arXiv subjects

H. Klahr

Publications and source records attributed to H. Klahr.

50 records · Page 3Linked to original sources

arXiv2011

The baroclinic instability in the context of layered accretion. Self-sustained vortices and their magnetic stability in local compressible unstratified models of protoplanetary disks

Turbulence and angular momentum transport in accretion disks remains a topic of debate. With the realization that dead zones are robust features of protoplanetary disks, the search for hydrodynamical sources of turbulence continues. A possible source is the baroclinic instability (BI), which has been shown to exist in unmagnetized non-barotropic disks. We present shearing box simulations of baroclinicly unstable, magnetized, 3D disks, in order to assess the interplay between the BI and other instabilities, namely the magneto-rotational instability (MRI) and the magneto-elliptical instability. We find that the vortices generated and sustained by the baroclinic instability in the purely hydrodynamical regime do not survive when magnetic fields are included. The MRI by far supersedes the BI in growth rate and strength at saturation. The resulting turbulence is virtually identical to an MRI-only scenario. We measured the intrinsic vorticity profile of the vortex, finding little radial variation in the vortex core. Nevertheless, the core is disrupted by an MHD instability, which we identify with the magneto-elliptic instability. This instability has nearly the same range of unstable wavelengths as the MRI, but has higher growth rates. In fact, we identify the MRI as a limiting case of the magneto-elliptic instability, when the vortex aspect ratio tends to infinity (pure shear flow). We conclude that vortex excitation and self-sustenance by the baroclinic instability in protoplanetary disks is viable only in low ionization, i.e., the dead zone. Our results are thus in accordance with the layered accretion paradigm. A baroclinicly unstable dead zone should be characterized by the presence of large-scale vortices whose cores are elliptically unstable, yet sustained by the baroclinic feedback. As magnetic fields destroy the vortices and the MRI outweighs the BI, the active layers are unmodified.

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arXiv2009

Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks

As accretion in protoplanetary disks is enabled by turbulent viscosity, the border between active and inactive (dead) zones constitutes a location where there is an abrupt change in the accretion flow. The gas accumulation that ensues triggers the Rossby wave instability, that in turn saturates into anticyclonic vortices. It was suggested that the trapping of solids within them leads to a burst of planet formation on very short timescales. We perform two-dimensional global simulations of the dynamics of gas and solids in a non-magnetized thin protoplanetary disk with the Pencil Code. We use multiple particle species of radius 1, 10, 30, and 100 cm, solving for the particles' gravitational interaction by a particle-mesh method. The dead zone is modeled as a region of low viscosity. Adiabatic and locally isothermal equations of state are used. We find that the Rossby wave instability is triggered under a variety of conditions, thus making vortex formation a robust process. Inside the vortices, fast accumulation of solids occurs and the particles collapse into objects of planetary mass in timescales as short as five orbits. Because the drag force is size-dependent, aerodynamical sorting ensues within the vortical motion, and the first bound structures formed are composed primarily of similarly-sized particles. In addition to erosion due to ram pressure, we identify gas tides from the massive vortices as a disrupting agent of formed protoplanetary embryos. We also estimate the collisional velocity history of the particles that compose the most massive embryo by the end of the simulation, finding that the vast majority of them never experienced a collision with another particle at speeds faster than 1 m/s.

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arXiv2009

A high-order Godunov scheme for global 3D MHD accretion disks simulations. I. The linear growth regime of the magneto-rotational instability

We employ the PLUTO code for computational astrophysics to assess and compare the validity of different numerical algorithms on simulations of the magneto-rotational instability in 3D accretion disks. In particular we stress on the importance of using a consistent upwind reconstruction of the electro-motive force (EMF) when using the constrained transport (CT) method to avoid the onset of numerical instabilities. We show that the electro-motive force (EMF) reconstruction in the classical constrained transport (CT) method for Godunov schemes drives a numerical instability. The well-studied linear growth of magneto-rotational instability (MRI) is used as a benchmark for an inter-code comparison of PLUTO and ZeusMP. We reproduce the analytical results for linear MRI growth in 3D global MHD simulations and present a robust and accurate Godunov code which can be used for 3D accretion disk simulations in curvilinear coordinate systems.

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arXiv2008

The effect of stellar feedback on the formation and evolution of gas and dust tori in AGN

Recently, the existence of geometrically thick dust structures in Active Galactic Nuclei (AGN) has been directly proven with the help of mid-infrared interferometry. The observations are consistent with a two-component model made up of a geometrically thin and warm central disk, surrounded by a colder, fluffy torus component. In an exploratory study, we investigate one possible physical mechanism, which could produce such a structure, namely the effect of stellar feedback from a young nuclear star cluster on the interstellar medium in centres of AGN. The model is realised with the help of the hydrodynamics code TRAMP. We follow the evolution of the interstellar medium by taking discrete mass loss and energy ejection due to stellar processes, as well as optically thin radiative cooling into account. In a post-processing step, we calculate observable quantities (spectral energy distributions and images) with the help of the radiative transfer code MC3D. The interplay between injection of mass, supernova explosions and radiative cooling leads to a two-component structure made up of a cold geometrically thin, but optically thick and very turbulent disk residing in the vicinity of the angular momentum barrier, surrounded by a filamentary structure. The latter consists of cold long radial filaments flowing towards the disk and a hot tenuous medium in between, which shows both inwards and outwards directed motions. This modelling is able to reproduce the range of observed neutral hydrogen column densities of a sample of Seyfert galaxies as well as the relation between them and the strength of the silicate 10 micron spectral feature. Despite being quite crude, our mean Seyfert galaxy model is even able to describe the SEDs of two intermediate type Seyfert galaxies observed with the Spitzer Space Telescope.

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arXiv2008

Standing on the shoulders of giants: Trojan Earths and vortex trapping in low mass self-gravitating protoplanetary disks of gas and solids

Centimeter and meter sized solid particles in protoplanetary disks are trapped within long lived high pressure regions, creating opportunities for collapse into planetesimals and planetary embryos. We study the accumulations in the stable Lagrangian points of a giant planet, as well as in the Rossby vortices launched at the edges of the gap it carves. We employ the Pencil Code, tracing the solids with a large number of interacting Lagrangian particles, usually 100,000. For particles of 1 cm to 10 cm radii, gravitational collapse occurs in the Lagrangian points in less than 200 orbits. For 5 cm particles, a 2 Earth mass planet is formed. For 10 cm, the final maximum collapsed mass is around 3 Earth masses. The collapse of the 1 cm particles is indirect, following the timescale of depletion of gas from the tadpole orbits. In the edges of the gap vortices are excited, trapping preferentially particles of 30 cm radii. The rocky planet that is formed is as massive as 17 Earth masses, constituting a Super-Earth. By using multiple particle species, we find that gas drag modifies the streamlines in the tadpole region around the classical L4 and L5 points. As a result, particles of different radii have their stable points shifted to different locations. Collapse therefore takes longer and produces planets of lower mass. Three super-Earths are formed in the vortices, the most massive having 4.4 Earth masses. We conclude that a Jupiter mass planet can induce the formation of other planetary embryos in the outer edge of its gas gap. Trojan Earth mass planets are readily formed, and although not existing in the solar system, might be common in the exoplanetary zoo.

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arXiv2008

Embryos grown in the dead zone: Assembling the first protoplanetary cores in low mass self-gravitating circumstellar disks of gas and solids

In the borders of the dead zones of protoplanetary disks, the inflow of gas produces a local density maximum that triggers the Rossby wave instability. The vortices that form are efficient in trapping solids. We aim to assess the possibility of gravitational collapse of the solids within the Rossby vortices. We perform global simulations of the dynamics of gas and solids in a low mass non-magnetized self-gravitating thin protoplanetary disk with the Pencil code. We use multiple particle species of radius 1, 10, 30, and 100 cm. The dead zone is modeled as a region of low viscosity. The Rossby vortices excited in the edges of the dead zone are very efficient particle traps. Within 5 orbits after their appearance, the solids achieve critical density and undergo gravitational collapse into Mars sized objects. The velocity dispersions are of the order of 10 m/s for newly formed embryos, later lowering to less than 1 m/s by drag force cooling. After 200 orbits, 38 gravitationally bound embryos were formed inside the vortices, half of them being more massive than Mars. The embryos are composed primarily of same-sized particles. We conclude that the presence of a dead zone naturally gives rise to a population of protoplanetary cores in the mass range of 0.1-0.6 Earth masses, on very short timescales.

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arXiv2008

Turbulent AGN tori

Recently, the MID-infrared Interferometric instrument (MIDI) at the VLTI has shown that dust tori in the two nearby Seyfert galaxies NGC 1068 and the Circinus galaxy are geometrically thick and can be well described by a thin, warm central disk, surrounded by a colder and fluffy torus component. By carrying out hydrodynamical simulations with the help of the TRAMP code (Klahr et al. 1999), we follow the evolution of a young nuclear star cluster in terms of discrete mass-loss and energy injection from stellar processes. This naturally leads to a filamentary large scale torus component, where cold gas is able to flow radially inwards. The filaments open out into a dense and very turbulent disk structure. In a post-processing step, we calculate observable quantities like spectral energy distributions or images with the help of the 3D radiative transfer code MC3D (Wolf 2003). Good agreement is found in comparisons with data due to the existence of almost dust-free lines of sight through the large scale component and the large column densities caused by the dense disk.

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arXiv2008

Global magnetohydrodynamical models of turbulence in protoplanetary disks I. A cylindrical potential on a Cartesian grid and transport of solids

We present global 3D MHD simulations of disks of gas and solids, aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks. A second goal is to show that Cartesian codes are comparable to cylindrical and spherical ones in handling the magnetohydrodynamics of the disk simulations, as the disk-in-a-box models presented here develop and sustain MHD turbulence. We investigate the dependence of the magnetorotational instability on disk scale height, finding evidence that the turbulence generated by the magnetorotational instability grows with thermal pressure. The turbulent stresses depend on the thermal pressure obeying a power law of 0.24+/-0.03, compatible with the value of 0.25 found in shearing box calculations. The ratio of stresses decreased with increasing temperature. We also study the dynamics of boulders in the hydromagnetic turbulence. The vertical turbulent diffusion of the embedded boulders is comparable to the turbulent viscosity of the flow. Significant overdensities arise in the solid component as boulders concentrate in high pressure regions.

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arXiv2007

Survival of the mm-cm size grain population observed in protoplanetary disks

Millimeter interferometry provides evidence for the presence of mm to cm size "pebbles" in the outer parts of disks around pre-main-sequence stars. The observations suggest that large grains are produced relatively early in disk evolution (< 1 Myr) and remain at large radii for longer periods of time (5 to 10 Myr). Simple theoretical estimates of the radial drift time of solid particles, however, imply that they would drift inward over a time scale of less than 0.1 Myr. In this paper, we address this conflict between theory and observation, using more detailed theoretical models, including the effects of sedimentation, collective drag forces and turbulent viscosity. We find that, although these effects slow down the radial drift of the dust particles, this reduction is not sufficient to explain the observationally determined long survival time of mm/cm-sized grains in protoplanetary disks. However, if for some reason the gas to dust ratio in the disk is reduced by at least a factor of 20 from the canonical value of 100 (for instance through photoevaporation of the gas), then the radial drift time scales become sufficiently large to be in agreement with observations.

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arXiv2006

A comparative study of disc-planet interaction

We perform numerical simulations of a disc-planet system using various grid-based and smoothed particle hydrodynamics (SPH) codes. The tests are run for a simple setup where Jupiter and Neptune mass planets on a circular orbit open a gap in a protoplanetary disc during a few hundred orbital periods. We compare the surface density contours, potential vorticity and smoothed radial profiles at several times. The disc mass and gravitational torque time evolution are analyzed with high temporal resolution. There is overall consistency between the codes. The density profiles agree within about 5% for the Eulerian simulations while the SPH results predict the correct shape of the gap although have less resolution in the low density regions and weaker planetary wakes. The disc masses after 200 orbital periods agree within 10%. The spread is larger in the tidal torques acting on the planet which agree within a factor 2 at the end of the simulation. In the Neptune case the dispersion in the torques is greater than for Jupiter, possibly owing to the contribution from the not completely cleared region close to the planet.

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arXiv2005

Two-dimensional models of layered protoplanetary discs - II. The effect of a residual viscosity in the dead zone

We study axisymmetric models of layered protoplanetary discs taking radiative transfer effects into account, and allowing for a residual viscosity in the dead zone. We also explore the effect of different viscosity prescriptions. In addition to the ring instability reported in the first paper of the series we find an oscillatory instability of the dead zone, accompanied by variations of the accretion rate onto the central star. We provide a simplified analytical description explaining the mechanism of the oscillations. Finally, we find that the residual viscosity enables stationary accretion in large regions of layered discs. Based on results obtained with the help of a simple 1-D hydrocode we identify these regions, and discuss conditions in which layered discs can give rise to FU~Orionis phenomena.

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arXiv2005

3D-radiation hydro simulations of disk-planet interactions: I. Numerical algorithm and test cases

We study the evolution of an embedded protoplanet in a circumstellar disk using the 3D-Radiation Hydro code TRAMP, and treat the thermodynamics of the gas properly in three dimensions. The primary interest of this work lies in the demonstration and testing of the numerical method. We show how far numerical parameters can influence the simulations of gap opening. We study a standard reference model under various numerical approximations. Then we compare the commonly used locally isothermal approximation to the radiation hydro simulation using an equation for the internal energy. Models with different treatments of the mass accretion process are compared. Often mass accumulates in the Roche lobe of the planet creating a hydrostatic atmosphere around the planet. The gravitational torques induced by the spiral pattern of the disk onto the planet are not strongly affected in the average magnitude, but the short time scale fluctuations are stronger in the radiation hydro models. An interesting result of this work lies in the analysis of the temperature structure around the planet. The most striking effect of treating the thermodynamics properly is the formation of a hot pressure--supported bubble around the planet with a pressure scale height of H/R ~ 0.5 rather than a thin Keplerian circumplanetary accretion disk. We also observe an outflow of gas above and below the planet during the gap opening phase.

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arXiv2005

Dust Distribution in Gas Disks II: Self Induced Ring Formation Through a Clumping Instability

Debris rings of dust are found around young luminous stars such as HR4796A and HD141569. Some of these entities have sharp edges and gaps which have been interpreted as evidence for the presence of shepherding and embedded planets. Here we show that gaps and sharp edges in the debris disks of dust can also be spontaneously self generated if they are embedded in optically thin regions of gaseous disks. This clumping instability arises in regions where an enhancement in the dust density leads to local gas temperature and pressure increases. Consequently, the relative motion between the gas and the dust is modified. The subsequent hydrodynamic drag on the dust particles leads to further enhancement of their concentration. We show that this process is linearly unstable and leads to the formation of ring-like structures within the estimated life time of such young objects. Once the gas is removed (e.g. by photo evaporation) the structures are ``frozen'' and will persist, even when the gas might not be observable anymore.

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arXiv2005

2-D models of layered protoplanetary discs: I. The ring instability

In this work we use the radiation hydrodynamic code TRAMP to perform a two-dimensional axially symmetric model of the layered disc. Using this model we follow the accumulation of mass in the dead zone due to the radially varying accretion rate. We found a new type of instability which causes the dead zone to split into rings. This "ring instability" works due to the positive feedback between the thickness of the dead zone and the mass accumulation rate. We give an analytical description of this instability, taking into account non-zero thickness of the dead zone and deviations from the Keplerian rotational velocity. The analytical model agrees reasonably well with results of numerical simulations. Finally, we speculate about the possible role of the ring instability in protoplanetary discs and in the formation of planets.

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