arXiv subjects

T. Birnstiel

Publications and source records attributed to T. Birnstiel.

52 records · Page 3Linked to original sources

arXiv2013

Imaging diagnostics for transitional discs

Transitional discs are a special type of protoplanetary discs where planet formation is thought to be taking place. These objects feature characteristic inner cavities and/or gaps of a few tens of AUs in the sub-millimitre images of the disc. This signature suggests a localised depletion of matter in the disc that could be caused by planet formation processes. However, recent observations have revealed differences in the structures imaged at different wavelengths in some of these discs. In this paper, we aim to explain these observational differences using self-consistent physical 2-D hydrodynamical and dust evolution models of such objects, assuming their morphology is indeed generated by the presence of a planet. We use these models to derive the distribution of gas and dust in a theoretical planet-hosting disc, for various planet masses and orbital separations. We then simulate observations of the emitted and scattered light from these models with VLT/SPHERE ZIMPOL, Subaru/HiCIAO, VLT/VISIR and ALMA. We do this by first computing the full resolution images of the models at different wavelengths, and then simulating the observations accounting for the characteristics of each particular instrument. The presence of the planet generates pressure bumps in the gas distribution of the disc whose characteristics strongly depend on the planet mass and position. These bumps cause large grains to accumulate while small grains are allowed into inner regions. This spatial differentiation of the grain sizes explains the differences in the observations since different wavelengths and observing techniques trace different parts of the dust size distribution. Based on this effect, we conclude that the combination of visible/near-infrared polarimetric and sub-mm images is the best strategy to constrain the properties of the unseen planet responsible for the disc structure.

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arXiv2013

Explaining millimeter-sized particles in brown dwarf disks

Planets have been detected around a variety of stars, including low-mass objects, such as brown dwarfs. However, such extreme cases are challenging for planet formation models. Recent sub-millimeter observations of disks around brown dwarf measured low spectral indices of the continuum emission that suggest that dust grains grow to mm-sizes even in these very low mass environments. To understand the first steps of planet formation in scaled-down versions of T-Tauri disks, we investigate the physical conditions that can theoretically explain the growth from interstellar dust to millimeter-sized grains in disks around brown dwarf. We modeled the evolution of dust particles under conditions of low-mass disks around brown dwarfs. We used coagulation, fragmentation and disk-structure models to simulate the evolution of dust, with zero and non-zero radial drift. For the non-zero radial drift, we considered strong inhomogeneities in the gas surface density profile that mimic long-lived pressure bumps in the disk. We studied different scenarios that could lead to an agreement between theoretical models and the spectral slope found by millimeter observations. We find that fragmentation is less likely and rapid inward drift is more significant for particles in brown dwarf disks than in T-Tauri disks. We present different scenarios that can nevertheless explain millimeter-sized grains. As an example, a model that combines the following parameters can fit the millimeter fluxes measured for brown dwarf disks: strong pressure inhomogeneities of $\sim$ 40% of amplitude, a small radial extent $\sim$ 15 AU, a moderate turbulence strength $α_{\mathrm{turb}}= 10^{-3}$, and average fragmentation velocities for ices $v_f = 10 m s^{-1}$.

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arXiv2013

Protoplanetary Disk Structure With Grain Evolution: the ANDES Model

We present a self-consistent model of a protoplanetary disk: 'ANDES' ('AccretioN disk with Dust Evolution and Sedimentation'). ANDES is based on a flexible and extendable modular structure that includes 1) a 1+1D frequency-dependent continuum radiative transfer module, 2) a module to calculate the chemical evolution using an extended gas-grain network with UV/X-ray-driven processes surface reactions, 3) a module to calculate the gas thermal energy balance, and 4) a 1+1D module that simulates dust grain evolution. For the first time, grain evolution and time-dependent molecular chemistry are included in a protoplanetary disk model. We find that grain growth and sedimentation of large grains to the disk midplane lead to a dust-depleted atmosphere. Consequently, dust and gas temperatures become higher in the inner disk (R < 50 AU) and lower in the outer disk (R > 50 AU), in comparison with the disk model with pristine dust. The response of disk chemical structure to the dust growth and sedimentation is twofold. First, due to higher transparency a partly UV-shielded molecular layer is shifted closer to the dense midplane. Second, the presence of big grains in the disk midplane delays the freeze-out of volatile gas-phase species such as CO there, while in adjacent upper layers the depletion is still effective. Molecular concentrations and thus column densities of many species are enhanced in the disk model with dust evolution, e.g., CO2, NH2CN, HNO, H2O, HCOOH, HCN, CO. We also show that time-dependent chemistry is important for a proper description of gas thermal balance.

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arXiv2013

Lopsided dust rings in transition disks

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 Péclet 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.

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arXiv2012

Ring shaped dust accumulation in transition disks

Context.Transition disks are believed to be the final stages of protoplanetary disks, during which a forming planetary system or photoevaporation processes open a gap in the inner disk, drastically changing the disk structure. From theoretical arguments it is expected that dust growth, fragmentation and radial drift are strongly influenced by gas disk structure, and pressure bumps in disks have been suggested as key features that may allow grains to converge and grow efficiently. Aims. We want to study how the presence of a large planet in a disk influences the growth and radial distribution of dust grains, and how observable properties are linked to the mass of the planet. Methods. We combine two-dimensional hydrodynamical disk simulations of disk-planet interactions with state-of-the-art coagulation/fragmentation models to simulate the evolution of dust in a disk which has a gap created by a massive planet. We compute images at different wavelengths and illustrate our results using the example of the transition disk LkCa15. Results. The gap opened by a planet and the long-range interaction between the planet and the outer disk create a single large pressure bump outside the planetary orbit. Millimeter-sized particles form and accumulate at the pressure maximum and naturally produce ring-shaped sub-millimeter emission that is long-lived because radial drift no longer depletes the large grain population of the disk. For large planet masses around 9 $M_{\mathrm{Jup}}$, the pressure maximum and, therefore, the ring of millimeter particles is located at distances that can be more than twice the star-planet separation, creating a large spatial separation between the gas inner edge of the outer disk and the peak millimeter emission. Smaller grains do get closer to the gap and we predict how the surface brightness varies at different wavelengths.

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arXiv2012

Can grain growth explain transition disks?

Aims: Grain growth has been suggested as one possible explanation for the diminished dust optical depths in the inner regions of protoplanetary "transition" disks. In this work, we directly test this hypothesis in the context of current models of grain growth and transport. Methods: A set of dust evolution models with different disk shapes, masses, turbulence parameters, and drift efficiencies is combined with radiative transfer calculations in order to derive theoretical spectral energy distributions (SEDs) and images. Results: We find that grain growth and transport effects can indeed produce dips in the infrared SED, as typically found in observations of transition disks. Our models achieve the necessary reduction of mass in small dust by producing larger grains, yet not large enough to be fragmenting efficiently. However, this population of large grains is still detectable at millimeter wavelengths. Even if perfect sticking is assumed and radial drift is neglected, a large population of dust grains is left behind because the time scales on which they are swept up by the larger grains are too long. This mechanism thus fails to reproduce the large emission cavities observed in recent millimeter-wave interferometric images of accreting transition disks.

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arXiv2012

A simple model for the evolution of the dust population in protoplanetary disks

Context: The global size and spatial distribution of dust is an important ingredient in the structure and evolution of protoplanetary disks and in the formation of larger bodies, such as planetesimals. Aims: We aim to derive simple equations that explain the global evolution of the dust surface density profile and the upper limit of the grain size distribution and which can readily be used for further modeling or for interpreting of observational data. Methods: We have developed a simple model that follows the upper end of the dust size distribution and the evolution of the dust surface density profile. This model is calibrated with state-of-the-art simulations of dust evolution, which treat dust growth, fragmentation, and transport in viscously evolving gas disks. Results: We find very good agreement between the full dust-evolution code and the toy model presented in this paper. We derive analytical profiles that describe the dust-to-gas ratios and the dust surface density profiles well in protoplanetary disks, as well as the radial flux by solid material "rain out", which is crucial for triggering any gravity assisted formation of planetesimals. We show that fragmentation is the dominating effect in the inner regions of the disk leading to a dust surface density exponent of -1.5, while the outer regions at later times can become drift-dominated, yielding a dust surface density exponent of -0.75. Our results show that radial drift is not efficient in fragmenting dust grains. This supports the theory that small dust grains are resupplied by fragmentation due to the turbulent state of the disk.

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arXiv2011

The TW Hya Disk at 870 microns: Comparison of CO and Dust Radial Structures

We present high resolution (0.3" = 16 AU), high signal-to-noise ratio Submillimeter Array observations of the 870 microns (345 GHz) continuum and CO J=3--2 line emission from the protoplanetary disk around TW Hya. Using continuum and line radiative transfer calculations, those data and the multiwavelength spectral energy distribution are analyzed together in the context of simple two-dimensional parametric disk structure models. Under the assumptions of a radially invariant dust population and (vertically integrated) gas-to-dust mass ratio, we are unable to simultaneously reproduce the CO and dust observations with model structures that employ either a single, distinct outer boundary or a smooth (exponential) taper at large radii. Instead, we find that the distribution of millimeter-sized dust grains in the TW Hya disk has a relatively sharp edge near 60 AU, contrary to the CO emission (and optical/infrared scattered light) that extends to a much larger radius of at least 215 AU. We discuss some possible explanations for the observed radial distribution of millimeter-sized dust grains and the apparent CO-dust size discrepancy, and suggest that they may be hallmarks of substructure in the dust disk or natural signatures of the growth and radial drift of solids that might be expected for disks around older pre-main sequence stars like TW Hya.

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arXiv2011

Trapping dust particles in the outer regions of protoplanetary disks

In order to explain grain growth to mm sized particles and their retention in outer regions of protoplanetary disks, as it is observed at sub-mm and mm wavelengths, we investigate if strong inhomogeneities in the gas density profiles can slow down excessive radial drift and can help dust particles to grow. We use coagulation/fragmentation and disk-structure models, to simulate the evolution of dust in a bumpy surface density profile which we mimic with a sinusoidal disturbance. For different values of the amplitude and length scale of the bumps, we investigate the ability of this model to produce and retain large particles on million years time scales. In addition, we introduced a comparison between the pressure inhomogeneities considered in this work and the pressure profiles that come from magnetorotational instability. Using the Common Astronomy Software Applications ALMA simulator, we study if there are observational signatures of these pressure inhomogeneities that can be seen with ALMA. We present the favorable conditions to trap dust particles and the corresponding calculations predicting the spectral slope in the mm-wavelength range, to compare with current observations. Finally we present simulated images using different antenna configurations of ALMA at different frequencies, to show that the ring structures will be detectable at the distances of the Taurus Auriga or Ophiucus star forming regions.

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arXiv2011

The Evolution of Gas and Dust in Protoplanetary Accretion Disks

Dust constitutes only about one percent of the mass of circumstellar disks, yet it is of crucial importance for the modeling of planet formation, disk chemistry, radiative transfer and observations. The initial growth of dust from sub-micron sized grains to planetesimals and also the radial transport of dust in disks around young stars is the topic of this thesis. Circumstellar dust is subject to radial drift, vertical settling, turbulent mixing, collisional growth, fragmentation and erosion. We approach this subject from three directions: analytical calculations, numerical simulations, and comparison to observations. We describe the physical and numerical concepts that go into a model which is able to simulate the radial and size evolution of dust in a gas disk which is viscously evolving over several million years. The resulting dust size distributions are compared to our analytical predictions and a simple recipe for obtaining steady-state dust size distributions is derived. With the numerical model at hand, we show that grain fragmentation can explain the fact that circumstellar disks are observed to be dust-rich for several million years. Finally, we investigate the challenges that observations present to the theory of grain evolution, namely that grains of millimeter sizes are observed at large distances from the star. We have found that under the assumption that radial drift is ineffective, we can reproduce some of the observed spectral indices and fluxes. Fainter objects point towards a reduced dust-to-gas ratio or lower dust opacities.

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arXiv2011

The mm-colors of a young binary disk system in the Orion Nebula Cluster

We present new EVLA continuum observations at 7 mm of the 253-1536 binary disk system in the Orion Nebula Cluster. The measured fluxes were combined with data in the sub-mm to derive the millimeter spectral index of each individual disk component. We show how these observations can be used to test the models of dust evolution and early growth of solids in protoplanetary disks. Our analysis indicates that the disk with lower density and higher temperature hosts larger grains than the companion disk. This result is the opposite of what predicted by the dust evolution models. The models and observational results can be reconciled if the viscosity $α$-parameter differs by more than a factor of ten in the two disks, or if the distribution of solids in the disks is strongly affected by radial motions. This analysis can be applied to future high-angular resolution observations of young disks with EVLA and ALMA to provide even stronger observational constraints to the models of dust evolution in protoplanetary disks.

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arXiv2010

Impact of grain evolution on the chemical structure of protoplanetary disks

We study the impact of dust evolution in a protoplanetary disk around a T Tauri star on the disk chemical composition. For the first time we utilize a comprehensive model of dust evolution which includes growth, fragmentation and sedimentation. Specific attention is paid to the influence of grain evolution on the penetration of the UV field in the disk. A chemical model that includes a comprehensive set of gas phase and grain surface chemical reactions is used to simulate the chemical structure of the disk. The main effect of the grain evolution on the disk chemical composition comes from sedimentation, and, to a lesser degree, from the reduction of the total grain surface area. The net effect of grain growth is suppressed by the fragmentation process which maintains a population of small grains, dominating the total grain surface area. We consider three models of dust properties. In model GS both growth and sedimentation are taken into account. In models A5 and A4 all grains are assumed to have the same size (10(-5) cm and 10(-4) cm, respectively) with constant gas-to-dust mass ratio of 100. Like in previous studies, the "three-layer" pattern (midplane, molecular layer, hot atmosphere) in the disk chemical structure is preserved in all models, but shifted closer to the midplane in models with increased grain size (GS and A4). Unlike other similar studies, we find that in models GS and A4 column densities of most gas-phase species are enhanced by 1-3 orders of magnitude relative to those in a model with pristine dust (A5), while column densities of their surface counterparts are decreased. We show that column densities of certain species, like C2H, HC(2n+1)N (n=0-3), H2O and some other molecules, as well as the C2H2/HCN abundance ratio which are accessible with Herschel and ALMA can be used as observational tracers of early stages of the grain evolution process in protoplanetary disks.

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arXiv2010

Dust size distributions in coagulation/fragmentation equilibrium: Numerical solutions and analytical fits

Context. Grains in circumstellar disks are believed to grow by mutual collisions and subsequent sticking due to surface forces. Results of many fields of research involving circumstellar disks, such as radiative transfer calculations, disk chemistry, magneto-hydrodynamic simulations largely depend on the unknown grain size distribution. Aims. As detailed calculations of grain growth and fragmentation are both numerically challenging and computationally expensive, we aim to find simple recipes and analytical solutions for the grain size distribution in circumstellar disks for a scenario in which grain growth is limited by fragmentation and radial drift can be neglected. Methods. We generalize previous analytical work on self-similar steady-state grain distributions. Numerical simulations are carried out to identify under which conditions the grain size distributions can be understood in terms of a combination of power-law distributions. A physically motivated fitting formula for grain size distributions is derived using our analytical predictions and numerical simulations. Results. We find good agreement between analytical results and numerical solutions of the Smoluchowski equation for simple shapes of the kernel function. The results for more complicated and realistic cases can be fitted with a physically motivated "black box" recipe presented in this paper. Our results show that the shape of the dust distribution is mostly dominated by the gas surface density (not the dust-to-gas ratio), the turbulence strength and the temperature and does not obey an MRN type distribution.

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arXiv2010

Testing the theory of grain growth and fragmentation by millimeter observations of protoplanetary disks

Context. Observations at sub-millimeter and mm wavelengths will in the near future be able to resolve the radial dependence of the mm spectral slope in circumstellar disks with a resolution of around a few AU at the distance of the closest star-forming regions. Aims. We aim to constrain physical models of grain growth and fragmentation by a large sample of (sub-)mm observations of disks around pre-main sequence stars in the Taurus-Auriga and Ophiuchus star-forming regions. Methods. State-of-the-art coagulation/fragmentation and disk-structure codes are coupled to produce steady-state grain size distributions and to predict the spectral slopes at (sub-)mm wavelengths. Results. This work presents the first calculations predicting the mm spectral slope based on a physical model of grain growth. Our models can quite naturally reproduce the observed mm-slopes, but a simultaneous match to the observed range of flux levels can only be reached by a reduction of the dust mass by a factor of a few up to about 30 while keeping the gas mass of the disk the same. This dust reduction can either be due to radial drift at a reduced rate or during an earlier evolutionary time (otherwise the predicted fluxes would become too low) or due to efficient conversion of dust into larger, unseen bodies.

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arXiv2010

Gas- and dust evolution in protoplanetary disks

Context. Current models of the size- and radial evolution of dust in protoplanetary disks generally oversimplify either the radial evolution of the disk (by focussing at one single radius or by using steady state disk models) or they assume particle growth to proceed monodispersely or without fragmentation. Further studies of protoplanetary disks - such as observations, disk chemistry and structure calculations or planet population synthesis models - depend on the distribution of dust as a function of grain size and radial position in the disk. Aims. We attempt to improve upon current models to be able to investigate how the initial conditions, the build-up phase, and the evolution of the protoplanetary disk influence growth and transport of dust. Methods. We introduce a new version of the model of Brauer et al. (2008) in which we now include the time-dependent viscous evolution of the gas disk, and in which more advanced input physics and numerical integration methods are implemented. Results. We show that grain properties, the gas pressure gradient, and the amount of turbulence are much more influencing the evolution of dust than the initial conditions or the build-up phase of the protoplanetary disk. We quantify which conditions or environments are favorable for growth beyond the meter size barrier. High gas surface densities or zonal flows may help to overcome the problem of radial drift, however already a small amount of turbulence poses a much stronger obstacle for grain growth.

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arXiv2009

Dust retention in protoplanetary disks

Context: Protoplanetary disks are observed to remain dust-rich for up to several million years. Theoretical modeling, on the other hand, raises several questions. Firstly, dust coagulation occurs so rapidly, that if the small dust grains are not replenished by collisional fragmentation of dust aggregates, most disks should be observed to be dust poor, which is not the case. Secondly, if dust aggregates grow to sizes of the order of centimeters to meters, they drift so fast inwards, that they are quickly lost. Aims: We attempt to verify if collisional fragmentation of dust aggregates is effective enough to keep disks 'dusty' by replenishing the population of small grains and by preventing excessive radial drift. Methods: With a new and sophisticated implicitly integrated coagulation and fragmentation modeling code, we solve the combined problem of coagulation, fragmentation, turbulent mixing and radial drift and at the same time solve for the 1-D viscous gas disk evolution. Results: We find that for a critical collision velocity of 1 m/s, as suggested by laboratory experiments, the fragmentation is so effective, that at all times the dust is in the form of relatively small particles. This means that radial drift is small and that large amounts of small dust particles remain present for a few million years, as observed. For a critical velocity of 10 m/s, we find that particles grow about two orders of magnitude larger, which leads again to significant dust loss since larger particles are more strongly affected by radial drift.

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