arXiv subjects

Hubert Klahr

Publications and source records attributed to Hubert Klahr.

At least 19 recordsLinked to original sources

arXiv2026

Gas dynamics around dust asymmetries in turbulent disks

High-resolution ALMA observations have revealed asymmetric dust crescents in several protoplanetary disks, suggesting efficient dust trapping mechanisms potentially linked to gas vortices. While such features have been associated with vortices--whether induced by massive planets, turbulence , or other disk processes--their origin remains unclear. In this study, we investigate the viability of dust trapping by vortices that are self-sustained in disks dominated by Vertical Shear Instability (VSI) turbulence. We perform 3D hydrodynamic simulations using the PLUTO code with Lagrangian particles of three sizes (1 mm, 500~$\mu$m, 100~$\mu$m) to analyze the gas-dust dynamics around vortices. Our simulations reveal the formation of multiple vortices, including two characteristic large-scale, long-lived vortices that are able to capture the dust particles. We also find that dust vertical diffusion is reduced within vortices, suggesting that these structures preferentially enhance radial and azimuthal motions. Finally we generate synthetic dust continuum images at different wavelength bands and velocity residuals to compare the observable properties with ALMA observations. No clear spiral features are observed in either the synthetic dust images or the velocity residuals, unlike in vortices triggered by planets. Projection effects at high disk inclinations can obscure dust asymmetries, implying that more disks may host dust crescents than currently reported.

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arXiv2025

Exoplanet formation inference using conditional invertible neural networks

The interpretation of the origin of observed exoplanets is usually done only qualitatively due to uncertainties of key parameters in planet formation models. To allow a quantitative methodology which traces back in time to the planet birth locations, we train recently developed conditional invertible neural networks (cINN) on synthetic data from a global planet formation model which tracks growth from dust grains to evolved final giant planets. In addition to deterministic single planet formation runs, we also include gravitationally interacting planets in multiplanetary systems, which include some measure of chaos. For the latter case, we treat them as individual planets or choose the two or three planets most likely to be discovered by telescopes. We find that training on multiplanetary data, each planet treated as individual point, is promising. The single-planet data only covers a small range of planets and does not extrapolate well to planet properties not included in the training data. Extension to planetary systems will require more training data due to the higher dimensionality of the problem.

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arXiv2025

The Origins & Reservoirs of Exocomets

Small bodies exist in distinct populations within their planetary systems. These reservoir populations hold a range of compositions, which to first order are dependent on formation location relative to their star. We provide a general overview of the nature of the reservoirs that source exocomets, from the influence of the stellar environment through planetesimal formation to comparisons with Solar System populations. Once transitioned from a young protoplanetary disc to a debris disc, a star can expect to be rained with exocomets. While exocomets are predominantly detected to date at A-type stars, planetesimals plausibly exist across a range of stellar masses, based on exoplanet abundance, debris disc occurrence and white dwarf infall.

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arXiv2025

Feasibility of interferometric observations and characterization of planet-induced structures at sub au to au scales in protoplanetary disks

Interferometric observations of protoplanetary disks by VLTI and ALMA have greatly improved our understanding of the detailed structure of these planetary birthplaces. These observations have revealed a variety of large-scale disk substructures, including rings, gaps, and spirals, spanning tens to hundreds of au, supporting the predictions of planet formation models. Recent instruments, such as MATISSE at the VLTI, allow one to resolve and investigate the inner few au of protoplanetary disks in nearby star formation regions, shedding light on the traces of planet formation and evolution at these small scales. The aim of this work is to assess the feasibility of interferometric observations of small-scale planet-induced substructures in protoplanetary disks in nearby star-forming regions. We aim to characterize these substructures in multi-wavelength and multi-epoch observations and subsequently differentiate between simulation parameters. On the basis of 3D hydrodynamic simulations of embedded planetary companions and subsequent 3D Monte Carlo radiative transfer simulations, we calculated and analyzed interferometric observables, assuming observations with the VLTI in the K, L, M, and N bands. The hydrodynamic simulations exhibit mass-dependent planet-induced density waves that create observable substructures, most notably for the considered case of a 300 $M_{\oplus}$ planet. These substructures share similarities with observed large-scale structures and feature a prominent accretion region around the embedded planet. The visibilities show a detectable variability for multi-epoch VLTI/GRAVITY and VLTI/MATISSE observations, caused by the orbital motion of the planet, that are distinguishable from other sources of variability due to their unique combination of timescale and amplitude.

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arXiv2025

Multidimensional half-moment multigroup radiative transfer. Improving moment-based thermal models of circumstellar disks

Common moment-based radiative transfer methods, such as flux-limited diffusion (FLD) and the M1 closure, suffer from artificial interactions between crossing beams. In protoplanetary disks, this leads to an overestimation of the midplane temperature due to the merging of inward and outward vertical fluxes. Methods that avoid these artifacts typically require angular discretization, which can be computationally expensive. In the spirit of the two-stream approximation, we introduced a half-moment (HM) closure that integrates the radiative intensity over hemispheres, thereby suppressing beam interactions along a fixed spatial direction. We derived a multidimensional HM closure via entropy maximization and replaced this closure with an approximate expression that closely matches it, coinciding with it in the diffusion and free-streaming regimes while remaining expressible through simple operations. We implemented HM and M1 closures via implicit-explicit schemes, including multiple frequency groups. We tested these methods in numerical benchmarks such as computing the temperature in an irradiated disk around a T Tauri star, comparing our results with Monte Carlo (MC) radiative transfer simulations. The HM closure correctly reproduces the diffusion limit and prevents crossing flux interactions in a chosen spatial direction. In disk simulations, our multigroup HM method closely matches midplane temperature distributions obtained with classical MC methods. While the M1 closure produces midplane temperatures 44% higher than MC with one frequency group and 21% higher with 22 groups, HM reduces this discrepancy to 6% with 22 groups. Even with just three groups, HM significantly outperforms M1, with maximum departures of 8% compared to M1's 23%. Our results show that combining HM with a multigroup treatment yields more realistic disk temperatures than M1, particularly in optically thick regions.

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arXiv2025

Monte Carlo post-processing for radiation hydro simulations of accreting planets in protoplanetary disks

This paper is part of a series investigating the observational appearance of planets accreting from their nascent protoplanetary disk (PPD). We evaluate the differences between gas temperature distributions determined in our radiation hydrodynamical (RHD) simulations and those recalculated via post-processing with a Monte Carlo (MC) radiative transport (RT) scheme. Our MCRT simulations were performed for global PPD models, each composed of a local 3D high-resolution RHD model embedded in an axisymmetric global disk simulation. We report the level of agreement between the two approaches and point out several caveats that prevent a perfect match between the temperature distributions with our respective methods of choice. Overall, the level of agreement is high, with a typical discrepancy between the RHD and MCRT temperatures of the high-resolution region of only about 10 percent. The largest differences were found close to the disk photosphere, at the transition layer between optically dense and thin regions, as well as in the far-out regions of the PPD, occasionally exceeding values of 40 percent. We identify several reasons for these discrepancies, which are mostly related to general features of typical radiative transfer solvers used in hydrodynamical simulations (angle- and frequency-averaging and ignored scattering) and MCRT methods (ignored internal energy advection and compression and expansion work). This provides a clear pathway to reduce systematic temperature inaccuracies in future works. Based on MCRT simulations, we finally determined the expected error in flux estimates, both for the entire PPD and for planets accreting gas from their ambient disk, independently of the amount of gas piling up in the Hill sphere and the used model resolution.

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arXiv2024

Kinetic Field Theory Applied to Planetesimal Formation I: Freely Streaming Dust Particles

Planet formation in the solar system was started when the first planetesimals were formed from the gravitational collapse of pebble clouds. Numerical simulations of this process, especially in the framework of streaming instability, produce various power laws for the initial mass function for planetesimals. While recent advances have shed light on turbulence and its role in particle clustering, a comprehensive theoretical framework linking turbulence characteristics to particle cluster properties and planetesimal mass function remains incomplete. Recently, a kinetic field theory for ensembles of point-like classical particles in or out of equilibrium has been applied to cosmic structure formation. This theory encodes the dynamics of a classical particle ensemble by a generating functional specified by the initial probability distribution of particles in phase space and their equations of motion. Here, we apply kinetic field theory to planetesimal formation. A model for the initial probability distribution of dust particles in phase space is obtained from a quasi-initial state for a three-dimensional streaming-instability simulation that is a particle distribution with velocities for gas and particles from the Nakagawa relations. The equations of motion are chosen for the simplest case of freely streaming particles. We calculate the non-linearly evolved density power spectrum of dust particles and find that it develops a universal $k^{-3}$ tail at small scales, suggesting scale-invariant structure formation below a characteristic and time-dependent length scale. Thus, the KFT analysis indicates that the initial state for streaming instability simulations does not impose a constraint on structure evolution during planetesimal formation.

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arXiv2024

TriPoD: Tri-Population size distributions for Dust evolution. Coagulation in vertically integrated hydrodynamic simulations of protoplanetary disks

Context. Dust coagulation and fragmentation impact the structure and evolution of protoplanetary disks and set the initial conditions for planet formation. Dust grains dominate the opacities, they determine the cooling times of the gas, they influence the ionization state of the gas, and the grain surface area is an important parameter for the chemistry in protoplanetary disks. Therefore, dust evolution should not be ignored in numerical studies of protoplanetary disks. Available dust coagulation models are, however, too computationally expensive to be implemented in large-scale hydrodynamic simulations. This limits detailed numerical studies of protoplanetary disks, including these effects, mostly to one-dimensional models. Aims. We aim to develop a simple - yet accurate - dust coagulation model that can be implemented in hydrodynamic simulations of protoplanetary disks. Our model shall not significantly increase the computational cost of simulations and provide information about the local grain size distribution. Methods. The local dust size distributions are assumed to be truncated power laws. Such distributions can be characterized by two dust fluids (large and small grains) and a maximum particle size, truncating the power law. We compare our model to state-of-the-art dust coagulation simulations and calibrate it to achieve a good fit with these sophisticated numerical methods. Results. Running various parameter studies, we achieved a good fit between our simplified three-parameter model and DustPy, a state-of-the-art dust coagulation software. Conclusions. We present TriPoD, a sub-grid dust coagulation model for the PLUTO code. With TriPoD, we can perform two-dimensional, vertically integrated dust coagulation simulations on top of a hydrodynamic simulation. Studying the dust distributions in two-dimensional vortices and planet-disk systems is thus made possible.

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arXiv2024

Can gap-edge illumination excite spirals in protoplanetary disks? Three-temperature radiation hydrodynamics and NIR image modelling

The advent of high-resolution, near-infrared instruments such as VLT/SPHERE and Gemini/GPI has helped uncover a wealth of substructure in planet-forming disks, including large, prominent spiral arms in MWC 758, SAO 206462, and V1247 Ori among others. In the classical theory of disk-planet interaction, these arms are consistent with Lindblad-resonance driving by multi-Jupiter-mass companions. Despite improving detection limits, evidence for such massive bodies in connection with spiral substructure has been inconclusive. In search of an alternative explanation, we use the PLUTO code to run 3D hydrodynamical simulations with two comparatively low planet masses (Saturn-mass, Jupiter-mass) and two thermodynamic prescriptions (three-temperature radiation hydrodynamics, and the more traditional $\beta$-cooling) in a low-mass disk. In the radiative cases, an $m = 2$ mode, potentially attributable to the interaction of stellar radiation with gap-edge asymmetries, creates an azimuthal pressure gradient, which in turn gives rise to prominent spiral arms in the upper layers of the disk. Monte Carlo radiative transfer (MCRT) post-processing with RADMC3D reveals that in near-infrared scattered light, these gap-edge spirals are significantly more prominent than the traditional Lindblad spirals for planets in the mass range tested. Our results demonstrate that even intermediate-mass protoplanets -- less detectable, but more ubiquitous, than super-Jupiters -- are capable of indirectly inducing large-scale spiral disk features, and underscore the importance of including radiation physics in efforts to reproduce observations.

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arXiv2024

Vertical shear instability with dust evolution and consistent cooling times. On the importance of the initial dust distribution

Context. Gas in protoplanetary disks mostly cools via thermal accommodation with dust particles. Thermal relaxation is thus highly sensitive to the local dust size distributions and the spatial distribution of the grains. So far, the interplay between thermal relaxation and gas turbulence has not been dynamically modeled in hydrodynamic simulations of protoplanetary disks with dust. Aims. We aim to study the effects of the vertical shear instability (VSI) on the thermal relaxation times, and vice versa. We are particularly interested in the influence of the initial dust grain size on the VSI and whether the emerging turbulence is sustained over long timescales. Results. We find that the emergence of the VSI is strongly dependent on the initial dust grain size. Coagulation also counteracts the emergence of hydrodynamic turbulence in our simulations, as shown by others before. Starting a simulation with larger grains (100 $\mu$m) generally leads to a less turbulent outcome. While the inner disk regions (within $\sim$ 70 au) develop turbulence in all three simulations, we find that the simulations with larger particles do not develop VSI in the outer disk. Conclusions. Our simulations with dynamically calculated thermal accommodation times based on the drifting and settling dust distribution show that the VSI, once developed in a disk, can be sustained over long timescales, even if grain growth is occurring. The VSI corrugates the dust layer and even diffuses the smaller grains into the upper atmosphere, where they can cool the gas. Whether the instability can emerge for a specific stratification depends on the initial dust grain sizes and the initial dust scale height. If the grains are initially $\gtrsim$ 100 $\mu$m and if the level of turbulence is initially assumed to be low, we find no VSI turbulence in the outer disk regions.

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arXiv2024

Three-temperature radiation hydrodynamics with PLUTO: Thermal and kinematic signatures of accreting protoplanets

In circumstellar disks around young stars, the gravitational influence of nascent planets produces telltale patterns in density, temperature, and kinematics. To better understand these signatures, we first performed 3D hydrodynamical simulations of a 0.012 $M_{\odot}$ disk, with a Saturn-mass planet orbiting circularly in-plane at 40 au. We tested four different disk thermodynamic prescriptions (in increasing order of complexity, local isothermality, $\beta$-cooling, two-temperature radiation hydrodynamics, and three-temperature radiation hydrodynamics), finding that $\beta$-cooling offers a reasonable approximation for the three-temperature approach when the planet is not massive or luminous enough to substantially alter the background temperature and density structure. Thereafter, using the three-temperature scheme, we relaxed this assumption, simulating a range of different planet masses (Neptune-mass, Saturn-mass, Jupiter-mass) and accretion luminosities (0, $10^{-3} L_{\odot}$) in the same disk. Our investigation revealed that signatures of disk-planet interaction strengthen with increasing planet mass, with circumplanetary flows becoming prominent in the high-planet-mass regime. Accretion luminosity, which adds pressure support around the planet, was found to weaken the midplane Doppler-flip, potentially visible in optically thin tracers like C$^{18}$O, while strengthening the spiral signature, particularly in upper disk layers sensitive to thicker lines, like those of $^{12}$CO.

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arXiv2024

Thermal baroclinic instabilities in accretion disks I: Combined dispersion relation for Goldreich-Schubert-Fricke Instability and Convective Overstability in disks around young stars

This paper discusses the Goldreich-Schubert-Fricke instability (GSF) and the convective overstability (COS) in the context of baroclinic thermal instabilities in rotating disks around young stars. The vertical shear instability (VSI) is a global extension of the GSF that affects geometrically thin disks but follows the same stability criterion. The COS, on the other hand, also possesses a twin for stellar interiors, specifically, Shibahashi's vibrational stability of rotating stars. We derive a combined dispersion relation for GSF and COS with arbitrary cooling times for local perturbations and determine a new stability criterion beyond the Solberg-Høiland\ criterion. The paper shows that in extension to the stability criterion for the vertically unstratified case ($N^2_R > 0$), one also needs a barotropic disk structure to ensure stability towards COS modes. We demonstrate that a baroclinic disk atmosphere always has a buoyantly unstable direction, although not necessarily in the radial nor vertical direction. The paper predicts that for cooling times longer than the critical cooling time for VSI, GSF modes will always be accompanied by COS modes of similar growth rate. The numerical companion paper II tests the predictions of growth rates from this paper.

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arXiv2023

Dust Coagulation Reconciles Protoplanetary Disk Observations with the Vertical Shear Instability. I. Dust Coagulation and the VSI Dead Zone

Protoplanetary disks exhibit a vertical gradient in angular momentum, rendering them susceptible to the Vertical Shear Instability (VSI). The most important condition for the onset of this mechanism is a short timescale of thermal relaxation ($\lesssim 0.1$ orbital timescales). Simulations of fully VSI active disks are characterized by turbulent, vertically extended dust layers. This is in contradiction with recent observations of the outer regions of some protoplanetary disks, which appear highly settled. In this work, we demonstrate that the process of dust coagulation can diminish the cooling rate of the gas in the outer disk and extinct the VSI activity. Our findings indicate that the turbulence strength is especially susceptible to variations in the fragmentation velocity of the grains. A small fragmentation velocity of $\approx 100 \mathrm{\, cm \,s^{-1}}$ results in a fully turbulent simulation, whereas a value of $\approx 400 \mathrm{\, cm \,s^{-1}}$ results in a laminar outer disk, being consistent with observations. We show that VSI turbulence remains relatively unaffected by variations in the maximum particle size in the inner disk regions. However, we find that dust coagulation can significantly suppress the occurrence of VSI turbulence at larger distances from the central star.

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arXiv2023

Vertical shear instability in two-moment radiation-hydrodynamical simulations of irradiated protoplanetary disks I. Angular momentum transport and turbulent heating

We studied the linear and nonlinear evolution of the Vertical Shear Instability (VSI) in axisymmetric models of protoplanetary disks, focusing on the transport of angular momentum, the produced temperature perturbations, and the applicability of local stability conditions. We modeled the gas-dust mixture via high-resolution two-moment (M1) radiation-hydrodynamical simulations including stellar irradiation with frequency-dependent opacities. We found that, given sufficient depletion of small grains (with a dust-to-gas mass ratio of $10\%$ of our nominal value of $10^{-3}$ for $<0.25$ $μ$m grains), the VSI can operate in surface disk layers while being inactive close to the midplane, resulting in a suppression of the VSI body modes. The VSI reduces the initial vertical shear in bands of approximately uniform specific angular momentum, whose formation is likely favored by the enforced axisymmetry. Similarities with Reynolds stresses and angular momentum distributions in 3D simulations suggest that the VSI-induced angular momentum mixing in the radial direction may be predominantly axisymmetric. The stability regions in our models are well explained by local stability criteria, while the employment of global criteria is still justifiable up to a few scale heights above the midplane, at least as long as VSI modes are radially optically thin. Turbulent heating produces only marginal temperature increases of at most $0.1\%$ and $0.01\%$ in the nominal and dust-depleted models, respectively, peaking at a few (approximately three) scale heights above the midplane. We conclude that it is unlikely that the VSI can, in general, lead to any significant temperature increase since that would either require it to efficiently operate in largely optically thick disk regions or to produce larger levels of turbulence than predicted by models of passive irradiated disks.

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arXiv2023

Vertical shear instability in two-moment radiation-hydrodynamical simulations of irradiated protoplanetary disks II. Secondary instabilities and stability regions

The vertical shear instability (VSI) is a hydrodynamical instability likely to produce turbulence in the dead zones of protoplanetary disks. Various aspects of this instability remain to be understood, including the disk regions where it can operate and the physical phenomena leading to its saturation. In this work, we studied the growth and evolution of secondary instabilities parasitic to the VSI, examining their relation with its saturation in axisymmetric radiation-hydrodynamical simulations of protoplanetary disks. We also constructed stability maps for our disk models, considering temperature stratifications enforced by stellar irradiation and radiative cooling and incorporating the effects of dust-gas collisions and molecular line emission. We found that the flow pattern produced by the interplay of the axisymmetric VSI modes and the baroclinic torque forms bands of nearly uniform specific angular momentum. In the high-shear regions in between these bands, the Kelvin-Helmholtz instability (KHI) is triggered. The significant transfer of kinetic energy to small-scale eddies produced by the KHI and possibly even the baroclinic acceleration of eddies limit the maximum energy of the VSI modes, likely leading to the saturation of the VSI. A third instability mechanism, consisting of an amplification of eddies by baroclinic torques, forms meridional vortices with Mach numbers up to $\sim 0.4$. Our stability analysis suggests that protoplanetary disks can be VSI-unstable in surface layers up to tens of au for reasonably high gas emissivities, even in regions where the midplane is stable. This picture is consistent with current observations of disks showing thin midplane millimeter-sized dust layers while appearing vertically extended in optical and near-infrared wavelengths.

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arXiv2023

Three-temperature radiation hydrodynamics with PLUTO: Tests and applications to protoplanetary disks

In circumstellar disks around T Tauri stars, visible and near-infrared stellar irradiation is intercepted by dust at the disk's optical surface and reprocessed into thermal infrared; this subsequently undergoes radiative diffusion through the optically thick bulk of the disk. The gas component -- overwhelmingly dominant by mass, but contributing little to the opacity -- is heated primarily by gas-grain collisions. In hydrodynamical simulations, however, typical models for this heating process (local isothermality, $β$-cooling, two-temperature radiation hydrodynamics) incorporate simplifying assumptions that limit their ranges of validity. To build on these methods, we develop a ``three-temperature" numerical scheme, which self-consistently models energy exchange between gas, dust, and radiation, as a part of the PLUTO radiation-hydrodynamics code. With a range of test problems in 0D, 1D, 2D, and 3D, we demonstrate the efficacy of our method, and make the case for its applicability to a wide range of problems in disk physics, including hydrodynamic instabilities and disk-planet interaction.

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arXiv2023

High Resolution Study of Planetesimal Formation by Gravitational Collapse of Pebble Clouds

Planetary embryos are built through the collisional growth of 10-100 km sized objects called planetesimals, a formerly large population of objects, of which asteroids, comets and Kuiper-Belt objects represent the leftovers from planet formation in our solar system. Here, we follow the paradigm that turbulence created over-dense pebble clouds, which then collapse under their own self-gravity. We use the multi-physics code GIZMO to model the pebble cloud density as a continuum, with a polytropic equation of state to account for collisional interactions and capturing the phase transition to a quasi-incompressible solid object, i.e. a planetesimal in hydrostatic equilibrium. Thus we study cloud collapse effectively at the resolution of the forming planetesimals, allowing us to derive an initial mass function for planetesimals in relation to the total pebble mass of the collapsing cloud. The redistribution of angular momentum in the collapsing pebble cloud is the main mechanism leading to multiple fragmentation. The angular momentum of the pebble cloud and thus the centrifugal radius increases with distance to the sun, but the solid size of the forming planetesimals is constant. Therefore we find that with increasing distance to the sun, the number of forming planetesimals per pebble cloud increases. For all distances the formation of binaries occurs within higher hierarchical systems. The size distribution is top heavy and can be described with a Gaussian distribution of planetesimal mass. For the asteroid belt, we can infer a most likely size of 125 km, all stemming from pebble clouds of equivalent size 152 km.

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arXiv2023

Thermal instabilities in accretion disks II: Numerical Experiments for the Goldreich-Schubert-Fricke Instability and the Convective Overstability in disks around young stars

The linear stability analysis of a stratified rotating fluid (see paper I) showed that disks with a baroclinic stratification under the influence of thermal relaxation will become unstable to thermal instabilities. One instability is the Goldreich-Schubert-Fricke instability (GSF), which is the local version of the Vertical Shear Instability (VSI) and the other is a thermal overstability, the Convective Overstability (COS). In the present paper we reproduce the analytic predicted growth rates for both instabilities in numerical experiments of small axisymmetric sections of vertically isothermal disks with a radial temperature gradient, especially for cooling times longer than the critical cooling time for VSI. In this cooling time regime our simulations reveal the simultaneous and independent growth of both modes: COS and GSF. We consistently observe that GSF modes exhibit a faster growth rate compared to COS modes. Near the midplane, GSF modes eventually stop growing, while COS modes continue to grow and ultimately dominate the flow pattern. Away from the midplane, we find GSF modes to saturate, when bands of constant angular momentum have formed. In these bands we observe the formation and growth of eddies driven by the baroclinic term, further enhancing the velocity perturbations. In geophysics this effect is known as horizontal convection or sea-breeze instability. Three-dimensional simulations will have to show whether similar effects will occur when axisymmetry is not enforced. Our local simulations help to reveal the numerical resolution requirements to observe thermal instabilities in global simulations of disks around young stars.

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