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Hubert Klahr

Publications and source records attributed to Hubert Klahr.

At least 91 records · Page 5Linked to original sources
arXiv2010

Circumventing the radiation pressure barrier in the formation of massive stars via disk accretion

We present radiation hydrodynamics simulations of the collapse of massive pre-stellar cores. We treat frequency dependent radiative feedback from stellar evolution and accretion luminosity at a numerical resolution down to 1.27 AU. In the 2D approximation of axially symmetric simulations, it is possible for the first time to simulate the whole accretion phase (up to the end of the accretion disk epoch) for the forming massive star and to perform a broad scan of the parameter space. Our simulation series show evidently the necessity to incorporate the dust sublimation front to preserve the high shielding property of massive accretion disks. While confirming the upper mass limit of spherically symmetric accretion, our disk accretion models show a persistent high anisotropy of the corresponding thermal radiation field. This yields to the growth of the highest-mass stars ever formed in multi-dimensional radiation hydrodynamics simulations, far beyond the upper mass limit of spherical accretion. Non-axially symmetric effects are not necessary to sustain accretion. The radiation pressure launches a stable bipolar outflow, which grows in angle with time as presumed from observations. For an initial mass of the pre-stellar host core of 60, 120, 240, and 480 Msun the masses of the final stars formed in our simulations add up to 28.2, 56.5, 92.6, and at least 137.2 Msun respectively.

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arXiv2010

Fast and accurate frequency-dependent radiation transport for hydrodynamics simulations in massive star formation

Context: Radiative feedback plays a crucial role in the formation of massive stars. The implementation of a fast and accurate description of the proceeding thermodynamics in pre-stellar cores and evolving accretion disks is therefore a main effort in current hydrodynamics simulations. Aims: We introduce our newly implemented three-dimensional frequency dependent radiation transport algorithm for hydrodynamics simulations of spatial configurations with a dominant central source. Methods: The module combines the advantage of the speed of an approximate Flux Limited Diffusion (FLD) solver with the high accuracy of a frequency dependent first order ray-tracing routine. Results: We prove the viability of the scheme in a standard radiation benchmark test compared to a full frequency dependent Monte-Carlo based radiative transfer code. The setup includes a central star, a circumstellar flared disk, as well as an envelope. The test is performed for different optical depths. Considering the frequency dependence of the stellar irradiation, the temperature distributions can be described precisely in the optically thin, thick, and irradiated transition regions. Resulting radiative forces onto dust grains are reproduced with high accuracy. The achievable parallel speedup of the method imposes no restriction on further radiative (magneto-) hydrodynamics simulations. Conclusions: The proposed approximate radiation transport method enables frequency dependent radiation hydrodynamics studies of the evolution of pre-stellar cores and circumstellar accretion disks around an evolving massive star in a highly efficient and accurate manner.

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arXiv2010

Trapping Solids at the Inner Edge of the Dead Zone: 3-D Global MHD Simulations

The poorly-ionized interior of the protoplanetary disk is the location where dust coagulation processes may be most efficient. However even here, planetesimal formation may be limited by the loss of solid material through radial drift, and by collisional fragmentation of the particles. Our aim is to investigate the possibility that solid particles are trapped at local pressure maxima in the dynamically evolving disk. We perform the first 3-D global non-ideal MHD calculations of the disk treating the turbulence driven by the magneto-rotational instability. The domain contains an inner MRI-active region near the young star and an outer midplane dead zone, with the transition between the two modeled by a sharp increase in the magnetic diffusivity. The azimuthal magnetic fields generated in the active zone oscillate over time, changing sign about every 150 years. We thus observe the radial structure of the `butterfly pattern' seen previously in local shearing-box simulations. The mean magnetic field diffuses from the active zone into the dead zone, where the Reynolds stress nevertheless dominates. The greater total accretion stress in the active zone leads to a net reduction in the surface density, so that after 800 years an approximate steady state is reached in which a local radial maximum in the midplane pressure lies near the transition radius. We also observe the formation of density ridges within the active zone. The dead zone in our models possesses a mean magnetic field, significant Reynolds stresses and a steady local pressure maximum at the inner edge, where the outward migration of planetary embryos and the efficient trapping of solid material are possible.

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arXiv2009

Discovery of the Coldest Imaged Companion of a Sun-Like Star

We present the discovery of a brown dwarf or possible planet at a projected separation of 1.9" = 29 AU around the star GJ 758, placing it between the separations at which substellar companions are expected to form by core accretion (~5 AU) or direct gravitational collapse (typically >100 AU). The object was detected by direct imaging of its thermal glow with Subaru/HiCIAO. At 10-40 times the mass of Jupiter and a temperature of 550-640 K, GJ 758 B constitutes one of the few known T-type companions, and the coldest ever to be imaged in thermal light around a Sun-like star. Its orbit is likely eccentric and of a size comparable to Pluto's orbit, possibly as a result of gravitational scattering or outward migration. A candidate second companion is detected at 1.2" at one epoch.

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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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arXiv2009

Zonal Flows and Long-Lived Axisymmetric Pressure Bumps in Magnetorotational Turbulence

We study the behavior of magnetorotational turbulence in shearing box simulations with a radial and azimuthal extent up to ten scale heights. Maxwell and Reynolds stresses are found to increase by more than a factor two when increasing the box size beyond two scale heights in the radial direction. Further increase of the box size has little or no effect on the statistical properties of the turbulence. An inverse cascade excites magnetic field structures at the largest scales of the box. The corresponding 10% variation in the Maxwell stress launches a zonal flow of alternating sub- and super-Keplerian velocity. This in turn generates a banded density structure in geostrophic balance between pressure and Coriolis forces. We present a simplified model for the appearance of zonal flows, in which stochastic forcing by the magnetic tension on short time-scales creates zonal flow structures with life-times of several tens of orbits. We experiment with various improved shearing box algorithms to reduce the numerical diffusivity introduced by the supersonic shear flow. While a standard finite difference advection scheme shows signs of a suppression of turbulent activity near the edges of the box, this problem is eliminated by a new method where the Keplerian shear advection is advanced in time by interpolation in Fourier space.

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arXiv2008

A coagulation-fragmentation model for the turbulent growth and destruction of preplanetesimals

To treat the problem of growing protoplanetary disc solids across the meter barrier, we consider a very simplified two-component coagulation-fragmentation model that consists of macroscopic boulders and smaller dust grains, the latter being the result of catastrophic collisions between the boulders. Boulders in turn increase their radii by sweeping up the dust fragments. An analytical solution to the dynamical equations predicts that growth by coagulation-fragmentation can be efficient and allow agglomeration of 10-meter-sized objects within the time-scale of the radial drift. These results are supported by computer simulations of the motion of boulders and fragments in 3-D time-dependent magnetorotational turbulence. Allowing however the fragments to diffuse freely out of the sedimentary layer of boulders reduces the density of both boulders and fragments in the mid-plane, and thus also the growth of the boulder radius, drastically. The reason is that the turbulent diffusion time-scale is so much shorter than the collisional time-scale that dust fragments leak out of the mid-plane layer before they can be swept up by the boulders there. Our conclusion that coagulation-fragmentation is not an efficient way to grow across the meter barrier in fully turbulent protoplanetary discs confirms recent results by Brauer, Dullemond, & Henning who solved the coagulation equation in a parameterised turbulence model with collisional fragmentation, cratering, radial drift, and a range of particle sizes. We find that a relatively small population of boulders in a sedimentary mid-plane layer can populate the entire vertical extent of the disc with small grains and that these grains are not first generation dust, but have been through several agglomeration-destruction cycles during the simulations.

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arXiv2007

Supplementary Information for ``Rapid planetesimal formation in turbulent circumstellar discs''

This document contains refereed supplementary information for the paper ``Rapid planetesimal formation in turbulent circumstellar discs''. It contains 15 sections (\S1.1 -- \S1.15) that address a number of subjects related to the main paper. We describe in detail the Poisson solver used to find the self-potential of the solid particles, including a linear and a non-linear test problem (\S1.3). Dissipative collisions remove energy from the motion of the particles by collisional cooling (\S1.4), an effect that allows gravitational collapse to occur in somewhat less massive discs (\S1.7). A resolution study of the gravitational collapse of the boulders is presented in \S1.6. We find that gravitational collapse can occur in progressively less massive discs as the grid resolution is increased, likely due to the decreased smoothing of the particle-mesh self-gravity solver with increasing resolution. In \S1.10 we show that it is in good agreement with the Goldreich & Ward (1973) stability analysis to form several-hundred-km-sized bodies, when the analysis is applied to 5 AU and to regions of increased boulder column density. \S11 is devoted to the measurement of random speeds and collision speeds between boulders. We find good agreement between our measurements and analytical theory for the random speeds, but the measured collision speeds are 3 times lower than expected from analytical theory. Higher resolution studies, and an improved analytical theory of collision speeds that takes into account epicyclic motion, will be needed to determine whether collision speeds have converged. In \S1.12 we present models with no magnetic fields. The boulder layer still exhibits strong clumping, due to the streaming instability, if the global solids-to-gas ratio is increased by a factor 3. Gravitational collapse occurs as readily as in magnetised discs.

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arXiv2007

Rapid planetesimal formation in turbulent circumstellar discs

The initial stages of planet formation in circumstellar gas discs proceed via dust grains that collide and build up larger and larger bodies (Safronov 1969). How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem (Dominik et al. 2007): boulders stick together poorly (Benz 2000), and spiral into the protostar in a few hundred orbits due to a head wind from the slower rotating gas (Weidenschilling 1977). Gravitational collapse of the solid component has been suggested to overcome this barrier (Safronov 1969, Goldreich & Ward 1973, Youdin & Shu 2002). Even low levels of turbulence, however, inhibit sedimentation of solids to a sufficiently dense midplane layer (Weidenschilling & Cuzzi 1993, Dominik et al. 2007), but turbulence must be present to explain observed gas accretion in protostellar discs (Hartmann 1998). Here we report the discovery of efficient gravitational collapse of boulders in locally overdense regions in the midplane. The boulders concentrate initially in transient high pressures in the turbulent gas (Johansen, Klahr, & Henning 2006), and these concentrations are augmented a further order of magnitude by a streaming instability (Youdin & Goodman 2005, Johansen, Henning, & Klahr 2006, Johansen & Youdin 2007) driven by the relative flow of gas and solids. We find that gravitationally bound clusters form with masses comparable to dwarf planets and containing a distribution of boulder sizes. Gravitational collapse happens much faster than radial drift, offering a possible path to planetesimal formation in accreting circumstellar discs.

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arXiv2006

Turbulent diffusion in protoplanetary discs: the effect of an imposed magnetic field

We study the effect of an imposed vertical magnetic field on the turbulent mass diffusion properties of magnetorotational turbulence in protoplanetary discs. It is well-known that the effective viscosity generated by the turbulence depends strongly on the magnitude of such an external field. In this letter we show that the turbulent diffusion of the flow also grows, but that the diffusion coefficient does not rise with increasing vertical field as fast as the viscosity does. The vertical Schmidt number, i.e. the ratio between viscosity and vertical diffusion, can be close to 20 for high field magnitudes, whereas the radial Schmidt number is increased from below unity to around 3.5. Our results may have consequences for the interpretation of observations of dust in protoplanetary discs and for chemical evolution modelling of these discs.

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arXiv2006

Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations

We perform numerical simulations of the Kelvin-Helmholtz instability in the mid-plane of a protoplanetary disk. A two-dimensional corotating slice in the azimuthal--vertical plane of the disk is considered where we include the Coriolis force and the radial advection of the Keplerian rotation flow. Dust grains, treated as individual particles, move under the influence of friction with the gas, while the gas is treated as a compressible fluid. The friction force from the dust grains on the gas leads to a vertical shear in the gas rotation velocity. As the particles settle around the mid-plane due to gravity, the shear increases, and eventually the flow becomes unstable to the Kelvin-Helmholtz instability. The Kelvin-Helmholtz turbulence saturates when the vertical settling of the dust is balanced by the turbulent diffusion away from the mid-plane. The azimuthally averaged state of the self-sustained Kelvin-Helmholtz turbulence is found to have a constant Richardson number in the region around the mid-plane where the dust-to-gas ratio is significant. Nevertheless the dust density has a strong non-axisymmetric component. We identify a powerful clumping mechanism, caused by the dependence of the rotation velocity of the dust grains on the dust-to-gas ratio, as the source of the non-axisymmetry. Our simulations confirm recent findings that the critical Richardson number for Kelvin-Helmholtz instability is around unity or larger, rather than the classical value of 1/4

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arXiv2005

Formation of Giant Planets by Concurrent Accretion of Solids and Gas inside an Anti-Cyclonic Vortex

We study the formation of a giant gas planet by the core--accretion gas--capture process, with numerical simulations, under the assumption that the planetary core forms in the center of an anti-cyclonic vortex. The presence of the vortex concentrates particles of centimeter to meter size from the surrounding disk, and speeds up the core formation process. Assuming that a planet of Jupiter mass is forming at 5 AU from the star, the vortex enhancement results in considerably shorter formation times than are found in standard core--accretion gas--capture simulations. Also, formation of a gas giant is possible in a disk with mass comparable to that of the minimum mass solar nebula.

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arXiv2005

Gravoturbulent formation of planetesimals

We explore the effect of magnetorotational turbulence on the dynamics and concentrations of boulders in local box simulations of a sub-Keplerian protoplanetary disc. The solids are treated as particles each with an independent space coordinate and velocity. We find that the turbulence has two effects on the solids. 1) Meter and decameter bodies are strongly concentrated, locally up to a factor 100 times the average dust density, whereas decimeter bodies only experience a moderate density increase. The concentrations are located in large scale radial gas density enhancements that arise from a combination of turbulence and shear. 2) For meter-sized boulders, the concentrations cause the average radial drift speed to be reduced by 40%. We find that the densest clumps of solids are gravitationally unstable under physically reasonable values for the gas column density and for the dust-to-gas ratio due to sedimentation. We speculate that planetesimals can form in a dust layer that is not in itself dense enough to undergo gravitational fragmentation, and that fragmentation happens in turbulent density fluctuations in this sublayer.

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arXiv2005

Dust diffusion in protoplanetary discs by magnetorotational turbulence

We measure the turbulent diffusion coefficient of dust grains embedded in magnetorotational turbulence in a protoplanetary disc directly from numerical simulations and compare it to the turbulent viscosity of the flow. The simulations are done in a local coordinate frame comoving with the gas in Keplerian rotation. Periodic boundary conditions are used in all directions, and vertical gravity is not applied to the gas. Using a two-fluid approach, small dust grains of various sizes (with friction times up to $\varOmega_0 τ_{\rm f}=0.02$) are allowed to move under the influence of friction with the turbulent gas. We measure the turbulent diffusion coefficient of the dust grains by applying an external sinusoidal force field acting in the vertical direction on the dust component only. This concentrates the dust around the mid-plane of the disc, and an equilibrium distribution of the dust density is achieved when the vertical settling is counteracted by the turbulent diffusion away from the mid-plane. Comparing with analytical expressions for the equilibrium concentration we deduce the vertical turbulent diffusion coefficient. The vertical diffusion coefficient is found to be lower than the turbulent viscosity and to have an associated vertical diffusion Prandtl number of about 1.5. A similar radial force field also allows us to measure the radial turbulent diffusion coefficient. We find a radial diffusion Prandtl number of about 0.85 and also find that the radial turbulent diffusion coefficient is around 70% higher than the vertical. We also find evidence for trapping of dust grains of intermediate friction time in turbulent eddies.

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arXiv2004

The Global Baroclinic Instability in Accretion Disks. II: Local Linear Analysis

This paper contains a local linear stability analysis for accretion disks under the influence of a global radial entropy gradient beta = - d log T / d log r for constant surface density. Numerical simulations suggested the existence of an instability in two- and three-dimensional models of the solar nebula. The present paper tries to clarify, quantify, and explain such a global baroclinic instability for two-dimensional flat accretion disk models. As a result linear theory predicts a transient linear instability that will amplify perturbations only for a limited time or up to a certain finite amplification. This can be understood as a result of the growth time of the instability being longer than the shear time which destroys the modes which are able to grow. So only non-linear effects can lead to a relevant amplification. Nevertheless, a lower limit on the entropy gradient ~beta = 0.22 for the transient linear instability is derived, which can be tested in future non-linear simulations. This would help to explain the observed instability in numerical simulations as an ultimate result of the transient linear instability, i.e. the Global Baroclinic Instability.

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arXiv2002

Turbulence in Accretion Disks. Vorticity Generation and Angular Momentum Transport via the Global Baroclinic Instability

In this paper we present the global baroclinic instability as a source for vigorous turbulence leading to angular momentum transport in Keplerian accretion disks. We show by analytical considerations and three-dimensional radiation hydro simulations that, in particular, protoplanetary disks have a negative radial entropy gradient, which makes them baroclinic. Two-dimensional numerical simulations show that a baroclinic flow is unstable and produces turbulence. These findings are tested for numerical effects by performing a simulation with a barotropic initial condition which shows that imposed turbulence rapidly decays. The turbulence in baroclinic disks transports angular momentum outward and creates a radially inward bound accretion of matter. Potential energy is released and excess kinetic energy is dissipated. Finally the reheating of the gas supports the radial entropy gradient, forming a self consistent process. We measure accretion rates in our 2D and 3D simulations of dotM= - 1E-9 - 1E-7 Msun/yr and viscosity parameters of alpha = 1E-4 - 1E-2, which fit perfectly together and agree reasonably with observations. The turbulence creates pressure waves, Rossby waves, and vortices in the R-phi plane of the disk. We demonstrate in a global simulation that these vortices tend to form out of little background noise and to be long-lasting features, which have already been suggested to lead to the formation of planets.

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arXiv2002

Large-scale Vortices in Protoplanetary Disks: On the observability of possible early stages of planet formation

We investigate the possibility of mapping large-scale anti-cyclonic vortices, resulting from a global baroclinic instability, as pre-cursors of planet formation in proto-planetary disks with the planned Atacama Large Millimeter Array (ALMA). On the basis of three-dimensional radiative transfer simulations, images of a hydrodynamically calculated disk are derived which provide the basis for the simulation of ALMA. We find that ALMA will be able to trace the theoretically predicted large-scale anti-cyclonic vortex and will therefore allow testing of existing models of this very early stage of planet formation in circumstellar disks.

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