arXiv subjects

Willy Kley

Publications and source records attributed to Willy Kley.

At least 19 recordsLinked to original sources

arXiv2013

The formation of systems with closely spaced low-mass planets and the application to Kepler-36

The Kepler-36 system consists of two planets that are spaced unusually close together, near the 7:6 mean motion resonance. While it is known that mean motion resonances can easily form by convergent migration, Kepler-36 is an extreme case due to the close spacing and the relatively high planet masses of 4 and 8 times that of the Earth. In this paper, we investigate whether such a system can be obtained by interactions with the protoplanetary disc. These discs are thought to be turbulent and exhibit density fluctuations which might originate from the magneto-rotational instability. We adopt a realistic description for stochastic forces due to these density fluctuations and perform both long term hydrodynamical and N-body simulations. Our results show that planets in the Kepler-36 mass range can be naturally assembled into a closely spaced planetary system for a wide range of migration parameters in a turbulent disc similar to the minimum mass solar nebula. The final orbits of our formation scenarios tend to be Lagrange stable, even though large parts of the parameter space are chaotic and unstable.

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arXiv2012

Stellar irradiated discs and implications on migration of embedded planets I: equilibrium discs

The strength and direction of migration of low mass planets depends on the disc's thermodynamics. In discs where the viscous heating is balanced by radiative transport, the migration can be directed outwards, a process which extends the lifetime of growing planetary embryos. We investigate the influence of opacity and stellar irradiation on the disc thermodynamics. Utilizing the resulting disc structure, we determine the regions of outward migration. We perform two-dimensional numerical simulations of equilibrium discs with viscous heating, radiative cooling and stellar irradiation. We use the hydrodynamical code NIRVANA that includes a full tensor viscosity and stellar irradiation, as well as a two temperature solver that includes radiation transport in the flux-limited diffusion approximation. The migration is studied by using torque formulae. In the constant opacity case, we reproduce the analytical results of a black-body disc: the stellar irradiation dominates in the outer regions -- leading to flaring -- while the viscous heating dominates close to the star. We find that the inner edge of the disc should not be significantly puffed-up by the stellar irradiation. If the opacity depends on the local density and temperature, the structure of the disc is different, and several bumps in the aspect ratio H/r appear, due to transitions between different opacity regimes. The bumps in the disc can shield the outer disc from stellar irradiation. Stellar irradiation is an important factor for determining the disc structure and has dramatic consequences for the migration of embedded planets. Compared to discs with only viscous heating, a stellar irradiated disc features a much smaller region of outward migration for a range of planetary masses. This suggests that the region where the formation of giant planet cores takes place is smaller, which in turn might lead to a shorter growth phase.

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arXiv2011

Range of outward migration and influence of the disc's mass on the migration of giant planet cores

The migration of planets plays an important role in the early planet-formation process. An important problem has been that standard migration theories predict very rapid inward migration, which poses problems for population synthesis models. However, it has been shown recently that low-mass planets (20-30 Earth Masses) that are still embedded in the protoplanetary disc can migrate outwards under certain conditions. Simulations have been performed mostly for planets at given radii for a particular disc model. Here, we plan to extend previous work and consider different masses of the disc to quantify the influence of the physical disc conditions on planetary migration. We perform three-dimensional (3D) radiation hydrodynamical simulations of embedded planets in protoplanteary discs. For planets on circular orbits at various locations we measure the radial dependece of the torques. For all considered planet masses (20-30 Earth masses) in this study we find outward migration within a limited radial range of the disc, typically from about 0.5 up to 1.5-2.5 a_Jup. Inside and outside this intervall, migration is inward and given by the Lindblad value for large radii. Because outward migration stops at a certain location in the disc, there exists a zero-torque distance for planetary embryos, where they can continue to grow without moving too fast. For higher disc masses (M_disc > 0.02 M_Sol) convection ensues, which changes the structure of the disc and therefore the torque on the planet as well. Outward migration stops at different points in the disc for different planetary masses, resulting in a quite extended region where the formation of larger cores might be easier. In higher mass discs, convection changes the disc's structure resulting in fluctuations in the surface density, which influence the torque acting on the planet, and therefore its migration rate.

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arXiv2011

Evolution of inclined planets in three-dimensional radiative discs

While planets in the solar system only have a low inclination with respect to the ecliptic there is mounting evidence that in extrasolar systems the inclination can be very high, at least for close-in planets. One process to alter the inclination of a planet is through planet-disc interactions. Recent simulations considering radiative transport have shown that the evolution of migration and eccentricity can strongly depend on the thermodynamic state of the disc. We extend previous studies to investigate the planet-disc interactions of fixed and moving planets on inclined and eccentric orbits. We also analyse the effect of the disc's thermodynamic properties on the orbital evolution of embedded planets in detail. The protoplanetary disc is modelled as a viscous gas where the internally produced dissipation is transported by radiation. For locally isothermal discs, we confirm previous results and find inclination damping and inward migration for planetary cores. For low inclinations i < 2 H/r, the damping is exponential, while di/dt is proportional to i^-2 for larger i. For radiative discs, the planetary migration is very limited, as long as their inclination exceeds a certain threshold. If the inclination is damped below this threshold, planetary cores with a mass up to approximately 33 Earth masses start to migrate outwards, while larger cores migrate inwards right from the start. The inclination is damped for all analysed planet masses. In a viscous disc an initial inclination of embedded planets will be damped for all planet masses. This damping occurs on timescales that are shorter than the migration time. If the inclination lies beneath a certain threshold, the outward migration in radiative discs is not handicapped. Outward migration is strongest for circular and non-inclined orbits.

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arXiv2011

Orbital Migration Models under Test

Planet-disk interaction predicts a change in the orbital elements of an embedded planet. Through linear and fully hydrodynamical studies it has been found that migration is typically directed inwards. Hence, this migration process gives natural explanation for the presence of the 'hot' planets orbiting close to the parent star, and it plays a mayor role in explaining the formation of resonant planetary systems. However, standard migration models for locally isothermal disks indicate a too rapid inward migration for small mass planets, and a large number of massive planets are found very far away from the star. Recent studies, including more complete disk physics, have opened up new paths to slow down or even reverse migration. The new findings on migration are discussed and connected to the observational properties of planetary systems.

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arXiv2010

Orbital evolution of eccentric planets in radiative discs

With an average eccentricity of about 0.29, the eccentricity distribution of extrasolar planets is markedly different from the solar system. Among other scenarios considered, it has been proposed that eccentricity may grow through planet-disc interaction. Recently, it has been noticed that the thermodynamical state of the disc can significantly influence the migration properties of growing protoplanets. However, the evolution of planetary eccentricity in radiative discs has not been considered yet. In this paper we study the evolution of planets on eccentric orbits that are embedded in a three-dimensional viscous disc and analyse the disc's effect on the orbital evolution of the planet. We use the three-dimensional hydrodynamical code NIRVANA that includes full tensor viscosity and implicit radiation transport in the flux-limited diffusion approximation. The code uses the FARGO-algorithm to speed up the simulations. First we measure the torque and power exerted on the planet by the disc for fixed orbits, and then we let the planet start with initial eccentricity and evolve it in the disc. For locally isothermal we confirm previous results and find eccentricity damping and inward migration for planetary cores. In the case of radiative discs, the planets experience an inward migration as long as its eccentricity lies above a certain threshold. After the damping of eccentricity cores with masses below 33 Earthmasses begin to migrate outward in radiative discs, while higher mass cores always migrate inward. For all planetary masses studied (up to 200 Earthmasses) we find eccentricity damping. In viscous discs the orbital eccentricity of embedded planets is damped during the evolution independent of the mass. Hence, planet-disc interaction does not seem to be a viable mechanism to explain the observed high eccentricity of exoplanets.

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arXiv2010

Variable accretion as a mechanism for brightness variations in T Tau S

(Note: this is a shortened version of the original A&A-style structured abstract). The physical nature of the strong photometric variability of T Tau Sa, the more massive member of the Southern "infrared companion" to T Tau, has long been debated. Intrinsic luminosity variations due to variable accretion were originally proposed but later challenged in favor of apparent fluctuations due to time-variable foreground extinction. In this paper we use the timescale of the variability as a diagnostic for the underlying physical mechanism. Because the IR emission emerging from Sa is dominantly thermal emission from circumstellar dust at <=1500K, we can derive a minimum size of the region responsible for the time-variable emission. In the context of the variable foreground extinction scenario, this region must be (un-) covered within the variability timescale, which implies a minimum velocity for the obscuring foreground material. If this velocity supercedes the local Kepler velocity we can reject foreground extinction as a valid variability mechanism. The variable accretion scenario allows for shorter variability timescales since the variations in luminosity occur on much smaller scales, essentially at the surface of the star, and the disk surface can react almost instantly on the changing irradiation with a higher or lower dust temperature and according brightness. We have detected substantial variations at long wavelengths in T Tau S: +26% within four days at 12.8 micron. We show that this short-term variability cannot be due to variable extinction and instead must be due to variable accretion. Using a radiative transfer model of the Sa disk we show that variable accretion can in principle also account for the much larger (several magnitude) variations observed on timescales of several years. For the long-term variability, however, also variable foreground extinction is a viable mechanism.

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arXiv2009

Formation of massive planets in binary star systems

As of today over 40 planetary systems have been discovered in binary star systems. In all cases the configuration appears to be circumstellar, where the planets orbit around one of the stars, the secondary acting as a perturber. The formation of planets in binary star systems is more difficult than around single stars due to the gravitational action of the companion on the dynamics of the protoplanetary disk. In this contribution we first briefly present the relevant observational evidence for planets in binary systems. Then the dynamical influence that a secondary companion has on a circumstellar disk will be analyzed through fully hydrodynamical simulations. We demonstrate that the disk becomes eccentric and shows a coherent precession around the primary star. Finally, fully hydrodynamical simulations of evolving protoplanets embedded in disks in binary star systems are presented. We investigate how the orbital evolution of protoplanetary embryos and their mass growth from cores to massive planets might be affected in this very dynamical environment. We consider, in particular, the planet orbiting the primary in the system Gamma Cephei.

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arXiv2009

Modelling the evolution of planets in disks

To explain important properties of extrasolar planetary systems (eg. close-in hot Jupiters, resonant planets) an evolutionary scenario which allows for radial migration of planets in disks is required. During their formation protoplanets undergo a phase in which they are embedded in the disk and interact gravitationally with it. This planet-disk interaction results in torques (through gravitational forces) acting on the planet that will change its angular momentum and result in a radial migration of the planet through the disk. To determine the outcome of this very important process for planet formation, dedicated high resolution numerical modeling is required. This contribution focusses on some important aspects of the numerical approach that we found essential for obtaining successful results. We specifically mention the treatment of Coriolis forces, Cartesian grids, and the FARGO method.

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arXiv2009

Planet migration in three-dimensional radiative discs

The migration of growing protoplanets depends on the thermodynamics of the ambient disc. Standard modelling, using locally isothermal discs, indicate in the low planet mass regime an inward (type-I) migration. Taking into account non-isothermal effects, recent studies have shown that the direction of the type-I migration can change from inward to outward. In this paper we extend previous two-dimensional studies, and investigate the planet-disc interaction in viscous, radiative discs using fully three-dimensional radiation hydrodynamical simulations of protoplanetary accretion discs with embedded planets, for a range of planetary masses. We use an explicit three-dimensional (3D) hydrodynamical code NIRVANA that includes full tensor viscosity. We have added implicit radiation transport in the flux-limited diffusion approximation, and to speed up the simulations significantly we have newly adapted and implemented the FARGO-algorithm in a 3D context. First, we present results of test simulations that demonstrate the accuracy of the newly implemented FARGO-method in 3D. For a planet mass of 20 M_earth we then show that the inclusion of radiative effects yields a torque reversal also in full 3D. For the same opacity law used the effect is even stronger in 3D than in the corresponding 2D simulations, due to a slightly thinner disc. Finally, we demonstrate the extent of the torque reversal by calculating a sequence of planet masses. Through full 3D simulations of embedded planets in viscous, radiative discs we confirm that the migration can be directed outwards up to planet masses of about 33 M_earth. Hence, the effect may help to resolve the problem of too rapid inward migration of planets during their type-I phase.

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arXiv2007

On the evolution of eccentric and inclined protoplanets embedded in protoplanetary disks

Young planets embedded in their protoplanetary disk interact gravitationally with it leading to energy and angular momentum exchange. This interaction determines the evolution of the planet through changes to the orbital parameters. We investigate changes in the orbital elements of a 20 Earth--mass planet due to the torques from the disk. We focus on the non-linear evolution of initially non-vanishing eccentricity $e$ and/or inclination $i$. We treat the disk as a two- or three-dimensional viscous fluid and perform hydrodynamical simulations with an embedded planet. We find rapid exponential decay of the planet orbital eccentricity and inclination for small initial values of $e$ and $i$, in agreement with linear theory. For larger values of $e > 0.1$ the decay time increases and the decay rate scales as $\dot{e} \propto e^{-2}$, consistent with existing theoretical models. For large inclinations ($i$ > 6 deg) the inclination decay rate shows an identical scaling $di/dt \propto i^{-2}$. We find an interesting dependence of the migration on the eccentricity. In a disk with aspect ratio $H/r=0.05$ the migration rate is enhanced for small non-zero eccentricities ($e < 0.1$), while for larger values we see a significant reduction by a factor of $\sim 4$. We find no indication for a reversal of the migration for large $e$, although the torque experienced by the planet becomes positive when $e \simeq 0.3$. This inward migration is caused by the persisting energy loss of the planet. For non gap forming planets, eccentricity and inclination damping occurs on a time scale that is very much shorter than the migration time scale. The results of non linear hydrodynamic simulations are in very good agreement with linear theory for small $e$ and $i$.

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arXiv2007

On the Formation and Dynamical Evolution of Planets in Binaries

Among the extrasolar planetary systems about 30 are located in a stellar binary orbiting one of the stars, preferably the more massive primary. The dynamical influence of the second companion alters firstly the orbital elements of the forming protoplanet directly and secondly the structure of the disk from which the planet formed which in turn will modify the planet's evolution. We present detailed analysis of these effects and present new hydrodynamical simulations of the evolution of protoplanets embedded in circumstellar disks in the presence of a companion star, and compare our results to the system $γ$ Cep. To analyse the early formation of planetary embryos, we follow the evolution of a swarm of planetesimals embedded in a circumstellar disk. Finally, we study the evolution of planets embedded in circumbinary disks.

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arXiv2006

On the evolution of the resonant planetary system HD128311

A significant number of the known multiple exoplanetary systems are containing a pair of giant planets engaged in a low order mean motion resonance. Such a resonant condition protects the dynamics of these planets resulting in very stable orbits. According to recent studies the capture into a resonance is the result of a planetary migration process induced by the interaction of the planets with a protoplanetary disk. If the migration is slow enough (adiabatic) next to a mean motion resonance, the two planets will also be in apsidal corotation. The recently refined orbital parameters of the system HD 128311 suggest that the two giant planets are in a 2:1 mean motion resonance, however without exhibiting apsidal corotation. Thus the evolution of this system can not be described by an adiabatic migration process alone. We present possible evolution scenarios of this system combining migration processes and sudden perturbations. We model migration scenarios through numerical integration of the gravitational N-body problem with additional non-conservative forces. Planet-planet scattering has been investigated by N-body simulations. We show that the present dynamical state of the system HD128311 may be explained by such evolutionary processes.

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arXiv2005

Modeling the resonant planetary system GJ876

The two planets about the star GJ 876 appear to have undergone extensive migration from their point of origin in the protoplanetary disk -- both because of their close proximity to the star (30 and 60 day orbital periods) and because of their occupying three stable orbital resonances at the 2:1 mean-motion commensurability. The resonances were most likely established by converging differential migration of the planets leading to capture into the resonances. A problem with this scenario is that continued migration of the system while it is trapped in the resonances leads to orbital eccentricities that rapidly exceed the observational upper limits of e_1 = 0.31 and e_2 = 0.05. As seen in forced 3-body simulations, lower eccentricities would persist during migration only for an applied eccentricity damping. Here we explore the evolution of the GJ 876 system using two-dimensional hydrodynamical simulations that include viscous heating and radiative effects. We find that a hydrodynamic evolution within the resonance, where only the outer planet interacts with the disk, always rapidly leads to large values of eccentricities that exceed those observed. Only if mass is removed from the disk on a time scale of the order of the migration time scale (before there has been extensive migration after capture), as might occur for photoevaporation in the late phases of planet formation, can we end up with eccentricities that are consistent with the observations.

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arXiv2004

Evolution of Planets in Disks

The main properties of the observed extrasolar planets are reviewed with respect to their relevance to the formation scenario of planetary systems. Results of numerical computations of embedded planets in viscously evolving disks are presented. Emphasis is given to the accretion and migration process. New calculations on inviscid disks are shown. The second part of the talk concentrates on resonant planetary systems. Among the observed extrasolar systems there are 3 confirmed cases, Gl 876, HD 82943 and 55 Cnc, where the planets orbit their central star in a low order mean motion resonance. Results of numerical simulations modeling the formation and evolution of such systems are presented.

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arXiv2003

Thermo-Hydrodynamics of Circumstellar Disks with High-mass Planets

With a series of numerical simulations, we analyze the thermo-hydrodynamical evolution of circumstellar disks containing Jupiter-size protoplanets. In the framework of the two-dimensional approximation, we consider an energy equation that includes viscous heating and radiative effects in a simplified, yet consistent form. Multiple nested grids are used in order to study both global and local features around the planet. By means of different viscosity prescriptions, we investigate various temperature regimes. A planetary mass range from 0.1 to 1 Mj is examined. Computations show that gap formation is a general property which affects density, pressure, temperature, optical thickness, and radiated flux distributions. However, it remains a prominent feature only when the kinematic viscosity is on the order of 10^(15) cm^2/s or lower. Around accreting planets, a circumplanetary disk forms that has a surface density profile decaying exponentially with the distance and whose mass is 5-6 orders of magnitudes smaller than Jupiter's mass. Circumplanetary disk temperature profiles decline roughly as the inverse of the distance from the planet. Temperatures range from some 10 to ~1000 K. Planetary accretion and migration rates depend on the viscosity regime, with discrepancies within an order of magnitude. Estimates of growth and migration time scales inferred by these models are on the same orders of magnitude as those previously obtained with locally isothermal simulations.

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arXiv2003

Orbital Migration and Mass Accretion of Protoplanets in 3D Global Computations with Nested Grids

We investigate the evolution of protoplanets with different masses embedded in an accretion disk, via global fully three-dimensional hydrodynamical simulations. We consider a range of planetary masses extending from one and a half Earth's masses up to one Jupiter's mass, and we take into account physically realistic gravitational potentials of forming planets. In order to calculate accurately the gravitational torques exerted by disk material and to investigate the accretion process onto the planet, the flow dynamics has to be thoroughly resolved on long as well as short length scales. We achieve this strict resolution requirement by applying a nested-grid refinement technique which allows to greatly enhance the local resolution. Our results from altogether 51 simulations show that for large planetary masses, approximately above a tenth of the Jupiter's mass, migration rates are relatively constant, as expected in type II migration regime and in good agreement with previous two-dimensional calculations. In a range between seven and fifteen Earth's masses, we find a dependency of the migration speed on the planetary mass that yields time scales considerably longer than those predicted by linear analytical theories. This property may be important in determining the overall orbital evolution of protoplanets. The growth time scale is minimum around twenty Earth-masses, but it rapidly increases for both smaller and larger mass values. Significant differences between two- and three-dimensional calculations are found in particular for objects with masses smaller than ten Earth-masses. We also derive an analytical approximation for the numerically computed mass growth rates.

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arXiv2003

Dynamical Evolution of Planets in Disks

We study the evolution of a system consisting of two protoplanets still embedded in a protoplanetary disk. Results of two different numerical approaches are presented. In the first kind of model the motion of the disk material is followed by fully viscous hydrodynamical simulations, and the planetary motion is determined by N-body calculations including exactly the gravitational potential from the disk material. In the second kind we only solve the N-body part and add additional analytically given forces which model the effect of the torques of the disk. This type of modeling is of course orders of magnitudes faster than the full hydro-model. Another advantage of this two-fold approach is the possibility of adjusting the otherwise unknown parameters of the simplified model. The results give very good agreement between the methods. Using two different initial setups for the planets and disk, we obtain in the first case a resonant trapping into the 3:1 resonance, and in the second case a trapping into the 2:1 resonance. Resonant capture leads to a rise in the eccentricity and to an alignment of the of the spatial orientation of orbits. The characteristics of the numerical results agree very favorably with those of 3 observed planetary systems (GJ 876, HD 82943, and 55 Cnc) known to be in mean motion resonances.

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