arXiv subjects

Tilman Birnstiel

Publications and source records attributed to Tilman Birnstiel.

At least 37 records · Page 2Linked to original sources

arXiv2023

Leaky dust traps: How fragmentation impacts dust filtering by planets

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.

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arXiv2022

Rapid Formation of Massive Planetary Cores in a Pressure Bump

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.

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arXiv2022

Constraining the turbulence and the dust disk in IM Lup: onset of planetesimal formation

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.

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arXiv2022

A Neural Network Subgrid Model of the Early Stages of Planet Formation

Planet formation is a multi-scale process in which the coagulation of $\mathrm{μm}$-sized dust grains in protoplanetary disks is strongly influenced by the hydrodynamic processes on scales of astronomical units ($\approx 1.5\times 10^8 \,\mathrm{km}$). Studies are therefore dependent on subgrid models to emulate the micro physics of dust coagulation on top of a large scale hydrodynamic simulation. Numerical simulations which include the relevant physical effects are complex and computationally expensive. Here, we present a fast and accurate learned effective model for dust coagulation, trained on data from high resolution numerical coagulation simulations. Our model captures details of the dust coagulation process that were so far not tractable with other dust coagulation prescriptions with similar computational efficiency.

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arXiv2022

DustPy: A Python Package for Dust Evolution in Protoplanetary Disks

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.

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arXiv2022

A large population study of protoplanetary disks: Explaining the millimeter size-luminosity relation with or without sub-structure

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 $α$ 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.

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arXiv2022

Mineral Snowflakes on Exoplanets and Brown Dwarfs: Coagulation and Fragmentation of Cloud Particles with {\sc HyLandS}

Brown dwarfs and exoplanets provide unique atmospheric regimes that hold information about their formation routes and evolutionary states. Modelling mineral cloud particle formation is key to prepare for missions and instruments like CRIRES+, JWST and ARIEL as well as possible polarimetry missions like {\sc PolStar}. The aim is to support more detailed observations that demand greater understanding of microphysical cloud processes. We extend our kinetic cloud formation model that treats nucleation, condensation, evaporation and settling of mixed material cloud particles to consistently model cloud particle-particle collisions. The new hybrid code, {\sc HyLandS}, is applied to a grid of {\sc Drift-Phoenix} (T, p)-profiles. Effective medium theory and Mie theory are used to investigate the optical properties. Turbulence is the main driving process of collisions, with collisions becoming the dominant process at the cloud base ($p>10^{-4}\,{\rm bar}$). Collisions produce one of three outcomes: fragmenting atmospheres ($\log_{10}(g)=3$), coagulating atmospheres ($\log_{10}(g)=5$, $T_{\rm eff} \leq 1800\, {\rm K}$) and condensational growth dominated atmospheres ($\log_{10}(g\,)=5$, $T_{\rm eff} > 1800\, {\rm K}$). Cloud particle opacity slope at optical wavelengths (HST) is increased with fragmentation, as are the silicate features at mid-infrared wavelengths. The hybrid moment-bin method {\sc HyLandS} demonstrates the feasibility of combining a moment and a bin method whilst assuring element conservation. It provides a powerful and fast tool for capturing general trends of particle collisions, consistently with other microphysical processes. Collisions are important in exoplanet and brown dwarf atmospheres but cannot be assumed to be hit-and-stick only. The spectral effects of collisions complicates inferences of cloud particle size and material composition from observational data.

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arXiv2021

Mass determination of protoplanetary disks from dust evolution

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.

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arXiv2021

Thermal Wave Instability as an Origin of Gap and Ring Structures in Protoplanetary Disks

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 $Δr/r \sim$ 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.

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arXiv2021

A search for companions via direct imaging in the DSHARP planet-forming disks

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.

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arXiv2020

The Disk Substructures at High Angular Resolution Project (DSHARP): II. Characteristics of Annular Substructures

The Disk Substructures at High Angular Resolution Project used ALMA to map the 1.25 millimeter continuum of protoplanetary disks at a spatial resolution of ~5 au. We present a systematic analysis of annular substructures in the 18 single-disk systems targeted in this survey. No dominant architecture emerges from this sample; instead, remarkably diverse morphologies are observed. Annular substructures can occur at virtually any radius where millimeter continuum emission is detected and range in widths from a few au to tens of au. Intensity ratios between gaps and adjacent rings range from near-unity to just a few percent. In a minority of cases, annular substructures co-exist with other types of substructures, including spiral arms (3/18) and crescent-like azimuthal asymmetries (2/18). No clear trend is observed between the positions of the substructures and stellar host properties. In particular, the absence of an obvious association with stellar host luminosity (and hence the disk thermal structure) suggests that substructures do not occur preferentially near major molecular snowlines. Annular substructures like those observed in DSHARP have long been hypothesized to be due to planet-disk interactions. A few disks exhibit characteristics particularly suggestive of this scenario, including substructures in possible mean-motion resonance and "double gap" features reminiscent of hydrodynamical simulations of multiple gaps opened by a planet in a low-viscosity disk.

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arXiv2020

Constraining the parameter space for the Solar Nebula

If we want to understand planetesimal formation, the only data set we have is our own Solar System. It is particularly interesting as it is so far 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, once the gas disk is gone. 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. 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 perform a parameter study with nine different disk parameters like the initial disk mass, initial disk size, initial dust-to-gas ratio, turbulence level, and more. We find that the distribution of mass in planetesimals in the disk depends on the planetesimal formation timescale and the pebbles' drift timescale. Multiple disk parameters can influence pebble properties and thus planetesimal formation. However, it is still possible to draw some conclusions on potential parameter ranges. Pebble flux-regulated planetesimal formation seems to be very robust, allowing simulations with a wide range of parameters to meet the initial planetesimal constraints for the Solar Nebula. I.e., it does not require a lot of fine tuning.

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arXiv2020

Planet-induced Vortices with Dust Coagulation in Protoplanetary Disks

In this work, we study how the dust coagulation/fragmentation will influence the evolution and observational appearances of vortices induced by a massive planet embedded in a low viscosity disk by performing global 2D high-resolution hydrodynamical simulations. Within the vortex, due to its higher gas surface density and steeper pressure gradients, dust coagulation, fragmentation and drift (to the vortex center) are all quite efficient, producing dust particles ranging from micron to $\sim 1.0\ {\rm cm}$, as well as overall high dust-to-gas ratio (above unity). In addition, the dust size distribution is quite non-uniform inside the vortex, with the mass weighted average dust size at the vortex center ($\sim 4.0$ mm) being a factor of $\sim10$ larger than other vortex regions. Both large ($\sim$ mm) and small (tens of micron) particles contribute strongly to affect the gas motion within the vortex. As such, we find that the inclusion of dust coagulation has a significant impact on the vortex lifetime and the typical vortex lifetime is about 1000 orbits. After the initial gaseous vortex is destroyed, the dust spreads into a ring with a few remaining smaller gaseous vortices with a high dust concentration and a large maximum size ($\sim$ mm). At late time, the synthetic dust continuum images for the coagulation case show as a ring inlaid with several hot spots at 1.33 mm band, while only distinct hot spots remain at 7.0 mm.

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arXiv2020

A multi-frequency ALMA characterization of substructures in the GM Aur protoplanetary disk

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 $α$ 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."

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arXiv2019

Ring Morphology with Dust Coagulation in Protoplanetary Disks

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.

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arXiv2019

One Solution to the Mass Budget Problem for Planet Formation: Optically Thick Disks with Dust Scattering

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 $α$ can be either larger or smaller than 2 depending on if the dust albedo increases or decreases with wavelength. Using the DSHARP opacity, $α<2$ corresponds to $s_{max}$ of 0.03-0.3 mm. We describe how this optically thick scattering scenario could explain the observed scaling between submm continuum sizes and luminosities, and might help ease the tension between the dust size constraints from polarization and dust continuum measurements. We suggest that a significant amount of disk mass can be hidden from ALMA observations at short millimeter wavelengths. For compact disks smaller than 30 au, we can easily underestimate the dust mass by more than a factor of 10. Longer wavelength observations (e.g. VLA or SKA) are desired to probe the dust mass in disks.

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arXiv2019

Effects of Ringed Structures and Dust Size Growth on Millimeter Observations of Protoplanetary Disks

The growth of solids from sub-micron to millimeter and centimeter sizes is the early step toward the formation of planets inside protoplanetary disks (PPDs). However, such processes and their potential impact on the later stages of solid growth are still poorly understood. In this work, we test the hypothesis that most disks contain at least one ringed structure with a relative small radius. We have carried out a large family of 1D two-fluid (gas+dust) hydrodynamical simulations by evolving the gas and dust motion self-consistently while allowing dust size to evolve via coagulation and fragmentation. We investigate the joint effects of ringed structures and dust size growth on the overall sub-millimeter and millimeter (mm) flux and spectral index of PPDs. Ringed structures slow down the dust radial drift and speed up the dust growth. In particular, we find that those unresolved disks with a high fragmentation velocity ($\sim10\ {\rm m~s^{-1}}$) and a high dust surface density ($\sim10\ {\rm g\ cm^{-2}}$ in the ring) can have mm spectral indices as low as $\sim2.0$, consistent with mm observations of faint disks in nearby star forming regions. Furthermore, disks with more than one ringed structure can potentially reproduce brighter disks with spectral indices lower than $\sim2.5$. Future multi-wavelength high-resolution observations of these low spectral index sources can be used to test the existence of the ringed structures in the unresolved disks and differentiate the effects of dust size growth from optical depth.

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arXiv2019

Planetesimal Population Synthesis: Pebble Flux Regulated Planetesimal Formation

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 $α$-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.

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