow line produces a ring-like structure with a minimum at {\alpha}_mm ~ 2 in the optically thick regime, possibly similar to what has been measured with ALMA in the innermost region of the HL Tau disk., Comment: 6 pages, 4 figures, accepted for publication in ApJ Letters

Recent imaging of protoplanetary disks with high resolution and contrast have revealed a striking variety of substructure. Of particular interest are cases where near-infrared scattered light images show evidence for low-intensity annular "gaps." The origins of such structures are still uncertain, but the interaction of the gas disk with planets is a common interpretation. We study the impact that the evolution of the solid material can have on the observable properties of disks in a simple scenario without any gravitational or hydrodynamical disturbances to the gas disk structure. Even with a smooth and continuous gas density profile, we find that the scattered light emission produced by small dust grains can exhibit ring-like depressions similar to those presented in recent observations. The physical mechanisms responsible for these features rely on the inefficient fragmentation of dust particles. The occurrence and position of the proposed "gap" features depend most strongly on the dust-to-gas ratio, the fragmentation threshold velocity, the strength of the turbulence, and the age of the disk, and should be generic (at some radius) for typically adopted disk parameters. The same physical processes can affect the thermal emission at optically thin wavelengths ($\sim$1 mm), although the behavior can be more complex; unlike for disk-planet interactions, a "gap" should not be present at these longer wavelengths., 6 pages, 4 figures, accepted for publication in ApJL, fixed typos

Astronomy and Astrophysics 573 (2015): A19 reproduced with permission from Astronomy & Astrophysics, Context. The Cep OB2 region, with its two intermediate-aged clusters Tr 37 and NGC7160, is a paradigm of sequential star formation and an ideal site for studies of protoplanetary disk evolution. Aims. We use Herschel data to study the protoplanetary disks and the star formation history of the region. Methods. Herschel/PACS observations at 70 and 160 μm probe the disk properties (mass, dust sizes, structure) and the evolutionary state of a large number of young stars. Far-IR data also trace the remnant cloud material and small-scale cloud structure. Results. We detect 95 protoplanetary disks at 70 μm, 41 at 160 μm, and obtain upper limits for more than 130 objects. The detection fraction at 70 μm depends on the spectral type (88% for K4 or earlier stars, 17% for M3 or later stars) and on the disk type (∼50% for full and pre-transitional disks, ∼35% for transitional disks, no low-excess/depleted disks detected). Non-accreting disks are not detected, suggesting significantly lower masses. Accreting transition and pre-transition disks have systematically higher 70 μm excesses than full disks, suggestive of more massive, flared and/or thicker disks. Herschel data also reveal several mini-clusters in Tr 37, which are small, compact structures containing a few young stars surrounded by nebulosity. Conclusions. Far-IR data are an excellent probe of the evolution of disks that are too faint for sub-millimetre observations. We find a strong link between far-IR emission and accretion, and between the inner and outer disk structure. Herschel confirms the dichotomy between accreting and non-accreting transition disks. Accretion is a powerful measure of global disk evolution: substantial mass depletion and global evolution need to occur to shut down accretion in a protoplanetary disk, even if the disk has inner holes. Disks likely follow different evolutionary paths: low disk masses do not imply opening inner holes, and having inner holes does not require low disk masses. The mini-clusters reveal multi-episodic star formation in Tr 37. The long survival of mini-clusters suggest that they formed from the fragmentation of the same core. Their various morphologies favour different formation/triggering mechanisms acting within the same cluster. The beads-on-a-string structure in one mini-cluster is consistent with gravitational fragmentation or gravitational focusing, acting on very small scales (solar-mass stars in ∼0.5 pc filaments). Multi-episodic star formation could also produce evolutionary variations between disks in the same region. Finally, Herschel also unveils what could be the first heavy mass loss episode of the O6.5 star HD206267 in Tr 37, A.S.A. acknowledges support by the Spanish MICINN/MINECO “Ramón y Cajal” program, grant number RYC-2010-06164. A.S.A. and M.F. acknowledge support by the action “Proyectos de Investigación fundamental no orientada”, grant number AYA2012-35008. C.E. is partly supported by Spanish MICINN/MINECO grant AYA2011-26202. V.R. is supported by the DLR grant number 50 OR 1109 and by the Bayerischen Gleichstellungsförderung (BGF). T.B. acknowledges support from NASA Origins of Solar Systems grant NNX12AJ04G. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France

We present sub-arcsecond resolution observations of continuum emission associated with the GG Tau quadruple star system at wavelengths of 1.3, 2.8, 7.3, and 50 mm. These data confirm that the GG Tau A binary is encircled by a circumbinary ring at a radius of 235 AU with a FWHM width of ~60 AU. We find no clear evidence for a radial gradient in the spectral shape of the ring, suggesting that the particle size distribution is spatially homogeneous on angular scales of ~0.1". A central point source, likely associated with the primary component (GG Tau Aa), exhibits a composite spectrum from dust and free-free emission. Faint emission at 7.3 mm is observed toward the low-mass star GG Tau Ba, although its origin remains uncertain. Using these measurements of the resolved, multifrequency emission structure of the GG Tau A system, models of the far-infrared to radio spectrum are developed to place constraints on the grain size distribution and dust mass in the circumbinary ring. The non-negligible curvature present in the ring spectrum implies a maximum particle size of 1-10 mm, although we are unable to place strong constraints on the distribution shape. The corresponding dust mass is 30-300 M_earth, at a temperature of 20-30 K. We discuss how this significant concentration of relatively large particles in a narrow ring at a large radius might be produced in a local region of higher gas pressures (i.e., a particle "trap") located near the inner edge of the circumbinary disk., ApJ, in press

Overdensity of dust with respect to the gas in the planet forming regions is a crucial prerequisite to form larger bodies and eventually planets. We use a state-of-the-art code to simulate dust evolution processes in gas-rich circumstellar discs, including the viscous gas evolution. We find significant deviations of the radial distribution of dust from that of the gas as early as 1-2Myr. These deviations are closely related to the efficiency of grain growth. Apparent discrepancies between dust and gas distributions are suggested by the current millimetre interferometer observations, and ALMA will allow us tointerpret any such discrepancies in the context of dust evolution.

HD 100546 is a well-studied Herbig Be star-disk system that likely hosts a close-in companion with compelling observational evidence for an embedded protoplanet at 68 AU. We present ALMA observations of the HD 100546 disk which resolve the gas and dust structure at (sub)mm wavelengths. The CO emission (at 345.795 GHz) originates from an extensive molecular disk (390+/-20 AU in radius) whereas the continuum emission is more compact (230+/-20 AU in radius) suggesting radial drift of the mm-sized grains. The CO emission is similar in extent to scattered light images indicating well-mixed gas and um-sized grains in the disk atmosphere. Assuming azimuthal symmetry, a single-component power-law model cannot reproduce the continuum visibilities. The visibilities and images are better reproduced by a double-component model: a compact ring with a width of 21 AU centered at 26 AU and an outer ring with a width of 75+/-3 AU centered at 190+/-3 AU. The influence of a companion and protoplanet on the dust evolution is investigated. The companion at 10 AU facilitates the accumulation of mm-sized grains within a compact ring, ~ 20 - 30 AU, by ~ 10 Myr. The injection of a protoplanet at 1 Myr hastens the ring formation (~ 1.2 Myr) and also triggers the development of an outer ring (~ 100 - 200 AU). These observations provide additional evidence for the presence of a close-in companion and hint at dynamical clearing by a protoplanet in the outer disk., Comment: Accepted for publication in the Astrophysical Journal Letters

The expectation that aerodynamic drag will force the solids in a gas-rich protoplanetary disk to spiral in toward the host star on short timescales is one of the fundamental problems in planet formation theory. The nominal efficiency of this radial drift process is in conflict with observations, suggesting that an empirical calibration of solid transport mechanisms in a disk is highly desirable. However, the fact that both radial drift and grain growth produce a similar particle size segregation in a disk (such that larger particles are preferentially concentrated closer to the star) makes it difficult to disentangle a clear signature of drift alone. We highlight a new approach, by showing that radial drift leaves a distinctive "fingerprint" in the dust surface density profile that is directly accessible to current observational facilities. Using an analytical framework for dust evolution, we demonstrate that the combined effects of drift and (viscous) gas drag naturally produce a sharp outer edge in the dust distribution (or, equivalently, a sharp decrease in the dust-to-gas mass ratio). This edge feature forms during the earliest phase in the evolution of disk solids, before grain growth in the outer disk has made much progress, and is preserved over longer timescales when both growth and transport effects are more substantial. The key features of these analytical models are reproduced in detailed numerical simulations, and are qualitatively consistent with recent millimeter-wave observations that find gas/dust size discrepancies and steep declines in dust continuum emission in the outer regions of protoplanetary disks., 12 pages, 5 figures, accepted to ApJ

Context. Particle trapping in local or global pressure maxima in protoplanetary disks is one of the new paradigms in the theory of the first stages of planet formation. However, finding observational evidence for this effect is not easy. Recent work suggests that the large ring-shaped outer disks observed in transition disk sources may in fact be lopsided and constitute large banana-shaped vortices. Aims. We wish to investigate how effective dust can accumulate along the azimuthal direction. We also want to find out if the size- sorting resulting from this can produce a detectable signatures at millimeter wavelengths. Methods. To keep the numerical cost under control we develop a 1+1D method in which the azimuthal variations are treated sepa- rately from the radial ones. The azimuthal structure is calculated analytically for a steady-state between mixing and azimuthal drift. We derive equilibration time scales and compare the analytical solutions to time-dependent numerical simulations. Results. We find that weak, but long-lived azimuthal density gradients in the gas can induce very strong azimuthal accumulations of dust. The strength of the accumulations depends on the P\'eclet number, which is the relative importance of advection and diffusion. We apply our model to transition disks and our simulated observations show that this effect would be easily observable with ALMA and in principle allows to put constraints on the strength of turbulence and the local gas density., Comment: 4 pages, 4 figures, accepted for publication in A&A Letters