arXiv subjects

Wilhelm Kley

Publications and source records attributed to Wilhelm Kley.

At least 19 recordsLinked to original sources

arXiv2025

Viscous circumbinary protoplanetary discs -- II. Disc effects on the binary orbit

More than half of all stars are part of binaries, and many form in a common circumbinary disc. The interaction with the binary shapes the disc to feature a large eccentric inner cavity and spirals in the inner disc. The shape of the cavities is linked to binary and disc properties like viscosity and scale height, and the disc and cavity shape influences the orbital evolution of the binary stars. This is the second part of the study in which we use 2D hydrodynamic long-term simulations for a range of viscous parameters relevant to protoplanetary discs to understand the interaction between young stars and the circumbinary disc. The long-term simulations allow us to study how disc shape and exchange of mass, momentum and energy between binary and disc depend on the precession angle between disc and binary orbit on time scales of thousands of binary orbits. We find a considerable, periodic interaction between the precession of the disc and the binary eccentricity that can significantly exceed the precession-averaged change in eccentricity. We further confirm that thin discs ($H/R<0.05$) lead to shrinking binary orbits, also in the regime of low viscosity, $\alpha=10^{-3}$. In general, the disc can excite eccentricity in binaries with initial eccentricities in the range of $e_\mathrm{bin}=0.05-0.4$. In most cases, the terms aiding shrinking or expansion and circularisation or excitation are nearly balanced, and the evolution of the binary semi-major axis and eccentricity will be sensitive to the ratio of mass accretion between the secondary and primary components.

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arXiv2024

Viscous circumbinary protoplanetary discs -- I. Structure of the inner cavity

Many of the most intriguing features, including spirals and cavities, in the current disc observations are found in binary systems like GG Tau, HD 142527 or HD 100453. Such features are evidence of the dynamic interaction between binary stars and the viscous disc. Understanding these dynamic interactions and how they result in the structure and growth of asymmetric circumbinary discs is a difficult problem, for which there is no complete analytical solution, that predicts the shape of the observed disc accurately. We use numeric simulation to evolve circumbinary discs with varying disc viscosities and investigate the size and shape of the inner cavities in such protoplanetary discs. We have simulated over 140 locally isothermal 2D grid-based disc models for > 3e4 binary orbits each and mapped out the parameter space relevant for protoplanetary discs. With this, it becomes possible to create parametrised profiles for individual discs to compare to observation and find limits to their binary eccentricity or internal viscosity from the simulation data. In the long-term simulations larger cavity sizes than previously considered are possible within the parameter space (< 6 binary separations). As an example, we find that the eccentricity of the disc around HD 142527 suggests the impact of the binary dynamics on the disc. However, even considering the larger cavity sizes, the large size of the cavity in HD 142527 remains unexplained by the simulations considering the most recent orbital constraints.

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arXiv2024

Overstability of the 2:1 mean motion resonance: Exploring disc parameters with hydrodynamic simulations

Resonant planetary migration in protoplanetary discs can lead to an interplay between the resonant interaction of planets and their disc torques called overstability. While theoretical predictions and N-body simulations hinted at its existence, there was no conclusive evidence until hydrodynamical simulations were performed. Our primary purpose is to find a hydrodynamic setup that induces overstability in a planetary system with two moderate-mass planets in a first-order 2:1 mean motion resonance. We also aim to analyse the impact of key disc parameters, namely the viscosity, surface density, and aspect ratio, on the occurrence of overstability in this planetary system when the masses of the planets are kept constant. We performed 2D locally isothermal hydrodynamical simulations of two planets, with masses of 5 and 10 $M_{\oplus}$, in a 2:1 resonance. Upon identifying the fiducial model in which the system exhibits overstability, we performed simulations with different disc parameters to explore the effects of the disc on the overstability of the system. We observe an overstable planetary system in our hydrodynamic simulations. In the parameter study, we note that overstability occurs in discs characterised by low surface density and low viscosity. Increasing the surface density reduces the probability of overstability within the system. A limit cycle was observed in a specific viscous model with $\alpha_{\nu} = 10^{-3}$. In almost all our models, planets create partial gaps in the disc, which affects both the migration timescale and structure of the planetary system. We demonstrate the existence of overstability using hydrodynamic simulations but find deviations from the analytic approximation and show that the main contribution to this deviation can be attributed to dynamic gap opening.

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arXiv2024

FargoCPT: A 2D Multi-Physics Code for Simulating the Interaction of Disks with Stars, Planets and Particles

Context: Planet-disk interactions play a crucial role in the understanding of planet formation and disk evolution. There are multiple numerical tools available to simulate these interactions, including the often-used FARGO code and its variants. Many of the codes were extended over time to include additional physical processes with a focus on their accurate modeling. Aims: We introduce FargoCPT, an updated version of FARGO incorporating other previous enhancements to the code, to provide a simulation environment tailored to study interactions between stars, planets, and disks, ensuring accurate representation of planet systems, hydrodynamics, and dust dynamics with a focus on usability. Methods: The radiation-hydrodynamics part of FargoCPT uses a second-order upwind scheme in 2D polar coordinates supporting multiple equations of state, radiation transport, heating and cooling, and self-gravity. Shocks are considered using artificial viscosity. Integration of the N-body system is achieved by leveraging the REBOUND code. The dust module utilizes massless tracer particles, adapting to drag laws for the Stokes and Epstein regimes. Moreover, FargoCPT provides mechanisms to simulate accretion onto the stars and planets. Results: The code has been tested in practice by its use in various publications. Additionally, it comes with an automated test suite to test the physics modules. Conclusions: FargoCPT offers a unique set of simulation capabilities within the current landscape of publicly available planet-disk interaction simulation tools. Its structured interface and underlying technical updates are intended to assist researchers in the ongoing exploration of planet formation.

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arXiv2023

Stability of coorbital planets around binaries

In previous hydrodynamical simulations, we found a mechanism for nearly circular binary stars, like Kepler-413, to trap two planets in a stable 1:1 resonance. Therefore, the stability of coorbital configurations becomes a relevant question for planet formation around binary stars. Here, we investigate the coorbital planet stability using a Kepler-413 analogue as example and then expanding the parameters to study general n-body stability of planet pairs in eccentric horseshoe orbits around binaries. The stability is tested by evolving the planet orbits for $10^5$ binary periods with varying initial semi-major axes and planet eccentricities. The unstable region of a single circumbinary planet is used as a comparison to the investigated coorbital configurations in this work. We confirm previous findings on the stability of single planets and find a first order linear relation between orbit eccentricity and pericentre to identify stable orbits for various binary configurations. Such a linear relation is also found for the stability of 1:1 resonant planets around binaries. Stable orbits for eccentric horseshoe configurations exist with a pericentre closer than seven binary separations and, in the case of Kepler-413, the pericentre of the first stable orbit can be approximated by $r_{c,peri} = (2.88 e_p + 2.46) a_{bin}$.

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arXiv2022

Hydrodynamic turbulence in disks with embedded planets

The vertical shear instability (VSI) is a source of hydrodynamic turbulence that can drive vigorous vertical mixing and moderate levels of accretion in protoplanetary disks, and it could be observable in the near future. With high-resolution three-dimensional numerical hydrodynamics simulations, we modeled the behavior of the VSI in protoplanetary disks with and without embedded planets. We then measured its accretion and mixing capabilities by comparing the full Reynolds stress, which includes the contribution of nonaxisymmetric features, such as spiral arms and vortices, to the Reynolds stress due to the azimuthally averaged velocity field, which can be attributed to good approximation to the VSI. We verified that the VSI can contribute to the accretion stress and showed that, depending on disk conditions, an embedded planet can coexist with or suppress VSI turbulent stress. Specifically, the presence of spiral shocks launched by a planet or planet-generated vortices can interfere with the VSI near the planet's vicinity, with the instability recovering at large enough distances from the planet or vortex. Our results suggest that observations of VSI signatures are unlikely in disks that contain massive, nonaxisymmetric features.

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arXiv2022

How cooling influences circumbinary discs

Circumbinary disc observations and simulations show large, eccentric inner cavities. Recent work has shown that the shape and size of these cavities depend on the aspect ratio and viscosity of the disc, as well as the binary eccentricity and mass ratio. It has been further shown that, for gaps created by planets, the cooling timescale significantly affects the shape and size of the gap. In this study, we consider the effect of different cooling models on the cavity shape in a circumbinary disc. We compare locally isothermal and radiatively cooled disc models to ones with a parametrised cooling timescale ($β$-cooling), implemented in 2D numerical simulations for varying binary eccentricities. While the shape of the cavity for radiative and locally isothermal models remains comparable, the inner disc structure changes slightly, leading to a change in the precession rate of the disc. With $β$-cooled models, the shape and size of the cavity changes dramatically towards values of $β$=1. Based on our findings, we introduce a parametrised $β$ model that accounts for the shorter cooling timescale inside the cavity while adequately reproducing the results of the radiative model, and we highlight that accurate treatment of the thermodynamics inside the cavity has a significant impact in modelling circumbinary systems.

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arXiv2022

Binary orbital evolution driven by a circumbinary disc

The question whether the interaction of a circumbinary disc with the central binary system leads to shrinking or expansion of the binary orbit has attracted considerable interest as it impacts the evolution of binary black holes and stellar binary stars in their formation phase. We performed two-dimensional hydrodynamical simulations of circumbinary discs for a large parameter set of disc viscosities and thicknesses and two different binary mass ratios for binaries on circular orbits. For those we measured carefully the net angular momentum and mass transfer between disc and binary system, and evaluate the normalised specific angular momentum accretion, $j_\mathrm{s}$ . This is compared to the theoretical, critical specific angular momentum change $j_\mathrm{s,crit}$ that separates contracting from expanding cases which depends on the the binary's mass ratio and the relative accretion onto the two stars. Using finite and infinite disc models we show that the inferred binary evolution is very similar for both setups and confirm that $j_\mathrm{s}$ can be measured accurately with cylindrical simulations that do not include the central binary. However, to obtain the relative accretion onto the stars for non-equal mass binaries, simulations that cover the whole domain including the binary are required. We find that for thick discs with aspect ratio $h = 0.1$ the binaries expand for all viscosities, while discs with $h = 0.05$ lead to an expansion only for larger viscosities with $α$ exceeding $\sim 0.005$. Overall, the regime of binary expansion extends to a much wider parameter space than previously anticipated, but for thin, low viscosity discs the orbits shrink.

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arXiv2021

Survival of planet-induced vortices in 2D disks

Context: Several observations of protoplanetary disks display non-axisymmetric features, often interpreted as vortices. Numerical modeling has repeatedly shown that gap-opening planets are capable of producing large and long-lasting vortices at their outer gap edge, making massive planets popular candidates as the source of such features. Aims: We explore the lifetime of vortices generated by Jupiter-sized planets as a function of the thermal relaxation timescale, the level of turbulence, and the effect of disk self-gravity. Methods: We conduct 2D numerical simulations using the hydrodynamics codes PLUTO and FARGO, scanning through several physical and numerical parameters. Vortex properties are automatically extracted from thousands of simulation snapshots. Results: We find that vortices that spawn at the outer gap edge can survive for about 100-3000 planetary orbits, with the shortest lifetimes occurring for moderately efficient dissipation and cooling. However, we also observe a different regime of long-lasting vortices with lifetimes of at least 15 000 orbits for very low viscosity and very short thermal relaxation timescales. Disk self-gravity significantly shortens the lifetime of regular vortices but still allows long-lived ones to survive. Conclusions: Our results suggest that the cooling timescale plays an important role in vortex formation and lifetime and that planet-generated vortices should be observable at large distances from the star for typical thermal relaxation timescales and low turbulence levels.

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arXiv2021

Disks in close binary stars: γ-Cephei revisited

Close binaries ($a_{bin} < 20$ au) are known to harbor planets, yet planet formation is unlikely to succeed in such systems. Studying the dynamics of disks in close binaries can help to understand how those planets could have formed. We study the impact that numerical and physical parameters have on the dynamics of disks in close binaries. We use the $γ$-Cephei system as an example and focus on disk quantities such as disk eccentricity and the precession rate as indicators for the dynamical state of the disks. We simulate disks in close binaries by performing two-dimensional radiative hydrodynamical simulations using a modified version of the Fargo code. First, we perform a parameter study for different numerical parameters to confirm that our results are robust. In the second part, we study the effects of different masses and different viscosities on the disks' dynamics. Previous studies on radiative disks in close binaries used too low resolutions and too small simulation domains, which impacted the disk's dynamics. We find that radiative disks in close binaries, after an initialization phase, become eccentric with mean eccentricities between 0.06 to 0.27 and display a slow retrograde precession with periods ranging from $4 - 40T_{bin}$ which depends quadratically on the disk's mean aspect ratio. In general, the disks show a coherent, rigid precession which can be broken, however, by changes in the opacity law reducing the overall eccentricity of the disk.

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arXiv2021

Giant planet migration during the disc dispersal phase

Transition discs are expected to be a natural outcome of the interplay between photoevaporation (PE) and giant planet formation. Massive planets reduce the inflow of material from the outer to the inner disc, therefore triggering an earlier onset of disc dispersal due to PE through a process known as Planet-Induced PhotoEvaporation (PIPE). In this case, a cavity is formed as material inside the planetary orbit is removed by PE, leaving only the outer disc to drive the migration of the giant planet. We investigate the impact of PE on giant planet migration and focus specifically on the case of transition discs with an evacuated cavity inside the planet location. This is important for determining under what circumstances PE is efficient at halting the migration of giant planets, thus affecting the final orbital distribution of a population of planets. For this purpose, we use 2D FARGO simulations to model the migration of giant planets in a range of primordial and transition discs subject to PE. The results are then compared to the standard prescriptions used to calculate the migration tracks of planets in 1D planet population synthesis models. The FARGO simulations show that once the disc inside the planet location is depleted of gas, planet migration ceases. This contradicts the results obtained by the impulse approximation, which predicts the accelerated inward migration of planets in discs that have been cleared inside the planetary orbit. These results suggest that the impulse approximation may not be suitable for planets embedded in transition discs. A better approximation that could be used in 1D models would involve halting planet migration once the material inside the planetary orbit is depleted of gas and the surface density at the 3:2 mean motion resonance location in the outer disc reaches a threshold value of $0.01\,\mathrm{g\,cm^{-2}}$.

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arXiv2020

Modeling the nonaxisymmetric structure in the HD 163296 disk with planet-disk interaction

High resolution ALMA observations revealed a variety of rich substructures in numerous protoplanetary disks. These structures consist of rings, gaps and asymmetric features. It is debated whether planets can be accounted for these substructures in the dust continuum. Characterizing the origin of asymmetries as seen in HD 163296 might lead to a better understanding of planet formation and the underlying physical parameters of the system. We test the possibility of the formation of the crescent-shaped asymmetry in the HD 163296 disk through planet-disk interaction. The goal is to obtain constraints on planet masses and eccentricities and disk viscosities. Two dimensional, multi-fluid, hydrodynamical simulations are performed with the FARGO3D code including three embedded planets. Dust is described with the pressureless fluid approach and is distributed over eight size bins. Resulting grids are post-processed with the radiative transfer code RADMC-3D and the CASA software to model synthetic observations. We find that the crescent-shaped asymmetry can be qualitatively modeled with a Jupiter mass planet at a radial distance of 48 au. Dust is trapped preferably in the trailing Lagrange point L5 with a mass of 10 to 15 earth masses. Increased values of eccentricity of the innermost Jupiter mass planet damages the stability of the crescent-shaped feature and does not reproduce the observed radial proximity to the first prominent ring in the system. Generally, a low level of viscosity ($α\leq 2\cdot10^{-3}$) is necessary to allow the existence of such a feature. Including dust feedback the leading point L4 can dominantly capture dust for dust grains with an initial Stokes number $\leq 3.6\cdot 10^{-2}$. The observational results suggest a negligible effect of dust feedback since only one such feature has been detected so far.

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arXiv2020

Migration jumps of planets in transition disks

Transition disks form a special class of protoplanetary disks that are characterized by a deficiency of disk material close to the star. In a subgroup, inner holes in these disks can stretch out to a few tens of au while there is still mass accretion onto the central star observed. We analyse the proposition that this type of wide transition disks is generated by the interaction of the disk with a system of embedded planets. We performed 2D hydrodynamics simulations of a flat disk using either a locally isothermal equation of state or considering also radiative effects. Two 3 to 9 Jupiter mass planets were embedded in the disk and their dynamical evolution due to disk-planet interaction was followed for over 100 000 years. The simulations account for mass accretion onto the star and planets. We included models with parameters geared to the system PDS 70. To assess the observability of features in our models we performed synthetic ALMA observations. For systems with a more massive inner planet there are phases where both planets migrate outward engaged in a 2:1 mean motion resonance via the Masset-Snellgrove mechanism. In sufficiently massive disks the formation of a vortex in the outer disk can trigger rapid outward migration of the outer planet where its distance increases by tens of au within a few thousand years. Later, the outer planet migrates back inwards settling again into resonance with the inner planet. We call this emerging composite phenomenon a 'migration jump'. Outward migration and the migration jumps are accompanied by a high mass accretion rate onto the star. The synthetic images reveal numerous substructures depending on the type of dynamical behaviour. Our results suggest that the outward migration of two embedded planets is a prime candidate for the explanation of the observed high stellar mass accretion rate in wide transition disks.

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arXiv2020

High Resolution Parameter Study of the Vertical Shear Instability

Theoretical models of protoplanetary disks have shown the Vertical Shear Instability (VSI) to be a prime candidate to explain turbulence in the dead zone of the disk. However, simulations of the VSI have yet to show consistent levels of key disk turbulence parameters like the stress-to-pressure ratio $α$. We aim to reconcile these different values by performing a parameter study on the VSI with focus on the disk density gradient $p$ and aspect ratio $h := H/R$. We use full 2$π$ 3D simulations of the disk for chosen set of both parameters. All simulations are evolved for 1000 reference orbits, at a resolution of 18 cells per h. We find that the saturated stress-to-pressure ratio in our simulations is dependent on the disk aspect ratio with a \review{strong} scaling of $α\propto h^{2.6}$, in contrast to the traditional $α$ model, where viscosity scales as $ν\propto αh^2$ with a constant $α$. We also observe consistent formation of large scale vortices across all investigated parameters. The vortices show uniformly aspect ratios of $χ\approx 10$ and radial widths of approximately 1.5 $H$. With our findings we can reconcile the different values reported for the stress-to-pressure ratio from both isothermal and radiation hydrodynamics models, and show long-term evolution effects of the VSI that could aide in the formation of planetesimals.

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arXiv2020

Solid accretion onto planetary cores in radiative disks

The solid accretion rate, necessary to grow gas giant planetary cores within the disk lifetime, has been a major constraint for theories of planet formation. We tested the solid accretion rate efficiency on planetary cores of different masses embedded in their birth disk, by means of 3D radiation-hydrodynamics, where we followed the evolution of a swarm of embedded solids of different sizes. We found that using a realistic equation of state and radiative cooling, the disk at 5 au is able to cool efficiently and reduce its aspect ratio. As a result, the pebble isolation mass is reached before the core grows to 10 Earth masses, stopping efficiently the pebble flux and creating a transition disk. Moreover, the reduced isolation mass halts the solid accretion before the core reaches the critical mass, leading to a barrier to giant planet formation, and it explains the large abundance of super-Earth planets in the observed population.

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arXiv2020

Importance of radiative effects in gap opening by planets in protoplanetary disks

Recent ALMA observations revealed concentric annular structures in several young class-II objects. In an attempt to produce the rings and gaps in some of these systems, they have been modeled numerically with a single embedded planet assuming a locally isothermal equation of state. This is often justified by observations targeting the irradiation-dominated outer regions of disks (approximately 100 au). We test this assumption by conducting hydrodynamics simulations of embedded planets in thin locally isothermal and radiative disks that mimic the systems HD 163296 and AS 209 in order to examine the effect of including the energy equation in a seemingly locally isothermal environment as far as planet-disk interaction is concerned. We find that modeling such disks with an ideal equation of state makes a difference in terms of the number of produced rings and the spiral arm contrast in the disk. Locally isothermal disks produce sharper annular or azimuthal features and overestimate a single planet's gap-opening capabilities by producing multiple gaps. In contrast, planets in radiative disks carve a single gap for typical disk parameters. Consequently, for accurate modeling of planets with semimajor axes up to about 100 au, radiative effects should be taken into account even in seemingly locally isothermal disks. In addition, for the case of AS 209, we find that the primary gap is significantly different between locally isothermal and radiative models. Our results suggest that multiple planets are required to explain the ring-rich structures in such systems.

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arXiv2019

The impact of planet wakes on the location and shape of the water iceline in a protoplanetary disk

Context: Planets in accretion disks can excite spiral shocks, and---if massive enough---open gaps in their vicinity. Both of these effects can influence the overall disk thermal structure. Aims: We model planets of different masses and semimajor axes in disks of various viscosities and accretion rates to examine their impact on disk thermodynamics and highlight the mutable, non-axisymmetric nature of icelines in systems with massive planets. Methods: We conduct a parameter study using numerical hydrodynamics simulations where we treat viscous heating, thermal cooling and stellar irradiation as additional source terms in the energy equation, with some runs including radiative diffusion. Our parameter space consists of a grid containing different combinations of planet and disk parameters. Results: Both gap opening and shock heating can displace the iceline, with the effects being amplified for massive planets in optically thick disks. The gap region can split an initially hot (T>170 K) disk into a hot inner disk and a hot ring just outside of the planet's location, while shock heating can reshape the originally axisymmetric iceline into water-poor islands along spirals. We also find that radiative diffusion does not alter the picture significantly in this context. Conclusions: Shock heating and gap opening by a planet can effectively heat up optically thick disks and in general move and/or reshape the water iceline. This can affect the gap structure and migration torques. It can also produce azimuthal features that follow the trajectory of spiral arms, creating hot zones, "islands" of vapor and ice around spirals which could affect the accretion or growth of icy aggregates.

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arXiv2019

1:1 orbital resonance of circumbinary planets

The recent detection of the third planet in Kepler-47 has shown that binary stars can host several planets in circumbinary orbits. To understand the evolution of such systems we have performed two-dimensional hydrodynamic simulations of the circumbinary disc with two embedded planets for several Kepler systems. In two cases, Kepler-47 and -413, the planets are captured in a 1:1 mean-motion resonance at the planet parking position near the inner edge of the disc. The orbits are fully aligned, have mean eccentricities of about 0.25 to 0.30, and the planets are entangled in a horseshoe type of motion. Subsequent n-body simulations without the disc show that the configurations are stable. Our results point to the existence of a new class of stable resonant orbits around binary stars. It remains to be seen if such orbits exist in reality.

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